P(x) = 4x^3 + 7x + 9, D(x) = 2x + 1

Question

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).

P(x) =

Answer 1

If we use synthetic division, we would just need to write 2x+1 as 2(x+1/2) and then simply divide our resultant quotient by 2:

-1/2 | 4 0 7 9

________-2 1-4_

______4 -2 8|5

4x³+7x+9 = (x+1/2)(4x²-2x+8) + 5/(x+1/2)

4x³+7x+9 = (2x+1)(2x²-x+4) + 10

Hope this helped!