Dividing Polynomials.

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Presentation transcript:

Dividing Polynomials

Long Division of Polynomials

Long Division of Polynomials

Long Division of Polynomials

Long Division of Polynomials with Missing Terms You need to leave a hole when you have missing terms. This technique will help you line up like terms. See the dividend above.

Divide using Long Division and check your answer. Example Divide using Long Division and check your answer.

Divide using Long Division. Answer Divide using Long Division.

Divide using Long Division and check your answer. Example Divide using Long Division and check your answer.

Divide using Long Division. Answer Divide using Long Division.

Example Divide using Long Division and check your answer.

Divide using Long Division. Answer Divide using Long Division.

Dividing Polynomials Using Synthetic Division

Comparison of Long Division and Synthetic Division of X3 +4x2-5x+5 divided by x-3

Steps of Synthetic Division dividing 5x3+6x+8 by x+2 Put in a 0 for the missing term.

ANSWER: Steps of Synthetic Division dividing 5x3+6x+8 by x+2 Put in a 0 for the missing term.

Using synthetic division instead of long division. Notice that the divisor has to be a binomial of degree 1 with no coefficients. Thus:

Example Divide using synthetic division.

Divide using synthetic division. Answer Divide using synthetic division.

Divide using synthetic division. Example Divide using synthetic division.

Divide using synthetic division. Answer Divide using synthetic division.

Complete the problems below. Find the value f(2) for the given function. Use Synthetic Division to divide: f(x)=x3- 4x2+5x+3 What do you notice?

The Remainder Theorem

If you are given the function f(x)=x3- 4x2+5x+3 and you want to find f(2), then the remainder of this function when divided by x-2 will give you f(2) f(2)=5

Example Use synthetic division and the remainder theorem to find the indicated function value.

Example Use synthetic division and the remainder theorem to find the indicated function value.

(a) (b) (c) (d)

(a) (b) (c) (d)

(a) (b) (c) (d)

(a) (b) (c) (d)