Chapter 8.6, Problem 6AGP

To determine

To factor: The polynomial $4r^2-r+7$ , if possible. If the polynomial cannot be factored using integers write prime.

Answer to Problem 6AGP

Prime

Explanation of Solution

Given:

  $4r^2-r+7$

Calculation:

The given polynomial is $4r^2-r+7$

This is a quadratic expression with $a=4,b=-1,c=7$

Here, $ac=28$ . So, in order to factor the polynomial chose the factor of 28 whose sum/difference is equal to b .

There is no such factor whose sum/difference gives b .

Therefore, the polynomial cannot be factored and hence it is a prime polynomial.