x^2-5x-24 factor into two binomonials

- anonymous

x^2-5x-24 factor into two binomonials

- jamiebookeater

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- anonymous

- anonymous

- anonymous

In order to do this you want to get two factors of -24 that will equal to -5. What two factors of -24 equal -5?

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## More answers

- anonymous

hmm its 1 because they have no other common factor :/

- anonymous

For example factors of 6 are 3 and 2, 1 and 6, -3 and 2, and -1 and 6

- anonymous

When they are multiplied they equal 6.

- anonymous

Step 1: Find multiples for -24.
Step 2: (After getting a few), add together these numbers and see which one gets you -5
Step 3: Use those two numbers that get -5 that multiply to -24
Your numbers should be -8 and 3.
Step 4: Apply these to your x.
(x-8) (x+3) ---> also roots
If you wanted to find the zeroes as well, you would make them both equal to zero. For example, (x-8) would be x-8=0. Do simple math, and your zero is 8.
For now, though, refer to roots.
((I believe I did this right, but the question could be asking something different. We never referred to them as separate binomials in Alg 2, unless what the question is asking is different than what I'm thinking))

- anonymous

ik but 24 and 5 only have -1 in common

- anonymous

So 6 and 4 multiplied equal 24 right?

- anonymous

Yes they do

- anonymous

Okay added up what do they equal?

- anonymous

6 and 4?

- anonymous

10

- anonymous

Good that doesn't equal -5. But what about 8 and 3? That would equal 11, however what if we did -8 and 3? Try adding -8 and 3 what do you get?

- anonymous

ok its negative 5 so -5

- anonymous

yes so now you take those factors and make it into a binomial. So (x-8)(x+3). Now check your work. And multiply the binomials

- anonymous

What do you get when you multiply (x-8) and (x+3)?

- anonymous

(x-5)?

- anonymous

No. what is x*x? or x^(1+1)?

- anonymous

Oh yeah X is always 1

- anonymous

What???? No x multiplied by x is x^2

- anonymous

Oh ok.....

- anonymous

Now what is 3 times x?

- anonymous

- anonymous

its 3x

- anonymous

Good job. Now what is -8 times x?

- anonymous

-8x

- anonymous

Good job. Finally, what is -8 times 3?

- anonymous

-24

- anonymous

Good so now that we have FOILed we will add the answers up so
x^2 + 3x - 8x -24
Combine like terms. 3x - 8x is -5x
x^2 - 5x -24
Does that look like the original problem?

- anonymous

Yes a little bit

- anonymous

A lot of bit because that is what is asking you to factor so we said the answer before and checked it so what is your factored binomial we checked?

- anonymous

x^2 + 3x - 8x -24

- anonymous

No that is not the binomial. That is what the binomial equals, come on we just said it (x-8)(x+3).
So your final answer is (x-8)(x+3). The reason we checked it to see if it was like the question is to ensure accuracy. Hope this helped!

- anonymous

Oh ok thanks you very much

- anonymous

No problem have a great day!

- anonymous

If you need anymore help just tag me.

- anonymous

ok :P

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