Question

The expression 2x^3+hx^2−6x+1 leaves a remainder of 2k when divided by (x+2) and when the same expression is divided by (x-1), the remainder obtained is k. Find the values of h and k.

Answer 1

Answer:

Let f(x)=

$2x ^{3} −kx ^{2} +7x−1.$

Now according to the remainder theorem, when f(x) is divided by x−1 then the remainder is f(1).

Now, f(1)=2−k+7−1=8−k.

According to the problem,

8−k=3

or, k=5.

Answer 2

Correcting the slip by anonymous in equation 2 to get

h-k =-3

So i get,

-2x^3+3x^2+11x-6

Using algebraic long division of given factor (x-2)

To obtain f(x) = (x-2)(-2x^2+7x-3)

And factorising the quatratic by inspection

We obtain

f(x)=(x-2)(-2x+1)(x-3)

here, I answered your question!!