factoring polynomials: need to factor r^3 + 6r^2 + 11r + 6

[tku]

r^3+6r^2+11r+6 Need to factor this. I have the answer but not sure how to arrive at it. Thanks

 

[masters]

Re: factoring polynomials

r^3+6r^2+11r+6 Need to factor this. I have the answer but not sure how to arrive at it. Thanks

Hi tku,

The first thing I might suggest to do is use the Rational Roots Theorem to try and find a factor of this polynomial. Set \(\displaystyle f(x)=0\) using these possible zeros \(\displaystyle \pm 1, \pm 2, \pm 3, \pm 6\)

I found \(\displaystyle f(-1)=0\), so -1 is a zero and \(\displaystyle (x+1)\) is a factor.

Use synthetic division to create the depressed quadratic which should be easier to factor.

-1 | 1  6  11  6
       -1  -5 -6
------------------
     1  5   6  0

The depressed quadratic polynomial is \(\displaystyle x^2+5x+6\) You should be able to easily factor this to find your other two factors.