Dividing Polynomials – Part 2

Honors Math – Grade 8

nnn 5)1210( 2

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial. n

nn

5

12102

Divide each term by 5n

nn

n

n

n

5

12

5

10

5

2

225 2)1254( xxx

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial. 2

25

2

1254

x

xx

Divide each term by 2x2

22

2

2

5

2

12

2

5

2

4

xx

x

x

x

)4()243( 2 xxxLong division can be used to divide a polynomial by a binomial as well as factoring.

Setup a division house.

Step 1. Divide the first term of the dividend, x2, by the first term of the divisor, x.

2434 2 xxxxxx 2x

Multiply x and x – 4.

xx 42 Subtract. Be careful of the integer rules.

x7

Bring down. Start over.

24

77 xx

7

Multiply 7 and x – 4.

287 x44

47

x

x

)3()123( 2 yyyLong division can be used to divide a polynomial by a binomial as well as factoring.

Setup a division house.

Step 1. Divide the first term of the dividend, y2, by the first term of the divisor, y.

1233 2 yyyxxx 2y

Multiply y and y + 3.

yy 32 Subtract. Be careful of the integer rules.

0

Bring down. Start over.

12

012 y

0

Multiply 0 and y + 3.

00123

12

y

y

)5()1593( 2 bbbLong division can be used to divide a polynomial by a binomial as well as factoring.

Setup a division house.

Step 1. Divide the first term of the dividend, x2, by the first term of the divisor, x.

15935 2 bbbbbb 33 2 b3

Multiply 3b and b + 5.

bb 153 2 Subtract. Be careful of the integer rules.

b6

Bring down. Start over.

15

66 bb

6

Multiply -6 and b + 5.

306 b155

1563

b

b

)2()248( 3 aaaLong division can be used to divide a polynomial by a binomial as well as factoring.

Setup a division house. The a2 term is missing. Insert one with a coefficient of 0.

Step 1. Divide the first term of the dividend, a3, by the first term of the divisor, a.

24802 23 aaaa23 aaa

2a

Multiply a2 and a – 2.23 2aa

Subtract. Be careful of the integer rules.

22a

Bring down. Start over.

a8

aaa 22 2

a2

Multiply -2a and a – 2.

aa 42 2 a12

1222 aa24

1212 aa

12Multiply 12 and a – 2.

2412 a0

)5()4534( 3 xxxLong division can be used to divide a polynomial by a binomial as well as factoring.

Setup a division house. The x2 term is missing. Insert one with a coefficient of 0.

Step 1. Divide the first term of the dividend, x3, by the first term of the divisor, x.

453405 23 xxxx23 xxx

2x

Multiply x2 and x – 5.23 5xx

Subtract. Be careful of the integer rules.

25x

Bring down. Start over.

x34

xxx 55 2

x5

Multiply 5x and x – 5.

xx 255 2 x9

952 xx45

99 xx

9Multiply -9 and x – 5.

459 x0