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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