What are the factors of y=4x^2 + 2x - 30?
First, divide 2 out of this expression. y = 2(2x^2 + x - 30)
One way to factor this would be to find the roots using the quadratic formula:
Since a=2, b=1 and c= -15,
-1 plus or minus sqrt(1^2-4(2)(-15)
x = -------------------------------------------------
4
-1 plus or minus sqrt(121) -1 plus or minus 11
= -------------------------------------- = ----------------------------
4 4
One such solution is -12/4, or -3. The corresponding factor is (x+3), and the other is 5/2, leading to the factor (2x-5).
Therefore, 4x^2 + 2x - 30 = y = 2(2x-5)(x+3).