Find the Degree, Leading Term, and Leading Coefficient (x-1)(x-2)^2(x-pi)^3

$(x - 1) {(x - 2)}^{2} {(x - π)}^{3}$

Step 1

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

Rewrite ${(x - 2)}^{2}$ as $(x - 2) (x - 2)$ .

$(x - 1) ((x - 2) (x - 2)) {(x - π)}^{3}$

Expand $(x - 2) (x - 2)$ using the FOIL Method.

Apply the distributive property.

$(x - 1) (x (x - 2) - 2 (x - 2)) {(x - π)}^{3}$

Apply the distributive property.

$(x - 1) (x \cdot x + x \cdot - 2 - 2 (x - 2)) {(x - π)}^{3}$

Apply the distributive property.

$(x - 1) (x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2) {(x - π)}^{3}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$(x - 1) (x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2) {(x - π)}^{3}$

Move $- 2$ to the left of $x$ .

$(x - 1) (x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2) {(x - π)}^{3}$

Multiply $- 2$ by $- 2$ .

$(x - 1) (x^{2} - 2 x - 2 x + 4) {(x - π)}^{3}$

Subtract $2 x$ from $- 2 x$ .

$(x - 1) (x^{2} - 4 x + 4) {(x - π)}^{3}$

Expand $(x - 1) (x^{2} - 4 x + 4)$ by multiplying each term in the first expression by each term in the second expression.

$(x \cdot x^{2} + x (- 4 x) + x \cdot 4 - 1 x^{2} - 1 (- 4 x) - 1 \cdot 4) {(x - π)}^{3}$

Simplify terms.

Simplify each term.

Multiply $x$ by $x^{2}$ by adding the exponents.

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$(x^{1} x^{2} + x (- 4 x) + x \cdot 4 - 1 x^{2} - 1 (- 4 x) - 1 \cdot 4) {(x - π)}^{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{1 + 2} + x (- 4 x) + x \cdot 4 - 1 x^{2} - 1 (- 4 x) - 1 \cdot 4) {(x - π)}^{3}$

Add $1$ and $2$ .

$(x^{3} + x (- 4 x) + x \cdot 4 - 1 x^{2} - 1 (- 4 x) - 1 \cdot 4) {(x - π)}^{3}$

Rewrite using the commutative property of multiplication.

$(x^{3} - 4 x \cdot x + x \cdot 4 - 1 x^{2} - 1 (- 4 x) - 1 \cdot 4) {(x - π)}^{3}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$(x^{3} - 4 (x \cdot x) + x \cdot 4 - 1 x^{2} - 1 (- 4 x) - 1 \cdot 4) {(x - π)}^{3}$

Multiply $x$ by $x$ .

$(x^{3} - 4 x^{2} + x \cdot 4 - 1 x^{2} - 1 (- 4 x) - 1 \cdot 4) {(x - π)}^{3}$

Move $4$ to the left of $x$ .

$(x^{3} - 4 x^{2} + 4 \cdot x - 1 x^{2} - 1 (- 4 x) - 1 \cdot 4) {(x - π)}^{3}$

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

$(x^{3} - 4 x^{2} + 4 x - x^{2} - 1 (- 4 x) - 1 \cdot 4) {(x - π)}^{3}$

Multiply $- 4$ by $- 1$ .

$(x^{3} - 4 x^{2} + 4 x - x^{2} + 4 x - 1 \cdot 4) {(x - π)}^{3}$

Multiply $- 1$ by $4$ .

$(x^{3} - 4 x^{2} + 4 x - x^{2} + 4 x - 4) {(x - π)}^{3}$

Simplify by adding terms.

Subtract $x^{2}$ from $- 4 x^{2}$ .

$(x^{3} - 5 x^{2} + 4 x + 4 x - 4) {(x - π)}^{3}$

Add $4 x$ and $4 x$ .

$(x^{3} - 5 x^{2} + 8 x - 4) {(x - π)}^{3}$

Use the Binomial Theorem.

$(x^{3} - 5 x^{2} + 8 x - 4) (x^{3} + 3 x^{2} (- π) + 3 x {(- π)}^{2} + {(- π)}^{3})$

Simplify each term.

Multiply $- 1$ by $3$ .

$(x^{3} - 5 x^{2} + 8 x - 4) (x^{3} - 3 x^{2} π + 3 x {(- π)}^{2} + {(- π)}^{3})$

Apply the product rule to $- π$ .

