find values

**mark** · September 19th 2009, 05:42 AM

hi, i've got the question:

the polynomials f(x) and g(x) are defined by $f(x) = x^3 + px^2 - x + 5$ , $g(x) = x^3 - x^2 + px + 1$ where p is a constant. when f(x) and g(x) are divided by x - 2 the remainder is R in each case. find the values of p and R

i got it down to
R = f(2) = 8 + 4p - 2 + 5 = 11 + 4p and
R = g(2) = 8 - 4 + 2p + 1 = 5 + 2p but i'm not sure if either of those are right.

can someone show me the way to do it please? thanks

**VonNemo19** · September 19th 2009, 05:48 AM

Originally Posted by mark

hi, i've got the question:

the polynomials f(x) and g(x) are defined by $f(x) = x^3 + px^2 - x + 5$ , $g(x) = x^3 - x^2 + px + 1$ where p is a constant. when f(x) and g(x) are divided by x - 2 the remainder is R in each case. find the values of p and R

i got it down to
R = f(2) = 8 + 4p - 2 + 5 = 11 + 4p and
R = g(2) = 8 - 4 + 2p + 1 = 5 + 2p but i'm not sure if either of those are right.

can someone show me the way to do it please? thanks

I would start by dividing each by x-2, then set the remainders equal.

**galactus** · September 19th 2009, 05:52 AM

$\frac{x^{3}+px^{2}-x+5}{x-2}=\underbrace{\frac{4p+11}{x-2}}_{\text{remainder}}$

$\frac{x^{3}-x^{2}+px+1}{x-2}=\underbrace{\frac{2p+5}{x-2}}_{\text{remainder}}$

$4p+11=2p+5\Rightarrow p=-3$

$R=-1$

Therefore, the remainder in each case would be $\frac{-1}{x-2}$

$\frac{x^{3}-x^{2}-3x+1}{x-2}=\boxed{\frac{-1}{x-2}}+x^{2}+x-1$

$\frac{x^{3}-3x^{2}-x+5}{x-2}=\boxed{\frac{-1}{x-2}}+x^{2}-x-3$

**pacman** · September 19th 2009, 06:48 AM

Galactus, your latexing method is as good as that of soroban, excellent!

**mark** · September 19th 2009, 07:45 AM

ok i understand it now up to $\frac {-1}{x - 2}$ , when you get to that, wouldn't x have to be 3 for the final answer to be -1? how do you know the value of x?

**galactus** · September 19th 2009, 08:33 AM

Yes, p=-3. Sub that in and we get R=-1

Thread: find values

LinkBack

Thread Tools

Display

find values

Similar Math Help Forum Discussions

For the limit below, find values of δ that correspond to the ε values.

help with find values

Find the values of F1 and F2

Find values of variable for which trigonometric expression takes only +ve values?

find all possible values

Search Tags