3w^2 +8w -16
2007-07-26 10:25:08 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
3w^2 + 8w - 16 =
(3w - 4)(w + 4)
2007-07-26 10:28:49 · answer #1 · answered by N E 7 · 0⤊ 0⤋
3w^2 +8w -16
3w² + 8w – 16
(aw + b)(cw + d)
acw² + (ad + bc)w + bd
ac=3, so one of them probably equals 3, and the other 1. I say “probably” because 2 and 1.5 are also factors of 3… and there are a whole lot more. But two things make me think otherwise. First, there are no weird fractions anywhere (in the trinomial. Second, this is a pretty elementary problem, and unlikely to have weird stuff like fractional coefficients to trip you up.
So far we have
(3w + b)(w + d)
3w² + (3d + b)w + bd
Now we have to consider b and d.
bd= -16
Because the product is negative, one of them is positive and the other is negative.
The factors or 16 are
1 and 16, 8
2 and 8, and
4 and 4.
Keeping in mind that 3d+b=8…
We can eliminate d=16 and 8 because there’s no way to get 8 from 48 or 24 from there.
We can eliminate d=1 because 16-3 is 13.
We can eliminate d=2 because -6 = 2… What about 8+6? Nope. They have to have different signs.
That leaves 4 and 4. The product of 3 and 4 is 12, and 12-4 is 8…
3w² + 8w – 16 = (3w-4) (w+4)
CHECK
(3w-4) (w+4) = (3w-4)(w)( + (3w-4)(4)
= (3w)(w) + (-4)(w) + (3w)(4) + (-4)(4)
= 3w² + (-4)(w) + (12)(w) + (-16)
= 3w² +(-4 + 12)w - 16
= 3w² + 8w - 16 CHECKS
2007-07-26 17:59:16 · answer #2 · answered by gugliamo00 7 · 0⤊ 0⤋
(3w+4)(w-4)
use foil to check answer
The trick is to factor 16 into 2 numbers that multiply to 16
and when subtracted from each other after multiplying one of them by 3 U get 8.
2007-07-26 17:32:54 · answer #3 · answered by 037 G 6 · 0⤊ 0⤋
(3w-4)(w+4)
2007-07-26 17:28:10 · answer #4 · answered by Andrea 1 · 1⤊ 0⤋