Question

determination the number k so that the polynomial x^3+kx^2-kx+9 gets a factor x+3

Answer 1

are you familiar with remainder theorem?

Answer 2

psst @kalemale ..you there?

Answer 3

no

Answer 4

does not say anything about that in my book

Answer 5

well that's a bummer...how about long division? familar?

Answer 6

yes

Answer 7

let's go with that...

Answer 8

x^2 + (k-3)x + (-4k + 9)
______________________
x + 3 | x^3 + kx^2 -kx + 9
x^3 + 3x^2
===============
(k-3)x^2 - kx
(k-3)x^2+(3k-9)x
================
(-4k+9)x + 9
(-4k+9)x +(-12k +27)

since it's a factor, the remainder should be 0 so

9 - (-12k+27) = 0
9 + 12k -27 = 0
-18 + 12k = 0
12k = 18
k = 18/12
k = 3/2

do you get that?

Answer 9

ye I see now can you do one with the remainder therom? It seems much easier. Thanks for all the help!

Answer 10

now i'll show you the remainder theorem to prove im right

since x + 3 is a factor, x = -3 is a root

therefore p(-3) = 0

P(-3) = (-3)^3 + k(-3)^2 - k(-3) + 9
-27 + 9k + 3k + 9 = 0
12k - 18 = 0
12k = 18
k = 18/12
k = 3/2

Answer 11

Thanks!!!! =)

Answer 12

welcome ^_^