SOLUTION: A polynomial P(x) and a divisor d(x) are given. 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)

Algebra ->  Equations -> SOLUTION: A polynomial P(x) and a divisor d(x) are given. 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)      Log On


   



Question 367590: A polynomial P(x) and a divisor d(x) are given. 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 + 3x2 + 18 d(x) = x2 – 3

Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
x4 + 3x2 + 18 | x2 – 3 = d(x)
-----------------------
x4 - 3x2......| x2 + 6 = Q(x)
--------------|
6x2 + 18......|
6x2 - 18......|
--------------|
......36 = R(x)

Hence : x4 + 3x2 + 18 = (x2 - 3)(x2 + 6) + 36