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Polynomial and Synthetic Division

Objective: In this lesson you learned how to use long division and
synthetic division to divide polynomials by other
polynomials.

Important Vocabulary Define each term or concept.

Division Algorithm

Improper

Proper

Synthetic division

I. Long Division of Polynomials (Pages 284-286)

Dividing polynomials is useful when . . .

When dividing a polynomial f (x) by another polynomial d(x), if
the remainder r(x) = 0, d(x) ________________ into f(x).

The result of a division problem can be checked by . . .

What you should learn
How to use long division
to divide polynomials by
other
polynomials

Example 1: Divide 3x^3 + 4x - 2 by x^2 + 2x +1.

II. Synthetic Division (Page 287)

Can synthetic division be used to divide a polynomial by x^2 - 5?
Explain.

Can synthetic division be used to divide a polynomial by x + 4?
Explain.

What you should learn
How to use synthetic
division to divide
polynomials by binomials
of the form (x -k)

Example 2: Fill in the following synthetic division array to
divide 2x^4 + 5x^2 - 3 by x - 5. Then carry out the
synthetic division and indicate which entry
represents the remainder.

III. The Remainder and Factor Theorems (Pages 288-289)

The Remainder Theorem states that . . .

To use the Remainder Theorem to evaluate a polynomial
function f(x) at x = k, . . .

What you should learn
How to use the
Remainder Theorem and
the Factor Theorem

Example 3: Use the Remainder Theorem to evaluate the
function f (x) = 2x^4 + 5x^2 - 3 at x = 5.

The Factor Theorem states that . . .

To use the Factor Theorem to show that (x - k) is a factor of a
polynomial function f(x), . . .

List three facts about the remainder r, obtained in the synthetic
division of f(x) by x - k:

1)

2)

3)

Homework Assignment
Page(s)
Exercises

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