Chapter 6.5, Problem 2BCYP

To determine

To find: the factor of the given polynomial and check whether the polynomial is factored or prime.

Answer to Problem 2BCYP

Prime polynomial.

Explanation of Solution

Given:

The given polynomial is $13ax+18bz-15by-14az-32bx+9ay$ .

Calculation:

The given polynomial is $13ax+18bz-15by-14az-32bx+9ay$ .

Now, to find the factor of the given polynomial. Therefore,

  $\begin{array}{l}13ax+18bz-15by-14az-32bx+9ay\left\{\text{given polynomial}\right\}\\ =\left(13ax-14az+9ay\right)+\left(18bz-15by-32bx\right)\left\{\text{group the}\text{polynomial}\right\}\\ =a\left(13x-14z+9y\right)+b\left(18z-15y-32x\right)\left\{\text{factor out the GCF}\right\}\end{array}$

Here, the polynomial cannot be factorized using the sum. It cannot be factored by quadratic methods or GCF methods.

Hence, the given polynomial is prime polynomial.