Use synthetic division to find a value of k such that f(x) is divisible by d(x)
f(x)= kx^4 + 8x^2 + 5k d(x)= x-1
PLEASE HELP THANK YOU

Question

Use synthetic division to find a value of k such that f(x) is divisible by d(x)
f(x)= kx^4 + 8x^2 + 5k    d(x)= x-1
PLEASE HELP THANK YOU

kirbykirby · Answer

If $f(x)$ is divisible by $d(x)$, then it must be that $\dfrac{f(x)}{d(x)}$ doesn't leave a remainder. Or in other words, $d(x)$ must be a factor of $f(x)$. 

From the factor theorem, a polynomial $f(x)$ has factor $x-a$ if $f(a)=0$. 

Here, we have that $a=1$ (since $d(x)=x-1$).  So it must be that $f(1)=0$. Now try to solve that, by plugging in $x=1$ and setting $f(x)=0$, and solve for $k$.

anonymous · Answer

YAY got it thanks!!

anonymous · Answer

Could I ask you another question kind of similar??

kirbykirby · Answer

This though is a much faster method than using synthetic division, and gives you same same answer. But, if you do synthetic division, all you have to do is set the remainder  equal to 0, and solve for k.

kirbykirby · Answer

:)

kirbykirby · Answer

sure

anonymous · Answer

Find a value of k such that the remainder in the division of f(x)= 3x^2 - 5kx +1 by d(x) = x + 5  is r=-24... And yes that makes sense setting the remainder to  haha thanks

kirbykirby · Answer

Well it is similar to the previous idea, but now dividing f(x) with $(x+5)$, so $f(-5)=-24$

kirbykirby · Answer

Cause the remainder of dividing a polynomial $f(x)$ by $x-a$ is is equal to $f(a)$

kirbykirby · Answer

Or again, do synthetic division, and set the remainder equal to -24 and solve for k :)

anonymous · Answer

so I would put -5 in for x and solve...

kirbykirby · Answer

yes, and just set that expression equal to -24

anonymous · Answer

oh cool. so -24=3(-5)^2 -5k(-5)+1

anonymous · Answer

so awesome i got -4

anonymous · Answer

thank you so much!!!

kirbykirby · Answer

yay =]