Download Adding and Subtracting Polynomials Guide

Mayansky/Finizio
Algeo I
Quiz Date: 12/14/04
Section 4.1 and 4.2
Study Guide
Section 4.1: Exponents
Important Information
Exponential Form
a6
52
53
24
Expanded Form
aaaaaa
55
555
2222
Words
“a to the 6th power”
“5 squared”
“5 Cubed”
“2 to the 4th power”
24  16
(2)4  16
Area of a Rectangle = Length x Width
Sample Problem #1
Write the following expression in exponential form.
666666
Answer:
Step #1: This is written in
expanded form. In order to
write it in exponential form
you must keep the number
(6) and count the total
number of 6’s. In this case
there are 6.
66
Step #2: Therefore your
answer is “Six to the Sixth
Power.”
Sample Problem #2:
Simplify
2  32
29
11
Step #1: Remember your order of operations PEMDAS
(Parenthesis, Exponents, Multiplication, Division, Adding, and
Subtraction. Because of this you must take care of the exponent
first.
After Step #1
Final Answer
Simplified
a6
25
125
16
Sample Problem #3
Evaluate the Following if a = 3 and x = 2.
( a  x) 2
(3  2) 2
(3  2) 2
(5) 2
Step #1: Re-Write the
equation with the numbers
provided.
Step #2: Simplify this expression. Remember your
order of operations PEMDAS (Parenthesis,
Exponents, Multiplication, Division, Adding, and
Subtraction.
According to your order of operations, you must
simplify what is in the parenthesis first. After doing
this you move to your exponents.
25
Sample Problem #4
Find the area of the rectangle.
Area of a Rectangle = Length x Width
5x
3x
Step #1: Write an equation
using the Area of a Rectangle
Formula. In this rectangle 5x is
the length and 3x is the width.
5x 3x
15x 2
Step #2: Multiply. In order to
multiply you must first multiply your
coefficient #’s. In this case they are 5
and 3. After that you must multiply
your X’s.
Section 4.2: Adding and Subtracting Polynomials
Sample Problem #1:
Simplify
Step #1: Recognize like terms. Draw a line under each
6 x3  3x 2  x 2  6 x3
4 x 2  12 x3
like term. In this problem you can combine 6 x  6 x .
3
You may also combine 3x  x
2
3
2
Step #2: Add or subtract. Remember to order your
terms according to exponent number.
Sample Problem #2:
Simplify
(2 x  5)  ( x  2)
2x  5  x  2
x 3
Step #1: Remove parenthesis. In order to do this in this equation
you must distribute the negative to all terms that follow it.
Step #2: Combine like terms. In this statement you may combine 2x  x
you may also combine 5  2 . After you do this your statement is in simplest
form.
Practice Problems
1. Simplify
2. Simplify
2 4
3. Simplify
(2  3) 2
4. Simplify
2  32
25
5. Evaluate if a=3 and
6. Evaluate if a=3 and
7. Evaluate if a=3 and
8. Evaluate if a=3 and
x=2
x=2
x=2
x=2
ax
2
(ax)
2
( x  a)
3
x4  a4
9. Evaluate if a=3 and x=2
10. Evaluate if
11. Evaluate if a=3 and
12. Evaluate if a=3 and x=2
xa
a=3 and x=2
2
x=2
a3  x3
4
13. Find the Area
.
x a
ax
14. Find the Area
3
15. Find the Area
5x
3y
3x
2
17.
(2 x  5 y  2)  (5 x  6 y  7)
21.
4z
2
6x
2z
4
18.
19.
22.
23.
(2 x  5)  ( x  2) (3m  5)  (2m  3)
(3n  5n  6)  (n  3n  3) (4 y  12)  (6 y  4) (3x  5)  (4 x  2)
2
16. Find the Area
20.
(2 p  7q  4)  (3q  2 p  1)
24.
( y  6 y  5)  ( y 2  3 y  1)
2