Presentation on theme: "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."— 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)
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:
The Factor Theorem Since the remainder is 0, x-3 is a factor of the polynomial.
When you divide the polynomial by one of the binomial factors, the quotient is called a depressed equation. The Factor Theorem
(x-2) Is NOT a factor Remainder = 6, therefore
The Factor Theorem Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some factors may not be binomials.