the remainder is 3. find the value of k.

thanks in advanced :)

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- Jan 8th 2009, 10:41 AMcoyoteflarex^3+kx+7 is divided by (x-2) ....
the remainder is 3. find the value of k.

thanks in advanced :) - Jan 8th 2009, 10:53 AMMoo
Hello,

We have $\displaystyle P(x)=x^3+kx+7$

So there exists a polynomial $\displaystyle Q(x)$ such that :

$\displaystyle P(x)=Q(x)(x-2)+3$

One simple way to solve it is to let $\displaystyle x=2$

So we have :

$\displaystyle P(2)=Q(2)(2-2)+3=3$

$\displaystyle (2)^3+2k+7=3$

$\displaystyle 8+2k+7=3$

$\displaystyle k=\dots$