Question

On dividing x4+2x3+3x2+2x+20 by a polynomial g(x) the quotient obtained is (x2+1) and remainder is 18. Find the value of g(x).

Answer 1

Answer:

g(x) = x^2 + 2 x + 2

Step-by-step explanation:

Given  

On dividing x4+2x3+3x2+2x+20 by a polynomial g(x) the quotient obtained is (x2+1) and remainder is 18. Find the value of g(x).

ANSWER

Given by dividing we can write as

 X^4 + 2 x^3 + 3 x^2 + 2 x + 20 / g(x) = (x^2 + 1) + 18

So  

 X^4 + 2 x^3 + 3 x^2 + 2 x + 20 = g(x) x (x^2 + 1) + 18

 X^4 + 2 x^3 + 3 x^2 + 2 x + 2 = g(x) x (x^2 + 1)

So g(x) = X^4 + 2 x^3 + 3 x^2 + 2 x + 2 / x^2 + 1

Now we can write as

 g(x) = X^4 + 2 x^3 + 2 x^2 + x^2 + 2 x + 2 / x^2 + 1

        = x^2(x^2 + 2 x + 2) + 1(x^2 + 2 x + 2) / x^2 + 1

         = (x^2 + 1) (x^2 + 2 x + 2) / x^2 + 1

g(x) = x^2 + 2 x + 2

Answer 2

Answer:

Step-by-step explanation: