# The Remainder Theorem question

• Oct 18th 2012, 08:03 AM
Danthemaths
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
• Oct 18th 2012, 08:14 AM
Plato
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.
• Oct 18th 2012, 08:22 AM
Danthemaths
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???
• Oct 18th 2012, 09:55 AM
Plato
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\$