Download Dividing a Polynomial by a Binomial Divisor

Math 102
4.1 "Dividing Polynomials"
Objectives:
*
Divide a polynomial by a binomial divisor.
*
Use synthetic division to determine the quotient and remainder for division problems.
Dividing a Polynomial by a Binomial Divisor
Division Algorithm for Polynomials:
If f (x) and g (x) are polynomials and g (x) 6= 0; then unique polynomials q (x) and r (x) exist such that
where r (x) = 0 or the degree of r (x) is less than the degree of g (x) :
Example 1: (Dividing polynomials using the division algorithm)
Find the quotient and remainder for each division problem.
a)
20x2
c)
8y 3
39x + 18
y2
y+5
(5x
6)
y2 + y
b)
x5
d)
3x2
Page: 1
1
(x + 1)
2xy
9y 2
(x
2y)
Notes by Bibiana Lopez
College Algebra by Kaufmann and Schwitters
4.1
Synthetic Division
Example 2: (Dividing polynomials using synthetic division)
Use synthetic division to determine the quotient and remainder for each division problem.
a)
2x2
5x
c)
4x4
5x2 + 1
3
(x
x
3)
b)
4x2 + 5x
1
2
c)
2x3 + 3x2
Page: 2
4
(x + 2)
2x + 3
x+
1
2
Notes by Bibiana Lopez