Question

Determine the value of k , such that the first polinomial is divisible by the second k^2x^4-3kx^2-4 ; x-1

Answer 1

f(x) = 2(x2 - 3x) + 4 : factor 2 out in the first two terms
= 2(x2 - 3x + (-3/2)2 - (-3/2)2) + 4 : add and subtract (-3/2)2
= 2(x - 3/2))2 + 17/2 : complete square and group like terms

this a aid 2 finish u r task!
hope this helps!! :-)

Answer 2

x-1=0
x=1

so we want x=1 to be a zero of the polynomial
which means we want
f(1)=0

where f(x)=polynomial of course

Answer 3

Once you know the second binomial is a factor of first polynomial, By remainder theorem,
f(1) = k^2(1)^4-3k(1)^2-4 =0
Then, you'll get k^2 - 3k -4 =0
Do the facorization for left hand side, you'll get
(k-4)(k+1) =0
Solve the equation and you'll get 2 values for k.