Question

① Find the remainder when x⁴ +2x³ - 3x²+ x-1 is divided by x‐2 using remainder theorem
​

Answer 1

Let,

p(x) = x⁴ + 2x³ - 3x² + x - 1 and, - Dividend

g(x) = x - 2 - Divisor

Zero of g(x) :-

x - 2 = 0

→ x = 2

Putting the value of (x) in p(x).

∵ p(x) = x⁴ + 2x³ - 3x² + x - 1

∴ p(2) = 2⁴ + 2(2)³ - 3(2)² + 2 - 1

= 16 + 16 - 12 + 2 - 1

= 32 - 10 - 1

= 32 - 11

= 21 (Remainder)

Required Solition:-

➯ Dividing (x - 2) with (x⁴ + 2x³ - 3x² + x - 1) leaves a remainder of 21.

Answer 2

Reminder Theorem :

g(x) = x - 2

→ x - 2 = 0

→ x = 0 + 2

.°. x = 2

___________....

p(x) = x⁴ + 2x³ - 3x²+ x - 1

p(2) = (2)⁴ + 2(2)³ - 3(2)² + 2 - 1

p(2) = 16 + 2(8) - 3(4) + 1

p(2) = 16 + 16 - 12 + 1

p(2) = 32 - 13

p(2) = 21

.°. The remainder is 21...