Question

determine the value o k such that the first polynomial is divisible by the second k²x⁴-3kx²-4 : x-1

Answer 1

apply mind+formulae

Answer 2

If the polynomial were divisible by x-1, that means if you plug in 1 for x, you should end up with a result of 0.

Answer 3

the second polynomial will be divisible by x-1 if we divide the polynomial by x-1 aand have a remainder of zero. Recall from remainder theorem that the remainder R we will get from dividing any polynomial f(x) by a polynomial x-a could be found by, R=f(a)
now since we are finding the value of k, such that the function will be divisible by x-1, then we know that the remainder will be 0. so we'll have:
f(x)=k^2x^4-3kx^2-4 our a in this case is one...
f(1)=R
f(1)=0
k^2-3k-4=0
(k-4)(k+1)=0
so we have two answers, which are k=4 and k=-1