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

$f (x) = {(x + 3)}^{2} {(x - 2)}^{3} (x - 1)$

Step 1

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

Rewrite ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

$f (x) = (x + 3) (x + 3) {(x - 2)}^{3} (x - 1)$

Expand $(x + 3) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$f (x) = (x (x + 3) + 3 (x + 3)) {(x - 2)}^{3} (x - 1)$

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $3$ to the left of $x$ .

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

Multiply $3$ by $3$ .

$f (x) = (x^{2} + 3 x + 3 x + 9) {(x - 2)}^{3} (x - 1)$

Add $3 x$ and $3 x$ .

$f (x) = (x^{2} + 6 x + 9) {(x - 2)}^{3} (x - 1)$

Use the Binomial Theorem.

$f (x) = (x^{2} + 6 x + 9) (x^{3} + 3 x^{2} \cdot - 2 + 3 x {(- 2)}^{2} + {(- 2)}^{3}) (x - 1)$

Simplify each term.

Multiply $- 2$ by $3$ .

$f (x) = (x^{2} + 6 x + 9) (x^{3} - 6 x^{2} + 3 x {(- 2)}^{2} + {(- 2)}^{3}) (x - 1)$

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

$f (x) = (x^{2} + 6 x + 9) (x^{3} - 6 x^{2} + 3 x \cdot 4 + {(- 2)}^{3}) (x - 1)$

Multiply $4$ by $3$ .

$f (x) = (x^{2} + 6 x + 9) (x^{3} - 6 x^{2} + 12 x + {(- 2)}^{3}) (x - 1)$

Raise $- 2$ to the power of $3$ .

$f (x) = (x^{2} + 6 x + 9) (x^{3} - 6 x^{2} + 12 x - 8) (x - 1)$

Expand $(x^{2} + 6 x + 9) (x^{3} - 6 x^{2} + 12 x - 8)$ by multiplying each term in the first expression by each term in the second expression.

$f (x) = (x^{2} x^{3} + x^{2} (- 6 x^{2}) + x^{2} (12 x) + x^{2} \cdot - 8 + 6 x \cdot x^{3} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Simplify terms.

Simplify each term.

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

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

$f (x) = (x^{2 + 3} + x^{2} (- 6 x^{2}) + x^{2} (12 x) + x^{2} \cdot - 8 + 6 x \cdot x^{3} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Add $2$ and $3$ .

$f (x) = (x^{5} + x^{2} (- 6 x^{2}) + x^{2} (12 x) + x^{2} \cdot - 8 + 6 x \cdot x^{3} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Rewrite using the commutative property of multiplication.

$f (x) = (x^{5} - 6 x^{2} x^{2} + x^{2} (12 x) + x^{2} \cdot - 8 + 6 x \cdot x^{3} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

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

Move $x^{2}$ .

$f (x) = (x^{5} - 6 (x^{2} x^{2}) + x^{2} (12 x) + x^{2} \cdot - 8 + 6 x \cdot x^{3} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

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

$f (x) = (x^{5} - 6 x^{2 + 2} + x^{2} (12 x) + x^{2} \cdot - 8 + 6 x \cdot x^{3} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Add $2$ and $2$ .

$f (x) = (x^{5} - 6 x^{4} + x^{2} (12 x) + x^{2} \cdot - 8 + 6 x \cdot x^{3} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Rewrite using the commutative property of multiplication.

$f (x) = (x^{5} - 6 x^{4} + 12 x^{2} x + x^{2} \cdot - 8 + 6 x \cdot x^{3} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

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

Move $x$ .

$f (x) = (x^{5} - 6 x^{4} + 12 (x \cdot x^{2}) + x^{2} \cdot - 8 + 6 x \cdot x^{3} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

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

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

$f (x) = (x^{5} - 6 x^{4} + 12 (x \cdot x^{2}) + x^{2} \cdot - 8 + 6 x \cdot x^{3} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

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

$f (x) = (x^{5} - 6 x^{4} + 12 x^{1 + 2} + x^{2} \cdot - 8 + 6 x \cdot x^{3} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Add $1$ and $2$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} + x^{2} \cdot - 8 + 6 x \cdot x^{3} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Move $- 8$ to the left of $x^{2}$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 \cdot x^{2} + 6 x \cdot x^{3} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

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

Move $x^{3}$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 (x^{3} x) + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

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

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

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 (x^{3} x) + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

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

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{3 + 1} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Add $3$ and $1$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} + 6 x (- 6 x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Rewrite using the commutative property of multiplication.

