Trinomials with coefficient of one!

1
Trinomials with coefficient of one!

• Trinomials are 3 sets of numbers that are not
  alike in any ways. In order to solve trinomials,
  you need to know your factors and distributive
  property!

Try these examples
Rose Felisme
2
Finding the Equation of a Line Given Two Points
X Y
-3 -1
6 -4
How to do it The table shows the coordinates of
two points on the graph of a linear function.

• Description If you know two points on a line,
  first find the slope. Then follow these steps
• Use the slope and one of the two points to find
  the y-intercept
• Write the slope-intercept form using ymxb
• Check your answer by graphing the line. It should
  pass through the two points.

Step 1 Find the slope of the line containing the
points. m y2-y1 Slope formula x2-x1
-4-(-1) (x1,y1)(-3,-1) and (x2,y2)(6,-4)
6-(-3) -3 or-1 Simplify. 9
3 Step 2 Use the slope and one of the two
points to find the y-intercept. y mxb
Slope-intercept form -4 -1(6) b Replace m
with -1,x with 6, and y with -4. 3
3 -4 -2 b Multiply. -2
b Add 2 to each side. Step 3 Write the
slope-intercept form using m-1 and b-2 y
mxb Slope-intercept form 3 y -1x-2
Replace m with -1, and b with -2. 3
3

• Problems for you to try
• (2,3) (6,4) B. (2,4) (2,1)
• C. (-1,12) (4,-8) D. (36,15) (22,10)

Alexis Clark
3
Simplifying square Roots using perfect square
EXAMPLE
square Roots is a quantity of which a given
quantity is the square. Perfect squares are a
rational number that is equal to the square of
another rational number.
The first thing you need to know while
simplifying square roots using perfect squares
is if the number your dealing with is a perfect
square. In this case our number is 81 and its a
perfect square because 9 times itself gives you
81.
The second thing you need to do is find the
square roots of y2 which is y because y times
itself is equal to y2
Lastly you just put it all together and the
answer is 9y
Practice Problems
Kennie Rebecca
4
Solving inequalities using all operations
An inequality can be use when we dont know
what an expression is equal to instead of an
equal sigh we an use this symbol lt gt
For example12x-4lt8 12xlt12(add 4 to each side of
the inequality) Xlt1 ( divide both sides of the
inequality by 12)
One important rule you should always remember if
you multiplying or dividing both sides of an
inequality by a negative number reverse the
direction of the inequality sigh
Four practice problems 1)5x-8lt12 2)4-2x2x-4 3)-13
mgt-26 4)14ggt56
Tamarre Cynthia Jabouin
5
Solving absolute value Open Sentence
24ylt6
Four Examples 5d 1 9 2-2y gt8 3-n
4 I -w8I 11
Description An Open Sentence is mathematical
statement that can be either true or false
depending on what values are used. Because this
equation has the absolute value in it, you would
have to solve it using a positive, and negative
solution.
Rewrite the inequality then solve
24y gt -6
24y lt 6
Subtract 2 from each side
-2 -2
-2 -2
4y gt -8
4y lt 4
4 4
Divide by 4
4 4
y gt -2
y lt 1
Answer
Solution Set
-4 -3 -2 -1 0 1 2 3
Nia Rogers
6
Graphing an equation that is presented in
slope-intercept form

• Description
• A way to graph a equation in slope-intercept
  form, the equation is ymxb m is the slope and
  b is the y-intercept and y and x is the points.
  Slope is the steepness of the line and intercept
  is where the line connects and intersects with
  the y axis.

