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## anonymous one year ago what are the factors of x^3-2x^2-29x+30 Please explain the steps too?

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1. anonymous

I know the answers are (x-6) (x-1) (x+5) but how do I explain that?

2. zzr0ck3r

Well you can foil those out or you can notice that $$1$$ is a solution, and then divide the whole thing by $$(x-1)$$ then factor that.

3. zzr0ck3r

Do you know how to do that?

4. anonymous

yes thank you

5. UsukiDoll

1. use the rational root theorem - find all factors of the last term in the polynomial so in that case it's 30 . We need the positive and negative versions 1, 2, 3, 5, 6, 10, 15, 30 -1, -2, -3, -5, -6, -10, -15, -30 2. Plug in one of these numbers and see if our result is 0. If our result is 0, then we have found one of the roots. If not, then we continue until we find a number that can give us 0 For example, if we let x = 1 $1^3-2(1^2)-29(1)+30 \rightarrow 1-2-29+30 =-30+30 = 0$ 3.since we obtained one of the roots. Use long division or synthetic division to find the remaining roots.

6. UsukiDoll

I'm gonna use synthetic division because long division will take some time |dw:1439178108445:dw|

7. UsukiDoll

now we factor $x^2-x-30$ the middle term has to be -1 and the last term is -30 suppose we use this combination 5 x -6 = -30 then 5-6 = -1 so we need a positive 5 and a negative 6 (x+5)(x-6)

8. UsukiDoll

so now we got the remaining roots using synthetic division (you can use long division too... takes time but the results are the same) we have (x-1) from the rational root theorem and (x+5)(x-6) with synthetic division therefore (x-1)(x+5)(x-6)

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