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

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1 Answer

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!