1. ## Is this correct?

I was assigned homework for the long weekend. I was asked to answer the following question:

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

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

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

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

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

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: $(2x^4-11x^3+12x^2+x-4)$

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

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

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

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

Am I correct?
$2x^4-11x^3+12x^2+x-4 = (x-1)(x-1)(2x^2-7x-4)$

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

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

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

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