Question

If x⁵- 8 x⁴+ 16 x³ +3x² - 22x + 19 is divided by x - 4, then what is the remainder ?
1. - 21
2. 21
3. 19
4. - 19

Answer 1

Correct Answer - Option 1 : - 21

Given:

Dividend = x⁵- 8 x⁴+ 16 x³ +3x² - 22x + 19

Divisor = x - 4

Concept:

Remainder theorem: According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn’t essentially an element of the polynomial; you will find a smaller polynomial along with a remainder. This remainder that has been obtained is actually a value of P(x) at x = a.

Calculation:

Let us consider, x - 4 = 0

⇒ x = 4

⇒ f(x) = x⁵- 8 x⁴+ 16 x³ +3x² - 22x + 19

When f(x) is divided by (x - 4) then reminder is equal to f(4).

⇒ f(4) = 4⁵- 8 × 4⁴+ 16 × 4³ + 3 × 4² - 22 × 4 + 19

⇒ f(4) = 1024 - 2048 + 1024 + 48 - 88 + 19

⇒ f(4) = -21

∴ If x⁵- 8 x⁴+ 16 x³ +3x² - 22x + 19 is divided by x - 4, then reminder is -21.