Algebra Examples

8 x^{2} - 4 x + 10

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

x + 2

$x + 2$

Step 1

x + 2

$x + 2$ 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

$x$ when the factor

x + 2

$x + 2$ is equal to

0

$0$ .

x + 2 = 0

$x + 2 = 0$

Step 2

Solve the equation for

x

$x$ .

x = - 2

$x = - 2$

Step 3

Replace

x

$x$ with

- 2

$- 2$ in

8 x^{2} - 4 x + 10

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

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

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

Step 4

Simplify each term.

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Step 4.1

Raise

- 2

$- 2$ to the power of

2

$2$ .

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

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

Step 4.2

Multiply

8

$8$ by

4

$4$ .

32 - 4 \cdot - 2 + 10

$32 - 4 \cdot - 2 + 10$

Step 4.3

Multiply

- 4

$- 4$ by

- 2

$- 2$ .

32 + 8 + 10

$32 + 8 + 10$

32 + 8 + 10

$32 + 8 + 10$

Step 5

Simplify by adding numbers.

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Step 5.1

Add

32

$32$ and

8

$8$ .

40 + 10

$40 + 10$

Step 5.2

Add

40

$40$ and

10

$10$ .

50

$50$

50

$50$

Step 6

Since

x = - 2

$x = - 2$ is not a root of the polynomial,

x + 2

$x + 2$ is not a factor of the polynomial.

x + 2

$x + 2$ is not a factor of

8 x^{2} - 4 x + 10

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

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