Homework Help

[slhartman]

I'm not sure how to factor the following two problems. Could you please help me?

#1 aA^2 b+ 2ab - 15b

#2 x^3 +2x^2 - 5x - 6 given that the following binomial is a factor of the polynomial x+3

Thank you Scarlet

 

[wjm11]

I'm not sure how to factor the following two problems. Could you please help me?

#1 aA^2 b+ 2ab - 15b

#2 x^3 +2x^2 - 5x - 6 given that the following binomial is a factor of the polynomial x+3

Is "A" really supposed to be in the first problem? I'm guessing, "No". Factor b out first, then factor the trinomial into to two binomials.

For the second one, use long division or synthetic division to factor x+3 out of x^3 +2x^2 - 5x - 6. Then you'll be left with a quadratic trinomial, which can be easily factored.

 

[slhartman]

On the first one I ended up with the answer b(a+5)(a-3) and I'm pretty sure that is right.

As far as the second one goes I'm sorry, but I don't understand a word of what you just said. Well, I take that back, I do understand the factor out x+3, but I can't figure out how.

 

[mmm4444bot]

?

Please check number (1) for typographical error(s). That upper-case A looks suspect, to me.

On number (2), you will get another factor, if you divide the cubic polynomial by the given linear polynomial.

It's the same principle as if asked to factor 34, given that a factor of 2 is known.

We would divide 34 by 2 and get a quotient of 17 and no remainder, yes?

That means the factorization of 34 is (2)(17).

So, you divide, too.

?

If you have not yet learned how to divide polynomials by hand, try looking the subject up in your textbook index.

I will also look for some on-lin references.

?

 

[mmm4444bot]

?

Whoops, I jumped the gun.

 

[mmm4444bot]

?
Click here for some lessons on how to divide one polynomial into another, longhand.

?

 

[mmm4444bot]

?

Here's a video lesson at the Khan Academy:

http://www.youtube.com/watch?v=4u8_AMac ... tube_gdata

?

 

[mmm4444bot]

?

If dividing polynomials is something that you've never seen before, then wjm is probably on the right track.

You can reason it out, if you have experience factoring.

(x + 3)*(ax^2 + bx + c) = x^3 +2x^2 - 5x - 6

It's pretty obvious what numbers a and c must be, yes?

?

Another approach, is to use the Rational Roots Theorem. Does that ring any bells?

I really have no way to tell what topics your class is studying, right now.

Verifying potential roots provided by the Rational Roots Theorem gives you the other two factors because, if some root R is verified, then we know (x - R) is a factor.

?

The more specific the information about your situation you provide, the better tailored the responses will be.


?

 

[mmm4444bot]

?

On the first one I ended up with the answer b(a+5)(a-3) and I'm pretty sure that is right. CORRECT!

?