Examples

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

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

x - 4

$x - 4$

Step 1

x - 4

$x - 4$ 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 - 4

$x - 4$ is equal to

0

$0$ .

x - 4 = 0

$x - 4 = 0$

Step 2

Solve the equation for

x

$x$ .

x = 4

$x = 4$

Step 3

Replace

x

$x$ with

4

$4$ in

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

$x^{3} - 3 x^{2} - 2 x + 6$ to find if it is a root of the polynomial.

{(4)}^{3} - 3 {(4)}^{2} - 2 \cdot 4 + 6

${(4)}^{3} - 3 {(4)}^{2} - 2 \cdot 4 + 6$

Step 4

Simplify each term.

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Step 4.1

Raise

4

$4$ to the power of

3

$3$ .

64 - 3 {(4)}^{2} - 2 \cdot 4 + 6

$64 - 3 {(4)}^{2} - 2 \cdot 4 + 6$

Step 4.2

Raise

4

$4$ to the power of

2

$2$ .

64 - 3 \cdot 16 - 2 \cdot 4 + 6

$64 - 3 \cdot 16 - 2 \cdot 4 + 6$

Step 4.3

Multiply

- 3

$- 3$ by

16

$16$ .

64 - 48 - 2 \cdot 4 + 6

$64 - 48 - 2 \cdot 4 + 6$

Step 4.4

Multiply

- 2

$- 2$ by

4

$4$ .

64 - 48 - 8 + 6

$64 - 48 - 8 + 6$

64 - 48 - 8 + 6

$64 - 48 - 8 + 6$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Subtract

48

$48$ from

64

$64$ .

16 - 8 + 6

$16 - 8 + 6$

Step 5.2

Subtract

8

$8$ from

16

$16$ .

8 + 6

$8 + 6$

Step 5.3

Add

8

$8$ and

6

$6$ .

14

$14$

14

$14$

Step 6

Since

x = 4

$x = 4$ is not a root of the polynomial,

x - 4

$x - 4$ is not a factor of the polynomial.

x - 4

$x - 4$ is not a factor of

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

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

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