 Remainder and Factor Theorems

Presentation on theme: "Remainder and Factor Theorems"— Presentation transcript:

Remainder and Factor Theorems
Section 7.4

The Remainder Theorem If a polynomial f(x) is divided by x-a, the remainder is the constant f(a), and Dividend=quotient *divisor +remainder Where is a polynomial with degree one less than the degree of f(x)

Remember Lesson 5-3 for Synthetic Division
The Remainder Theorem Remember Lesson 5-3 for Synthetic Division

The Remainder Theorem Remainder = 1

Your Turn: Use synthetic substitution to find g(3) for the function:

Since the remainder is 0, x-3 is a factor of the polynomial.
The Factor Theorem Since the remainder is 0, x-3 is a factor of the polynomial.

The Factor Theorem When you divide the polynomial by one of the binomial factors , the quotient is called a depressed equation.

The Factor Theorem Remainder = 6 , therefore (x-2) Is NOT a factor

The Factor Theorem Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some factors may not be binomials.