Question

How do you factor `16b^2 +10b -21`?

Answer 1

`f(x) = 16x^2 + 10x - 21 = (x - p)(x - q)`
Converted function:`f'(x) = x^2 + 10 x - 336 =` (x - p')(x - q')
Compose factor pairs of (-336). Proceed:... (-12, 28)(-14, 24). This last sum is: -14 + 24 = 10 = b. Then p' = -14 and q' = 24.

We get: `p = (p')/a = -14/16 = -7/8` and `q = (q')/a = 24/16 = 3/2`

Factored form of f(x):
`f(x) = (x - 7/8)(x + 3/2) = (8x - 7)(2x + 3)`

Check by developing:
`f(x) = 16x^2 + 24x - 14x - 21 = 16x^2 + 10x - 21.` OK