CCSS.Math.Content.HSA.APR Arithmetic with Polynomials & Rational

CCSS.Math.Content.HSA.APR Arithmetic with Polynomials & Rational Expressions - High School Algebra Mathematics - Common Core State Standards

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Authors: National Governors Association Center for Best Practices, Council of Chief State School Officers
Title: CCSS.Math.Content.HSA.APR Arithmetic with Polynomials & Rational Expressions - High School Algebra Mathematics Common Core State Standards
Publisher: National Governors Association Center for Best Practices, Council of Chief State School Officers, Washington D.C.
Copyright Date: 2010
(Page last edited 10/08/2017)

CCSS.Math.Content.HSA.APR.A.1
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
CCSS.Math.Content.HSA.APR.B.2
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
CCSS.Math.Content.HSA.APR.B.3
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
CCSS.Math.Content.HSA.APR.C.4
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x² + y²)² = (x² - y²)² + (2xy)² can be used to generate Pythagorean triples.
CCSS.Math.Content.HSA.APR.C.5
(+) Know and apply the Binomial Theorem for the expansion of (x + y)ⁿ in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.¹
CCSS.Math.Content.HSA.APR.D.6
Rewrite simple rational expressions in different forms; write ^a(x)/_b(x) in the form q(x) + ^r(x)/_b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
CCSS.Math.Content.HSA.APR.D.7
(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions

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CCSS.Math.Content.HSA.APR.A.1	Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
CCSS.Math.Content.HSA.APR.B.2	Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
CCSS.Math.Content.HSA.APR.B.3	Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
CCSS.Math.Content.HSA.APR.C.4	Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x² + y²)² = (x² - y²)² + (2xy)² can be used to generate Pythagorean triples.
CCSS.Math.Content.HSA.APR.C.5	(+) Know and apply the Binomial Theorem for the expansion of (x + y)ⁿ in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.¹
CCSS.Math.Content.HSA.APR.D.6	Rewrite simple rational expressions in different forms; write ^a(x)/_b(x) in the form q(x) + ^r(x)/_b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
CCSS.Math.Content.HSA.APR.D.7	(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions