Question

Factor x²-7x+12
Can you show me how to do this?

Answer 1

Factor x²-7x+12
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What are two numbers that multiply to 12 and add to -7 ?

Answer 2

The options are
a. (x-3)(x+4)
b.(x-3)(x-4)
c.(x-6)(x-2)
d.(x-1)(x-12)

Answer 3

*-3 and -4

Answer 4

x²-7x+12 = x^2 - 3x -4x +12

Answer 5

x^2 - 3x -4x +12 = x(x - 3) -4(x - 3)

Answer 6

x(x - 3) -4(x - 3) = (x-3) (x - 4)

Answer 7

ok thanks! I'll try the rest on my own and post them to make sure i get it.

Answer 8

That's a good idea.

I used "busting the b" to do the factoring. I'll try to find where I wrote up the technique and post it here for you to use as an example to help learn to factor.

Answer 9

that would be great, thanks

Answer 10

"Bust the b" technique for factoring

4 x² -1x + 18

a = 4 and c = 18 and b = -1.

The task on "bust the b" is to find numbers that mutiply to a*c AND add to b.

In this case, numbers that multiply to 4*18 and add to -1.

14 * 18 breaks aparts into the product of prime factors : 2*2*2*3*3

Look at those five factor of 14 * 18 and try to put them in the form of 2 numbers that differ by -1.

2*2*2 and 3*3 appear to differ by 1. That would be 8 and 9.

"b" has been "busted into 8 and - 9 whose sum is -1 which equals "b" in this problem.

4x - x+ 18 = 4 x² + 8 x - 9 x - 1.

The "b" has been busted.

Factoring by grouping comes next.

4 x² + 8 x - 9 x - 18 =

4x ( x + 2) - 9 ( x + 2 ) = --> On this step, (x + 2) is the common factor of the expression.

[ (x + 2) ] ( 4x - 9 ) =

( x + 2 ) ( 4x - 9)