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

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

Step 1

Simplify and reorder the polynomial.

Rewrite ${(x + 4)}^{2}$ as $(x + 4) (x + 4)$ .

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

Expand $(x + 4) (x + 4)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $4$ by $4$ .

$(x^{2} + 4 x + 4 x + 16) {(x - 3)}^{3} (x - 2)$

Add $4 x$ and $4 x$ .

$(x^{2} + 8 x + 16) {(x - 3)}^{3} (x - 2)$

Use the Binomial Theorem.

$(x^{2} + 8 x + 16) (x^{3} + 3 x^{2} \cdot - 3 + 3 x {(- 3)}^{2} + {(- 3)}^{3}) (x - 2)$

Simplify each term.

Multiply $- 3$ by $3$ .

$(x^{2} + 8 x + 16) (x^{3} - 9 x^{2} + 3 x {(- 3)}^{2} + {(- 3)}^{3}) (x - 2)$

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

$(x^{2} + 8 x + 16) (x^{3} - 9 x^{2} + 3 x \cdot 9 + {(- 3)}^{3}) (x - 2)$

Multiply $9$ by $3$ .

$(x^{2} + 8 x + 16) (x^{3} - 9 x^{2} + 27 x + {(- 3)}^{3}) (x - 2)$

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

$(x^{2} + 8 x + 16) (x^{3} - 9 x^{2} + 27 x - 27) (x - 2)$

Expand $(x^{2} + 8 x + 16) (x^{3} - 9 x^{2} + 27 x - 27)$ by multiplying each term in the first expression by each term in the second expression.

$(x^{2} x^{3} + x^{2} (- 9 x^{2}) + x^{2} (27 x) + x^{2} \cdot - 27 + 8 x \cdot x^{3} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

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.

$(x^{2 + 3} + x^{2} (- 9 x^{2}) + x^{2} (27 x) + x^{2} \cdot - 27 + 8 x \cdot x^{3} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Add $2$ and $3$ .

$(x^{5} + x^{2} (- 9 x^{2}) + x^{2} (27 x) + x^{2} \cdot - 27 + 8 x \cdot x^{3} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Rewrite using the commutative property of multiplication.

$(x^{5} - 9 x^{2} x^{2} + x^{2} (27 x) + x^{2} \cdot - 27 + 8 x \cdot x^{3} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

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

Move $x^{2}$ .

$(x^{5} - 9 (x^{2} x^{2}) + x^{2} (27 x) + x^{2} \cdot - 27 + 8 x \cdot x^{3} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

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

$(x^{5} - 9 x^{2 + 2} + x^{2} (27 x) + x^{2} \cdot - 27 + 8 x \cdot x^{3} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Add $2$ and $2$ .

$(x^{5} - 9 x^{4} + x^{2} (27 x) + x^{2} \cdot - 27 + 8 x \cdot x^{3} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Rewrite using the commutative property of multiplication.

$(x^{5} - 9 x^{4} + 27 x^{2} x + x^{2} \cdot - 27 + 8 x \cdot x^{3} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

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

Move $x$ .

$(x^{5} - 9 x^{4} + 27 (x \cdot x^{2}) + x^{2} \cdot - 27 + 8 x \cdot x^{3} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

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

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

$(x^{5} - 9 x^{4} + 27 (x^{1} x^{2}) + x^{2} \cdot - 27 + 8 x \cdot x^{3} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

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

$(x^{5} - 9 x^{4} + 27 x^{1 + 2} + x^{2} \cdot - 27 + 8 x \cdot x^{3} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Add $1$ and $2$ .

$(x^{5} - 9 x^{4} + 27 x^{3} + x^{2} \cdot - 27 + 8 x \cdot x^{3} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Move $- 27$ to the left of $x^{2}$ .

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 \cdot x^{2} + 8 x \cdot x^{3} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

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

Move $x^{3}$ .

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 (x^{3} x) + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

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

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

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 (x^{3} x^{1}) + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

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

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{3 + 1} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Add $3$ and $1$ .

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} + 8 x (- 9 x^{2}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Rewrite using the commutative property of multiplication.

