Chapter 4.4, Problem 40E

To determine

To check: whether $x+7$ is a factor of the given polynomial or not.

Answer to Problem 40E

  $x+7$ is a not factor of the given polynomial.

Explanation of Solution

Given information:

A polynomial is given as

  $g\left(x\right)=3x^3-28x^2+29x+140$

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.

  $g\left(x\right)=3x^3-28x^2+29x+140$

If $x+7$ is a factor of the given polynomial, then $g\left(-7\right)=0$ .

Now, check whether $g\left(-7\right)=0$ or not.

  $\begin{array}{c}g\left(-7\right)=3{\left(-7\right)}^3-28{\left(-7\right)}^2+29\left(-7\right)+140\\ =3\left(-343\right)-28\left(49\right)-203+140\\ =1029-1372-63\\ =-2464\\ \ne 0\end{array}$

Therefore, $x+7$ is a not factor of the given polynomial $g\left(x\right)=3x^3-28x^2+29x+140$ .