Do Now

• Pass out calculators. • Write down the weeks

assignments. • Pick up a worksheet from the back

and wait for instructions.

Objective:

• To divide polynomials.

SOLUTION

Divide a polynomial by a monomial

EXAMPLE 1

Divide 4x3 + 8x2 + 10x by 2x.

Method 1: Write the division as a fraction.

Write as fraction.

Divide each term by 2x.

= 2x2 + 4x + 5

8x24x3

2x 2x10x2x+ +=

Simplify.

(4x3 + 8x2 + 10x) 2x 4x3 + 8x2 +10x2x=

Divide a polynomial by a monomial

EXAMPLE 1

CHECK 2x(2x2 + 4x + 5) = 4x3 + 8x2 + 10x?

2x(2x2) + 2x(4x) + 2x(5) = 4x3 + 8x2 + 10x?

4x3 2x = ?

Think8x2 2x = ?

Think

10x 2x = ?

Think

+ 4x + 5

ANSWER (4x3 + 8x2 + 10x) 2x = 2x2 + 4x + 5

2x 4x3 + 8x2 + 10x)2x2

4x3 + 8x2 + 10x = 4x3 + 8x2 + 10x

GUIDED PRACTICE for Example 1

(6x3 + 3x2 –12x) 3x1.

2x2 + x – 4

ANSWER

(12y4 – 16y3 + 20y2) 4y2.

ANSWER

3y3 – 4y2 + 5y

SOLUTION

EXAMPLE 2 Divide a polynomial by a binomial

Divide x2 + 2x – 3 by x – 1.

STEP 1Divide the first term of x2 + 2x – 3 by the first term of x – 1.

Multiply x and x – 1.

xx – 1 x2 + 2x – 3

x2 – x3x Subtract x2 – x from x2 + 2x.

Think: x2 x = ?

EXAMPLE 2 Divide a polynomial by a binomial

Bring down –3. Then divide the first term of 3x – 3 by the first term of x – 1.

+ 3

3x – 30

Multiply 3 and x – 1.

Subtract 3x – 3 from 3x – 3.

STEP 2

Think: 3x x = ?

ANSWER (x2 + 2x – 3) (x – 1) = x + 3

x – 1 x2 + 2x – 3x2 – x

3x – 3

x

EXAMPLE 3 Divide a polynomial by a binomial

Divide 2x2 + 11x – 9 by 2x – 3.x

2x2 –3x2x – 3 2x2 + 11x – 9

14x – 9

12

Multiply x and 2x – 3.

Subtract 2x2 – 3x. Bring down – 9.

Multiply 7 and 2x – 3.

Subtract 14x – 21.

ANSWER (2x2 + 11x – 9) (2x – 3) = x + 7 + 12

2x – 3

14x – 21

+ 7

GUIDED PRACTICE for Examples 2 and 3

3. Divide: (a2 + 3a – 4) (a + 1)

a + 2 +ANSWER– 6a + 1

4. Divide: (9b2 + 6b + 8) (3b – 4)

ANSWER 3b + 6 +32

3b – 4

EXAMPLE 4 Rewrite polynomials

Divide 5y + y2 + 4 by 2 + y.

Rewrite polynomials.

Multiply y and y + 2.y2 + 2ySubtract y2 + 2y. Bring down 4.3y + 4Multiply 3 and y + 2.3y + 6Subtract 3y + 6.– 2

y + 2 y2 + 5y + 4y

ANSWER

(5y + y2 + 4) (2 + y) = y + 3 + y + 2– 2

+ 3

EXAMPLE 5 Insert missing terms

Divide 13 + 4m2 by – 1 + 2m.

Rewrite polynomials, Insert missing term.2m

2m – 1 4m2 + 0m + 13Multiply 2m and 2m – 1.4m2 – 2mSubtract 4m2 – 2m. Bring down 13.2m + 13

Multiply 1 and 2m – 1.2m – 1

Subtract 2m – 1.14

ANSWER

(13 + 4m2) (– 1 + 2m) = 2m + 1 + 2m – 114

+ 1

GUIDED PRACTICE for Examples 4, 5, and 6

5. Divide: (8m – 7 + 4m2) (5 + 2m)

ANSWER

2m – 1+2m + 5– 2

6. Divide: (n2 – 6) (– 3 + n)

n + 3 +

ANSWER

n – 3 3

Exit Ticket:

1. Divide 6x3 – 12x2 + 9x by 3x.

1. Divide x2 + x – 6 by x + 3.

1. Divide 3x2 + 17x + 13 by 3x + 2.

1. Divide -12 + 4y2 by -1 + 2y.