Transcript 8.4 Dividing Polynomials CORD Math Mrs. Spitz Fall 2006 Objective • Divide polynomials by binomials.

8.4 Dividing Polynomials
CORD Math
Mrs. Spitz
Fall 2006
Objective
• Divide polynomials by binomials
Upcoming
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8.4 Monday 10/23
8.5 Tuesday/Wednesday – Skip 8.6
8.7 Thursday 10/26
8.8 Friday 10/27
8.9 Monday 10/30
8.10 Tuesday/Wed
Chapter 8 Review Wed/Thur
Chapter 8 Test Friday
Assignment
• Pg. 320 #3-31 all
Introduction
• To divide a polynomial by a polynomial,
you can use a long division process similar
to that used in arithmetic. For example,
you can divide x2 + 8x +15 by x + 5 as
shown on the next couple of slides.
Step 1
• To find the first term
of the quotient, divide
the first term of the
dividend (x2) by the
first term of the divisor
(x).
x
x  5 x  8 x  15
2
x  5x
2
3x + 15
Step 2
• To find the next term
of the quotient, divide
the first term of the
partial dividend (3x)
by the first term of the
divisor (x).
x+3
x  5 x  8 x  15
2
x  5x
2
3x + 15
3x - 15
0
Therefore, x2 + 8x + 15 divided by x + 5 is x + 3. Since the
remainder is 0, the divisor is a factor of the divident. This
means that (x + 5)(x + 3) = x2 + 8x + 15.
What happens if it doesn’t go evenly?
• If the divisor is NOT a factor of the
dividend, there will be a non-zero
remainder. The quotient can be
expressed as follows:
remainder
Quotient = partial quotient +
divisor
Ex. 1: Find (2x2 -11x – 20)  (2x + 3).
x-7
2 x  3 2 x 2  11x  20
2 x  3x
- 14x - 20
+ 14x+ 21
2
+1
← Multiply by x(2x+3)
← Subtract, then bring down - 20
← Multiply -7(2x+3)
← Subtract. The remainder is 1
The quotient is x – 7 with a remainder of 1. Thus,
1
2
(2x -11x – 20)  (2x + 3) = x – 7 + 2 x  3 .
Other note . . .
• In an expression like s3 +9, there is no s2
term and no s term. In such situations,
rename the expression using 0 as a
coefficient of these terms as follows:
s3 + 9 = s3 + 0s2 + 0s + 9
s 9
Ex. 2: Find
s 3
3
s2+3s + 9
s  3 s 3  0s 2  0s  9
s  3s
3
← Insert 0s2 and 0s. Why?
← Multiply by s2
2
3s2 + 0s
3s2 - 9s
9s + 9
-9s + 27
← Subtract, then bring down 0s
← Multiply 3s(s - 3)
← Subtract. The remainder is 36
+ 36
The quotient is s2+3s+9 with a remainder of 36. Thus,
36
3
.
(s + 9)  (s - 3) = s2 + 3s + 9 +
s 3