Question

remainder theorum

Consider the polynomial P(x)=(kx^3)+(2x^2)-5x+4.
Find the value of k such that the remainder is -14 when P(x) is divided by x-2

k=?

Answer 1

P(x)=(x-2)Q(x)-14

Answer 2

not sure how to set this one up

Answer 3

Have you done the remainder theorem before?

Answer 4

somewhat

Answer 5

its like 13/5=2 r 3
then 13=5*2+3

Answer 6

P(x)/(x-a)=q(x)+r

Answer 7

then P(x)=(x-a)q(x)+r

Answer 8

Yeah, also--this is key--when you plug in the "a" to get "P(a)", the answer is "r"

Answer 9

So calculate "P(2)" and tell me what you get

Answer 10

its not 2

Answer 11

its -2

Answer 12

No, no, what I mean is this: Take your initial polynomial and plug in "2" for x and tell me the resulting expression.

Answer 13

i got it thanks

Answer 14

But you mentioned "x-a", right? Well, if you have "x-2" then that means that "a" is equal to "2"

Answer 15

(x-(-2))

Answer 16

k(2)^3+2(2)^2-5(2)+4=-14

Answer 17

But in your initial question you said you were dividing by "(x-2)"?

Answer 18

ok, now simplify...

Answer 19

8k+8-10+4=14
8k+2=-14
8k=-16
k=-2

Answer 20

i just need to keep practicing it

Answer 21

Ok, ok. You're right -- k=-2. When you said "it's -2" i didn't know what you were referring to.

Answer 22

:)

Answer 23

so the polynomial is equal to: -2k^3 + 2x^2 ... and do on

Answer 24

thanks for your time @Splash_Dance

Answer 25

Yeah, that was good--you got the answer fast!

Answer 26

Good luck with the rest of your problems