Trinomials with coefficient of one Trinomials are 3

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

Finding the Equation of a Line Given Two Points X Y -3 Step 1: Find the slope of the line containing the points. 6 m= y 2 -y 1 Slope formula x 2 -x 1 = -4 -(-1)(x 1, y 1)=(-3, -1) and (x 2, y 2)=(6, -4) 6 -(-3) = -3 or-1 Simplify. 9 3 Step 2: Use the slope and one of the two points to find the yintercept. y = mx+b 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 = mx+b Slope-intercept form 3 y = -1 x-2 Replace m with -1, and b with -2. 3 3 -1 -4 Problems for you to try: A. (2, 3) (6, 4) B. (2, 4) (2, 1) C. (-1, 12) (4, -8) D. (36, 15) (22, 10) 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 yintercept • Write the slopeintercept form using y=mx+b • Check your answer by graphing the line. It should pass through the two points. How to do it: The table shows the coordinates of two points on the graph of a linear function. Alexis Clark

Simplifying square Roots using perfect 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. EXAMPLE 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 y 2 which is y because y times itself is equal to y 2 Practice Problems Lastly you just put it all together and the answer is 9 y Kennie Rebecca

Solving inequalities using all operations An inequality can be use when we don’t know what an expression is equal to… instead of an equal sigh we an use this symbol < ≥ > ≤ Four practice problems 1)5 x-8<12 2)4 -2 x≤ 2 x-4 3)-13 m>-26 4)14 g>56 For example: 12 x-4<8 12 x<12(add 4 to each side of the inequality) X<1 ( 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 Tamarre Cynthia Jabouin

Solving absolute value Open Sentence |2+4 y|<6 Description: An Rewrite the inequality then solve: 2+4 y > -6 Subtract 2 from each side Divide by 4 Answer: -2 2+4 y < 6 -2 4 y > -8 ÷ 4 y > -2 -2 -2 4 y < 4 ÷ 4 y < 1 Solution Set: 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. -4 -3 -2 -1 0 1 2 3 Nia Rogers

Graphing an equation that is presented in slope-intercept form Description: A way to graph a equation in slopeintercept form, the equation is y=mx+b: 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

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 10 d 2 + 17 d - 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 who’s 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 10 d 2 -8 d + 25 d-20 4 is to split the problem so it is separated by the middle operation (10 d 2 -8 d )+ (25 d-20) GCF= 5 GCF=2 d Find the GCF of both sides of the equation 3 -Distribute the GCF to each of the terms to each equation using division instead of multiplying 2 d(5 d-4) + 5(5 d-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. (2 d-5) (5 d-4) Answer Practice Problems By Jamari Robinson 2 10 x +21 x-10 12 q 2+34 q-28 8 z 2+20 z-48 12 y 2 -4 y-5

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 10 d 2 + 17 d - 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 who’s 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 10 d 2 -8 d + 25 d-20 4 is to split the problem so it is separated by the middle operation (10 d 2 -8 d )+ (25 d-20) GCF= 5 GCF=2 d Find the GCF of both sides of the equation 3 -Distribute the GCF to each of the terms to each equation using division instead of multiplying 2 d(5 d-4) + 5(5 d-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. (2 d-5) (5 d-4) Answer Practice Problems By Jamari Robinson 2 10 x +21 x-10 12 q 2+34 q-28 8 z 2+20 z-48 12 y 2 -4 y-5

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 wouldn’t be too different you would just find the variables, the exponents and the coefficient and instead of adding you would subtract. -William Higgins

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 Simplify the equation Practice problems Subtract both sides Divide both sides After you divide them you get the answer. Guervens Charles

Finding the equation of a line given two points Description 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 yintercept of a line using two points. 4 practice problems (-2, 0) (8, 4) (-3, 0) (3, 3) (2, 4) (4, 8) (8, 16) (16, 32) Example • (-1, 0) (1, 4) • Find the slope • Slope= • Find the y-intercept • You have to solve for b (y-intercept) • Let (1, 4) be x and y Replace the letters by their values Multiply the slope and the x value Minus two on both sides The answer is 2. • The equation is y=2 x+2 Rubens Lacouture

Multiplying A Binomial By A Binomial Kasie Okafor ls a i m o n i rly b e o p o tw r p y l ve en tip i l t u u. b To m y distri do wh umber u l app as yo - digit n e c i o c i a r w r t o w b t y e l m g l u tip s. a l s u m n e r m A e th t f s i o o This ession e of tw c r exp ifferen d the Examples: 1. 2. 3. 4. Add The Result: The Answer

Solving Inequalities using all operations Description: An Inequalities is the condition of being unequal lack of equality disparity. 4 Practice 2 x+ 6 > 4 x- 16 Problems: : s e l p Exam First you -3 x to both sides , then you have 9>3 x-12 you have to +12 to both sides. Then you have 213 >3 x3 you cross 3 x3 out and 7> x. Your answer x>7. 9 x -5 < 45 x +12 8 x-9>7 x+12 8 x-5<23 x+13 Jennifer Jean-Louis

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: Step 1: Step 2: 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. (4 x+8+2) 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. 4 Practice Problems: Step 3: Answer: Mykala Jordan

