P(x) = 4x^2 + 5x − 3, D(x) = x + 3

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

-3 4 5 -3

-12 21

_________

4 -7 18

4x^2 + 5x - 3 = (x + 3)(4x - 7) + 18

Note also that P(-3) = 18 from Remainder Theorm

4(-3)^2 + 5(-3) - 3 = 18