Question

How do you factor `16x^3 - 28x^2 - 30x`?

Answer 1

`y = 2x(8x^2 - 14x -15)`

Factor `(8x^2 - 14x - 15)` = (x - p)(x - q).
Converted trinomial: `(x^2 - 14x - 120)` = (x - p')(x - q').
Find p' and q' by composing factor pairs of a.c = -120. Proceed:...(-4, 30)(-6, 20). This sum is 14 = -b. Then p' = 6 and q' = -20.

Then,`p = (p')/a = 6/8 = 3/4` and `q = (q')/a = -20/8 = -5/2.`

Finally: `y = 2x(x + 3/4)(x - 5/2) = 2x(4x + 3)(2x - 5))`