8.4 Dividing Polynomials CORD Math Mrs. Spitz Fall 2006.
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Transcript of 8.4 Dividing Polynomials CORD Math Mrs. Spitz Fall 2006.
8.4 Dividing Polynomials
CORD Math
Mrs. Spitz
Fall 2006
Objective
• Divide polynomials by binomials
Upcoming
• 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).
xx
xxx
5
15852
2
x
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).
xx
xxx
5
15852
2
x + 3
3x + 153x - 15
0Therefore, 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:
Quotient = partial quotient + divisor
remainder
Ex. 1: Find (2x2 -11x – 20) (2x + 3).
xx
xxx
32
20112322
2
- 14x - 20+ 14x+ 21
x - 7
+ 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, (2x2 -11x – 20) (2x + 3) = x – 7 + .
32
1
x
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
Ex. 2: Find
23
23
3
9003
ss
ssss
3
93
s
s
3s2 + 0s
s2+3s + 9
+ 36
← Insert 0s2 and 0s. Why?
← Subtract, then bring down 0s
← Multiply 3s(s - 3)
← Subtract. The remainder is 36
The quotient is s2+3s+9 with a remainder of 36. Thus,
(s3 + 9) (s - 3) = s2 + 3s + 9 + .3
36
s
3s2 - 9s
9s + 9-9s + 27
← Multiply by s2