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.
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!
10 answers
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
Wait I got it! (3x+5)(4x-1). I have a few more...
2x(3x+4)-3(3x+4)
-2x(x+7)-(x+7)
-2x(x+7)-(x+7)
use the distributive property:
a(b+c) + d(b+c) = (a+d)(b+c)
So, the first is just
(2x-3)(3x+4)
a(b+c) + d(b+c) = (a+d)(b+c)
So, the first is just
(2x-3)(3x+4)
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?
ummm, -x = -1x
Ya, but one is x^2=14x+5
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
x^2 - 14x - 5 = 0
good luck factoring this one. Better use the quadratic formula:
x = (14±√216)/2 = 7±3√6
Oh! I get that now!
Thank u soo much!
Thank u soo much!
1 answer