SWBAT divide polynomial with Long Division

4.3 Dividing Polynomials: Long

Division and Synthetic Division

Dividend– the number being divided

Divisor– the number that will divide the dividend

Quotient– the answer to a division problem

Remainder– the amount left over after dividing

Vocabulary

Long Division Review

𝟕𝟖 ÷ 𝟑

26

𝟑)𝟕𝟖

-6

18

-18

00

Long Division of Polynomials

𝒙𝟐 + 𝟒𝒙 − 𝟓 ÷ 𝒙 − 𝟏

𝒙 + 𝟓

𝒙 − 𝟏)𝒙𝟐 + 𝟒𝒙 − 𝟓

−𝒙𝟐 + 𝟏𝒙

𝟓𝒙 − 𝟓

−𝟓𝒙 + 𝟓

0 0

Long Division of Polynomials

1. 𝟐𝒙𝟑 − 𝟗𝒙𝟐 + 𝟕𝒙 + 𝟔 ÷ 𝟐𝒙 + 𝟏

2. 𝟒𝒙𝟑 + 𝟏𝟑𝒙𝟐 − 𝟐𝒙 − 𝟏𝟓 ÷ 𝟒𝒙 + 𝟓

3. (𝟔𝒙𝟐 − 𝒙 − 𝟐) ÷ (𝒙 + 𝟏)

4. (𝟐𝒙𝟑 + 𝒙𝟐 − 𝟒𝒙 − 𝟑) ÷ (𝒙 − 𝟏)

Long Division of Polynomials

1. 𝒙𝟑 − 𝟖 ÷ 𝒙 − 𝟐

2. (𝒙𝟑 − 𝟏) ÷ (𝒙 − 𝟏)

Long Division of Polynomials

1. 𝟐𝒙𝟓 + 𝟑𝒙𝟐 + 𝟏𝟐 ÷ 𝒙𝟑 − 𝟑𝒙 − 𝟒

2. (𝟑𝒙𝟒 + 𝟐𝒙𝟑 + 𝒙𝟐 + 𝟒) ÷ (𝒙𝟐 + 𝟏)

Pop Quiz

Divide using long division (𝒙𝟐 − 𝟗) ÷ (𝒙 − 𝟐)

Dividing Polynomials: Long Division and Synthetic division

SWBAT divide Polynomials with synthetic division

A shorthand way of dividing a polynomial by a linear factor

Synthetic division

1. Write the division in synthetic form

list the coefficients of the dividend. Remember to use 0 for a placeholder

2. Bring down the first term in the dividend 3. Multiply and place the product up and to the right in the

second column 4. Add the values in the second column 5. Repeat step 3 and 4 6. Identify the quotient by assigning powers of x in

descending order the last term is the remainder

Steps for using Synthetic division

Divide using Synthetic Division

(𝒙𝟑 − 𝟐𝒙𝟐 + 𝟐𝒙 − 𝟒) ÷ (𝒙 + 𝟏)

Divide Using Synthetic Division

(𝟑𝒙𝟓 − 𝟐𝒙𝟑 + 𝒙𝟐 − 𝟕) ÷ (𝒙 + 𝟐)

Divide Using Synthetic Division

1. 𝟑𝒙𝟐 + 𝟕𝒙 + 𝟐 ÷ 𝒙 + 𝟐

2. 𝟐𝒙𝟑 − 𝒙 + 𝟑 ÷ 𝒙 − 𝟏

3. (𝒙𝟒 + 𝟏) ÷ (𝒙 + 𝟏)

4. (𝟐𝒙𝟒 − 𝟑𝒙𝟑 + 𝟕𝒙𝟐 − 𝟒) ÷ 𝒙 −𝟐

𝟑

Pop Quiz

Divide using Synthetic Division (𝒙𝟕 − 𝟖𝒙𝟒 + 𝟑𝒙𝟐 + 𝟏) ÷ (𝒙 − 𝟏)