Polynomial and Synthetic Division

1
Polynomial and Synthetic Division
2
By the Definition of Exponents
Notice that 5 3 2
3
Examples
4
Monomial division of a polynomial
5
Example 2
6
Long Division.
Check
7
Long Division.
Check
8
x2 times.
1. x goes into x3?
2. Multiply (x-1) by x2.
3. Change sign, Add.
4. Bring down 4x.
5. x goes into 2x2?
2x times.
6. Multiply (x-1) by 2x.
7. Change sign, Add
8. Bring down -6.
9. x goes into 6x?
6 times.
10. Multiply (x-1) by 6.
11. Change sign, Add .
9
Divide.
10
Example

Check
11
Synthetic Division.
1
-8
15
3
3
-15
0
1
-5
12
Synthetic Division.
1
-2
-8
3
3
3
-5
1
1
13
Synthetic Division

• Divide x4 10x2 2x 4 by x 3

1
0
-10
-2
4
-3
-3
9
-3
3
-1
1
1
1
-3
14
Homework

• Page 87 1 25 odd
• Page 88 1 13 odd, 16

15
Page 87
16
Page 87 A polynomial f and a factor of f are
given. Factor f completely.
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A polynomial f and one zero of f are given. Find
the other zeros of f.
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25. Geometry The volume of the box shown at the
right is given by

• V 2x3 11x2 10x 8
• Find an expression for the missing dimension.