Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) · Q(x) + R(x).

Question

P(x) = 20x⁴ + 16x³ + 9x²,    D(x) = 4x² + 1

Answer 1

20x^4+16x^3+9x^2= (5x^2+4x+1)(4x^2+1) +(-4x-1)

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

P(x) = 20x^4 +16x^3 + 9x^2

D(x) = 4x^2+1

Q(x)=5x^2+4x+1

R(x)=-4x-1

Answer 2