IDM College Maths Algebra Worksheet

(6) Let h(x) = x + ax2 + bx + c, where a, b, cER. It is given that x2 – 1 is a factor of h(x). Show
that b=-1.
It is also given that the remainder when h(x) is divided by x2 – 2x is 5x + k, where KER. Find
the value of k and show that h(x) can be written in the form (x – 2)2(x – 1), where a,uER.