Download Polynomial Functions 3 - Dividing Polynomials

Math 30-1
Polynomial Functions: Lesson #3
Dividing Polynomials
Objective: By the end of this lesson, you should be able to:
Recall: Long Division:
e.g. 1) Divide 327 by 11 using long division, then write a division statement in the forms
dividend
remainder
 quotient 
Dividend = Divisor  Quotient + Remainder and
.
divisor
divisor
Polynomials can be divided in a similar manner:
P x 
R
,
 Q x  
D x 
D x 
where Px is the original polynomial, Dx  is the divisor, Qx  is the quotient, and R is
the remainder.
e.g. 2) Divide x 2  7 x  17 by x  3 , then write the division statement
Math 30-1
Polynomial Functions: Lesson #3
This method will work for polynomials of any degree. But be careful: You must put in a
placeholder for every degree of x.
e.g. 3) Divide 2 x 3  x  8 by x  1 .
Synthetic Division:
Synthetic division can be used as a quicker method to divide when we are dividing by a binomial
of the form x  a or x  a .
e.g. 3) Divide 2 x 3  x  8 by x  1using synthetic division.
Steps:
1. Write the coefficients of the dividend in descending order of x.
2. Use the _________ rather than the factor.
3. Bring down the first coefficient.
4. Multiply by the zero and write the product under the next coefficient.
5. _______ the column.
6. Repeat steps 4 and 5 until there are no more terms left.
7. The numbers under the box are the coefficients of the quotient in descending order of x.
Start with degree of x _________________ than the dividend. The last number is the
_____________________.
Math 30-1
Polynomial Functions: Lesson #3
e.g. 2) Divide the following polynomials using synthetic division, and write the division
statement in the form Px  Dx  Qx  R .
a) 2 x 2  3x  8  x  2
b) x 4  6 x 3  x 2  14 x  13  x  3
If the remainder when you divide a polynomial by x  a is 0, then:


e.g. 3) Is x  2 a factor of each of the following polynomials?
a) x 3  8
b) 3x 4  14 x 3  7 x  78
Assignment:
Remainder Theorem Investigation
p. 124-125 #1-5, C3