Determine if the Given Expression is a Factor x+3 , x^3+5x^2-9x-45

$x + 3$ , $x^{3} + 5 x^{2} - 9 x - 45$

Step 1

If $x + 3$ 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 $x + 3$ is equal to $0$ .

$x + 3 = 0$

Step 2

Solve the equation for $x$ .

$x = - 3$

Step 3

Replace $x$ with $- 3$ in $x^{3} + 5 x^{2} - 9 x - 45$ to find if it is a root of the polynomial.

${(- 3)}^{3} + 5 {(- 3)}^{2} - 9 \cdot - 3 - 45$

Step 4

Simplify each term.

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

$- 27 + 5 {(- 3)}^{2} - 9 \cdot - 3 - 45$

Raise $- 3$ to the power of $2$ .

$- 27 + 5 \cdot 9 - 9 \cdot - 3 - 45$

Multiply $5$ by $9$ .

$- 27 + 45 - 9 \cdot - 3 - 45$

Multiply $- 9$ by $- 3$ .

$- 27 + 45 + 27 - 45$

Step 5

Simplify by adding and subtracting.

Add $- 27$ and $45$ .

$18 + 27 - 45$

Add $18$ and $27$ .

$45 - 45$

Subtract $45$ from $45$ .

$0$

Step 6

Since $x = - 3$ is a root of the polynomial, $x + 3$ is a factor of the polynomial.

$x + 3$ is a factor of $x^{3} + 5 x^{2} - 9 x - 45$

Determine if the Given Expression is a Factor x+3 , x^3+5x^2-9x-45

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