Originally Posted by

**lickman** For what value of b will the polynomial

P(x) = -2x^3+bx^2 -5x +2 have the same remainder when it is divided by x-2 and x + 1?

I thought of finding the remainder by using the remainder theorm and combine them both, and i thought of foiling it, but that wont work. u can't use divide it since b is still unkown. what do u do!! lol thanks

You could use synthetic division:

The synthetic division process for $\displaystyle \frac{-2x^3+bx^2-5x+2}{x-2}$

Code:

__
2| -2 b -5 2
-4 2b-8 4b-26
-------------------------------
-2 b-4 2b-13 |4b-24

We have a remainder of $\displaystyle 4b-24$

Now, the synthetic division process for $\displaystyle \frac{-2x^3+bx^2-5x+2}{x+1}$

Code:

__
-1| -2 b -5 2
2 -b-2 b+7
-------------------------------
-2 b+2 -b-7 |b+9

We have a remainder of $\displaystyle b+9$

Now, we want a value of $\displaystyle b$ that gives us the same remainder:

$\displaystyle 4b-24=b+9\implies 3b=33\implies \color{red}\boxed{b=11}$

I hope this makes sense!

--Chris