Ch 10: PolynomialsC) Dividing

Objective:

To divide polynomials using long division.

Rules1) Multiply the first term of the divisor by a value

that will eliminate the first term of the dividend

2) Distribute that value to the divisor and subtract it from the dividend

3) Repeat 1 & 2 until there is a remainder

Definitions

€

divisor dividendquotient

)

dividend ÷ divisor = quotient

Example 1(a2 – 11a + 36) ÷ (a – 7)

€

a − 7 a2 −11a+ 36)

a

a2 − 7a− ( )-4a + 36

-4

-4a + 28− ( )8

a – 4 + 8 a - 7

Example 2(x2 + 8x + 18) ÷ (x + 5)

€

x + 5 x 2 + 8x +18)

x

x2 + 5x− ( )3x + 18

+3

3x + 15− ( )3

x + 3 + 3 x + 5

Example 3(v2 + v − 57) ÷ (v + 8)

€

v + 8 v 2 + v − 57)

v

v2 + 8v− ( )-7v − 57

-7

-7v − 56− ( )-1

v – 7 + -1 v + 8

Example 4(5n2 − 23n − 33) ÷ (n − 6)

€

n − 6 5n2 − 23n − 33)

5n

5n2 − 30n− ( )7n − 33

+7

7n − 42− ( )9

5n + 7 + 9 n − 6

Classwork

1)

3)

2)

4)

(r2 + 15r + 61) ÷ (r + 7) (n2 – 3n – 32) ÷ (n + 5)

(m2 + 12m + 11) ÷ (m + 2) (x2 – x – 93) ÷ (x – 10)

r + 8 + 5 r + 7

n – 8 + 8 n + 5

m + 10 + -9 m + 2

x + 9 + -3 x − 10

5)

7)

6)

8)

(x2 + 8x + 18) ÷ (x + 5) (n2 + 11n + 21) ÷ (n + 3)

(x2 + x – 15) ÷ (x – 3) (8m2 + 39m – 57) ÷ (m + 6)

x + 3 + 3 x + 5

n + 8 + -3 n + 3

x + 4 + -3 x − 3

8m – 9 + -3 m + 6