math nation algebra 2 unit 1 lesson 3 homework

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Common Core Algebra II

The full experience and value of eMATHinstruction courses are achieved when units and lessons are followed in order.  Students learn skills in earlier units that they will then build upon later in the course.  Lessons can be used in isolation but are most effective when used in conjunction with the other lessons in this course. All Lesson/Homework files, and videos are available for free.  Other resources such as answer keys and more, are accessible with a paid membership.

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Standards Alignment – Powered by EdGate

• Table of Contents and Standards Alignment for Common Core Algebra II
• Unit 1 - Algebraic Essentials Review
• Unit 2 - Functions as the Cornerstones of Algebra II
• Unit 3 - Linear Functions, Equations, and Their Algebra
• Unit 4 - Exponential and Logarithmic Functions
• Unit 5 - Sequences and Series
• Unit 6 - Quadratic Functions and Their Algebra
• Unit 7 - Transformations of Functions
• Unit 8 - Radicals and the Quadratic Formula
• Unit 9 - Complex Numbers
• Unit 10 - Polynomial and Rational Functions
• Unit 11 - The Circular Functions
• Unit 12 - Probability
• Unit 13 - Statistics
• Statistical Simulators

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Dividing Polynomials Worksheet and Answer Key

Students will practice dividing polynomials .

This is a 4 part worksheet:

• Part I Model Problems
• Part II Practice
• Part III Challenge Problems
• Part IV Answer Key

Example Worksheet Questions

Directions: Divide the polynomials below:

Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there!

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Unit 1: Algebra foundations

Unit 2: solving equations & inequalities, unit 3: working with units, unit 4: linear equations & graphs, unit 5: forms of linear equations, unit 6: systems of equations, unit 7: inequalities (systems & graphs), unit 8: functions, unit 9: sequences, unit 10: absolute value & piecewise functions, unit 11: exponents & radicals, unit 12: exponential growth & decay, unit 13: quadratics: multiplying & factoring, unit 14: quadratic functions & equations, unit 15: irrational numbers, unit 16: creativity in algebra.

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About This Course

Welcome to the Math Medic Algebra 2 course! Here you will find a ready-to-be-taught lesson for every day of the school year, along with expert tips and questioning techniques to help the lesson be successful. Each lesson is designed to be taught in an Experience First, Formalize Later (EFFL) approach, in which students work in small groups on an engaging activity before the teacher formalizes the learning.

Our Algebra 2 course focuses on several function families and develops the graphical, analytical, verbal, and numerical analysis skills needed to flexibly work with these functions, with an emphasis on quadratics. The concept of function transformations is a big theme and woven throughout the course. This course was created using the Common Core State Standards as a guide. The standards taught in each Math Medic Algebra 2 lesson can be found here . The unit overviews and learning targets for the Math Medic Algebra 2 course can be found here .

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Mathematics Support

Algebra II | Unit 1 2 3 4 5 6

Polynomial and Rational Functions

Topic 1: Quadratic Expressions and Equations 

• Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. ( cK–12 Flexbook Unit 2 Topic 1 SLT 1 ) 

• Identify zeros of quadratic functions when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the quadratic expression. ( cK–12 Flexbook Unit 2 Topic 1 SLT 2 ) 

• Solve radical equations in one variable and identify extraneous solutions. ( cK–12 Flexbook Unit 2 Topic 1 SLT 3 ) 

• Explore complex numbers and their importance in mathematics.( cK–12 Flexbook Unit 2 Topic 1 SLT 4 ) 

• Define a complex number and determine its relationship to the real number system. ( cK–12 Flexbook Unit 2 Topic 1 SLT 5 ) 

• Add, subtract, and multiply complex numbers using properties of operations. ( cK–12 Flexbook Unit 2 Topic 1 SLT 6 ) 

• Solidify understanding of addition and multiplication within the complex number system. 

• Solve quadratic equations that have complex solutions. ( cK–12 Flexbook Unit 2 Topic 1 SLT 8 ) 

• Identify and describe characteristics of quadratic functions given graphs or equations. ( cK–12 Flexbook Unit 2 Topic 1 SLT 9) 

Topic 2: Radical Expressions and Equations 

• Explore functions at large positive and negative values of x . 

