GCF(Greatest Common Factor) and Factor by Grouping

Question

Factor Completely:

12x3+15−9x2−20x

Answer 1

(3x² - 5) (4x - 3)

can be factored.

3x^2 - 5 has the form of the difference of two squares:

3x^2 - 5 = ( x√3 + √5 ) ( x√3 - √5 )

So the completely factored form is

( x√3 + √5 ) ( x√3 - √5 ) ( 4x - 3 )

I would suggest you put both answers in case your teacher is not expecting you to go this additional step.

One important purpose of factoring is to determine the zeros of the expression. So factoring this last step is very helpful in finding all the zeros of an expression.

Answer 2

Hi Genesis O

(3x² - 5)(4x - 3)

12x³ + 15 -9x² - 20x

Factor Completely by Grouping

Reorder the terms according to the exponents

12x³ - 9x² - 20x + 15

Group first two terms

(12x³ - 9x²) - 20x + 15

Factor out Greatest common factor from each group

3x²(4x - 3) - 5(4x - 3)

Since (4x -3) is now the greatest common factor that leaves

(3x² - 5)(4x - 3)

I hope this helps.