If k is a constant, what is the value of the polynomial k^2x^3-6kx+9 is divisible by x-1?

Help please. I am not sure on what to do here.

Question

If k is a constant, what is the value of the polynomial k^2x^3-6kx+9 is divisible by x-1?

Help please. I am not sure on what to do here.

angel_kitty12 · Answer

$$k^2x^3-6kx+9 $$ divisible by x-1

angel_kitty12 · Answer

algebra 2 by the way

satellite73 · Answer

if it is divisible by $x-1$ that means when you replace $x$ by $1$ you get $0$

satellite73 · Answer

put $x=1$ set $$k^2-6k+9=0$$ solve for $k$

satellite73 · Answer

it is a way to get you to solve a quadratic equation is all

angel_kitty12 · Answer

Can you elaborate on that?

satellite73 · Answer

sure

satellite73 · Answer

if you have a polynomial $p(x)$ with $p(r)=0$ that means $x-r$ is a factor of $p(x)$

satellite73 · Answer

it is called the "factor theorem" or sommat
like if you know how to factor you can find the zeros, this says it works in reverse too
if you know a zero, you can factor

angel_kitty12 · Answer

So i would have to factor the equation? I'm sorry but this is very confusing to mw

satellite73 · Answer

the theorem is what leads you to the method for solving the question, which is why it is confusing when it is written this way

satellite73 · Answer

you don't have to factor $$k^2x^3-6kx+9$$ you are told that $x-1$ IS a factor
that means if you replace $x$ by $1$ you will get 0

angel_kitty12 · Answer

oh, i didn't see that post

angel_kitty12 · Answer

Oh, so x-1 would be x=1 which is a zero that could be used to plug in for x to solve k

satellite73 · Answer

yeah exactly 
put $x=1$ and set the result equal to zero
then solve for $k$

angel_kitty12 · Answer

is k equal to 3 ?

satellite73 · Answer

yes it is

satellite73 · Answer

want to check it /

angel_kitty12 · Answer

I am now

satellite73 · Answer

i mean check to see that $x-1$is a factor

angel_kitty12 · Answer

Yeah.. I realized that I couldn't plug in the numbers to check it like an ordinary equation. How do I check to see if x is the factor?

satellite73 · Answer

put $k=3$ get $$9x^3-18x+9$$ right?

angel_kitty12 · Answer

x-1 is the factor

satellite73 · Answer

has a common factor of 9. get $$9(x^3-2x+1)$$ and hat one factors

angel_kitty12 · Answer

Oh, I didn't factor the GCF. I was doing hard factoring. No wonder I couldn't factor this accordingly.

satellite73 · Answer

$$9(x-1)(x^2+x-1)$$

angel_kitty12 · Answer

okay, wait. I got confused over the x^3. How did you get (x-1) when factoring?

satellite73 · Answer

i guess i just knew how to factor it is all

angel_kitty12 · Answer

Okay, thanks