Find the Degree f(x)=(x+1)^2(x-4)^3(x-3)

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

Step 1

Simplify and reorder the polynomial.

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

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

Expand $(x + 1) (x + 1)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $x$ by $1$ .

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

Multiply $1$ by $1$ .

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

Add $x$ and $x$ .

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

Use the Binomial Theorem.

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

Simplify each term.

Multiply $- 4$ by $3$ .

$(x^{2} + 2 x + 1) (x^{3} - 12 x^{2} + 3 x {(- 4)}^{2} + {(- 4)}^{3}) (x - 3)$

Raise $- 4$ to the power of $2$ .

$(x^{2} + 2 x + 1) (x^{3} - 12 x^{2} + 3 x \cdot 16 + {(- 4)}^{3}) (x - 3)$

Multiply $16$ by $3$ .

$(x^{2} + 2 x + 1) (x^{3} - 12 x^{2} + 48 x + {(- 4)}^{3}) (x - 3)$

Raise $- 4$ to the power of $3$ .

$(x^{2} + 2 x + 1) (x^{3} - 12 x^{2} + 48 x - 64) (x - 3)$

Expand $(x^{2} + 2 x + 1) (x^{3} - 12 x^{2} + 48 x - 64)$ by multiplying each term in the first expression by each term in the second expression.

$(x^{2} x^{3} + x^{2} (- 12 x^{2}) + x^{2} (48 x) + x^{2} \cdot - 64 + 2 x \cdot x^{3} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

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.

$(x^{2 + 3} + x^{2} (- 12 x^{2}) + x^{2} (48 x) + x^{2} \cdot - 64 + 2 x \cdot x^{3} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Add $2$ and $3$ .

$(x^{5} + x^{2} (- 12 x^{2}) + x^{2} (48 x) + x^{2} \cdot - 64 + 2 x \cdot x^{3} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Rewrite using the commutative property of multiplication.

$(x^{5} - 12 x^{2} x^{2} + x^{2} (48 x) + x^{2} \cdot - 64 + 2 x \cdot x^{3} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

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

Move $x^{2}$ .

$(x^{5} - 12 (x^{2} x^{2}) + x^{2} (48 x) + x^{2} \cdot - 64 + 2 x \cdot x^{3} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

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

$(x^{5} - 12 x^{2 + 2} + x^{2} (48 x) + x^{2} \cdot - 64 + 2 x \cdot x^{3} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Add $2$ and $2$ .

$(x^{5} - 12 x^{4} + x^{2} (48 x) + x^{2} \cdot - 64 + 2 x \cdot x^{3} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Rewrite using the commutative property of multiplication.

$(x^{5} - 12 x^{4} + 48 x^{2} x + x^{2} \cdot - 64 + 2 x \cdot x^{3} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

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

Move $x$ .

$(x^{5} - 12 x^{4} + 48 (x \cdot x^{2}) + x^{2} \cdot - 64 + 2 x \cdot x^{3} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

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

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

$(x^{5} - 12 x^{4} + 48 (x^{1} x^{2}) + x^{2} \cdot - 64 + 2 x \cdot x^{3} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

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

$(x^{5} - 12 x^{4} + 48 x^{1 + 2} + x^{2} \cdot - 64 + 2 x \cdot x^{3} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Add $1$ and $2$ .

$(x^{5} - 12 x^{4} + 48 x^{3} + x^{2} \cdot - 64 + 2 x \cdot x^{3} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Move $- 64$ to the left of $x^{2}$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 \cdot x^{2} + 2 x \cdot x^{3} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

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

Move $x^{3}$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 (x^{3} x) + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

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

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

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 (x^{3} x^{1}) + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

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

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{3 + 1} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Add $3$ and $1$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} + 2 x (- 12 x^{2}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Rewrite using the commutative property of multiplication.

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} + 2 \cdot - 12 x \cdot x^{2} + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

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

Move $x^{2}$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} + 2 \cdot - 12 (x^{2} x) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

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

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

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} + 2 \cdot - 12 (x^{2} x^{1}) + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

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

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} + 2 \cdot - 12 x^{2 + 1} + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Add $2$ and $1$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} + 2 \cdot - 12 x^{3} + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Multiply $2$ by $- 12$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} - 24 x^{3} + 2 x (48 x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Rewrite using the commutative property of multiplication.

