Chapter 8.8, Problem 1STP

For Exercises $1-5,$ choose the correct letter.

What is the GCF of the first two terms of the polynomial $4y^3+8y^2+5y+10?$

A. $4y^{}$

B. $4y^2$

C. $4y^3$

D. 4

To determine

To find: The GCF of the first two terms of the given polynomial.

Answer to Problem 1STP

  $4y^2$ isthe GCF of first two terms of the given polynomial.

Explanation of Solution

Given information:The polynomial $4y^3+8y^2+5y+10$

First rewrite each term as product using the GCF.

  $4\cdot y\cdot y\cdot y+8\cdot y\cdot y+5\cdot y+10$

Here are find the GCF of first two term,

Therefore, take only first two terms,

  $4\cdot y\cdot y\cdot y+8\cdot y\cdot y$

Now, use the distributive property in reverse to factor the expression,

  $\begin{array}{l}4\cdot y\cdot y\cdot y+8\cdot y\cdot y+5\cdot y+10\\ 4\cdot y\cdot y\cdot y+8\cdot y\cdot y\\ 4\cdot y\cdot y\left(y+2\right)\\ 4y^2\left(y+2\right)\end{array}$

Therefore the GCF is common factor in both terms.

  $GCF=4y^2$