Chapter 8, Problem 74CR

To determine

To find:The GCF of the first two terms and the GCF of the last two terms of $8m^3+40m^2+6m+15$ .

Answer to Problem 74CR

  $8m^2,3$

Explanation of Solution

Given information:The expression $8m^3+40m^2+6m+15$

Calculation:

The prime factors of first two terms of the polynomial are,

  $\begin{array}{l}8m^3=2\cdot 2\cdot 2\cdot m\cdot m\cdot m\\ 40m^2=2\cdot 2\cdot 2\cdot 5\cdot m\cdot m\end{array}$

The GCF of first two terms is $2\cdot 2\cdot 2\cdot m\cdot m\text{ or }8m^2$ .

The prime factors of last two terms of the polynomial are,

  $\begin{array}{l}6m=2\cdot 3\cdot m\\ 15=3\cdot 5\end{array}$

The GCF of first two terms is $3$ .