# polynomial

• Sep 18th 2009, 09:19 AM
mark
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
• Sep 18th 2009, 09:21 AM
e^(i*pi)
Quote:

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
• Sep 18th 2009, 09:42 AM
VonNemo19
Quote:

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.
• Sep 18th 2009, 10:01 AM
mark
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