Question

If the polynomial 2x⁴ + kx³ - 75k is divided by x the remainder is 150, then the value of k will be:
1. 2
2. -1
3. -2
4. 1

Answer 1

Correct Answer - Option 3 : -2

Concept:

If a polynomial f (x) is divided by (x - a), the remainder is f (a).

f (x) = (x -a) Q (x) + f (a)

Calculation:

Now according to the remainder theorem, when f(x) is divided by x then the remainder is f(0)

Now, f(0) = 2(0)⁴ + k(0)³ - 75k

So, f(0) = - 75k

Now, -75 k = remainder = 150

∴ k = -2