$(x^{3} - 5 x^{2} + 8 x - 4) (x^{3} - 3 x^{2} π + 3 x ({(- 1)}^{2} π^{2}) + {(- π)}^{3})$

Raise $- 1$ to the power of $2$ .

$(x^{3} - 5 x^{2} + 8 x - 4) (x^{3} - 3 x^{2} π + 3 x (1 π^{2}) + {(- π)}^{3})$

Multiply $π^{2}$ by $1$ .

$(x^{3} - 5 x^{2} + 8 x - 4) (x^{3} - 3 x^{2} π + 3 x π^{2} + {(- π)}^{3})$

Apply the product rule to $- π$ .

$(x^{3} - 5 x^{2} + 8 x - 4) (x^{3} - 3 x^{2} π + 3 x π^{2} + {(- 1)}^{3} π^{3})$

Raise $- 1$ to the power of $3$ .

$(x^{3} - 5 x^{2} + 8 x - 4) (x^{3} - 3 x^{2} π + 3 x π^{2} - π^{3})$

Expand $(x^{3} - 5 x^{2} + 8 x - 4) (x^{3} - 3 x^{2} π + 3 x π^{2} - π^{3})$ by multiplying each term in the first expression by each term in the second expression.

$x^{3} x^{3} + x^{3} (- 3 x^{2} π) + x^{3} (3 x π^{2}) + x^{3} (- π^{3}) - 5 x^{2} x^{3} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Simplify terms.

Simplify each term.

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{3 + 3} + x^{3} (- 3 x^{2} π) + x^{3} (3 x π^{2}) + x^{3} (- π^{3}) - 5 x^{2} x^{3} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Add $3$ and $3$ .

$x^{6} + x^{3} (- 3 x^{2} π) + x^{3} (3 x π^{2}) + x^{3} (- π^{3}) - 5 x^{2} x^{3} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Rewrite using the commutative property of multiplication.

$x^{6} - 3 π x^{3} x^{2} + x^{3} (3 x π^{2}) + x^{3} (- π^{3}) - 5 x^{2} x^{3} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$x^{6} - 3 π (x^{2} x^{3}) + x^{3} (3 x π^{2}) + x^{3} (- π^{3}) - 5 x^{2} x^{3} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{6} - 3 π x^{2 + 3} + x^{3} (3 x π^{2}) + x^{3} (- π^{3}) - 5 x^{2} x^{3} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Add $2$ and $3$ .

$x^{6} - 3 π x^{5} + x^{3} (3 x π^{2}) + x^{3} (- π^{3}) - 5 x^{2} x^{3} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Rewrite using the commutative property of multiplication.

$x^{6} - 3 π x^{5} + 3 π^{2} x^{3} x + x^{3} (- π^{3}) - 5 x^{2} x^{3} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

$x^{6} - 3 π x^{5} + 3 π^{2} (x \cdot x^{3}) + x^{3} (- π^{3}) - 5 x^{2} x^{3} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $x$ by $x^{3}$ .

Raise $x$ to the power of $1$ .

$x^{6} - 3 π x^{5} + 3 π^{2} (x^{1} x^{3}) + x^{3} (- π^{3}) - 5 x^{2} x^{3} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{6} - 3 π x^{5} + 3 π^{2} x^{1 + 3} + x^{3} (- π^{3}) - 5 x^{2} x^{3} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Add $1$ and $3$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{2} x^{3} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 (x^{3} x^{2}) - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{3 + 2} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Add $3$ and $2$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} - 5 x^{2} (- 3 x^{2} π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} - 5 (x^{2} x^{2}) (- 3 π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} - 5 x^{2 + 2} (- 3 π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Add $2$ and $2$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} - 5 x^{4} (- 3 π) - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $- 3$ by $- 5$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 5 x^{2} (3 x π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 5 (x \cdot x^{2}) (3 π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 5 (x^{1} x^{2}) (3 π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 5 x^{1 + 2} (3 π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Add $1$ and $2$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 5 x^{3} (3 π^{2}) - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $3$ by $- 5$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} - 5 x^{2} (- π^{3}) + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $- 1$ by $- 5$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x \cdot x^{3} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 (x^{3} x) + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $x^{3}$ by $x$ .

