Chapter 4.4, Problem 41E

To determine

To check: whether $x+3$ is a factor of the given polynomial or not.

Answer to Problem 41E

  $x+3$ is a not factor of the given polynomial.

Explanation of Solution

Given information:

A polynomial is given as

  $h\left(x\right)=6x^5-15x^4-9x^3$

Concept used:

The factor theorem states that “A polynomial has a factor $x-a$ is and only if $f\left(a\right)=0$ ”.

Calculation:

Consider the given polynomial.

  $h\left(x\right)=6x^5-15x^4-9x^3$

If $x+3$ is a factor of the given polynomial, then $h\left(-3\right)=0$ .

Now, check whether $h\left(-3\right)=0$ or not.

  $\begin{array}{c}h\left(-3\right)=6{\left(-3\right)}^5-15{\left(-3\right)}^4-9{\left(-3\right)}^3\\ =6\left(-243\right)-15\left(81\right)-9\left(-27\right)\\ =-1458-1215+243\\ =-2430\\ \ne 0\end{array}$

Therefore, $x+3$ is a not factor of the given polynomial $h\left(x\right)=6x^5-15x^4-9x^3$ .