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

Answer 1

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 \(k\).

Answer 2

YAY got it thanks!!

Answer 3

Could I ask you another question kind of similar??

Answer 4

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.

Answer 5

:)

Answer 6

sure

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

yes, and just set that expression equal to -24

Answer 13

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

Answer 14

so awesome i got -4

Answer 15

thank you so much!!!

Answer 16

yay =]