Answer:
3(x - 2)(2x + 3)
Explanation:
6x² - 3x - 18 ← factor out GCF of 3 from each term
= 3(2x² - x - 6) ← factor the quadratic
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 6 = - 12 and sum = - 1
the factors are - 4 and + 3
use these factors to split the x- term
2x² - 4x + 3x - 6 ( factor the first/second and third/fourth terms )
= 2x(x - 2) + 3(x - 2) ← factor out (x - 2) from each term
= (x - 2)(2x + 3) ← in factored form
then
6x² - 3x - 18 = 3(x - 2)(2x + 3)