Question

Factorise 6x²-14x-12​

Answer 1

Answer:

2(x - 3)(3x + 2)

Step-by-step explanation:

Given

6x² - 14x - 12 ← factor out 2 from each term

= 2(3x² - 7x - 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 = 3 × - 6 = - 18 and sum = - 7

The factors are - 9 and + 2

Use these factors to split the x- term

3x² - 9x + 2x - 6 ( factor the first/second and third/fourth terms )

= 3x(x - 3) + 2(x - 3) ← factor out (x - 3) from each term

= (x - 3)(3x + 2)

Thus

3x² - 7x - 6 = (x - 3)(3x + 2) and

6x² - 14x - 12 = 2(x - 3)(3x + 2) ← in factored form