P(x): Polynomial function.
D(x): - The Divider (What you used to divide the polynomial function). “D is for Divider”.
R(x): - The Reminder (Quantity that is left over after the division operation).
The two ways to write a Deperessed Polynomial :
*P(x) = D(x)*Q(x)+R(x)*
OR
P(x)/D(x) = Q(x) + R(x)/D(x)
OR
If a polynomial P(x) is divided by (x-c), then the remainder ® is P©.
Proof:
P(x) = Q(x)(x-c) + r
P(c) = Q(c)(c-c) + r
P(c) = Q(c)(0) + r
P(c) = r
We can essentially rewrite P(x) = Q(x)(x-c) + r to P(x) = Q(x)(x-c) + P(c)
If P(x) is a polynomial and P© = 0; Then (x-c) is a factor of P(x). - That is… P(x) = Q(x)(x-c)