Question

factor the trinomial.
16s^2 + 8s - 35

Answer 1

Equation is of form: ax^2 + bx + c = 0
Here a = 16, b = 8, and c = -35
1. Is there a common factor in all three terms?
Answer: 16, 8, and -35 have no factor in common, so no.
2. Multiply ac together: 16 * -35 = -560
3. Now come up with two factors of ac, or 560, that add up to b, which is 8.
560 = 2 x 2 x 2 x 2 x 5 x 7
2 x 2 x 7 = 28
2 x 2 x 5 = 20
We need -20 and 28
4. Break up the middle term, 8s into a sum of these two numbers we found: 28s - 20s
and rewrite middle term.
16s^2 + 28s - 20s - 35
5. Now factor by parts. Take a factor out of first two terms, and take a factor out of
last two terms
16s^2 + 28s - 20s - 35
= 4s(4s +7) -5(4s + 7)
6. Now pull out common factor of (4s + 7)
(4s + 7)(4s - 5)