Examples

$8 x^{2} - 4 x + 10$ , $x + 2$

Step 1

If $x + 2$ is a factor of the polynomial, then it must be a root of the polynomial. To determine if the factor is a root, first find the value of $x$ when the factor $x + 2$ is equal to $0$ .

$x + 2 = 0$

Step 2

Solve the equation for $x$ .

$x = - 2$

Step 3

Replace $x$ with $- 2$ in $8 x^{2} - 4 x + 10$ to find if it is a root of the polynomial.

$8 {(- 2)}^{2} - 4 \cdot - 2 + 10$

Step 4

Simplify each term.

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Step 4.1

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

$8 \cdot 4 - 4 \cdot - 2 + 10$

Step 4.2

Multiply $8$ by $4$ .

$32 - 4 \cdot - 2 + 10$

Step 4.3

Multiply $- 4$ by $- 2$ .

$32 + 8 + 10$

Step 5

Simplify by adding numbers.

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Step 5.1

Add $32$ and $8$ .

$40 + 10$

Step 5.2

Add $40$ and $10$ .

$50$

Step 6

Since $x = - 2$ is not a root of the polynomial, $x + 2$ is not a factor of the polynomial.

$x + 2$ is not a factor of $8 x^{2} - 4 x + 10$

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