Question

Find the remainder when x^5 - 3x^3 + x - 5 is divided by x - 2​

Answer 1

Given info:- Find the remainder when x^5 - 3x^3 + x - 5 is divided by x - 2

Solution:-

Given,

p(x) = x^5 - 3x^3 + x - 5 , g(x) = x - 2

Let g(x) = x-2 will be the factor of p(x) if p(2) = 0.

Now, p(x) = x^5 - 3x^3 + x - 5

p(2) = (2)^5 - 3(2)^3 + 2 - 5

= (2*2*2*2*2) - 3(2*2*2) + 3 - 5

= 32 - 3(8) + 3 - 5

= 32 - 24 + 3 - 5

= 31 - 24 - 2

= 31 - 26

= 5 Remainder.

Hence, when x^5 - 3x^3 + x - 5 is divided by x - 2 , we get the remainder as 5.