How do i find the quotient and remainder R(x) when​ P(x) is divided by​ d(x) and express​ P(x) in the form ​d(x) times ​Q(x)+R(x).

Question

p(x)=x⁴-12x²-66

d(x)=x+4

Answer 1

You divide them.

A simple case:

Let P(x) = 9 and let D(x) = 2

4

2 | 9

8

----

1

So Q(x) = 4 and the R(x) = 1

Which means that 2•4 + 1 = 9 or D(x) • Q(x) + R(x) = P(x)

So to find Q(x):

Divide D(x) into P(x) and whatever is left over is the remainder or R(x)

x + 4 | x⁴ + 0x³ - 12x² + 0x - 66

Perform this division just like you would a long division problem with numbers in it