## Falling_In_Katt one year ago Which of the following expressions is a factor of the polynomial x ^ 2 +3/2 x - 1? A. x-1/2 B. x-2 C. x-1 D. x+3/2

1. Falling_In_Katt

@Luigi0210

2. Luigi0210

Is it this? $$\large x^2+\frac{3}{2}x-11$$?

3. Luigi0210

Whoops, that's suppose to be 1 not 11

4. Falling_In_Katt

yes

5. Luigi0210

If you know synthetic division it would work great here

6. Falling_In_Katt

I have no clue how to do that.

7. Luigi0210

Well synthetic division is another way of doing long division. All you have to do is take the coefficients of the polynomial and write in an upside down division bar like so: |dw:1436559961111:dw| Since the coefficients of $$x^2+3/2 x -1$$ are 1, 3/2, and -1 On left you put what you are dividing by, so let's try x-1/2 $$x-\frac{1}{2}=0$$ so $$x=\frac{1}{2}$$ |dw:1436560076049:dw|

8. Luigi0210

To solve, just bring down the first number: |dw:1436560162906:dw| Now just multiply by the left number and add it to the next number: |dw:1436560201845:dw|

9. Luigi0210

And just continue on till you get to the end: |dw:1436560295604:dw| And if you end up getting 0, then it means that it is a factor, so $$\large x-\frac{1}{2}$$ is a factor.

10. Falling_In_Katt

Oh..

11. Luigi0210

If you don't know synthetic division you can always go the quadratic formula way: $$\Large \frac{- b \pm \sqrt{b^2 -4ac}}{2a}$$ But knowing synthetic division would be great for you.

12. Falling_In_Katt

okay