1. 4.3 The Remainder & Factor Theorems
Objective: Find the factors of polynomials using the Remainder & Factor Theorems

2. P(x)=[x-r] · Q(x) + P(r),
Remainder Theorem:
If a polynomial P(x) is divided by x-r, the remainder is a constant P(r), and
P(x)=[x-r] · Q(x) + P(r),
where Q(x) is a polynomial with degree one less than the degree of P(x).
Factor Theorem:
The binomial x-r is a factor of the polynomial P(x) iff. P(r) = 0. (remainder is 0)
Synthetic Division:
Shortcut to long division

3. Ex. 1)
Ex. 2)
Ex. 3)
Use the remainder theorem to find the remainder when x³- x²- 5x- 3 is divided by
(x-3). State whether the binomial is a factor of the polynomial. Explain.
Ex. 4)
Determine the binomial factors of
x³- 2x²- 13x- 10

4. Ex. 5)
Find the value of j so that the remainder of
(x³+ 6x²- jx- 8) ÷ (x – 2) is 0.