Thread: polynomials

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

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

by the remainder theorem, we need P(2) = P(-1)

P(2) = P(-1) , so do u subsititue both of these to x? do u mean that both of these will result in the same remainder?

Originally Posted by lickman

P(2) = P(-1) , so do u subsititue both of these to x? do u mean that both of these will result in the same remainder?

the remainder theorem says, that if a polynomial P(x) is divided by (x - a) then the remainder is P(a)

so the remainder when P(x) is divided by x - 2 is P(2) and the remainder when P(x) is divided by x + 1 is P(-1). we want these to be equal, so we set them equal.

P(2) means you replace all the x's in P(x) with 2 and simplify. do the similar thing for P(-1). set the expressions equal to each other. you will have a linear equation in b, solve for b

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

Code:

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

We have a remainder of

Now, the synthetic division process for

Code:

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

We have a remainder of

Now, we want a value of that gives us the same remainder:



I hope this makes sense!

--Chris

lol hey, thanks for the effort really appreciate but i never learned the synthesis divison lol. so can u use the P(2) = P (-1) and show me haha thanks!?!?!?!

oh nvm, how stupid of me, i understand it thanks! i get it now LOL