# Remainder Theorm

• Dec 16th 2007, 09:09 AM
Chez_
Remainder Theorm
When x^3+kx+5 is divided by x-2 the remainder is 3. use the remainder theorm to find the value of k.

I have the remainder theorm, for a polynomial f(x). f(a) is the remainder when f(x) is divided by x-a.

but im not sure how to apply the theorm the the question..thanks for your time.
• Dec 16th 2007, 09:11 AM
DivideBy0
Quote:

Originally Posted by Chez_
When x^3+kx+5 is divided by x-2 the remainder is 3. use the remainder theorm to find the value of k.

I have the remainder theorm, for a polynomial f(x). f(a) is the remainder when f(x) is divided by x-a.

but im not sure how to apply the theorm the the question..thanks for your time.

By the remainder theorem, $\displaystyle f(2) = 3$, that is:

$\displaystyle (2)^3+k(2)+5=3$

Can you finished it off?
• Dec 16th 2007, 09:21 AM
Chez_
theorm
well i multiplied it out then solved it... not sure if its right tho

8+2k+5-3=0
8+5-3=k
_____
2

= 5/2=k
• Dec 16th 2007, 09:24 AM
Simplicity
Quote:

Originally Posted by Chez_
well i multiplied it out then solved it... not sure if its right tho

8+2k+5-3=0
8+5-3=k
_____
2

= 5/2=k

$\displaystyle 2^3+2k+5=3$
$\displaystyle 8+5-3 = -2k$
• Dec 16th 2007, 09:26 AM
Chez_
so, if its 8+5-3=-2k do i divide the whole thing by 2 and then gt 5/2
• Dec 16th 2007, 09:28 AM
Simplicity
Quote:

Originally Posted by Chez_
so, if its 8+5-3=-2k do i divide the whole thing by 2 and then gt 5/2

Sorry but I don't understand where you get $\displaystyle \frac{5}{2}$ from?

$\displaystyle 8+5-3=-2k$
$\displaystyle 10 = -2k$

What is $\displaystyle k$?
• Dec 16th 2007, 09:29 AM
Chez_
i miss read it lol i did 8+3-3 lol that wudnt b gd in exam lolk so is k 5
• Dec 16th 2007, 09:33 AM
Simplicity
Quote:

Originally Posted by Chez_
i miss read it lol i did 8+3-3 lol that wudnt b gd in exam lolk so is k 5

Correct. If you are in anyway unsure, just plug your answer back into the function and see if you get the remainder value.

E.G:
$\displaystyle f(x) = x^3-5x+5 = 3$
$\displaystyle f(2) = 2^3 -5(2) + 5 = 3$

EDIT: Remember to watch your sign too.