## anonymous one year ago Use the factor Theorem to factor the polynomial completely.

1. anonymous

Given that 2 is a solution; 2x^3+x^2-13x+6=0

2. anonymous

How would I go about solving this?

3. Nnesha

i guess it's p over q method $\huge\rm \frac{ p }{ q }= \frac{ constant }{ leading ~coefficient }$ find factors of leading coefficient and factors of constant term

4. Nnesha

like leading coefficient is 2 and factors 2 and 1 you will write it as $\frac{ constant }{ leading ~coefficinet }=\frac{ ? }{ \pm 2, \pm 1 }$

5. Nnesha

gtg sorry :(

6. anonymous

I'm still confused. The example problem uses synthetic division in the beginning...

7. anonymous

8. triciaal

given that 2 is a solution then (x-2) is a factor. (x-2) is a factor means when you divide the polynomial by the factor there is no remainder. Divide by (x-2) then factor the quadratic

9. triciaal

you already have the polynomial factored what do you need help with?

10. anonymous

The screenshot is an example problem, I was just confused as to what the question was asking.

11. triciaal

|dw:1441855710559:dw|

12. triciaal

|dw:1441855967549:dw|

13. triciaal

factor completely 2 x^3 +x^2-13 x + 6 = (x-2)(2 x-1)(x+3)

14. anonymous

I see!

15. triciaal

great

16. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @Thanasi99 Given that 2 is a solution; 2x^3+x^2-13x+6=0 $$\color{blue}{\text{End of Quote}}$$ ahh i was just looking at the equation didn't read the statement D:D