Question

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

Answer 1

Please check the explanation

Step-by-step 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)`