Question

25. Divide -6x4 + 5x + 1 + 11x by 2x2 + 1 and write down the quotient and the
remainder.
Also verify your answer.​

Answer 1

Answer:

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)

Step-by-step explanation: