Asked by Mathmat

Factor each quadratic equation:

8x^2+10x-3

25x^2+10x-3

9x^2-15x-14

12x^2+17x-5

I don't get how to even start these! Help!
Answered by Steve
The ability to do these quickly just comes from experience. Sometimes you can recognize standard setups, and others you just have to try a few guess, which will become better over time.

You know the first one will have the form
(8x+?)(x+?)
or
(4x+?)(2x+?)
where the ? may be negative. Now you want the outer and inner products to add up to 10. Since you have -3 at the end, the ? will be 1 or 3, plus or minus.
(8x-1)(x+3)? no, that gives 8x^2+23x-3
Now, 12-2 10, so
(4x-1)(2x+3)? YES

25x^2+10x-3
Since the middle number is relatively small, we probably will not have
(25x-?)(x+?)
So, that leaves
(5x-?)(5x+?)
10 = 15-5, so try
(5x-1)(5x+3) YES

Now try the others, and come back if you get stuck.
Answered by Mathmat
I got the third one (3x-7)(3x+2) but I can't figure out the 4th one. How do I do this that one? I know it can only be 5 and 1, but I tried all of the x values and it doesn't work! I tried 6 and 2, 12 and 1, and 4 and 3
Answered by Mathmat
Wait I got it! (3x+5)(4x-1). I have a few more...
Answered by Mathmat
2x(3x+4)-3(3x+4)

-2x(x+7)-(x+7)
Answered by Steve
use the distributive property:

a(b+c) + d(b+c) = (a+d)(b+c)

So, the first is just
(2x-3)(3x+4)
Answered by Mathmat
Ya I figured those out, but I put down your equation into my notes cause it made more sense than what I did. How do I factor with -x?
Answered by Steve
ummm, -x = -1x
Answered by Mathmat
Ya, but one is x^2=14x+5
Answered by Steve
x^2 = 14x+5
x^2 - 14x - 5 = 0
good luck factoring this one. Better use the quadratic formula:

x = (14±√216)/2 = 7±3√6
Answered by Mathmat
Oh! I get that now!
Thank u soo much!
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