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

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

Step 1

Simplify and reorder the polynomial.

Simplify the expression.

Add $- 2$ and $1$ .

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

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

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

Multiply ${(x - 3)}^{2}$ by $1$ .

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

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

$(x - 3) (x - 3) (x + 1)$

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

Apply the distributive property.

$(x (x - 3) - 3 (x - 3)) (x + 1)$

Apply the distributive property.

$(x \cdot x + x \cdot - 3 - 3 (x - 3)) (x + 1)$

Apply the distributive property.

$(x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3) (x + 1)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 3$ by $- 3$ .

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

Subtract $3 x$ from $- 3 x$ .

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

Expand $(x^{2} - 6 x + 9) (x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x + x^{2} \cdot 1 - 6 x \cdot x - 6 x \cdot 1 + 9 x + 9 \cdot 1$

Simplify terms.

Simplify each term.

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

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

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

$x^{2} x^{1} + x^{2} \cdot 1 - 6 x \cdot x - 6 x \cdot 1 + 9 x + 9 \cdot 1$

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

$x^{2 + 1} + x^{2} \cdot 1 - 6 x \cdot x - 6 x \cdot 1 + 9 x + 9 \cdot 1$

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot 1 - 6 x \cdot x - 6 x \cdot 1 + 9 x + 9 \cdot 1$

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

$x^{3} + x^{2} - 6 x \cdot x - 6 x \cdot 1 + 9 x + 9 \cdot 1$

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

Move $x$ .

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

Multiply $x$ by $x$ .

$x^{3} + x^{2} - 6 x^{2} - 6 x \cdot 1 + 9 x + 9 \cdot 1$

Multiply $- 6$ by $1$ .

$x^{3} + x^{2} - 6 x^{2} - 6 x + 9 x + 9 \cdot 1$

Multiply $9$ by $1$ .

$x^{3} + x^{2} - 6 x^{2} - 6 x + 9 x + 9$

Simplify by adding terms.

Subtract $6 x^{2}$ from $x^{2}$ .

$x^{3} - 5 x^{2} - 6 x + 9 x + 9$

Add $- 6 x$ and $9 x$ .

$x^{3} - 5 x^{2} + 3 x + 9$

Step 2

The largest exponent is the degree of the polynomial.

$3$

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

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