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} - 24 x^{3} + 2 \cdot 48 x \cdot x + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

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

Move $x$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} - 24 x^{3} + 2 \cdot 48 (x \cdot x) + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Multiply $x$ by $x$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} - 24 x^{3} + 2 \cdot 48 x^{2} + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Multiply $2$ by $48$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} - 24 x^{3} + 96 x^{2} + 2 x \cdot - 64 + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Multiply $- 64$ by $2$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} - 24 x^{3} + 96 x^{2} - 128 x + 1 x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Multiply $x^{3}$ by $1$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} - 24 x^{3} + 96 x^{2} - 128 x + x^{3} + 1 (- 12 x^{2}) + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Multiply $- 12 x^{2}$ by $1$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} - 24 x^{3} + 96 x^{2} - 128 x + x^{3} - 12 x^{2} + 1 (48 x) + 1 \cdot - 64) (x - 3)$

Multiply $48 x$ by $1$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} - 24 x^{3} + 96 x^{2} - 128 x + x^{3} - 12 x^{2} + 48 x + 1 \cdot - 64) (x - 3)$

Multiply $- 64$ by $1$ .

$(x^{5} - 12 x^{4} + 48 x^{3} - 64 x^{2} + 2 x^{4} - 24 x^{3} + 96 x^{2} - 128 x + x^{3} - 12 x^{2} + 48 x - 64) (x - 3)$

Simplify by adding terms.

Add $- 12 x^{4}$ and $2 x^{4}$ .

$(x^{5} - 10 x^{4} + 48 x^{3} - 64 x^{2} - 24 x^{3} + 96 x^{2} - 128 x + x^{3} - 12 x^{2} + 48 x - 64) (x - 3)$

Subtract $24 x^{3}$ from $48 x^{3}$ .

$(x^{5} - 10 x^{4} + 24 x^{3} - 64 x^{2} + 96 x^{2} - 128 x + x^{3} - 12 x^{2} + 48 x - 64) (x - 3)$

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

$(x^{5} - 10 x^{4} + 25 x^{3} - 64 x^{2} + 96 x^{2} - 128 x - 12 x^{2} + 48 x - 64) (x - 3)$

Add $- 64 x^{2}$ and $96 x^{2}$ .

$(x^{5} - 10 x^{4} + 25 x^{3} + 32 x^{2} - 128 x - 12 x^{2} + 48 x - 64) (x - 3)$

Subtract $12 x^{2}$ from $32 x^{2}$ .

$(x^{5} - 10 x^{4} + 25 x^{3} + 20 x^{2} - 128 x + 48 x - 64) (x - 3)$

Add $- 128 x$ and $48 x$ .

$(x^{5} - 10 x^{4} + 25 x^{3} + 20 x^{2} - 80 x - 64) (x - 3)$

Expand $(x^{5} - 10 x^{4} + 25 x^{3} + 20 x^{2} - 80 x - 64) (x - 3)$ by multiplying each term in the first expression by each term in the second expression.

$x^{5} x + x^{5} \cdot - 3 - 10 x^{4} x - 10 x^{4} \cdot - 3 + 25 x^{3} x + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

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 $1$ .

$x^{5} x^{1} + x^{5} \cdot - 3 - 10 x^{4} x - 10 x^{4} \cdot - 3 + 25 x^{3} x + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

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

$x^{5 + 1} + x^{5} \cdot - 3 - 10 x^{4} x - 10 x^{4} \cdot - 3 + 25 x^{3} x + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

Add $5$ and $1$ .

$x^{6} + x^{5} \cdot - 3 - 10 x^{4} x - 10 x^{4} \cdot - 3 + 25 x^{3} x + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

Move $- 3$ to the left of $x^{5}$ .

$x^{6} - 3 \cdot x^{5} - 10 x^{4} x - 10 x^{4} \cdot - 3 + 25 x^{3} x + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

Multiply $x^{4}$ by $x$ by adding the exponents.

