Question

x⁶ - 4x⁵ + 4x⁴ + 5x³ - 20x² + 22x - 10 when divided by x - 2 leaves a remainder _____.
1. 10
2. -10
3. 6
4. -6

Answer 1

Correct Answer - Option 4 : -6

Given:

The given algebric expression x6 - 4x5 + 4x4 + 5x3 - 20x2 + 22x - 10 is divided by x - 2

Concept used:

If any expression f(x) is completely divided by g(a), then f(a) = 0

Calculation:

Let f(x) = x6 - 4x5 + 4x4 + 5x3 - 20x2 + 22x - 10

And, g(a) = x - 2

Let g(a) divides f(x) completely

So. g(a) = 0

⇒ x - 2 = 0

⇒ x = 2

According to concept, we have

f(2) = 0

⇒ 26 - (4 × 25) + (4 × 24) + (5 × 23) - (20 × 22) + (22 × 2) - 10

⇒ 64 - 128 + 64 + 40 - 80 + 44 - 10

⇒ 212 - 218

⇒ -6

∴ When x6 - 4x5 + 4x4 + 5x3 - 20x2 + 22x - 10 when divided by x - 2 leaves a remainder -6.