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} + 8 \cdot - 9 x \cdot x^{2} + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

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

Move $x^{2}$ .

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} + 8 \cdot - 9 (x^{2} x) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

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

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

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} + 8 \cdot - 9 (x^{2} x^{1}) + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

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

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} + 8 \cdot - 9 x^{2 + 1} + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Add $2$ and $1$ .

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} + 8 \cdot - 9 x^{3} + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Multiply $8$ by $- 9$ .

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} - 72 x^{3} + 8 x (27 x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Rewrite using the commutative property of multiplication.

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} - 72 x^{3} + 8 \cdot 27 x \cdot x + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

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

Move $x$ .

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} - 72 x^{3} + 8 \cdot 27 (x \cdot x) + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Multiply $x$ by $x$ .

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} - 72 x^{3} + 8 \cdot 27 x^{2} + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Multiply $8$ by $27$ .

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} - 72 x^{3} + 216 x^{2} + 8 x \cdot - 27 + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Multiply $- 27$ by $8$ .

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} - 72 x^{3} + 216 x^{2} - 216 x + 16 x^{3} + 16 (- 9 x^{2}) + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Multiply $- 9$ by $16$ .

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} - 72 x^{3} + 216 x^{2} - 216 x + 16 x^{3} - 144 x^{2} + 16 (27 x) + 16 \cdot - 27) (x - 2)$

Multiply $27$ by $16$ .

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} - 72 x^{3} + 216 x^{2} - 216 x + 16 x^{3} - 144 x^{2} + 432 x + 16 \cdot - 27) (x - 2)$

Multiply $16$ by $- 27$ .

$(x^{5} - 9 x^{4} + 27 x^{3} - 27 x^{2} + 8 x^{4} - 72 x^{3} + 216 x^{2} - 216 x + 16 x^{3} - 144 x^{2} + 432 x - 432) (x - 2)$

Simplify by adding terms.

Add $- 9 x^{4}$ and $8 x^{4}$ .

$(x^{5} - x^{4} + 27 x^{3} - 27 x^{2} - 72 x^{3} + 216 x^{2} - 216 x + 16 x^{3} - 144 x^{2} + 432 x - 432) (x - 2)$

Subtract $72 x^{3}$ from $27 x^{3}$ .

$(x^{5} - x^{4} - 45 x^{3} - 27 x^{2} + 216 x^{2} - 216 x + 16 x^{3} - 144 x^{2} + 432 x - 432) (x - 2)$

Add $- 45 x^{3}$ and $16 x^{3}$ .

$(x^{5} - x^{4} - 29 x^{3} - 27 x^{2} + 216 x^{2} - 216 x - 144 x^{2} + 432 x - 432) (x - 2)$

Add $- 27 x^{2}$ and $216 x^{2}$ .

$(x^{5} - x^{4} - 29 x^{3} + 189 x^{2} - 216 x - 144 x^{2} + 432 x - 432) (x - 2)$

Subtract $144 x^{2}$ from $189 x^{2}$ .

$(x^{5} - x^{4} - 29 x^{3} + 45 x^{2} - 216 x + 432 x - 432) (x - 2)$

Add $- 216 x$ and $432 x$ .

$(x^{5} - x^{4} - 29 x^{3} + 45 x^{2} + 216 x - 432) (x - 2)$

Expand $(x^{5} - x^{4} - 29 x^{3} + 45 x^{2} + 216 x - 432) (x - 2)$ by multiplying each term in the first expression by each term in the second expression.

$x^{5} x + x^{5} \cdot - 2 - x^{4} x - x^{4} \cdot - 2 - 29 x^{3} x - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

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 $1$ .

$x^{5} x^{1} + x^{5} \cdot - 2 - x^{4} x - x^{4} \cdot - 2 - 29 x^{3} x - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

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

$x^{5 + 1} + x^{5} \cdot - 2 - x^{4} x - x^{4} \cdot - 2 - 29 x^{3} x - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

Add $5$ and $1$ .

