Identify the factors of the function
y = 4x2 + 2x - 12

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

Step-by-step 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

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