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Big Ideas Math Algebra 2 Answers | Big Ideas Math Book Algebra 2 Answer Key

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• Chapter 1 Linear Functions
• Chapter 2 Quadratic Functions
• Chapter 3 Quadratic Equations and Complex Numbers
• Chapter 4 Polynomial Functions
• Chapter 5 Rational Exponents and Radical Functions
• Chapter 6 Exponential and Logarithmic Functions
• Chapter 7 Rational Functions
• Chapter 8 Sequences and Series
• Chapter 9 Trigonometric Ratios and Functions
• Chapter 10 Probability
• Chapter 11 Data Analysis and Statistics

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BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015 HOUGHTON MIFFLIN HARCOURT

BIG IDEAS MATH Algebra 2: Common Core S... 15th Edition HOUGHTON MIFFLIN HARCOURT Publisher: Cengage Learning ISBN: 9781608408405

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The Multiplication of Polynomials

Related Topics: Lesson Plans and Worksheets for Algebra II Lesson Plans and Worksheets for all Grades More Lessons for Algebra Common Core For Algebra

Student Outcomes

• Students develop the distributive property for application to polynomial multiplication.
• Students connect multiplication of polynomials with multiplication of multi-digit integers.

New York State Common Core Math Algebra II, Module 1, Lesson 2

Worksheets for Algebra 2

Opening Exercise

Show that 28 × 27 = (20 + 8)(20 + 7) using an area model. What do the numbers you placed inside the four rectangular regions you drew represent?

Use the tabular method to multiply (𝑥 +8)(𝑥 + 7) and combine like terms.

Exercises 1–2

• Use the tabular method to multiply (𝑥 2 + 3𝑥 + 1)(𝑥 2 − 5𝑥 + 2) and combine like terms.
• Use the tabular method to multiply (𝑥 2 + 3𝑥 + 1)(𝑥 2 − 2) and combine like terms.

Multiply the polynomials (𝑥 − 1)(𝑥 4 + 𝑥 3 + 𝑥 2 + 𝑥 + 1) using a table. Generalize the pattern that emerges by writing down an identity for (𝑥 − 1)(𝑥 n + 𝑥 𝑛−1 + ⋯ + 𝑥 2 + 𝑥 + 1) for 𝑛 a positive integer.

Exercises 3–4

• Multiply (𝑥 − 𝑦)(𝑥 3 + 𝑥 2 𝑦 + 𝑥𝑦 2 + 𝑦 3 ) using the distributive property and combine like terms. How is this calculation similar to Example 2?
• Multiply (𝑥 2 − 𝑦 2 )(𝑥 2 + 𝑦 2 ) using the distributive property and combine like terms. Generalize the pattern that emerges to write down an identity for (𝑥 n − 𝑦 n )(𝑥 n + 𝑦 n ) for positive integers 𝑛.

Relevant Vocabulary

• EQUIVALENT POLYNOMIAL EXPRESSIONS: Two polynomial expressions in one variable are equivalent if, whenever a number is substituted into all instances of the variable symbol in both expressions, the numerical expressions created are equal.
• POLYNOMIAL IDENTITY: A polynomial identity is a statement that two polynomial expressions are equivalent. For example, (𝑥 + 3) 2 = 𝑥 2 + 6𝑥 + 9 for any real number 𝑥 is a polynomial identity.
• COEFFICIENT OF A MONOMIAL: The coefficient of a monomial is the value of the numerical expression found by substituting the number 1 into all the variable symbols in the monomial. The coefficient of 3𝑥 2 is 3, and the coefficient of the monomial (3𝑥𝑦𝑧) ⋅ 4 is 12.
• TERMS OF A POLYNOMIAL: When a polynomial is expressed as a monomial or a sum of monomials, each monomial in the sum is called a term of the polynomial.
• LIKE TERMS OF A POLYNOMIAL: Two terms of a polynomial that have the same variable symbols each raised to the same power are called like terms.
• STANDARD FORM OF A POLYNOMIAL IN ONE VARIABLE: A polynomial expression with one variable symbol, 𝑥, is in standard form if it is expressed as 𝑎 𝑛 𝑥 𝑛 +𝑎 𝑛 - 1 𝑥 𝑛 - 1 + ⋯ + 𝑎 1 𝑥 + 𝑎 0 , where 𝑛 is a non-negative integer, and 𝑎 0 , 𝑎 1 , 𝑎 2 … , 𝑎 𝑛 are constant coefficients with 𝑎 𝑛 ≠ 0. A polynomial expression in 𝑥 that is in standard form is often just called a polynomial in 𝑥 or a polynomial. The degree of the polynomial in standard form is the highest degree of the terms in the polynomial, namely 𝑛. The term 𝑎 𝑛 𝑥 𝑛 is called the leading term and 𝑎 𝑛 (thought of as a specific number) is called the leading coefficient. The constant term is the value of the numerical expression found by substituting 0 into all the variable symbols of the polynomial, namely 𝑎 0 .

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• List of Lessons

1.1 Multiply and Factor Polynomials

• 1.2 Advanced Factoring
• 1.3 Dividing Polynomials
• 1.4 Zeroes of Polynomials
• Unit 1 Review
• 2.1 Remainder Theorem
• 2.2 End Behavior
• 2.3 Sketching Polynomials
• 2.4 Graphing Polynomial Functions (Calc)
• Unit 2 Review
• 3.1 Simplify Rational Expressions
• 3.2 Multiply and Divide Rational Expressions
• 3.3 Add and Subtract Rational Expressions
• 3.4 Solve Rational Equations
• Unit 3 Review
• 4.1 Add/Sub Radicals
• 4.2 Mult/Div Radicals
• 4.3 Radical Equations
• Unit 4 Review
• 5.1 Transformations of Functions, Pt 1
• 5.2 Transformations of Functions, Pt 2
• 5.3 Systems of Equations
• Unit 5 Review
• 6.1 Imaginary Numbers
• 6.2 Complex Numbers
• 6.3 Quadratic Formula
• Unit 6 Review
• 7.1 Rational Exponents
• 7.2 Exponential Growth and Decay
• 7.3 Percent Change
• 7.4 Exponential Modeling
• Unit 7 Review
• 8.1 Intro to Logs
• 8.2 Logarithmic Graphs
• 8.3 Properties of Logarithms
• 8.4 Solving Exponential Equations
• Unit 8 Review
• 9.1 Intro to Trig
• 9.2 Reference Triangles
• 9.3 Unit Circle and Radians
• Unit 9 Review
• 10.1 Amplitude and Midline
• 10.2 Period
• 10.3 Modeling with Sine and Cosine
• Unit 10 Review
• 11.1 Sequences
• 11.2 Series
• Unit 11 Review
• 12.1 Introduction to Probability
• 12.2 Compound Events and Independence
• 12.3 Normal Distributions
• Unit 12 Review
• 13.1 Sampling Methods
• 13.2 Experimental Design
• 13.3 Simulations
• Unit 13 Review
• Teacher Resources

Practice Solutions

Corrective Assignment