Precalculus Examples

x^{2} - 4

$x^{2} - 4$ ,

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

x^{2} - 4

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

{(2)}^{2} - 4

${(2)}^{2} - 4$

Step 4

Raise

2

$2$ to the power of

2

$2$ .

4 - 4

$4 - 4$

Step 5

Subtract

4

$4$ from

4

$4$ .

0

$0$

Step 6

Since

x = 2

$x = 2$ is a root of the polynomial,

x - 2

$x - 2$ is a factor of the polynomial.

x - 2

$x - 2$ is a factor of

x^{2} - 4

$x^{2} - 4$

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