For Example
Y intercept 4
Y intercept 3
Gary Chen 5/31/12
7
Factoring a trinomial with leading coefficient
other than 1
Description- This is one way to factor a
polynomial. In this case there is a trinomial and
also a leading coefficient other that 1.
Factoring this is the inverse of the distributive
property that would result in two binomials
Example
10d2 17d - 20
1 -multiply the numbers of the two outside terms
and find factors that would equal the middle term
10 x -20 -200
2- Find two fractions whos sum add up to 17
-8 and 25 are factor of -200 that adds up to 17
3 substitute the middle term with the fractions
10d2-8d 25d-20
4 is to split the problem so it is separated by
the middle operation
(10d2-8d ) (25d-20)
GCF 5
Find the GCF of both sides of the equation
GCF2d
3-Distribute the GCF to each of the terms to each
equation using division instead of multiplying
2d(5d-4) 5(5d-4)
Now add the outside terms and multiply it to the
inside term (The terms inside the parentheses
should be the same in each part of the problem.
(2d-5) (5d-4)
Answer
Practice Problems
By Jamari Robinson
10x2 21x-10
12q234q-28
8z220z-48
12y2-4y-5
8
Factoring a trinomial with leading coefficient
other than 1
Description- This is one way to factor a
polynomial. In this case there is a trinomial and
also a leading coefficient other that 1.
Factoring this is the inverse of the distributive
property that would result in two binomials
Example
10d2 17d - 20
1 -multiply the numbers of the two outside terms
and find factors that would equal the middle term
10 x -20 -200
2- Find two fractions whos sum add up to 17
-8 and 25 are factor of -200 that adds up to 17
3 substitute the middle term with the fractions
10d2-8d 25d-20
4 is to split the problem so it is separated by
the middle operation
(10d2-8d ) (25d-20)
GCF 5
Find the GCF of both sides of the equation
GCF2d
3-Distribute the GCF to each of the terms to each
equation using division instead of multiplying
2d(5d-4) 5(5d-4)
Now add the outside terms and multiply it to the
inside term (The terms inside the parentheses
should be the same in each part of the problem.
(2d-5) (5d-4)
Answer
Practice Problems
By Jamari Robinson
10x2 21x-10
12q234q-28
8z220z-48
12y2-4y-5
9
Adding and Subtracting Polynomials

• When adding polynomials you must find all like
  terms for each variable, exponent and
  co-efficient and you must add them with each one
  that is the same term.
• Subtraction for polynomials wouldnt be too
  different you would just find the variables, the
  exponents and the co-efficient and instead of
  adding you would subtract.
• -William Higgins

10
Solving equations with multi step.
I am going to talk about how to solve multi step
equation as you can this equation below is a
multi step equation. It contain coefficient and
one variable and distribute to clear the
properties
Distribute the parentheses
Practice problems
Simplify the equation
Subtract both sides
Divide both sides
After you divide them you get the answer.
Guervens Charles
11
Finding the equation of a line given two points
Example
Description

• (-1,0) (1,4)
• Find the slope Slope
• Slope
• Find the y-intercept
• You have to solve for b (y-intercept)
• Let (1,4) be x and y
• The equation is y2x2

To be able to solve this concept, there is two
things that you need to know. First thing you
need to know is how to find the slope of a line
using two points. The second thing you need to
know is how to find the y-intercept of a line
using two points.
4 practice problems
Replace the letters by their values
Multiply the slope and the x value
(-2,0) (8,4) (-3,0) (3,3) (2,4) (4,8) (8,16) (16,
32)
Minus two on both sides
The answer is 2.
Rubens Lacouture
12
Multiplying A Binomial By A BinomialKasie Okafor
To multiply two binomials apply distributive
properly twice as you do when multiply two- digit
number. This is An algebraic expression of the
sum or the difference of two terms.
Add The Result
The Answer
Examples 1. 2. 3. 4.
13
Solving Inequalities using all operations

• Examples

Description
First you -3x to both sides , then you have
9gt3x-12 you have to 12 to both sides. Then you
have 21\3 gt3x\3 you cross 3x\3 out and 7gt x .
Your answer xgt7.
An Inequalities is the condition of being unequal
lack of equality disparity.
4 Practice Problems
2x 6 gt 4x- 16 9x -5 lt 45x 12 8x-9gt7x12
8x-5lt23x13
Jennifer Jean-Louis
14
Multiplying polynomials
A trinomial has three terms and a binomial has
two terms, but they are all polynomials. To
multiply polynomials you have to multiply each
term to every other term. An example of this is
To do this problem, you have to take the first
term which is x cubed, and multiply that by all
the other terms in the trinomial next to it.
(4x82) You have to continue to do this with
each term in the first trinomial. Once you do
this, you will get this for the answer. You get
this by combining all the like terms.
Step 1
Step 2
4 Practice Problems
Step 3
Answer
Mykala Jordan
15
Solving Equations using Elimination
You can use the Multiplication Property of
Equality so that adding or subtracting
eliminates one of the variables.
Practice Problems
By Mark Britt
16
Distributive property to simplify and solve
expressions.
expression
A mathematical equation which can contain
numbers, operators the four operation and
variable (like x, y) to represent equation or a
operation. Like 12x(4y2x)
3y(6y5zy) 10x(212y) 2(12b-6a) 100xy(7-2w)
France Wanise Saintil
17
Solving multi-step equations with all operations
Practice problems

• Practice problems

• Description, examples

1. To solve the problem above, you subtract 5
from both sides.
2.Then divide 5 to 5x, and 10, and you will get
x2. The variable is 2.