Solving Equations u on Property of ti a c li ip lt u M e th You can use liminates e g n ti c a tr b su r o ding Equality so that ad s. one of the variable sing Elimination Practice P roblems By: Mark Britt

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 12 x(4 y+2 x) 3 y(6 y+5 zy) 10 x(2+12 y) 2(12 b-6 a) 100 xy(7 -2 w) FRANCE WANISE SAINTIL

Solving multi-step equations with all Practice problems operations Practice problems • Description, examples 1. To solve the problem above, you subtract 5 from both sides. 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. 2. Then divide 5 to 5 x, and 10, and you will get x=2. The variable is 2. Here are some examples Jackson C. Ngo

Finding the equation of a line given two points By: Junior Tatis

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

Solving Systems of equations using 4 Practice substitution Example problems 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

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

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

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

DIVIDING MONOMIALS • First take the 12 and divide it by the three. 12 divided by 3 is 4. • Then were going to take the a’s 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 it’s a raised to the 3 rd 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 6 th power. At the end your answer should look like this. Jhlyik Lezama

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 Here is our variables inside the parenthesis with example the outside parenthesis 8(2 x -6) After multiplying it would give us our 8(2 x) 8(-6) final answer of 16 x – 48 16 x - 48 With that you are done and free to try some practice problems below. Vu Nguyen.

Multiplying a polynomial by a monomial. e can b rty e p o l by r a p i e m v o lyn buti i o to r t p s s i i a d a y ide ltipl The n u i a m and m l o t a e i d h nom use omial. T o m n fa a mo roduct o p if nd a omial. yn l o p a Examples: First thing is the distributive property. The next thing is to multiply After you multiplied you have to simply Brittany Odom

Example I 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 Practice Problem I find two solution. Substitute y=4 x-2 into the 1 y Distribute Multiplication Subtract 6 x-4 x 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 Answer is (1, 2) Fredens Altine

Solving Systems Of Equations Using Substitution 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. x - 2 y = 14 x + 3 y = 9 a. First, be sure that the variables are "lined up" under one another. In this problem, they are already "lined up". 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. 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. ) d. Solve this simple equation. Try these. . e. Plug "y = -1" into either of the ORIGINAL equations to get the value for "x". • 4 x + 3 y = -1 5 x + 4 y = 1 f. Check: substitute x = 12 and y = -1 into BOTH ORIGINAL equations. If these answers are correct, BOTH equations will be TRUE! • 4 x - y = 10 2 x = 12 - 3 y • x - 2 y = 14 x + 3 y = 9 P = 2 + 2 Q P = 10 – 6 Q x - 2 y = 14 x + 3 y = 9 x - 2 y = 14 -x - 3 y = - 9 - 5 y = 5 -5 y = 5 y = -1 x - 2 y = 14 x - 2(-1) = 14 x + 2 = 14 x = 12 x - 2 y = 14 12 - 2(-1) = 14 12 + 2 = 14 14 = 14 (check!) x + 3 y = 9 12 + 3(-1) = 9 12 - 3 = 9 9 = 9 (check!) SHAY WEBSTER

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. (2 x+3 y)+(4 x+9 y) {add the x’s first then the y’s} Practice problems for you to try…. • (5+4 n+2 m)+(-6 m-8) • (5 a+9 b)-(2 a+4 b) • (5 f+g-2)+(-2 f+3) • (11 m-7 n)-(2 m+6 n) 6 x+12 y 2. (6 s+5 t)+(4 t+8 s) {add the s’s first then the t’s} 14 s+9 t Jonique Tabb

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. 1. 3 x+10=100 2. 7 x+10=52 Were basically going to undo the probably by doing the opposite. So first I’m going to subtract 10 from both sides. That’s going to leave me with 3 x=90. -10 3 x=90 _ _ 3 3 X=30 Then were going to divide both sides by 3. 3 x 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 x=30. 7 x+10=52 -10 7 x=42 _ _ 7 Subtract 10 from both sides. Divide both sides by 7 7 X=6 There’s your answer Practice Problems 1. 3 x+5=14 2. 2 x - 3=-9 3. 3 x-2=10 4. 3 x+5=14 Cookie Bourne

Factoring Trinomials 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. 1 x²-10 n+25 1 x²+15 n+14 1 x²-8 n-48 1 x²+p-20 EXAMPLE 1 x² + 5 x – 36= (x + 9) * (x – 4) SOLUTION The problem asks me to factor the trinomial into two binomials. STEP 1 List 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 3 After that turn them into two binomials. Jimmy Lai

Graphing the Solution of an inequality on a number line EXAMPLE: 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 Graph: x < 4 Solution: The problem asks you to graph all numbers that are less than 4. STEP 1: Draw an open circle on the number 4. (Don’t draw a CLOSED circle because it does have the _ under the symbol. STEP 2: Draw a line going left, because x is less then 4. HERES THE SOLUTION X<-9 x > 24 | 2 x + 3 | < 6 5 >x Parmanand Jodhan

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. Practice problems (6 – 2 x) (10 – 7 x) (12 x + 4) (3 x + 7) First you do 3 x times 5 x and get 15 x. Next you do 2 times 4 and you get 8. after that its 2 times 5 x the answer is 10 x. lastly you do 3 x times 4 and it equals 12 x. (8 x – 9) (14 x – 13) (9 x+ 24) (5 x + 1) Alisha Cooper