How to factor x^2-26x-87

Question

anonymous · Answer

(x+3)(x-29)

anonymous · Answer

find multiples of -87

-29 * 3 = -87. turns out they add to -26; we're in business

(x - 29)(x + 3)

e.mccormick · Answer

In my case, the first thing that struck me was that 87 is only 3 away from 90.  I know 90 can be divided by 3, so that means 87 can too.  So I divided it by 3, got 29, and said "AH HA!  An easy one!"

anonymous · Answer

Im a bit confused, why did you look at the number with out the variable?

e.mccormick · Answer

Well, it is squared, so it is going to be two factors.  There is nothing in front of the $x^2$ so those factors will be in the form of $(x\pm ?)(x\pm ?)$


Another thing you can use is a little logic.

When you have negatives in a second degree polynomial it tells you a lot about the factors.

$ax^2+bx-c$ the -c means that there is a negative factor.  The + b means the + part needs to be more than the -.

$ax^2-bx-c$ the -c means that there is a negative factor.  The - b means the - part needs to be more than the +.

$ax^2-bx+c$ the -b but +c means there are two negative factors.

e.mccormick · Answer

Let me take $(x\pm 2)(x\pm 3)$ as an example.

The + part is larger:
$(x- 2)(x+ 3) \implies\ x^2-2x+3x-6 \implies\x^2+x-6$

The - part is larger:
$(x+ 2)(x- 3)  \implies\ x^2+2x-3x-6 \implies\x^2-x-6$

There are two -:
$(x- 2)(x- 3)  \implies\ x^2-2x-3x+6 \implies\x^2-5x+6$