How do you factor Cubic Polynomials?

[Starmaster29]

Hello, me and my friends are all attempting to use this site right now because we have no idea what we're doing. :lol:
Apparently, our math teacher gave us a bonus assignment for the weekend because one person in our class didn't turn in their homework. Unfortunately our teacher didn't explain how to do it... :x

How would you factor, say...

7x[sup:378ve5b1]3[/sup:378ve5b1] - 14x[sup:378ve5b1]2[/sup:378ve5b1] - 3x + 6

Please and thank you very much!!!

 

[Loren]

Re: How do you factor Quadratic Polynomials?

Try grouping the first two terms together and the last two terms together. See if you can find a monomial to factor out of the first two terms. Likewise for the second two terms. At that point it will be in the form am-bm where the m is a binomial. From there, you should get m(a-b).

 

[Starmaster29]

Re: How do you factor Quadratic Polynomials?

Try grouping the first two terms together and the last two terms together. See if you can find a monomial to factor out of the first two terms. Likewise for the second two terms. At that point it will be in the form am-bm where the m is a binomial. From there, you should get m(a-b).

Hmm... well, according to our book...

5x[sup:297vi11a]3[/sup:297vi11a] + 6x[sup:297vi11a]2[/sup:297vi11a] - 45x - 54

factors to

(5x + 6) (x + 3) (x - 3)

Would that method result to an answer like this?

Thanks for replying!

 

[Denis]

Re: How do you factor Quadratic Polynomials?

5x[sup:2p2exqdy]3[/sup:2p2exqdy] + 6x[sup:2p2exqdy]2[/sup:2p2exqdy] - 45x - 54
factors to
(5x + 6) (x + 3) (x - 3)

DO you "see" that 6 * 3 * -3 = -54 ?
And that 5x * x * x = 5x^3 ?

 

[Starmaster29]

Re: How do you factor Quadratic Polynomials?

5x[sup:38rv6uu9]3[/sup:38rv6uu9] + 6x[sup:38rv6uu9]2[/sup:38rv6uu9] - 45x - 54
factors to
(5x + 6) (x + 3) (x - 3)

DO you "see" that 6 * 3 * -3 = -54 ?
And that 5x * x * x = 5x^3 ?

I see; in fact, that was the first thing I saw. However, I don't know the formula (if one exists) for these types of problems. Heck, I wasn't even told what to do... :?

I'll just go backwards and not show work and fail my assignment...

 

[Loren]

Re: How do you factor Quadratic Polynomials?

Poor boy!
Try googling "factor by grouping".

Also, http://www.math.unt.edu/mathlab/emathla ... ouping.htm.

 

[Deleted member 4993]

Re: How do you factor Quadratic Polynomials?

\(\displaystyle 7x^3 \, - \, 14x^2 \, - \, 3x \, + \, 6\)

Loren has been telling you to group. Notice that

Notice that we can factor out 7x^2 from first two terms and 3 from next two terms.

Factor those and see what do you get.....

 

[Starmaster29]

Re: How do you factor Quadratic Polynomials?

Lol, just now I thought about what the polynomial was...

It's not quadratic; the highest exponent isn't two. The highest exponent is 3, so that would make the polynomial a CUBIC polynomial...

Comon, no one noticed that!?

 

[stapel]

It's not quadratic....

Comon, no one noticed that!?

I'd noticed. But the student seemed to be needing to apply simple factoring (the "by grouping" thing mentioned earlier) and then quadratic factoring (as the student had been instructed in class) to find the answer to this exercise, so pointing out the degree didn't seem particularly important.

But yes, the polynomial in question was indeed a cubic.

Eliz.