The Remainder Theorem question

Hey guys I am a bit stuck on how to do this question. Could you please go through step-by-step on how to get the answer! Thank You!

"The Remainder when x^3-2x^2+ax+5 is divided by x-3 is twice the remainder when the same expression is divided by x+1. Find the constant value of a."

I started off like: f(3)=2(x-1) but I am not sure if that is correct or not because I didn't get the right answer. Am I along the right lines but there are more steps or am I off the line completely? Once I can do this question I can answer some of the other questions which is a similar style to this.

Thanks

DantheMaths

Re: The Remainder Theorem question

Quote:

Originally Posted by

**Danthemaths** "The Remainder when x^3-2x^2+ax+5 is divided by x-3 is twice the remainder when the same expression is divided by x+1. Find the constant value of a."

$\displaystyle f(3)=27-18+3a+5~\&~f(-1)=-1-2-a+5$.

Now finish.

Re: The Remainder Theorem question

i did do that but for f(3) i got -14=3a cant remember what exactly and for f(-1) i got 2. I looked at the answer and it says the answer is 4! how can i possibly get to 4???

Re: The Remainder Theorem question

Quote:

Originally Posted by

**Danthemaths** Hey guys I am a bit stuck on how to do this question. Could you please go through step-by-step on how to get the answer! Thank You!

"The Remainder when x^3-2x^2+ax+5 is divided by x-3 is twice the remainder when the same expression is divided by x+1. Find the constant value of a."

I am not sure you understand this problem.

The Remainder when $\displaystyle f(x)=x^3-2x^2+ax+5$ is divided by $\displaystyle x-3$ is $\displaystyle f(3)$

The Remainder when $\displaystyle f(x)=x^3-2x^2+ax+5$ is divided by $\displaystyle x+1$ is $\displaystyle f(-1)$

So $\displaystyle f(3)=2f(-1)$. Solve for $\displaystyle a$