Question

What is the factor of y = 4x2 +2x -30

Answer 1

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).