• Multi-step equations are equations that takes
  more than 1 steps to solve that specific
  equation. Such as some examples below. They just
  basically requires more work.

Here are some examples
Jackson C. Ngo
18
Finding the equation of a line given two points
By Junior Tatis
19
Multiplying a Polynomials by a Monomials
Polynomials are just two or more monomials added
together. When an degree is asked for a
polynomial its usually asking for the highest
exponent for a variable.
Examples
In order to do all these you would have had to
had known distributive property
Try these, real fun!
Practicing will prepare you for success on the
Math Finals!
Tatyana Adams
20
Solving Systems of equations using substitution

• 4 Practice problems

• Example

Description Use the substitution method to
eliminate one of the variables in your
equation. When you find the answer to one of
the variables plug it in the equation to find
the other variable.
Nedcar Faugas
21
Using a Distributing property with simplifying -
is an algebra property which is used to multiply
a single term and two or more terms inside a set
of parentheses. Take a look at the problem below.
example-
Practice these four-
Nicholas Morales
22
Solving Inequalities Using All Operations
EXAMPLES
Solving Inequalities using all operations is when
you use all the steps and operations you learned
to solve inequalities. You need to know how to
add and subtract like terms. Also you would need
to know how to simplify equations. You will also
need to graph them on a number line.
Karan Richards
23
Multiplying a Polynomial by a Monomial
Try some for yourself D

• To solve this equation you need to use the
  distributive property. Distribute the Polynomial
  to all the Monomials in the parenthesis.

Yanick Cardoso
24

• DIVIDING MONOMIALS
• First take the 12 and divide it by the three. 12
  divided by 3 is 4.
• Then were going to take the as from up top, and
  at the bottom and see how many pairs we can cross
  out.

We crossed out 3 pairs so at that point. Now its
a raised to the 3rd power. So now were going to
do the same to the next variable which is C.
Practice Problems
We crossed out 6 pairs so that is going to be C
raised to the 6th power. At the end your answer
should look like this.
Jhlyik Lezama
25
Multiplying a polynomial by a monomial
We are going to do multiplying a polynomial by a
monomial. Where we multiply whatever is in the
parenthesis with the outside variable.
Our first step is to multiply both variables
inside the parenthesis with the outside
parenthesis After multiplying it would give us
our final answer of 16x 48 With that you are
done and free to try some practice problems below.
Here is our example
8(2x -6)
8(2x) 8(-6)
16x - 48

• Vu Nguyen.

26
Multiplying a polynomial by a monomial.
The distributive property can be used to multiply
a polynomial by a monomial. The main idea is to
find a product of a monomial and a polynomial.
First thing is the distributive property.
The next thing is to multiply
Examples
After you multiplied you have to simply
Brittany Odom ?
27
Solving System of Equation Using Substitution
When you Solving System of equation using
substitution you have to solve for y and x.
Because solving system of equation you know you
have to find two solution.
Example I
Practice Problem I
Substitute y4x-2 into the 1y
Distribute Multiplication
Subtract 6x-4x
Add 2 both side
Divide both side by 2
Practice Problem II
Sub the X answer from the previous Problem
Multiplication Subtract 4-2 to find Y
Fredens Altine
Answer is (1,2)
28
Solving Systems Of Equations Using Substitution


