SOLUTION: I am having a hard time with Variation, Progression, and Theorems. My question is Use the remainder theorem to determine the remainder when 5w^3 -2w+10 is divided by w+3? Can

Question 6613: I am having a hard time with Variation, Progression, and Theorems. My question is Use the remainder theorem to determine the remainder when 5w^3 -2w+10 is divided by w+3?
Can someone please help me, I have already tried to answer this question on my own and cannot seem to get the right answer? Please?
Found 2 solutions by rapaljer, Earlsdon:
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
There are two ways to find the remainder after division by a binomial such as w+3. The first most obvious way is to divide it out, using either long division or synthetic division. However, according to the Remainder Theorem, if a polynomial P(x) is divided by the binomial x-a, then the remainder is P(a).

In this case, using the remainder theorem, is divided by w+3, where a = -3, so the remainder is

. The remainder is -119.

You can check this by synthetic division. Write down the coefficients of the polynomial (be sure it is in descending powers of the variable, and if any terms are missing, be sure to put zero for the coefficients of missing terms).

-3 | 5 ` 0 `-2 ` 10
````` -15 45 -129
_____________________
``` 5 -15 43 -119
The last number is the remainder, -119, so it checks.

R^2 at SCC

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
The remainder theorem states:
If a polynomial P(x) is divided by (x-a), where a is a constant, then the remainder is P(a).
Starting with your polynomial: and the given divisor: (w+3), you should be able to find the remainder by noting that, in this case, a = -3.
The remainder then should be P(-3) Let's find out.

To check this solution, you will need to perform the division, either by long division or by synthetic division.
I have done this and indeed, -119 is the remainder after dividing the given polynomial by w+3
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