Move $x$ .

$x^{6} - 3 x^{5} - 10 (x \cdot x^{4}) - 10 x^{4} \cdot - 3 + 25 x^{3} x + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

Multiply $x$ by $x^{4}$ .

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

$x^{6} - 3 x^{5} - 10 (x^{1} x^{4}) - 10 x^{4} \cdot - 3 + 25 x^{3} x + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

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

$x^{6} - 3 x^{5} - 10 x^{1 + 4} - 10 x^{4} \cdot - 3 + 25 x^{3} x + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

Add $1$ and $4$ .

$x^{6} - 3 x^{5} - 10 x^{5} - 10 x^{4} \cdot - 3 + 25 x^{3} x + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

Multiply $- 3$ by $- 10$ .

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 x^{3} x + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

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

Move $x$ .

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 (x \cdot x^{3}) + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

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

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

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 (x^{1} x^{3}) + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

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

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 x^{1 + 3} + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

Add $1$ and $3$ .

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 x^{4} + 25 x^{3} \cdot - 3 + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

Multiply $- 3$ by $25$ .

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 x^{4} - 75 x^{3} + 20 x^{2} x + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

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

Move $x$ .

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 x^{4} - 75 x^{3} + 20 (x \cdot x^{2}) + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

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

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

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 x^{4} - 75 x^{3} + 20 (x^{1} x^{2}) + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

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

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 x^{4} - 75 x^{3} + 20 x^{1 + 2} + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

Add $1$ and $2$ .

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 x^{4} - 75 x^{3} + 20 x^{3} + 20 x^{2} \cdot - 3 - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

Multiply $- 3$ by $20$ .

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 x^{4} - 75 x^{3} + 20 x^{3} - 60 x^{2} - 80 x \cdot x - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

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

Move $x$ .

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 x^{4} - 75 x^{3} + 20 x^{3} - 60 x^{2} - 80 (x \cdot x) - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

Multiply $x$ by $x$ .

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 x^{4} - 75 x^{3} + 20 x^{3} - 60 x^{2} - 80 x^{2} - 80 x \cdot - 3 - 64 x - 64 \cdot - 3$

Multiply $- 3$ by $- 80$ .

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 x^{4} - 75 x^{3} + 20 x^{3} - 60 x^{2} - 80 x^{2} + 240 x - 64 x - 64 \cdot - 3$

Multiply $- 64$ by $- 3$ .

$x^{6} - 3 x^{5} - 10 x^{5} + 30 x^{4} + 25 x^{4} - 75 x^{3} + 20 x^{3} - 60 x^{2} - 80 x^{2} + 240 x - 64 x + 192$

Simplify by adding terms.

Subtract $10 x^{5}$ from $- 3 x^{5}$ .

$x^{6} - 13 x^{5} + 30 x^{4} + 25 x^{4} - 75 x^{3} + 20 x^{3} - 60 x^{2} - 80 x^{2} + 240 x - 64 x + 192$

Add $30 x^{4}$ and $25 x^{4}$ .

$x^{6} - 13 x^{5} + 55 x^{4} - 75 x^{3} + 20 x^{3} - 60 x^{2} - 80 x^{2} + 240 x - 64 x + 192$

Add $- 75 x^{3}$ and $20 x^{3}$ .

$x^{6} - 13 x^{5} + 55 x^{4} - 55 x^{3} - 60 x^{2} - 80 x^{2} + 240 x - 64 x + 192$

Subtract $80 x^{2}$ from $- 60 x^{2}$ .

$x^{6} - 13 x^{5} + 55 x^{4} - 55 x^{3} - 140 x^{2} + 240 x - 64 x + 192$

Subtract $64 x$ from $240 x$ .

$x^{6} - 13 x^{5} + 55 x^{4} - 55 x^{3} - 140 x^{2} + 176 x + 192$

Step 2

The largest exponent is the degree of the polynomial.

$6$

Find the Degree f(x)=(x+1)^2(x-4)^3(x-3)

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