Question

I don't know how to factor this polynomial.

r^3+6r^2+11r+6

Please help.

Answer 1

First see if any root that is an integer factor of 6 works in solving
r^3 + 6r^2 + 11r +6 = 0
Try these prime factors of 6:
+ or - 1,2,3, or 6.
+ roots won't work because all polynomial terms would be positive.
-1 works; therefore r+1 is a factor.

Divide (r+1) into r^3+6r^2+11r+6 for the other factor, using polynomial long division. You should get r^2 + 5r + 6.
That can also be factored. Do that and you're done.

Answer 2

That is confusing. We aren't learning it that way.

Answer 3

There is not way to make factoring cubic polynomials easy. The answer to your problem is (x-1)(x-2)(x-3). I did it the quickest way.

Answer 4

Hmmmm. If you are not learning it that way, you are missing a great lesson.

Answer 5

If you are not learning it in a way similar to the method drwls showed you, I would be very curious to know how "they" are teaching you to factor cubic polynomials

Answer 6

I made a mistake in my second post. I mixed up the polynomial equation roots (-1, -2, and -3) with the factors. The factors are (r+1)(r+2)(r+3). The polynomial is zero whenever a factor is zero. Sorry about the confusion.

Answer 7

Solve the following quadratic equation by factoring x^2-6x-16=0