x - 2y 14x 3y 9
  a.  First, be sure that the variables are "lined up" under one another.  In this problem, they are already "lined up".       x - 2y 14x 3y 9
  b.  Decide which variable ("x" or "y") will be easier to eliminate.  In order to eliminate a variable, the numbers in front of them (the coefficients) must be the same or negatives of one another.  Looks like "x" is the easier variable to eliminate in this problem since the x's already have the same coefficients.       x - 2y 14x 3y 9
  c.  Now, in this problem we need to subtract to eliminate the "x" variable.  Subtract ALL of the sets of lined up terms. (Remember  when you subtract signed numbers, you change the signs and follow the rules for adding signed numbers.)        x - 2y 14-x - 3y - 9        - 5y 5  
d.  Solve this simple equation.       -5y 5   y -1
  e.  Plug "y -1" into either of the ORIGINAL equations to get the value for "x".      x - 2y 14x - 2(-1) 14     x 2 14            x 12
  f.  Check  substitute x 12 and y -1 into BOTH ORIGINAL equations.  If these answers are correct, BOTH equations will be TRUE!     x - 2y 1412 - 2(-1) 14  12 2 14  14 14  (check!) x 3y 912 3(-1) 9 12 - 3 9  9 9  (check!)

• Steps to Solve Systems by Substitution
• Solve one of the equations for y
• Substitute the expression for y into the other
  equation.
• Solve for x.
• Substitute the value of x into either of the
  original equations to find the value of y
• Write the solution as a coordinate pair.

Try these ..

• 4x 3y -15x 4y 1

• 4x - y 102x  12 - 3y 

P 2 2QP 10 6Q

• x - 2y 14x 3y 9

SHAY WEBSTER
29
Adding and Subtracting polynomials
When you are adding/subtracting polynomials, you
have to add/subtract like terms. When you are
done adding like terms you have to put them in
order from largest to smallest, answers with
exponents always go first.
EXAMPLES! ? 1. (2x3y)(4x9y) add the xs
first then the ys 6x12y 2.
(6s5t)(4t8s) add the ss first then the
ts 14s9t

• Practice problems for you to try. ?
• (54n2m)(-6m-8)
• (5a9b)-(2a4b)
• (5fg-2)(-2f3)
• (11m-7n)-(2m6n)

Jonique Tabb
30
Solving Two Step Equations
One goal in solving an equation is to have only
variables on one side of the equal sign and
numbers on the other side of the equal sign. The
other goal is to have the number in front of the
variable equal to one. The variable does not
always have to be x. These equations can make use
of any letter as a variable.
2. 7x1052
1. 3x10100
Were basically going to undo the probably by
doing the opposite. So first Im going to
subtract 10 from both sides. Thats going to
leave me with 3x90.
Subtract 10 from both sides. Divide both sides
by 7 Theres your answer
-10 -10
_ 3
Then were going to divide both sides by 3. 3x
divided by 3 leaves you with x, and 90 divided by
three leaves you with 30. Your problem should be
finished off with x equaling something which is
30 so x30.
Practice Problems
Cookie Bourne
31
Factoring Trinomials
EXAMPLE1x² 5x 36(x 9) (x
4)SOLUTIONThe problem asks me to factor the
trinomial into two binomials.STEP 1List out all
the factor of the number with no variable.STEP
2 Add/Subtract the factors of that number and
see if it adds up to the middle number.STEP
3After that turn them into two binomials.
Factoring a trinomials means finding two
binomials that when multiplied together It makes
a trinomial. This is kind of like the opposite of
multiplying two binomials.
1x²-10n25 1x²15n14 1x²-8n-48 1x²p-20

• Jimmy Lai

32
Graphing the Solution of an inequality on a
number line
EXAMPLE Graph x lt 4 Solution The problem asks
you to graph all numbers that are less than 4.
STEP1 Draw an open circle on the number 4.
(Dont draw a CLOSED circle because it does have
the _ under the symbol. STEP2 Draw a line
going left, because x is less then 4.
Graphing inequalities on number line represent
the solution to inequalities . It aids in
visualizing the answer. Graphing inequalities is
simple once you learn the few simple steps to
solve a problem.
PRACTICE PROBLEMS
HERES THE SOLUTION
Xlt-9 x gt 24 2x 3 lt 6 5 gtx

• Parmanand Jodhan

33
Multiplying A Binomial By A Binomial
My project is to multiplying a binomial by a
binomial. When you multiply a binomial by a
binomial you have to multiply every number in the
problem by each other.
First you do 3x times 5x and get 15x. Next you do
2 times 4 and you get 8.after that its 2 times 5x
the answer is 10x.lastly you do 3x times 4 and
it equals 12x.
Practice problems
(6 2x) (10 7x) (12x 4) (3x 7) (8x
9) (14x 13) (9x 24) (5x 1)
Alisha Cooper