Raise $x$ to the power of $1$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 (x^{3} x^{1}) + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{3 + 1} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Add $3$ and $1$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} + 8 x (- 3 x^{2} π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} + 8 (x^{2} x) (- 3 π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} + 8 (x^{2} x^{1}) (- 3 π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} + 8 x^{2 + 1} (- 3 π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Add $2$ and $1$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} + 8 x^{3} (- 3 π) + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $- 3$ by $8$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} - 24 x^{3} π + 8 x (3 x π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} - 24 x^{3} π + 8 (x \cdot x) (3 π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $x$ by $x$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} - 24 x^{3} π + 8 x^{2} (3 π^{2}) + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $3$ by $8$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} - 24 x^{3} π + 24 x^{2} π^{2} + 8 x (- π^{3}) - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $- 1$ by $8$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} - 24 x^{3} π + 24 x^{2} π^{2} - 8 x π^{3} - 4 x^{3} - 4 (- 3 x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $- 3$ by $- 4$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} - 24 x^{3} π + 24 x^{2} π^{2} - 8 x π^{3} - 4 x^{3} + 12 (x^{2} π) - 4 (3 x π^{2}) - 4 (- π^{3})$

Multiply $3$ by $- 4$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} - 24 x^{3} π + 24 x^{2} π^{2} - 8 x π^{3} - 4 x^{3} + 12 x^{2} π - 12 (x π^{2}) - 4 (- π^{3})$

Multiply $- 1$ by $- 4$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} - 24 x^{3} π + 24 x^{2} π^{2} - 8 x π^{3} - 4 x^{3} + 12 x^{2} π - 12 x π^{2} + 4 π^{3}$

Simplify the expression.

Reorder factors in $x^{6} - 3 π x^{5} + 3 π^{2} x^{4} + x^{3} (- π^{3}) - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} - 24 x^{3} π + 24 x^{2} π^{2} - 8 x π^{3} - 4 x^{3} + 12 x^{2} π - 12 x π^{2} + 4 π^{3}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - x^{3} π^{3} - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} - 24 x^{3} π + 24 x^{2} π^{2} - 8 x π^{3} - 4 x^{3} + 12 x^{2} π - 12 x π^{2} + 4 π^{3}$

Move $x^{3}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - π^{3} x^{3} - 5 x^{5} + 15 x^{4} π - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} - 24 x^{3} π + 24 x^{2} π^{2} - 8 x π^{3} - 4 x^{3} + 12 x^{2} π - 12 x π^{2} + 4 π^{3}$

Move $x^{4}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - π^{3} x^{3} - 5 x^{5} + 15 π x^{4} - 15 x^{3} π^{2} + 5 x^{2} π^{3} + 8 x^{4} - 24 x^{3} π + 24 x^{2} π^{2} - 8 x π^{3} - 4 x^{3} + 12 x^{2} π - 12 x π^{2} + 4 π^{3}$

Move $x^{3}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - π^{3} x^{3} - 5 x^{5} + 15 π x^{4} - 15 π^{2} x^{3} + 5 x^{2} π^{3} + 8 x^{4} - 24 x^{3} π + 24 x^{2} π^{2} - 8 x π^{3} - 4 x^{3} + 12 x^{2} π - 12 x π^{2} + 4 π^{3}$

Move $x^{2}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - π^{3} x^{3} - 5 x^{5} + 15 π x^{4} - 15 π^{2} x^{3} + 5 π^{3} x^{2} + 8 x^{4} - 24 x^{3} π + 24 x^{2} π^{2} - 8 x π^{3} - 4 x^{3} + 12 x^{2} π - 12 x π^{2} + 4 π^{3}$

Move $x^{3}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - π^{3} x^{3} - 5 x^{5} + 15 π x^{4} - 15 π^{2} x^{3} + 5 π^{3} x^{2} + 8 x^{4} - 24 π x^{3} + 24 x^{2} π^{2} - 8 x π^{3} - 4 x^{3} + 12 x^{2} π - 12 x π^{2} + 4 π^{3}$

Move $x^{2}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - π^{3} x^{3} - 5 x^{5} + 15 π x^{4} - 15 π^{2} x^{3} + 5 π^{3} x^{2} + 8 x^{4} - 24 π x^{3} + 24 π^{2} x^{2} - 8 x π^{3} - 4 x^{3} + 12 x^{2} π - 12 x π^{2} + 4 π^{3}$

Move $x$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - π^{3} x^{3} - 5 x^{5} + 15 π x^{4} - 15 π^{2} x^{3} + 5 π^{3} x^{2} + 8 x^{4} - 24 π x^{3} + 24 π^{2} x^{2} - 8 π^{3} x - 4 x^{3} + 12 x^{2} π - 12 x π^{2} + 4 π^{3}$

