Question

Find the value of k so that x³ - 3x² + 4x + k is exactly divisible by x - 2.
1. 4
2. -4
3. -6
4. -8

Answer 1

Correct Answer - Option 2 : -4

Given:

x3 - 3x2 + 4x + k is divisible by x - 2

Concept used:

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

Calculation:

x3 - 3x2 + 4x + k is divisible by x - 2

So, x - 2 is a factor of x3 - 3x2 + 4x + k

x - 2 = 0

Hence, x = 2

Substituting x = 2 in x3 - 3x2 + 4x + k

x3 - 3x2 + 4x + k = 0

(2)³ - 3(2)² + 4(2) + k = 0

⇒ 8 - 12 + 8 + k = 0

⇒ k = -4

∴ The value of k is -4.