C.
1 2
x y 6 xy 8 x 2 y 2
2
When you have a binomial multiplied by a polynomial, you will use the distributive
property for each term in the first polynomial.
Another way to think about it is to use a method called FOIL (first, outside, inside,
last) when
7-8 Special Products of Binomials
Algebra I
Perfect-square trinomial- a trinomial that is the result of squaring a binomial
Difference of two squares- (a + b)(a b) = a2 b2. A binomial for the form a2 b2
is called the difference of two squares.
_
_
Ex 1: M
8-3: Factoring + +
When factoring x2
bx c:
If c If c is positive
and and b is positive, both factors are positive.
and and b is negative, both factors are negative.
Example 1: Factor t2 7t 10. Check your answer.
We need factors of 10 that sum to 7.
Facto
8-4: Factoring + +
What is different about factoring the quadratic trinomial compared to yesterday?
6 + 11 + 3
To factor when the value of a is greater than one, we can use the box method.
1) Write your first and last terms in a 4 by 4 box where the F an
8-1: Factors and Greatest Common Factors
A _has exactly two factors, itself and 1. The number 1 is not a prime number.
To write the prime factorization of a number, factor the number into its prime factors only.
Example 1: Find the prime factorization of
7-6 Adding and Subtracting Polynomials
Algebra I
Ex 1: Add or subtract.
A.
12p3 + 11p2 +8p3
B.
5x2 6 3x + 8
t2 + 2s2 4t2 s2
D.
10m2n + 4m2n -8m2n
Ex 2:
A.
(4m2 + 5) + (m2 m + 6)
B.
(10xy + x) + (-3xy + y)
C.
C.
D.
2013-03-01 09:36:36
(6x2 4y) + (-3x2 + 3y
7-3 Multiplication Properties of Exponents
Algebra I
_
Ex 1: Simplify.
A.
B.
3 2 * 35
2 4 * 34 * 2 2 * 32
C.
2013-02-25 09:52:07
q3 * r 2 * q6
D.
n3 * n 4 * n
1/2
Ch 7 Notes.pdf (2/15)
7-3 Algebra 1 Notes page 2
Ex 2: Light from the Sun travels as about 1
7-4 Division Properties of Exponents
Algebra I
_
Ex 1: Simplify.
27
A.
22
C.
2013-02-25 09:51:20
d 4e3
(de) 2
B.
x4
x3
D.
3 * 4 3 * 55
32 * 4 4 * 53
1/3
Ch 7 Notes.pdf (4/15)
7-4 Algebra 1 Notes page 2
Ex 2: Simplify (3 x 1010) (6 x 106) and write the ans
7-5 Polynomials
Algebra I
Monomial a number, a variable, or a product of numbers and variables with
whole number exponents
Degree of a monomial-the sum of the exponents of the variables. A constant has
a degree of 0.
Polynomial- a monomial or a sum or dif
8-2: Factoring by Greatest Common Factor
The Distributive Property states: a(b
c)
Factoring by GCF reverses the Distributive Property: ab
Factor 12y3
21y2
ac
15y.
Step 1: Find the GCF of all the terms in the polynomial.
The factors of 12y3 are:
The factor
6-5 Solving Linear Inequalities
A _ is similar to a linear equation, but
the equal sign is replaced by an inequality symbol.
A _ of a linear inequality is any ordered pair that makes
the inequality true.
or
indicates that the points on the boundary ARE so
6-2 Solving Systems by Substitution
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Solving Systems of Equations by Substitution
Solve for one variable in at least one equation, if necessary.
Substitute the resulting expression into the other equation.
Solve that
6-3 Solving Systems by Elimination
Solving Systems of Equations by Elimination
Step 1: Write the system so that like terms are aligned.
Step 2: Eliminate one of the variables by adding/subtracting the equations and
solve for the other variable.
Step 3: Su
6-6 Solving Systems of Linear Inequalities
A _is a set of two or more
linear inequalities containing two or more variables.
The _ consists of all the
ordered pairs that satisfy all the linear inequalities in the system.
Ex 1] Tell whether the ordered pair
6-4 Solving Special Systems
Consistent system: _
Inconsistent system: _
Independent system: _
Dependent system: _
Classification of Systems of Linear Equations
CLASSI CONSISTENT and
CONSISTENT and
FICATI INDEPENDENT
DEPENDENT
ON
# of
Solutio
ns
Descrip Di
6-1 Solving Systems by Graphing
A system of _ is a set of two or more linear
equations containing two or more variables.
A _ of a system of linear equations with two variables is an
ordered pair that satisfies each equation in the system.
If an ordered pa
Chapter 11 Section 4
Linear, Quadratic, Exponential Models
General Forms of Functions
Model
LINEAR
QUADRATIC
EXPONENTIAL
Pattern
Graph
Equation
Identify each of the following as linear, quadratic, or exponential
1
y =30,000(1.08)4
_
2
y = 3.75x + 74
_
3
y
Chapter 11 Section 1
Geometric Sequences
Terms
Geometric sequence: _
_
Common ratio: _
Example 1
Find the next 3 terms in the geometric sequence.
A. 1,3,9,27,
B. -16, 4, -1,
Formula For a Geometric Sequence
Example 2
A. The first term of a geometric seque
7-1 Integer Exponents
Algebra I
_
Ex 1: One cup is 2-4 gallons. Simplify this expression.
Ex 2: Simplify.
A.
4-3
C.
(-5)-4
B.
70
D.
-5-4
Ex 3: Evaluate each expression for the given value(s) of the variable(s).
A.
x-2 for x = 4
B.
-2a0b-4 for a = 5 and b
Chapter 11 Section 5
Square Root Functions
Terms
Square Root Function: _
Speed Function: _
Example 1
A. Find the speed of an object in free fall after it has fallen 4 feet.
B.
Find the speed of an object in free fall after it has fallen 50 feet. Round you