Chapter 5: Q. 509 (page 564)

Use the Factor Theorem to determine if $x + 3$ is a factor of $x^{3} + 8 x^{2} + 21 x + 18$ .

Short Answer

Expert verified

$x + 3$ is a factor of the given polynomial.

Step by step solution

Step 1. Given information

The given polynomial is $x^{3} + 8 x^{2} + 21 x + 18$ .
The given factor is $x + 3$ .

Step 2. Applying Factor Theorem

By factor theorem, if $x + 3$ is a factor, then the value of the polynomial at $x = - 3$ will be 0.
Find the value of the polynomial at $x = - 3$ .

$\begin{array}{rcl} {(- 3)}^{3} + 8 {(- 3)}^{2} + 21 (- 3) + 18 & = & - 27 + 72 - 63 + 18 \\ = & 0 \end{array}$

So, $x + 3$ is a factor of the polynomial $x^{3} + 8 x^{2} + 21 x + 18$ .

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Use the Factor Theorem to determine if $x + 3$ is a factor of $x^{3} + 8 x^{2} + 21 x + 18$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Applying Factor Theorem

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Use the Factor Theorem to determine if $x + 3$ is a factor of $x^{3} + 8 x^{2} + 21 x + 18$ .