A level C1 Polynomial question (factor theorem)

Struggling to do 12(c) on the attached question it makes no sense to me I have tried to make it = 0 and use trial and error with factor theorem but haven't go an answer. Btw k = 12.

Can somebody help me

as everybody disappeared this afternoon I will try to help you.

The Factor theorem states that if (x-2) is a factor of a polynomial f(x), then f(2) must equal zero.

So if you substitute x=2 into the polynomial you would expect to get zero,

see if this helps ...

I have done that part, its just 12(c) which I am stuck on

sorry I was busy and I did not look properly.

for (c) use the fact that a^6 = (a^2)^3 and use part (b)

sorry I was busy and I did not look properly.

for (c) use the fact that a^6 = (a^2)^3 and use part (b)

doesn't work

let y²=x in the second equation

Then say the y⁶=(y²)³

does this help?

yes i understand now but how did you work out that y^2 = x

it should be obvious that the coefficients of the two equations are the same (numbers in front of letters)

then x^3 goes to y^6
then x^2 goes to y^4
then x^1 goes to y^2

hope it makes sense