1. ## polynomial

the polynomial $\displaystyle P(x) = x^3 + 3x^2 - 2x + k$ has the factor of $\displaystyle x + 1$. find the remainder when P(x) is divided by $\displaystyle x - 3$

thanks for any help

2. Originally Posted by mark

the polynomial $\displaystyle P(x) = x^3 + 3x^2 - 2x + k$ has the factor of $\displaystyle x + 1$. find the remainder when P(x) is divided by $\displaystyle x - 3$

thanks for any help
By the factor theorem $\displaystyle P(-1) = 0$. Therefore k can be found.

Then use long division to find the remainder

3. Originally Posted by mark

the polynomial $\displaystyle P(x) = x^3 + 3x^2 - 2x + k$ has the factor of $\displaystyle x + 1$. find the remainder when P(x) is divided by $\displaystyle x - 3$

thanks for any help
Well, since you know that if (x-c) is a factor of some polynomial P(x), then x=c is a zero. Therefore, $\displaystyle P(-1)=0=(-1)^3+3(-1)^3-2(-1)+k$ will allow you to solve for k.

Then you must use polynomial division to find the indictated quantity.

4. i understand now, but i've got another question i'm not too sure how to tackle:

given that P(x), where $\displaystyle P(x) = x^3 + 3x^2 + kx + 4$ and k is a constant, is such that the remainder on dividing P(x) by (x - 1) is three times the remainder on dividing P(x) by (x + 1), find the value of k

could someone show me how it done? thankyou