Move $x^{2}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - π^{3} x^{3} - 5 x^{5} + 15 π x^{4} - 15 π^{2} x^{3} + 5 π^{3} x^{2} + 8 x^{4} - 24 π x^{3} + 24 π^{2} x^{2} - 8 π^{3} x - 4 x^{3} + 12 π x^{2} - 12 x π^{2} + 4 π^{3}$

Move $x$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - π^{3} x^{3} - 5 x^{5} + 15 π x^{4} - 15 π^{2} x^{3} + 5 π^{3} x^{2} + 8 x^{4} - 24 π x^{3} + 24 π^{2} x^{2} - 8 π^{3} x - 4 x^{3} + 12 π x^{2} - 12 π^{2} x + 4 π^{3}$

Move $- 8 π^{3} x$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - π^{3} x^{3} - 5 x^{5} + 15 π x^{4} - 15 π^{2} x^{3} + 5 π^{3} x^{2} + 8 x^{4} - 24 π x^{3} + 24 π^{2} x^{2} - 4 x^{3} + 12 π x^{2} - 8 π^{3} x - 12 π^{2} x + 4 π^{3}$

Move $24 π^{2} x^{2}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - π^{3} x^{3} - 5 x^{5} + 15 π x^{4} - 15 π^{2} x^{3} + 5 π^{3} x^{2} + 8 x^{4} - 24 π x^{3} - 4 x^{3} + 24 π^{2} x^{2} + 12 π x^{2} - 8 π^{3} x - 12 π^{2} x + 4 π^{3}$

Move $5 π^{3} x^{2}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - π^{3} x^{3} - 5 x^{5} + 15 π x^{4} - 15 π^{2} x^{3} + 8 x^{4} - 24 π x^{3} - 4 x^{3} + 5 π^{3} x^{2} + 24 π^{2} x^{2} + 12 π x^{2} - 8 π^{3} x - 12 π^{2} x + 4 π^{3}$

Move $- 15 π^{2} x^{3}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - π^{3} x^{3} - 5 x^{5} + 15 π x^{4} + 8 x^{4} - 15 π^{2} x^{3} - 24 π x^{3} - 4 x^{3} + 5 π^{3} x^{2} + 24 π^{2} x^{2} + 12 π x^{2} - 8 π^{3} x - 12 π^{2} x + 4 π^{3}$

Move $- π^{3} x^{3}$ .

$x^{6} - 3 π x^{5} + 3 π^{2} x^{4} - 5 x^{5} + 15 π x^{4} + 8 x^{4} - π^{3} x^{3} - 15 π^{2} x^{3} - 24 π x^{3} - 4 x^{3} + 5 π^{3} x^{2} + 24 π^{2} x^{2} + 12 π x^{2} - 8 π^{3} x - 12 π^{2} x + 4 π^{3}$

Move $3 π^{2} x^{4}$ .

$x^{6} - 3 π x^{5} - 5 x^{5} + 3 π^{2} x^{4} + 15 π x^{4} + 8 x^{4} - π^{3} x^{3} - 15 π^{2} x^{3} - 24 π x^{3} - 4 x^{3} + 5 π^{3} x^{2} + 24 π^{2} x^{2} + 12 π x^{2} - 8 π^{3} x - 12 π^{2} x + 4 π^{3}$

Step 2

The degree of a polynomial is the highest degree of its terms.

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$x^{6} \to 6$

$- 3 π x^{5} \to 5$

$- 5 x^{5} \to 5$

$3 π^{2} x^{4} \to 4$

$15 π x^{4} \to 4$

$8 x^{4} \to 4$

$- π^{3} x^{3} \to 3$

$- 15 π^{2} x^{3} \to 3$

$- 24 π x^{3} \to 3$

$- 4 x^{3} \to 3$

$5 π^{3} x^{2} \to 2$

$24 π^{2} x^{2} \to 2$

$12 π x^{2} \to 2$

$- 8 π^{3} x \to 1$

$- 12 π^{2} x \to 1$

$4 π^{3} \to 0$

The largest exponent is the degree of the polynomial.

$6$

Step 3

The leading term in a polynomial is the term with the highest degree.

$x^{6}$

Step 4

The leading coefficient of a polynomial is the coefficient of the leading term.

The leading term in a polynomial is the term with the highest degree.

$x^{6}$

The leading coefficient in a polynomial is the coefficient of the leading term.

$1$

Step 5

List the results.

Polynomial Degree: $6$

Leading Term: $x^{6}$

Leading Coefficient: $1$

Find the Degree, Leading Term, and Leading Coefficient (x-1)(x-2)^2(x-pi)^3

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