Easy Algebra Step-by-Step

Dividing Polynomials 111

To avoid sign errors when you are doing divi-

sion of polynomials, keep a − symbol with the

number that follows it. You likely will need to

properly insert a + symbol when you do this.

You will see this tactic illustrated in the following problem.

Problem Find the quotient and remainder.

a.

16

4

xx^323282828

− x

b.

−

−

12

3

xx^42 +++ 666

x

c.

4816

4

xy^438 xy^3416 xy

xy

88 xy^333 +

d.

61

2

4

4

x

x

e.

16

16

52

52

xy^5

xy^5

Solution

a.^16

4

xx^323282828

− x

Step 1. Divide each term of the polynomial by the monomial.

16 28

4

xx^322828

− x

=

−

+

−

↑ −

↓

16

4

28

4

x^32 ↓ 28

x

x

Insert x

Keep with 2 8

=− 47 xx^2 ++ 7

Step 2. State the quotient and remainder.

The quotient is − 47 xx^2 ++ 7 and the remainder is 0.

Sign errors are a major reason for

mistakes in division of polynomials.