Question

What two methods are the best choices to factor this expression 18x2-8

Answer 1

Answer:

Please check the explanation

Explanation:

The best two methods will be:

• Factor by grouping

• Factor out the GCF

Factor by grouping

Factor by grouping deals with establishing a smaller groups from each term.

$18x^2=\:\left(2\cdot 3\cdot 3\cdot x^2\right)$

$8\:=\:\:2\cdot 2\cdot 2$

Therefore, the expression becomes

$18x^2=\:\left(2\cdot 3\cdot 3\cdot x^2\right)-\left(2\cdot \:2\cdot \:2\right)$

Now factor out the greatest common factor (GCF) which is 2

         $=\:2\left(3\cdot \:\:3x^2-\left(2\right)\left(2\right)\right)$

           $=2\left(9x^2-2\cdot \:2\right)$

            $=2\left(9x^2-4\right)$

Factor out the GCF

Given the expression

$18x^2-8\:\:\:$

factor out common term 2

$=2\left(9x^2-4\right)$

$=2\left(3x+2\right)\left(3x-2\right)$          ∵ $Factors\:\:\left(9x^2-4\right)=\left(3x+2\right)\left(3x-2\right)$