Chapter 8.8, Problem 3P

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

$8t^3+36t^2+2t+9$

To determine

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

Answer to Problem 3P

The GCF of the first two terms is $4t^2$ and GCF of last two term 1.

Explanation of Solution

Given information: The polynomial $8t^3+36t^2+2t+9$

First rewrite each term as product using the GCF.

  $8\cdot t\cdot t\cdot t+36\cdot t\cdot t+2\cdot t+9$

Here are to find the GCF of first two terms, take only first two terms,

  $8\cdot t\cdot t\cdot t+36\cdot t\cdot t$

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

  $\begin{array}{l}8\cdot t\cdot t\cdot t+36\cdot t\cdot t\\ 4\cdot t\cdot t\left(2\cdot t+9\right)\\ 4t^2\left(2t+9\right)\end{array}$

Therefore the GCF is common factor in both terms.

  $GCF=4t^2$

Now, find the GCF of last two factor,

The GCF of last two terms, take only last two terms,

  $2\cdot t+9$

No common factor,

  $GCF=1$