# Is this correct?

• Oct 1st 2009, 12:15 PM
Barthayn
Is this correct?
I was assigned homework for the long weekend. I was asked to answer the following question:

Factor Completely: \$\displaystyle (2x^4-11x^3+12x^2+x-4)\$

I got \$\displaystyle (x-1)\$ as a factor. Then I divided \$\displaystyle (2x^4-11x^3+12x^2+x-4)\$ by \$\displaystyle (x-1)\$ to get \$\displaystyle (2x^3-9x^2+x+4)\$.

After I got that answer, I used \$\displaystyle (x-1)\$ as a factor, which it worked. So I divided \$\displaystyle (2x^3-9x^2+x+4)\$ by \$\displaystyle (x-1)\$. To get \$\displaystyle (2x^2+11x+14)+18/(x-1)\$.

After that I decomposed \$\displaystyle (2x^3-9x^2+x+4)\$ to get \$\displaystyle (x+2)(2x+7)\$.

After that I put my therefore stated as \$\displaystyle (x-1)(x+2)(2x+7)+18/(x-1) = (2x^4-11x^3+12x^2+x-4)\$. Therefore the zeros are: \$\displaystyle x = 1, -2, -7/2\$

Am I correct?
• Oct 1st 2009, 01:07 PM
Amer
Quote:

Originally Posted by Barthayn
I was assigned homework for the long weekend. I was asked to answer the following question:

Factor Completely: \$\displaystyle (2x^4-11x^3+12x^2+x-4)\$

I got \$\displaystyle (x-1)\$ as a factor. Then I divided \$\displaystyle (2x^4-11x^3+12x^2+x-4)\$ by \$\displaystyle (x-1)\$ to get \$\displaystyle (2x^3-9x^2+x+4)\$.

After I got that answer, I used \$\displaystyle (x-1)\$ as a factor, which it worked. So I divided \$\displaystyle (2x^3-9x^2+x+4)\$ by \$\displaystyle (x-1)\$. To get \$\displaystyle (2x^2+11x+14)+18/(x-1)\$.

After that I decomposed \$\displaystyle (2x^3-9x^2+x+4)\$ to get \$\displaystyle (x+2)(2x+7)\$.

After that I put my therefore stated as \$\displaystyle (x-1)(x+2)(2x+7)+18/(x-1) = (2x^4-11x^3+12x^2+x-4)\$. Therefore the zeros are: \$\displaystyle x = 1, -2, -7/2\$

Am I correct?

\$\displaystyle 2x^4-11x^3+12x^2+x-4 = (x-1)(x-1)(2x^2-7x-4)\$

since \$\displaystyle 2x^4-11x^3+12x^2+x-4 = (x-1)(2x^3-9x^2+3x+4)\$

and \$\displaystyle 2x^3-9x^2+3x+4=(x-1)(2x^2-7x-4)\$ and

\$\displaystyle 2x^2-7x-4 = (2x+1)(x-4)\$
• Oct 1st 2009, 06:34 PM
Barthayn
I do not understand where I went wrong. Can you explain more for me in words instead of mathematical equations?

EDIT: Never mind, I seen where I went wrong. Thank you for your help :D