Standard 4 : Polynomials (Archived)



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Perform operations on polynomials. Find factors of polynomials, learning special techniques for factoring quadratics. Understand the relationships among the solutions of polynomial equations, the zeros of a polynomial function, the x-intercepts of a graph, and the factors of a polynomial.

General Information

Number: MA.912.A.4
Title: Polynomials
Type: Standard
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 912
Body of Knowledge: Algebra

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.A.4.1: Simplify monomials and monomial expressions using the laws of integral exponents.
MA.912.A.4.2: Add, subtract, and multiply polynomials.
MA.912.A.4.3: Factor polynomial expressions.
MA.912.A.4.4: Divide polynomials by monomials and polynomials with various techniques, including synthetic division.
MA.912.A.4.5: Graph polynomial functions with and without technology and describe end behavior.
MA.912.A.4.6: Use theorems of polynomial behavior (including but not limited to the Fundamental Theorem of Algebra, Remainder Theorem, the Rational Root Theorem, Descartes' Rule of Signs, and the Conjugate Root Theorem) to find the zeros of a polynomial function.
MA.912.A.4.7: Write a polynomial equation for a given set of real and/or complex roots.
MA.912.A.4.8: Describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression with and without technology.
MA.912.A.4.9: Use graphing technology to find approximate solutions for polynomial equations.
MA.912.A.4.10: Use polynomial equations to solve real-world problems.
MA.912.A.4.11: Solve a polynomial inequality by examining the graph with and without the use of technology.
MA.912.A.4.12: Apply the Binomial Theorem.


Related Access Points

This cluster includes the following access points.

Independent

Access Point Number Access Point Title
MA.912.A.4.In.a: Simplify expressions with one unknown (variable) by identifying like terms.
MA.912.A.4.In.b: Solve equations with one unknown (variable) involving addition, subtraction, and multiplication.
MA.912.A.4.In.c: Combine like and unlike terms in number sentences representing real-world situations.
MA.912.A.4.In.d: Identify factors of expressions with whole numbers by dividing.

Supported

Access Point Number Access Point Title
MA.912.A.4.Su.a: Solve number sentences (equations) with one unknown involving addition and subtraction facts using physical and visual models.
MA.912.A.4.Su.b: Identify like and unlike terms in number sentences representing real-world situations.
MA.912.A.4.Su.c: Identify factors of whole numbers by using division facts.

Participatory

Access Point Number Access Point Title
MA.912.A.4.Pa.a: Identify a missing item from two or more sets.
MA.912.A.4.Pa.b: Recognize that joining sets of objects results in a larger quantity and separating sets of objects results in a smaller quantity.
MA.912.A.4.Pa.c: Separate groups of objects to 10 into sets with the same quantity.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Tutorial

Name Description
Multiplying Polynomials:

This resource is a step-by-step tutorial on how to multiply polynomials.

Unit/Lesson Sequence

Name Description
Variables and Patterns of Change: Translating Words Into Symbols; Linear Equations: Lesson Plan 1: Miles of Tiles - The Pool Border Problem, students will recognize patterns and represent situations using algebraic notation and variables. Lesson Plan 2: Cups and Chips - Solving Linear Equations Using Manipulatives, students use manipulatives to represent visually the steps they take to obtain a solution to an algebraic equation. They develop an understanding of the connections between the solution involving manipulatives and the symbolic solution. Students work in teams of four. Site includes a Topic Overview, Lesson Plans, Student Work, Teaching Strategies, Resources, and a video of Workshop 1; Part 1.

Video/Audio/Animation

Name Description
Teach Me How to Factor:

This video features a contrafactum of a popular rap song to teach students how to factor.

Virtual Manipulative

Name Description
Curve Fitting:

With a mouse, students will drag data points (with their error bars) and watch the best-fit polynomial curve form instantly. Students can choose the type of fit: linear, quadratic, cubic, or quartic. Best fit or adjustable fit can be displayed.



Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Virtual Manipulative

Title Description
Curve Fitting:

With a mouse, students will drag data points (with their error bars) and watch the best-fit polynomial curve form instantly. Students can choose the type of fit: linear, quadratic, cubic, or quartic. Best fit or adjustable fit can be displayed.



Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Tutorial

Title Description
Multiplying Polynomials:

This resource is a step-by-step tutorial on how to multiply polynomials.