how do i factor -8x^2 + 14x + 30

Question

i am very confused on how to factor will you help?

Answer 1

This is not an easy task, because factoring is a tough task that only becomes easier with experience. If the coefficient of x² was 1, you only have to worry about working with factors of 30 to get 14 in the middle. In this case you also have to try factors of -8.

The factors of -8 are 8 and -1, or 4 and -2, or these with the signs reversed. so I tried 8 and -1:

     (8x + ?)(-x +?)    Can we fill in the ? with factors of 30, so that I will get 14 in the middle term 

Let's try 30 and 1, 15 and 2, 10 and 3, 6 and 5

     (8x + 30)(-x + 1) = -8x² + 8x - 30x + 30  = -8x² - 22x + 30  DID NOT WORK

     (8x + 15)(-x + 2) = -8x2 + 16x - 15x + 30 = -8x² + x + 30 DID NOT WORK

     (8x + 10)(-x + 3) = -8x2 + 24x - 10x + 30 = -8x² + 14x + 30    WORKED!