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Master Equivalent Expressions of Polynomials | Math Guide

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

Intro

- Hi, welcome to this question right here. So we're trying to write an equivalent expression. Equivalent expression means something that is exactly the same. They don't look the same, but they are the same. Okay, but you need to have seven terms, so there's multiple of different ways of doing this, actually infinity number of ways in doing this question. So I'm just going to do one example, it's your choice to come up with different answers, okay? The idea is the same. You need to get x square plus 2x plus three as your final answer, okay? 
I can quickly show you how the first way I'm going to do this is-- Let's say how many ways we're going to x square. Maybe I have two x square minus an x square. That will also give me one x square, right? 
Simple enough. What about the 2x? Well, I can say plus, let's change to another color. Plus four x and then minus 2x because these two guys right here will give me two x in total so that is my final answer. So far I got one, two, three, four, four terms now. So I need three more terms to satisfy the question, right? The question says seven terms in total. I need a three at the very end. So any ideas to get a three. Again, the number of the answers you're going to get for this question is like, I don't know how many. Okay, tons and tons. So how do you get a three at the very end? Well, let's try this way. How about let's plus a 10. So 10, let's say you subtract a two. I ran out of space. Minus two is eight. How do you get a three? Well, eight minus five. So try another five. Okay? 
So clearly if you just look at the colors, we&apos;ve got two yellows, two greens and three purples. So all together it's seven terms in total, and if you simplify these guys over here. I can show you really quickly again but you probably know the answer anyway. Two x square minus x square is x square. See, they're the same so far. Take the green one again, so the green one, we have 4x minus 2x. So it's plus 2x. What about the last type of the variables, not variables. The constants here, 10 minus two, minus five? The answer is three, and that's what happens. We&apos;ve got x square plus 2x and the minus three. These guys here, and these guys here are equivalent, the same, but they are-- Well, originally they look different but once you put it all together, they are the same. Okay? This is just to check and your final answer is not this. Your final answer is here, all these guys. Okay? One, two, three, four, five, six, seven, seven terms in total. All right, thanks for watching.

A polynomial may contain multiple terms. The variable terms have a coefficient and a <a href="[[glossary.html|{"keyword":"Variable"}]]">variable</a>. Terms with the same variables are called like terms, and they can be combined together. It allows us to write equivalent expressions of polynomials with more or less terms.

Equivalent algebraic expressions

What are equivalent expressions of polynomials?

Understanding integer division

Applications of integer operations