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} + 6 \cdot (- 6 x \cdot x^{2}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

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

Move $x^{2}$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} + 6 \cdot (- 6 (x^{2} x)) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

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

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

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} + 6 \cdot (- 6 (x^{2} x)) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

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

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} + 6 \cdot (- 6 x^{2 + 1}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Add $2$ and $1$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} + 6 \cdot (- 6 x^{3}) + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Multiply $6$ by $- 6$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} - 36 x^{3} + 6 x (12 x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Rewrite using the commutative property of multiplication.

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} - 36 x^{3} + 6 \cdot (12 x \cdot x) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

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

Move $x$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} - 36 x^{3} + 6 \cdot (12 (x \cdot x)) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Multiply $x$ by $x$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} - 36 x^{3} + 6 \cdot (12 x^{2}) + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Multiply $6$ by $12$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} - 36 x^{3} + 72 x^{2} + 6 x \cdot - 8 + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Multiply $- 8$ by $6$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} - 36 x^{3} + 72 x^{2} - 48 x + 9 x^{3} + 9 (- 6 x^{2}) + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Multiply $- 6$ by $9$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} - 36 x^{3} + 72 x^{2} - 48 x + 9 x^{3} - 54 x^{2} + 9 (12 x) + 9 \cdot - 8) (x - 1)$

Multiply $12$ by $9$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} - 36 x^{3} + 72 x^{2} - 48 x + 9 x^{3} - 54 x^{2} + 108 x + 9 \cdot - 8) (x - 1)$

Multiply $9$ by $- 8$ .

$f (x) = (x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} - 36 x^{3} + 72 x^{2} - 48 x + 9 x^{3} - 54 x^{2} + 108 x - 72) (x - 1)$

Simplify by adding terms.

Combine the opposite terms in $x^{5} - 6 x^{4} + 12 x^{3} - 8 x^{2} + 6 x^{4} - 36 x^{3} + 72 x^{2} - 48 x + 9 x^{3} - 54 x^{2} + 108 x - 72$ .

Add $- 6 x^{4}$ and $6 x^{4}$ .

$f (x) = (x^{5} + 12 x^{3} - 8 x^{2} + 0 - 36 x^{3} + 72 x^{2} - 48 x + 9 x^{3} - 54 x^{2} + 108 x - 72) (x - 1)$

Add $x^{5} + 12 x^{3} - 8 x^{2}$ and $0$ .

$f (x) = (x^{5} + 12 x^{3} - 8 x^{2} - 36 x^{3} + 72 x^{2} - 48 x + 9 x^{3} - 54 x^{2} + 108 x - 72) (x - 1)$

Subtract $36 x^{3}$ from $12 x^{3}$ .

$f (x) = (x^{5} - 24 x^{3} - 8 x^{2} + 72 x^{2} - 48 x + 9 x^{3} - 54 x^{2} + 108 x - 72) (x - 1)$

Add $- 24 x^{3}$ and $9 x^{3}$ .

$f (x) = (x^{5} - 15 x^{3} - 8 x^{2} + 72 x^{2} - 48 x - 54 x^{2} + 108 x - 72) (x - 1)$

Add $- 8 x^{2}$ and $72 x^{2}$ .

$f (x) = (x^{5} - 15 x^{3} + 64 x^{2} - 48 x - 54 x^{2} + 108 x - 72) (x - 1)$

Subtract $54 x^{2}$ from $64 x^{2}$ .

$f (x) = (x^{5} - 15 x^{3} + 10 x^{2} - 48 x + 108 x - 72) (x - 1)$

Add $- 48 x$ and $108 x$ .

$f (x) = (x^{5} - 15 x^{3} + 10 x^{2} + 60 x - 72) (x - 1)$

Expand $(x^{5} - 15 x^{3} + 10 x^{2} + 60 x - 72) (x - 1)$ by multiplying each term in the first expression by each term in the second expression.

$f (x) = x^{5} x + x^{5} \cdot - 1 - 15 x^{3} x - 15 x^{3} \cdot - 1 + 10 x^{2} x + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

Simplify terms.

Simplify each term.

Multiply $x^{5}$ by $x$ by adding the exponents.

Multiply $x^{5}$ by $x$ .

