The Remainder and Factor Theorems. Solve by Using Long Division Example 1Example 2.

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Presentation transcript:

The Remainder and Factor Theorems

Solve by Using Long Division Example 1Example 2

How Might You Solve The Following Examples? Example 1Example 2

Factoring Polynomial Functions Using Long Division Based on the previous examples, how might you solve the following equation?

Solve by Using Long Division Example 1Example 2

Factoring Polynomial Functions Using Long Division Based on the previous examples, how might you solve the following equation?

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). From our previous example this means, P(x)=(x-2) (2x²+3x-8) + 6

Synthetic Division Synthetic division is a shortcut for dividing a polynomial by a binomial of the form x - r

Divide by Using Synthetic Division

Factor Theorem The binomial x - r is a factor of the polynomial P(x) if and only if P(r)=0

Practice Problems Divide using synthetic division.

Practice Problems Use the Remainder Theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial.