warm-up. warm-up answers dividing polynomials: objectives: ◦determine the best method to factor...

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Dividing Polynomials:Dividing Polynomials:

Objectives:

◦Determine the best method to factor rational expressions.

◦Divide rational expressions using long division and synthetic division.

◦Apply the methods to real-life situations.

Why is this important???Why is this important???

You can use polynomials to solve problems involving manufacturing and entertainment

ApplicationApplication

Joy, a senior at Burlington Township HS, spends one free period a day as a TA at the middle school located next to the high school. A magician was performing at the middle school and asked a member of the audience to participate in a number game.

Application continuedApplication continued

The magician said:choose any numberMultiply the number by 3Add the sum of your number and 8 to the

number you got when you multiplied.now divide by the sum of your number

and 2

Dividing PolynomialsDividing Polynomials

Polynomial by a Monomial

Dividing PolynomialsDividing Polynomials

Polynomial by a Monomial

Dividing PolynomialsDividing Polynomials

Polynomial by a Monomial

Divide using long division

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Dividing Polynomials using Dividing Polynomials using LONG DIVISIONLONG DIVISION

Polynomial by a Binomial

Dividing Polynomials using Dividing Polynomials using LONG DIVISIONLONG DIVISION

Polynomial by a Binomial

Dividing Polynomials using Dividing Polynomials using LONG DIVISIONLONG DIVISION

Polynomial by a Binomial

Dividing PolynomialsDividing Polynomials

Note: The leading coefficient of the divisor is not 1.

Dividing PolynomialsDividing Polynomials

NOTE: Polynomial with Missing Terms

Dividing PolynomialsDividing Polynomials

Polynomial with Missing Terms and/or divisor with a leading coefficient not equal to 1.

… … using Synthetic Divisionusing Synthetic Division

… … using Synthetic Divisionusing Synthetic Division

… … using Synthetic Divisionusing Synthetic Division

… … using Synthetic Divisionusing Synthetic Division Synthetic Division

1. Put the polynomial in the dividend in descending order.

2. Determine if the dividend has missing terms. – If there are any missing terms, hold

their space with a zero. – Write the coefficients and constant in a

row.

3. Solve the divisor for 0.

4. Drop the first number down. ◦ Multiply this number by the number

in the box.

◦ Add down.

◦ Multiply this number by the number in the box.

◦ Add down.

◦ Continue this pattern.

(x3 + 2x – 5) (x – 2)

2 1 0 2 -5

2 4 12

1 2 6 7

x2 x # R

Solution: x2 + 2x + 6 +

7x 2

Class work◦Sage and Scribe

TOTDTOTD

1. Illustrate why it is necessary to include terms with zero coefficients in the row of numbers for synthetic division.

2. Compare long division to synthetic division. Are there any advantages to either method? Which do you prefer? Why?

Homework

◦Worksheet, do it the exact same way we did the examples in class.

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