# 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.

**Improper**

**Proper**

**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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