DIVIDING POLYNOMIALS

Mr. Richard must have your “Un-Divided” attention for this

lesson!

Algebraic long division

Divide 2x³ + 3x² - x + 1 by x + 2

3 22 2 3 1x x x x x + 2 is the divisor

The quotient will be here.

2x³ + 3x² - x + 1 is the dividend

Algebraic long division

First divide the first term of the dividend, 2x³, by x (the first term of the divisor).

3 22 2 3 1x x x x

22xThis gives 2x². This will be the first term of the quotient.

Algebraic long division

Now multiply 2x² by x + 2

3 22 2 3 1x x x x 3 22 4x x

22x

2xand subtract

Algebraic long division

Bring down the next term, -x.

3 22 2 3 1x x x x 3 22 4x x

22x

2x x

Algebraic long division

Now divide –x², the first term of –x² - x, by x, the first term of the divisor

3 22 2 3 1x x x x 3 22 4x x

22x

2x x

x

which gives –x.

Algebraic long division

Multiply –x by x + 2

3 22 2 3 1x x x x 3 22 4x x

22x

2x x

x

2 2x x

xand subtract

Algebraic long division

Bring down the next term, 1 x

3 22 2 3 1x x x x 3 22 4x x

22x

2x x

x

2 2x x

1

Algebraic long division

Divide x, the first term of x + 1, by x, the first term of the divisor

13 22 2 3 1x x x x 3 22 4x x

22x

2x x

x

2 2x x

x 1which gives 1

Algebraic long division

Multiply x + 2 by 1

3 22 2 3 1x x x x 3 22 4x x

22x

2x x

x

2 2x x

x

1

12x 1and subtract

Algebraic long division

The remainder is –1.

3 22 2 3 1x x x x 3 22 4x x

22x

2x x

x

2 2x x

x

1

12x 1

The quotient is 2x² - x + 1

Try This One Yourself!

Try This ONE! 2

822

x

xx

822 2 xxxx

xx 22 x4 8

4

84 x0

Check

)2)(4( xx

8422 xxx

822 xx

x

x2

)2(xx

x

x4 )2(4 x

Try This One!1

124

x

xx

1001 234 xxxxx

3x

34 xx 3x 2x

2x

23 xx 22x x0

x2 x2

xx 22 2 x2 1

2

22 x3

1

3

x

Time 4 U 2 Get 2 Work!

• Quiz: Page 324 # 2, 4, 6, 8, 10

• Homework # 1, 3, 5, 7, 11