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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.337. (page 552)

Use the factor theorem to determine whether $x - 3$ a factor of $x^{3} - 7 x^{2} + 11 x + 3$ .

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

$x^{3} - 7 x^{2} + 11 x + 3$ and $x - 3$ is the factor of polynomial function.

02

Step 2. To simplify the polynomial function, by using remainder theorem.

According to the factor theorem, $x - 3$ is a factor of $f (x) = x^{3} - 7 x^{2} + 11 x + 3$ if $f (3) = 0$ .

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

$f (3) = {(3)}^{3} - 7 {(3)}^{2} + 11 (3) + 3 鈬� 27 - 63 + 33 + 3 鈬� 63 - 63 鈬� 0$

03

Step 3. Simplified answer.

Since $f (3) = 0$ , $x - 3$ is a factor of $f (x) = x^{3} - 7 x^{2} + 11 x + 3$ .

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