Question

Factor completely: 2x2 + 2x − 24

Answer 1

What two numbers can be multiplied to obtain the first term of your expression, then what two numbers can be multiplied to get the last term, AND add together to get the middle term?

Answer 2

2 and 12?

Answer 3

or 6 and 4

Answer 4

Start with the first term, (? ) (? )
What would you need to get your \(2x^{2}\)?

Answer 5

(2x )(2x )? i thinkk

Answer 6

or is it (x ) (x )?

Answer 7

x*x=\(x^2\)

Answer 8

so then (2x 4)(2x 6)?

Answer 9

If you FOIL that out, do you get your original expression?

Answer 10

no

Answer 11

is it (x )(2x )?

Answer 12

Yes, exactly.

Answer 13

So you have (2x )(x ), what creates the last term (noticing that one of them will be multiplied by 2)

Answer 14

(2x-4)(x+6)?

Answer 15

FOIL it, do you get your original equation?

Answer 16

No, do you switch 4 & 6?

Answer 17

No, what happens when you multiply the first terms? Can you see how one of the numbers you use will be increased by a factor of 2?

Answer 18

What other factors of -24 do you have?

Answer 19

When you get these difficult ones, I suggest making a table of your factors. You know by your first found term that one of the factors you find will be multiplied by 2. So you have to figure out two numbers that multiply and add with this new factor. So if you have factors A and B, you need to find two that A*B=-24 and 2A+B=2