Factoring Polynomials
The Remainder Theorem
The Remainder Theorem says that P(a) is equal to the remainder when you divide P(x) by (x - a)
P(a) is the value you get when you plug "a" into x in the polynomial
Example #1
The Remainder Theorem Example #2
The Remainder Theorem Example #3
The Factor Theorem
The Factor Theorem says that if P(a) = 0 (meaning the remainder of P(x) divided by (x - a) is 0), then (x - a) is a factor of P(x).
The Integral Zero Theorem (also called the Factor Property)
The Integral Zero Theorem says that in every factor (x - a) of a polynomial, the value of "a" is a factor of the constant term in the polynomial.
Factoring Polynomials
Find a factor of P(x) by plugging in different values of "a" into P(x) until it equals zero. When you find a factor, divide it by the original polynomial.
Example #1
Factoring Polynomials Example #2
- NOTE: in the final answer, I wrote (x + 3) as a factor, but it should be (x - 3), like I calculated earlier