x y 6 xy 8 x 2 y 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,
7-8 Special Products of Binomials
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
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.
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
Ex 1: Add or subtract.
12p3 + 11p2 +8p3
5x2 6 3x + 8
t2 + 2s2 4t2 s2
10m2n + 4m2n -8m2n
(4m2 + 5) + (m2 m + 6)
(10xy + x) + (-3xy + y)
(6x2 4y) + (-3x2 + 3y
7-3 Multiplication Properties of Exponents
Ex 1: Simplify.
3 2 * 35
2 4 * 34 * 2 2 * 32
q3 * r 2 * q6
n3 * n 4 * n
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
Ex 1: Simplify.
3 * 4 3 * 55
32 * 4 4 * 53
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
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
Factoring by GCF reverses the Distributive Property: ab
Step 1: Find the GCF of all the terms in the polynomial.
The factors of 12y3 are:
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.
indicates that the points on the boundary ARE so
6-2 Solving Systems by Substitution
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.
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
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
Identify each of the following as linear, quadratic, or exponential
y = 3.75x + 74
Chapter 11 Section 1
Geometric sequence: _
Common ratio: _
Find the next 3 terms in the geometric sequence.
B. -16, 4, -1,
Formula For a Geometric Sequence
A. The first term of a geometric seque
7-1 Integer Exponents
Ex 1: One cup is 2-4 gallons. Simplify this expression.
Ex 2: Simplify.
Ex 3: Evaluate each expression for the given value(s) of the variable(s).
x-2 for x = 4
-2a0b-4 for a = 5 and b
Chapter 11 Section 5
Square Root Functions
Square Root Function: _
Speed Function: _
A. Find the speed of an object in free fall after it has fallen 4 feet.
Find the speed of an object in free fall after it has fallen 50 feet. Round you