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- Common Core MathK - 8High School
Algebra: Arithmetic with Polynomials and Rational Expressions
722 questions44 skills
Algebra: Arithmetic with Polynomials and Rational Expressions
722 questions44 skills
HSA-APR.A.1
345 questions21 skills
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.
Multiply difference of squares
Add polynomials (intro)
Multiply binomials by polynomials
Multiply binomials intro
Multiply binomials by polynomials: area model
Polynomial special products: perfect square
Add & subtract polynomials: two variables
Multiply monomials by polynomials
Multiply monomials (advanced)
Polynomial special products: difference of squares
Multiply monomials by polynomials challenge
Multiply monomials
Add & subtract polynomials
Multiply binomials: area model
Add & subtract polynomials: two variables (intro)
Multiply monomials by polynomials (basic): area model
Multiply perfect squares of binomials
Multiply monomials by polynomials: area model
Add & subtract polynomials: find the error
Subtract polynomials (intro)
Multiply binomials
HSA-APR.B.2
27 questions2 skills
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).
HSA-APR.B.3
40 questions3 skills
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.
HSA-APR.C.4
20 questions1 skill
Prove polynomial identities and use them to describe numerical relationships.
HSA-APR.C.5
16 questions1 skill
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.
HSA-APR.D.6
116 questions8 skills
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.
Divide quadratics by linear expressions (no remainders)
Divide quadratics by linear expressions (with remainders)
Divide polynomials by x (no remainders)
Divide polynomials by monomials (with remainders)
Divide polynomials with remainders
Divide polynomials by linear expressions
Factor using polynomial division
Divide polynomials by x (with remainders)
HSA-APR.D.7
158 questions8 skills
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.
Multiply & divide rational expressions (advanced)
Add & subtract rational expressions
Multiply & divide rational expressions
Nested fractions
Add & subtract rational expressions (basic)
Multiply & divide rational expressions: Error analysis
Add & subtract rational expressions: factored denominators
Add & subtract rational expressions: like denominators