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Master Factoring Polynomials: ax^2 + bx + c | Step-by-Step

TX.AR.2.A

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Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Rate of change

Applications of linear relations

Arithmetic sequences

Geometric sequences

TX.AR.2.B

Relationship between two variables

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Reading linear relation graphs

Solving linear equations by graphing

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Characteristics of quadratic functions

TX.AR.2.C

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Graphing quadratic functions: General form VS. Vertex form

TX.AR.2.D

Word problems of graphing linear functions

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Applications of quadratic functions

TX.AR.3.A

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

Quadratic function in general form: y = ax^2 + bx + c

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Graphing exponential functions

TX.AR.3.B

Combining transformations of functions

Inverse functions

Even and odd functions

TX.AR.3.C

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Operations of Functions – In a Nutshell

TX.AR.3.D

Operations with functions

TX.AR.3.E

One to one functions

Function notation (advanced)

Composite functions

TX.AR.3.F

Difference quotient: applications of functions

TX.AR.4.A

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Multiplying and dividing monomials

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Multiplying polynomial by polynomial

TX.AR.4.B

Inequalities of combined functions

Inequalities of Combined Functions

TX.AR.4.C

Polynomial long division

Polynomial synthetic division

TX.AR.4.D

Solving polynomials with the unknown 

Solving polynomials with the unknown "b" from ax^2 + bx + c

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Rational zero theorem

Rational Zero Theorem

Common factors of polynomials

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

TX.AR.5.A

Adding and subtracting matrices

TX.AR.5.B

Matrix multiplication

TX.AR.5.C

Scalar multiplication of matrices

TX.AR.5.D

System of linear equations

Representing a linear system as a matrix

Solving a linear system with matrices using Gaussian elimination

TX.AR.5.E

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

The Inverse of a 2 x 2 matrix

The inverse of 3 x 3 matrices with matrix row operations

The inverse of 3 x 3 matrix with determinants and adjugate

2 x 2 invertible matrix

Solving linear systems using Cramer's Rule

Solving linear systems using Cramer"s Rule

Cramer"s Rule with 2 x 2 matrices

Solving linear systems using 2 x 2 inverse matrices

TX.AR.6.B

Introduction to linear equations

Solving quadratic equations by factoring

TX.AR.6.C

Solving logarithmic equations

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Solving exponential equations using exponent rules

TX.AR.7.A

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

TX.AR.7.C

Regression analysis

TX.AR.7.D

Equation of the best fit line

Algebraic Reasoning 

Modeling from data

Number and algebraic methods

Patterns and structure

math

Ex. 1:

Ex. 2:

Ex. 3:

Intro

- Hi, welcome to this question right here. So, here we are trying to do some factoring but this time we've got a number in the front of x square. So, this is a little bit harder, but this is a trick, okay? 
Before you may start with the bracket, bracket. We're gonna do a little bit something that's called a little bit of guessing, all right? First thing you do is, you have to think of the factor that gives you 9, the factors of 9 basically, we've got 1 and 9, 3 and 3. Now, personally I don't like the 1 and 9, I'd like to go with the 3 and 3. So, let's just go and do that, let's put the 3 and 3 just below the 9, okay? 
Now, on the other side over here, we have to look on the 2 over here. Now, the factors of 2 is just 1 and 2. So, let's say we're just gonna do randomly. Let's put 1 and 2 down. So, let's put a 1 right here, and then put a 2 right here. Now, the trick is you have to do something that is called cross multiply, all right? Why are we doing this? You will see. 3 times 1, or the cross multiplying here, 3 x 1 is 3, and 3 x 2 is a 6, okay? 
These two numbers here, you have to add them up to get you a positive 3. So, what that means is, this must be a 6 positive, and this one here must be a negative, a negative 3. So, where this negative come from? It has to come from the negative 1 at the front. Now, how does it make sense? Well, let's all go back to the very beginning. These two numbers here are the factors of 9. So what that means is 3 x 3 gives you the 9, which is true. These two numbers here are the factors of the 2, but remember this one? It was a negative, right? So 1 would had to be a negative, but we weren't sure yet so, that's why I just do the math, and then look at the answer over here, I know by adding or subtracting I need to get the 3, So, that means a negative 3 is here and that means this must be a negative 1, So, here let's just double check, 2 times negative 1 does give me negative 2. Cross multiplying 3 x negative 1 is negative 3, 3 x 2 is 6. By adding them I do get the middle number. Why is everything here and it makes sense perfectly, the final answer is just going to be bracket, bracket. But what do you put in the brackets? It's easy, take a look at the first one, that's your first bracket right there. You just have to add the x in by yourself. And this is a negative 1, so why not just put a negative 1 down there? The second one is the second bracket down here, it's a 3x again and you get yourself a positive 2. And that's it, there you go. That's the factor of that trinomial out there. Thanks for watching.

Before starting this lesson, check your understanding on how to factor \({x^2 + bx + c}\\  \) we talked about in the other lesson first. The coefficient, a, in front of \({x^2}\\  \) can make it a bit more challenging, but we will show you the tricks to make it easy!