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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 486 (page 563)

In the following exercises, use the Factor Theorem to determine if $x - c$ is a factor of the polynomial function.
Determine whether $x - 3$ is a factor of $x^{3} - 7 x^{2} + 11 x + 3$ .

Short Answer

Expert verified

$x - 3$ is a factor of $x^{3} - 7 x^{2} + 11 x + 3$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$x^{3} - 7 x^{2} + 11 x + 3$

The other expression is $x - 3$ .

02

Step 2. Determine whether the expression is a factor or not.

According to the Factor Theorem, if $f (c) = 0$ then $x - c$ is a factor of $f (x)$ .

The given expression can be written as:

$f (x) = x^{3} - 7 x^{2} + 11 x + 3$

Evaluate $f (3)$ .

$\begin{array}{rcl} f (3) & = & (3)^{3} - 7 (3)^{2} + 11 (3) + 3 \\ = & 27 - 63 + 33 + 3 \\ = & 0 \end{array}$

Since $f (3) = 0$ , therefore $x - 3$ is not a factor of $x^{3} - 7 x^{2} + 11 x + 3$ .

03

Step 3. Conclusion.

$x - 3$ is a factor of $x^{3} - 7 x^{2} + 11 x + 3$ .

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