Question

Find the quotient and remainder obtained on dividing p(x)=4x*x*x*x +11x³+2x²-11x+6 by x²+2x+2 and verify the remainder using remainder theorem

Answer 1

On dividing p(x) = 4x^4 + 11x^3 + 2x^2 - 11x - 6 by g(x) = x^2 + 2x + 2

We get,

q(x) = 4x^2 + 3x – 12

r(x) = 7x + 18

Using remainder theorem,

g(x) x q(x) + r(x)

= (x^2 + 2x + 2)( 4x^2 + 3x – 12) + 7x + 18                           

= (4x^4 + 3x^3 – 12x^2 + 6x^3 + 6x – 24 + 8x^2 + 6x – 24) + (7x + 18)          = 4x^4 + 11x^3 + 2x^2 - 11x – 6                           

= p(x)

Answer 2

Answer is in a picture

Given below