Algebra: Arithmetic with Polynomials and Rational Expressions722 questions44 skills
Algebra: Arithmetic with Polynomials and Rational Expressions
722 questions44 skills
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
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)
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).
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.
20 questions1 skill
Prove polynomial identities and use them to describe numerical relationships.
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.
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)
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
Add & subtract rational expressions (basic)
Multiply & divide rational expressions: Error analysis
Add & subtract rational expressions: factored denominators
Add & subtract rational expressions: like denominators