Determine if the Given Expression is a Factor x+6 , x^3+10x^2+19x-30

$x + 6$ , $x^{3} + 10 x^{2} + 19 x - 30$

Step 1

If $x + 6$ 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 $x + 6$ is equal to $0$ .

$x + 6 = 0$

Step 2

Solve the equation for $x$ .

$x = - 6$

Step 3

Replace $x$ with $- 6$ in $x^{3} + 10 x^{2} + 19 x - 30$ to find if it is a root of the polynomial.

${(- 6)}^{3} + 10 {(- 6)}^{2} + 19 (- 6) - 30$

Step 4

Simplify each term.

Raise $- 6$ to the power of $3$ .

$- 216 + 10 {(- 6)}^{2} + 19 (- 6) - 30$

Raise $- 6$ to the power of $2$ .

$- 216 + 10 \cdot 36 + 19 (- 6) - 30$

Multiply $10$ by $36$ .

$- 216 + 360 + 19 (- 6) - 30$

Multiply $19$ by $- 6$ .

$- 216 + 360 - 114 - 30$

Step 5

Simplify by adding and subtracting.

Add $- 216$ and $360$ .

$144 - 114 - 30$

Subtract $114$ from $144$ .

$30 - 30$

Subtract $30$ from $30$ .

$0$

Step 6

Since $x = - 6$ is a root of the polynomial, $x + 6$ is a factor of the polynomial.

$x + 6$ is a factor of $x^{3} + 10 x^{2} + 19 x - 30$

Determine if the Given Expression is a Factor x+6 , x^3+10x^2+19x-30

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