Chapter 8.8, Problem 7P

Find the GCF of the first two terms and the GCF of the last two terms for each polynomial.

$7r^3+16r^2-9r-72$

To determine

To find: The GCF of the first two terms and the GCF of the last two terms of $7r^3+16r^2-9r-72$

Answer to Problem 7P

The GCF of the first two terms is $r^2$ and last two terms is 9.

Explanation of Solution

Given information: $7r^3+16r^2-9r-72$

Calculation:

The prime factors of the first two terms of $7r^3+16r^2-9r-72$ is given by,

  $7r^3=7\cdot r\cdot r\cdot r$

  $16r^2=2\cdot 2\cdot 2\cdot 2\cdot r\cdot r$

Then GCF of first two terms $=r\cdot r=r^2$

The prime factors of the last two terms of $7r^3+16r^2-9r-72$ is given by,

  $9r=3\cdot 3\cdot r$

  $72=2\cdot 2\cdot 2\cdot 3\cdot 3$

Then GCF of last two terms $=3\cdot 3=9$

Thus, the GCF of the first two terms is $r^2$ and last two terms is 9.