1. ## Division & Remainder of Polynomials - please need help

Hi this is the question, I have no idea how to solve it so help would be appreciated.

Q: When a polynomial is dived by (2x+1)(x-3), the remainder is 3x -1. What is the remainder when the polynomial is divided by 2x + 1?

Please, help would be tremendously appreciated. Please show working out, and WHY you must do that working out.

Thank you very much everyone.

2. Originally Posted by SeaNanners
Hi this is the question, I have no idea how to solve it so help would be appreciated.

Q: When a polynomial is dived by (2x+1)(x-3), the remainder is 3x -1. What is the remainder when the polynomial is divided by 2x + 1?

Please, help would be tremendously appreciated. Please show working out, and WHY you must do that working out.

Thank you very much everyone.

The polynomial has a remainder $3x-1$ when divided by $(2x+1)(x-3)$

If $P(x)=(2x+1)(x-3)(3x-1)$

and you divide that by $(2x+1)(x-3)$, what will the answer be ?

The polynomial has a remainder $3x-1$ when divided by $(2x+1)(x-3)$

If $P(x)=(2x+1)(x-3)(3x-1)$

No, but 3x-1 is the remainder not a factor. So P(x) = Q(x).(2x+1)(x-3) + 3x -1. The question is asking what is the remainder if it is P(x)/2x+1, so P(x)=Q(x).(2x+1) + ......... Now the ......... is what must be found. I know its something to do with the remainder theorem but I don't know how to use it.

Thanks anyways.

4. That remainder! sorry!

$\displaystyle\frac{P(x)}{(2x+1)(x-3)}=A(x)+\frac{3x-1}{(2x+1)(x-3)}$

$\displaystyle\frac{P(x)}{(2x+1)}=\frac{P(x)[x-3]}{(2x+1)[x-3]}=A(x)[x-3]+\frac{(3x-1)[x-3]}{(2x+1)(x-3)}$

same remainder!