1. ## 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?

2. 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

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

3. 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