Long division to find the quotient

Question

Use long division to find the quotient​ Q(x) and the remainder​ R(x) when​ P(x) is divided by​ d(x) and express​ P(x) in the form

​d(x)•​Q(x)+​R(x).

     

​P(x)=x4−6x2−31

      

​d(x)=x+

Answer 1

x^4 -6x^2 -31 divided by x+1 = x^3 -x^2 -5x +5 =Q(x) with R(x) = -36

P(x) = d(x)Q(x) + R(x)

P(x) = (x+1)(x^3-x^2-5x +5) -36

= x^4 -6x^2 +5 -36

= x^4 -6x^2 -31