• Interpret end behavior of a variety of functions in multiple representations. ( cK–12 Flexbook Unit 2 Topic 2 SLT 11 ) 

• Interpret key features of polynomial functions given different representations. ( cK–12 Flexbook Unit 2 Topic 2 SLT 12 ) 

• Add and subtract polynomials graphically and symbolically. ( cK–12 Flexbook Unit 2 Topic 2 SLT 13 & 14: Add, Subtract ) 

• Multiply polynomials graphically and symbolically. ( cK–12 Flexbook Unit 2 Topic 2 SLT 13 & 14: Multiply ) 

• Graph polynomials in factored form. ( cK–12 Flexbook Unit 2 Topic 2 SLT 15 ) 

• Identify zeros of polynomial functions when suitable factorizations are available in order to graph the function and identify its key features. ( cK–12 Flexbook Unit 2 Topic 2 SLT 16 ) 

• Divide polynomial expressions using area models, partial quotients, and long division. ( cK–12 Flexbook Unit 2 Topic 2 SLT 17 ) 

• Apply the Remainder Theorem and polynomial division to find the zeros of a polynomial function. ( cK– 12 Flexbook Unit 2 Topic 2 SLT 18 ) 

• Make connections among the equation, graph, and features of a polynomial function. ( cK–12 Flexbook Unit 2 Topic 2 SLT 19 ) 

• Model a real-world situation using a polynomial function. 

Topic 3: Rational Expressions and Equations 

• Develop and graph a rational function that models inverse variations of the form k y x = and identify its key features. ( cK–12 Flexbook Unit 2 Topic 3 SLT 21 ) 

• Develop and graph a rational function that models inverse variations of the form 2 k y x = and identify its key features. ( cK–12 Flexbook Unit 2 Topic 3 SLT 22 ) 

• Identify the effect on the graph of a rational function of replacing ( ) f x by ( ) f x k + , ( ) k f x ∙ , and ( ) f x k + for specific values of k . ( cK–12 Flexbook Unit 2 Topic 3 SLT 23 ) 

• Rewrite rational expressions of the form ( ) ( ) a x b x as ( ) ( ) ( ) r x b x q x + to reveal characteristics of the associated function. ( cK–12 Flexbook Unit 2 Topic 3 SLT 24 ) 

• Solve simple rational equations in one variable. ( cK–12 Flexbook Unit 2 Topic 3 SLT 25 )

This document outlines concepts in each Topic for the Unit. When corresponding resources are available in cK12.org, a hyperlink is provided for the Flexbook. The cK12.org Flexbooks provide a variety of examples, definitions, and extra practice problems related to some of the concepts in Curriculum 2.0 Two-year Algebra 2, Algebra 2, and Honors Algebra 2. The concepts will be developed in greater depth and with appropriate vocabulary in the classroom. The materials in the Flexbooks are intended to provide additional support to the classroom expectations. The vocabulary and methods in these examples may differ slightly from the classroom expectation; however, the overall intent is consistent with the content expectation.

Introducing Polynomials

Select all points where relative minimum values occur on this graph of a polynomial function.

Point \(A\)

Point \(B\)

Point \(C\)

Point \(D\)

Point \(E\)

Point \(F\)

Point \(G\)

Point \(H\)

For access, consult one of our IM Certified Partners .

Add one term to the polynomial expression \(14x^{19}-9x^{15}+11x^4+5x^2+3\) to make it into a 22nd degree polynomial.

Identify the degree, leading coefficient, and constant value of each of the following polynomials:

• \(f(x)=x^3 - 8 x^2 - x + 8\)
• \(h(x)=2 x^4 + x^3 - 3 x^2 - x + 1\)
• \(g(x)=13.2 x^3+3 x^4 - x - 4.4\)

We want to make an open-top box by cutting out corners of a square piece of cardboard and folding up the sides. The cardboard is a 9 inch by 9 inch square. The volume \(V(x)\) in cubic inches of the open-top box is a function of the side length \(x\) in inches of the square cutouts.

• Write an expression for \(V(x)\) .
• What is the volume of the box when \(x=1\) ?
• What is a reasonable domain for \(V\) in this context?

Consider the polynomial function \(p\) given by \(p(x)=7x^3 - 2x^2 + 3x+10\) . Evaluate the function at \(x=\text-3\) .

An open-top box is formed by cutting squares out of an 11 inch by 17 inch piece of paper and then folding up the sides. The volume \(V(x)\) in cubic inches of this type of open-top box is a function of the side length \(x\) in inches of the square cutouts and can be given by  \(V(x)=(17-2x)(11-2x)(x)\) . Rewrite this equation by expanding the polynomial.