Chapter 4.4, Problem 10LC

Solution

To find: The GCF (greatest common factor) of the expression $21h^3+35h^2-28h$ .

The greatest common factor (GCF) of the expression is $7h$ .

Given:

The expression is $21h^3+35h^2-28h$ .

Concept used:

The greatest common factor (GCF) of an expression is the common factor of the terms in the expression having greatest exponent and the greatest coefficient.

Calculation:

The greatest common factor (GCF) of the expression $21h^3+35h^2-28h$ is evaluated as:

  $\begin{array}{c}21h^3+35h^2-28h=3\cdot 7\cdot h\cdot h^2+5\cdot 7\cdot h\cdot h-2\cdot 2\cdot 7\cdot h\mathrm{....}\left(\text{Factorize each term}\right)\\ =7\cdot h\cdot \left(3\cdot h^2+5\cdot h-2\cdot 2\right)\mathrm{....}\left(\begin{array}{l}\text{Take common factor }\\ \text{outside the expression}\end{array}\right)\\ =7h\cdot \left(3h^2+5h-4\right)\mathrm{....}\left(\begin{array}{l}\text{ Multiply the common}\\ \text{factors which is the GCF}\end{array}\right)\end{array}$

Now using the concept stated above, the greatest common factor (GCF) of the expression $21h^3+35h^2-28h$ is $7h$ .