Factor completely. 25x^2 – 15x – 4?

回答 (8)

2008-02-19 4:55 am

✔ 最佳答案

Come on:
(5x - 4)(5x + 1)
Sorry jumped out at me.

But here's how.
if 25x^2 - 15x - 4 is factorable, then there must be an a,b,c, and d such that
(ax + b)(cx + d) = 25x^2 - 15x - 4

That would make
ac = 25,
ad + bc = -15, and
bd = -4

a and c have to be 5 and 5 or 25 and 1
b and d have to have opposite signs because bd is negative. Were they both positive or both negative bd
so b and have to be 1 and -4, 2 and -2, or -1 and 4

Now we have to do some mental gymnastics with the factors to see what we can come up with for ad+bc

Quickly you can imagine the product of 25 and 4 is going to be way too large. So is the product of 25 and 2. The product of 25 and 1 is closer, but that leaves 1x4 as the other product, and the difference is 16, not 15, so that's out.

That leaves factors that look like
(5x + b)(5x + c)
2 and -2 are going to give us 25x^2 - 4.... not what we want
That means the factors look like
(5x + 4)(5x - 1), or
(5x - 4)(5x + 1)

The first pair give a +15 as the x coefficient. That leaves the second... and that's what I came up with originally.

Addendum: For those who "solved it," you have no idea what's 25x^2 - 15x - 4 is equal to. That makes it rather difficult to solve. ;-)

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