Answer:
y = 2(x + 2)(2x - 3)
Explanation:
Given
y = 4x² + 2x - 12 ← factor out 2 from each term
= 2(2x² + x - 6) ← factor the quadratic
Consider the factors of the product of the x² term and the constant 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)
Thus
2x² + x - 6 = (x + 2)(2x - 3) , and
y = 4x² + 2x - 12 = 2(x + 2)(2x - 3) ← in factored form