Download Dividing Polynomials

Elementary Algebra
Section 5.6
Page 1 of 4
Section 5.7: Dividing Polynomials
Big Idea: Dividing polynomials is a lot like doing arithmetic division.
Big Skill: You should be able to divide polynomials using long division and, when appropriate, synthetic
division.
Dividing a polynomial by a monomial: Divide the monomial into each term of the polynomial, and cancel
ab a b
 
when possible. This is allowable because of the arithmetic fraction rule that
c
c c
Practice:
24 z 5
1.

18 z 2
2.
9 p 4  12 p3  3 p 2

3p
3.
x 4 y 4  8 x 2 y 2  4 xy

4 x3 y
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Elementary Algebra
Section 5.6
Page 2 of 4
Dividing a polynomial by a polynomial using long division:
Long division of polynomials is a lot like long division of numbers:
a. Arrange divisor and dividend around the dividing symbol, and be sure to write them in
descending order of powers with all terms explicitly stated (even the terms with zero
coefficients).
b. Divide leading terms, then multiply and subtract.
c. Repeat until a remainder of order less than the divisor is obtained.
Compute 579 ÷ 16
Comparison between dividing integers and dividing polynomials
Dividend
Remainder
 Quotient 
Divisor
Divisor
Compute (5x2 + 7x +9) ÷ (x + 6)
Practice:
3x 2  4 x  7
1.

2x  5
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Elementary Algebra
2.
Section 5.6
Page 3 of 4
2 x3  x 2  7 x  13

x2
6 x3  7 x 2  6 x  6
3.

2x 1
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Elementary Algebra
4.
Section 5.6
Page 4 of 4
8  9 x  2 x 2  12 x3  5 x5

2x  3
8  9 x  2 x 2  12 x3  5 x5
5.

x2  3
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.