Question

The polynomial 2x^3-2x^2+x-a when divided by x-2 leaves the remainder 5. Find the value of a.​

Answer 1

ATQ, when polynomial 2x^3-2x^2+x-a when divided by x-2 leaves the remainder 5.

given :-

p(x) = 2x³ - 2x² + x - a

g(x) = x - 2

➡ x = 2

on putting values..

➡ p(2) = 2(2)³ - 2(2)² + 2 - a = 5 (since remainder is 5)

➡ 16 - 8 + 2 - a = 5

➡ 8 + 2 - a = 5

➡ 10 - a = 5

➡ -a = 5 - 10

➡ -a = -5

➡ a = 5

VERIFICATION :-

= 2(2)³ - 2(2)² + 2 - 5

= 16 - 8 - 3

= 8 - 3

= 5

hence, the value of a is 5.