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

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

Simplify and reorder the polynomial.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 1$ to the left of $x$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Multiply $- 1$ by $- 1$ .

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

Subtract $x$ from $- x$ .

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

Apply the distributive property.

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

Simplify.

Multiply $- 2$ by $4$ .

$(4 x^{2} - 8 x + 4 \cdot 1) (x^{2} + 2)$

Multiply $4$ by $1$ .

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

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

$4 x^{2} x^{2} + 4 x^{2} \cdot 2 - 8 x \cdot x^{2} - 8 x \cdot 2 + 4 x^{2} + 4 \cdot 2$

Simplify terms.

Simplify each term.

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

Move $x^{2}$ .

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

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

$4 x^{2 + 2} + 4 x^{2} \cdot 2 - 8 x \cdot x^{2} - 8 x \cdot 2 + 4 x^{2} + 4 \cdot 2$

Add $2$ and $2$ .

$4 x^{4} + 4 x^{2} \cdot 2 - 8 x \cdot x^{2} - 8 x \cdot 2 + 4 x^{2} + 4 \cdot 2$

Multiply $2$ by $4$ .

$4 x^{4} + 8 x^{2} - 8 x \cdot x^{2} - 8 x \cdot 2 + 4 x^{2} + 4 \cdot 2$

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

Move $x^{2}$ .

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

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

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

$4 x^{4} + 8 x^{2} - 8 (x^{2} x^{1}) - 8 x \cdot 2 + 4 x^{2} + 4 \cdot 2$

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

$4 x^{4} + 8 x^{2} - 8 x^{2 + 1} - 8 x \cdot 2 + 4 x^{2} + 4 \cdot 2$

Add $2$ and $1$ .

$4 x^{4} + 8 x^{2} - 8 x^{3} - 8 x \cdot 2 + 4 x^{2} + 4 \cdot 2$

Multiply $2$ by $- 8$ .

$4 x^{4} + 8 x^{2} - 8 x^{3} - 16 x + 4 x^{2} + 4 \cdot 2$

Multiply $4$ by $2$ .

$4 x^{4} + 8 x^{2} - 8 x^{3} - 16 x + 4 x^{2} + 8$

Add $8 x^{2}$ and $4 x^{2}$ .

$4 x^{4} + 12 x^{2} - 8 x^{3} - 16 x + 8$

The largest exponent is the degree of the polynomial.

$4$

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

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