use long divison 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)

Question

P(x)=x^3+7x^2-19x+112

d(x)=x+10

P(x)=(x+10)()+

Answer 1

x+10 into x^3 + 7x^2 -19x+ 112 P/d = Q+R, d(Q+R) = P

is x^2 -3x + 11 with remainder 2

or check with synthetic division

-10 1 7 -19 112

-10 30 -110

1 -3 11 2 which means Q = x^2 -3x +11, R=2 or Remainder = 2/(x+10)

x^3 +7x^2 -19x +112 = (x+10)(x^2 -3x +11 + 2/(x+10) = P(x) = d(Q(x) +R(x))