$x^{6} + x^{5} \cdot - 2 - x^{4} x - x^{4} \cdot - 2 - 29 x^{3} x - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

Move $- 2$ to the left of $x^{5}$ .

$x^{6} - 2 \cdot x^{5} - x^{4} x - x^{4} \cdot - 2 - 29 x^{3} x - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

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

Move $x$ .

$x^{6} - 2 x^{5} - (x \cdot x^{4}) - x^{4} \cdot - 2 - 29 x^{3} x - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

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

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

$x^{6} - 2 x^{5} - (x^{1} x^{4}) - x^{4} \cdot - 2 - 29 x^{3} x - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

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

$x^{6} - 2 x^{5} - x^{1 + 4} - x^{4} \cdot - 2 - 29 x^{3} x - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

Add $1$ and $4$ .

$x^{6} - 2 x^{5} - x^{5} - x^{4} \cdot - 2 - 29 x^{3} x - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

Multiply $- 2$ by $- 1$ .

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 x^{3} x - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

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

Move $x$ .

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 (x \cdot x^{3}) - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

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

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

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 (x^{1} x^{3}) - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

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

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 x^{1 + 3} - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

Add $1$ and $3$ .

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 x^{4} - 29 x^{3} \cdot - 2 + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

Multiply $- 2$ by $- 29$ .

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 x^{4} + 58 x^{3} + 45 x^{2} x + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

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

Move $x$ .

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 x^{4} + 58 x^{3} + 45 (x \cdot x^{2}) + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

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

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

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 x^{4} + 58 x^{3} + 45 (x^{1} x^{2}) + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

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

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 x^{4} + 58 x^{3} + 45 x^{1 + 2} + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

Add $1$ and $2$ .

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 x^{4} + 58 x^{3} + 45 x^{3} + 45 x^{2} \cdot - 2 + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

Multiply $- 2$ by $45$ .

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 x^{4} + 58 x^{3} + 45 x^{3} - 90 x^{2} + 216 x \cdot x + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

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

Move $x$ .

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 x^{4} + 58 x^{3} + 45 x^{3} - 90 x^{2} + 216 (x \cdot x) + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

Multiply $x$ by $x$ .

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 x^{4} + 58 x^{3} + 45 x^{3} - 90 x^{2} + 216 x^{2} + 216 x \cdot - 2 - 432 x - 432 \cdot - 2$

Multiply $- 2$ by $216$ .

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 x^{4} + 58 x^{3} + 45 x^{3} - 90 x^{2} + 216 x^{2} - 432 x - 432 x - 432 \cdot - 2$

Multiply $- 432$ by $- 2$ .

$x^{6} - 2 x^{5} - x^{5} + 2 x^{4} - 29 x^{4} + 58 x^{3} + 45 x^{3} - 90 x^{2} + 216 x^{2} - 432 x - 432 x + 864$

Simplify by adding terms.

Subtract $x^{5}$ from $- 2 x^{5}$ .

$x^{6} - 3 x^{5} + 2 x^{4} - 29 x^{4} + 58 x^{3} + 45 x^{3} - 90 x^{2} + 216 x^{2} - 432 x - 432 x + 864$

Subtract $29 x^{4}$ from $2 x^{4}$ .

$x^{6} - 3 x^{5} - 27 x^{4} + 58 x^{3} + 45 x^{3} - 90 x^{2} + 216 x^{2} - 432 x - 432 x + 864$

Add $58 x^{3}$ and $45 x^{3}$ .

$x^{6} - 3 x^{5} - 27 x^{4} + 103 x^{3} - 90 x^{2} + 216 x^{2} - 432 x - 432 x + 864$

Add $- 90 x^{2}$ and $216 x^{2}$ .

$x^{6} - 3 x^{5} - 27 x^{4} + 103 x^{3} + 126 x^{2} - 432 x - 432 x + 864$

Subtract $432 x$ from $- 432 x$ .

$x^{6} - 3 x^{5} - 27 x^{4} + 103 x^{3} + 126 x^{2} - 864 x + 864$

Step 2

The largest exponent is the degree of the polynomial.

$6$

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

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