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

$f (x) = x^{5} x + x^{5} \cdot - 1 - 15 x^{3} x - 15 x^{3} \cdot - 1 + 10 x^{2} x + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

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

$f (x) = x^{5 + 1} + x^{5} \cdot - 1 - 15 x^{3} x - 15 x^{3} \cdot - 1 + 10 x^{2} x + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

Add $5$ and $1$ .

$f (x) = x^{6} + x^{5} \cdot - 1 - 15 x^{3} x - 15 x^{3} \cdot - 1 + 10 x^{2} x + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

Move $- 1$ to the left of $x^{5}$ .

$f (x) = x^{6} - 1 \cdot x^{5} - 15 x^{3} x - 15 x^{3} \cdot - 1 + 10 x^{2} x + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

Rewrite $- 1 x^{5}$ as $- x^{5}$ .

$f (x) = x^{6} - x^{5} - 15 x^{3} x - 15 x^{3} \cdot - 1 + 10 x^{2} x + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

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

Move $x$ .

$f (x) = x^{6} - x^{5} - 15 (x \cdot x^{3}) - 15 x^{3} \cdot - 1 + 10 x^{2} x + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

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

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

$f (x) = x^{6} - x^{5} - 15 (x \cdot x^{3}) - 15 x^{3} \cdot - 1 + 10 x^{2} x + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

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

$f (x) = x^{6} - x^{5} - 15 x^{1 + 3} - 15 x^{3} \cdot - 1 + 10 x^{2} x + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

Add $1$ and $3$ .

$f (x) = x^{6} - x^{5} - 15 x^{4} - 15 x^{3} \cdot - 1 + 10 x^{2} x + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

Multiply $- 1$ by $- 15$ .

$f (x) = x^{6} - x^{5} - 15 x^{4} + 15 x^{3} + 10 x^{2} x + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

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

Move $x$ .

$f (x) = x^{6} - x^{5} - 15 x^{4} + 15 x^{3} + 10 (x \cdot x^{2}) + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

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

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

$f (x) = x^{6} - x^{5} - 15 x^{4} + 15 x^{3} + 10 (x \cdot x^{2}) + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

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

$f (x) = x^{6} - x^{5} - 15 x^{4} + 15 x^{3} + 10 x^{1 + 2} + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

Add $1$ and $2$ .

$f (x) = x^{6} - x^{5} - 15 x^{4} + 15 x^{3} + 10 x^{3} + 10 x^{2} \cdot - 1 + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

Multiply $- 1$ by $10$ .

$f (x) = x^{6} - x^{5} - 15 x^{4} + 15 x^{3} + 10 x^{3} - 10 x^{2} + 60 x \cdot x + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

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

Move $x$ .

$f (x) = x^{6} - x^{5} - 15 x^{4} + 15 x^{3} + 10 x^{3} - 10 x^{2} + 60 (x \cdot x) + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

Multiply $x$ by $x$ .

$f (x) = x^{6} - x^{5} - 15 x^{4} + 15 x^{3} + 10 x^{3} - 10 x^{2} + 60 x^{2} + 60 x \cdot - 1 - 72 x - 72 \cdot - 1$

Multiply $- 1$ by $60$ .

$f (x) = x^{6} - x^{5} - 15 x^{4} + 15 x^{3} + 10 x^{3} - 10 x^{2} + 60 x^{2} - 60 x - 72 x - 72 \cdot - 1$

Multiply $- 72$ by $- 1$ .

$f (x) = x^{6} - x^{5} - 15 x^{4} + 15 x^{3} + 10 x^{3} - 10 x^{2} + 60 x^{2} - 60 x - 72 x + 72$

Simplify by adding terms.

Add $15 x^{3}$ and $10 x^{3}$ .

$f (x) = x^{6} - x^{5} - 15 x^{4} + 25 x^{3} - 10 x^{2} + 60 x^{2} - 60 x - 72 x + 72$

Add $- 10 x^{2}$ and $60 x^{2}$ .

$f (x) = x^{6} - x^{5} - 15 x^{4} + 25 x^{3} + 50 x^{2} - 60 x - 72 x + 72$

Subtract $72 x$ from $- 60 x$ .

$f (x) = x^{6} - x^{5} - 15 x^{4} + 25 x^{3} + 50 x^{2} - 132 x + 72$

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.

$x^{6} \to 6$

$- x^{5} \to 5$

$- 15 x^{4} \to 4$

$25 x^{3} \to 3$

$50 x^{2} \to 2$

$- 132 x \to 1$

$72 \to 0$

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 f(x)=(x+3)^2(x-2)^3(x-1)

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