Need to know this: (x + a)(x + b) = x^2 + (a+b)x + ab
.
2x^2 - 5x - 3
We want 2x^2 - 5x - 3 to factor, hopefully with an (x-3) so the bottom (x-3) will cancel out.
(x - 3)( )
That 2x^2 means we have to do this:
(x - 3)(2x ?)
See how 2x^2 - 5x - 3 has a -3 on the end?
That means -3 * ? = -3
(it's the L in FOIL)
? = 1
(x - 3)(2x + 1)
Now the fraction
(x - 3)(2x + 1)/(x - 3)
The (x - 3)'s cancel out leaving us with
2x + 1
.
10x^2 - 26x - 12
(5x + 2)(?x ?)
5x * ?x = 10x^2, so that ? = 2
(5x + 2)(2x ?)
2 * ? = -12, so ? = -6
(5x + 2)(2x - 6)
Now the fraction
(5x + 2)(2x - 6)/(5x + 2)
The (5x + 2)'s cancel out, leaving:
2x - 6
.
x^2 - 5x - 2
(x + 3)( )
(x + 3)(x ?)
3? = -2, so ? = -2/3
(x + 3)(x - 2/3)
x^2 +(7/3)x - 3
We got (7/3) instead of -5 on the x, so (x + 3) doesn't factor out.
Answer: (x^2 - 5x - 2)/(x+3)
.
x^2 - 13x + 36
(x - 4)(x ?)
-4 * ? = 36, so ? = -9
(x - 4)(x - 9)
Now the fraction:
(x - 4)(x - 9)/(x - 4)
The (x-4)'s cancel out leaving:
x - 9