Need to know this: (x + a)(x + b) = x^2 + (a+b)x + ab

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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)

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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