When factored, the trinomials x2 − 12x + 35 and x2 − 2x − 35 have one binomial factor in common. What is this factor?
x − 7
x + 7
x − 5
x + 5

- some.random.cool.kid

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- some.random.cool.kid

@sammixboo @sleepyhead314 @freckles @robtobey @rvc @ParthKohli @Michele_Laino

- some.random.cool.kid

this is just the first one i have quite a few more.

- some.random.cool.kid

@AlexandervonHumboldt2 @kropot72 @ikram002p @Jaynator495 @Jesstho.-. @just_one_last_goodbye

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## More answers

- some.random.cool.kid

@Mehek14 @Data_LG2

- some.random.cool.kid

@inkyvoyd

- Maddy1251

(5 + -1X)(7 + -1X) = 0 is the first polynomial I have factored.

- some.random.cool.kid

ok

- some.random.cool.kid

so now distribute each correct?

- Maddy1251

the second one is (x+5)(x-7)

- Maddy1251

No. You look for a common factor they have.

- some.random.cool.kid

oh alright afterwards I just do this for each until they match a common factor?

- Maddy1251

Yup. Factor each polynomial out until you find them in the (x+n)(x-n) form, or however they need to be factored, and you will find a common factor for each.

- Maddy1251

x2 − 12x + 35 = (x-5)(x-7)

- Maddy1251

Looks like x-7 is your common factor.

- some.random.cool.kid

oh my gosh I just realized that there are two separate equations ok that makes much more sense now.

- some.random.cool.kid

and thank you very much.

- Maddy1251

Haha yeah! :-) You're welcome!

- some.random.cool.kid

ok well that helped didn't realize that think you can help with another bit different this time but same concept.

- Maddy1251

Yes.

- some.random.cool.kid

ok thanks
What is one factor of 20x2 + 6x − 8?
2x − 1
4x + 2
5x − 4
10x − 1
I was thinking that I can factor by two each? although that wouldn't work for the second half.

- Maddy1251

Well, We want to have a factor that can go into 20, 6, and 8. A does this, B does this, C and D do not.

- Maddy1251

So that helps eliminate half our answers.

- Maddy1251

Do you understand what I mean by that?

- some.random.cool.kid

uh so that factor would be 2? and I am not sure about the second half with the minus. all i know is that they all factor by two.

- Maddy1251

That's true. Correct. Well I can figure that out for you if you want it.

- Maddy1251

( 2x − 1)(10x+8)
20x^2+16x-10x-8. Does this equal the equation?

- some.random.cool.kid

yes I would like to learn it, im not sure why it is left over. Please explain.

- Maddy1251

\[20x ^{2}+6x-8\]

- some.random.cool.kid

hmm :o i see it now.

- Maddy1251

Yeah!

- Maddy1251

See why it isn't D either?

- Maddy1251

Because we need 10x+1. Not 10x-1.

- Maddy1251

I just did the factor concept to find our first factor.

- some.random.cool.kid

OH i was about t say I was confused because i thought the 20 divided by 2 becomes 10 but if it needs to + sign I guess that makes sense... during any of this do I have to flip signs?

- Maddy1251

No.. the only time I know about flipping signs is with inequalities, when you divide/multiply with negative numbers.

- Maddy1251

But remember 10/6 and 10/4 doesn't give whole numbers.

- some.random.cool.kid

ahhhh so since this needs a + sign does this meanyour left with 4x + 2?

- Maddy1251

No, your answer is A.

- some.random.cool.kid

yeah thats what i was confused about because the 10 feeds a decimal.

- some.random.cool.kid

:O please explain im lost.

- Maddy1251

Remember the factor of \[20x ^{2}+6x-8=(2x-1)(10x+8)\]

- Maddy1251

2 goes into 20, 6, and 8 in such a good manner. 4 only goes into 20 and 8.

- Maddy1251

And our second factor won't be (10x+8), or we would get a different polynomial

- some.random.cool.kid

ahah missed that part.

- Maddy1251

That's why 2x-1 works so well.

- Maddy1251

Yeah! They tried getting you with answer choice D.

- Maddy1251

It's their trick .

- some.random.cool.kid

I know funny thing is I almost fell for it to then figured I would go on openstudy to check. thanks. I have only a few more mind helping? I might have to pst a new thread though because OS sometimes crashes when the page is to long from the lag.

- Maddy1251

It's okay, it happens. :-) I would love to help, and go ahead and start a new thread and mention me in it.

- Maddy1251

While you do that, I will grab a bite to eat.

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