Hovedinnhold
Math
Common Core Math
High School: Algebra: Arithmetic with Polynomials and Rational Expressions
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.
- Add & subtract polynomials
- Add polynomials (intro)
- Adding and subtracting polynomials review
- Adding polynomials
- Binomial special products review
- Multiply binomials
- Multiply binomials by polynomials
- Multiply binomials by polynomials: area model
- Multiply binomials intro
- Multiply binomials: area model
- Multiply monomials by polynomials
- Multiply monomials by polynomials (basic): area model
- Multiply monomials by polynomials: area model
- Multiply monomials by polynomials: Area model
- Multiply monomials intro
- Multiply perfect squares of binomials
- Multiplying binomials
- Multiplying binomials by polynomials
- Multiplying binomials by polynomials review
- Multiplying binomials by polynomials: area model
- Multiplying binomials intro
- Multiplying binomials review
- Multiplying binomials: area model
- Multiplying monomials
- Multiplying monomials by polynomials
- Multiplying monomials by polynomials review
- Multiplying monomials by polynomials: area model
- Polynomial special products: difference of squares
- Polynomial special products: difference of squares
- Polynomial special products: perfect square
- Polynomial subtraction & set closure
- Special products of binomials
- Special products of binomials intro
- Special products of the form (ax+b)(ax-b)
- Special products of the form (x+a)(x-a)
- Squaring binomials of the form (ax+b)²
- Squaring binomials of the form (x+a)²
- Subtract polynomials (intro)
- Subtracting polynomials
- Warmup: Multiplying binomials
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).
- Intro to the Polynomial Remainder Theorem
- Proof of the Polynomial Remainder Theorem
- Remainder theorem and factors
- Remainder theorem examples
- Use the Polynomial Remainder Theorem
- Using the Polynomial Remainder Theorem: checking factors
- Using the Polynomial Remainder Theorem: finding coefficients
- Using the Polynomial Remainder Theorem: finding remainders
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.
- Find zeros of polynomials
- Graphs of polynomials
- Graphs of polynomials: Challenge problems
- Multiplicity of zeros of polynomials
- Zeros of polynomials (multiplicity)
- Zeros of polynomials (multiplicity)
- Zeros of polynomials (with factoring): common factor
- Zeros of polynomials (with factoring): grouping
- Zeros of polynomials & their graphs
- Zeros of polynomials & their graphs
- Zeros of polynomials introduction
- Zeros of polynomials: matching equation to graph
- Zeros of polynomials: matching equation to zeros
- Zeros of polynomials: plotting zeros
Prove polynomial identities and use them to describe numerical relationships.
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.
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 polynomials by x (no remainders)
- Divide polynomials by x (with remainders)
- Divide polynomials with remainders: binomial divisors
- Divide quadratics by linear expressions (no remainders)
- Divide quadratics by linear expressions (with remainders)
- Dividing polynomials by linear expressions
- Dividing polynomials by linear expressions: missing term
- Dividing polynomials by x (no remainders)
- Dividing polynomials with remainders: monomial divisors
- Dividing quadratics by linear expressions (no remainders)
- Dividing quadratics by linear expressions with remainders
- Dividing quadratics by linear expressions with remainders: missing x-term
- Factor using polynomial division
- Factoring using polynomial division
- Factoring using polynomial division: missing term
- Intro to long division of polynomials
- Polynomial division introduction
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.
- Add & subtract rational expressions
- Add & subtract rational expressions: factored denominators
- Add & subtract rational expressions: like denominators
- Add & subtract rational expressions: unlike denominators
- Adding & subtracting rational expressions (advanced)
- Adding & subtracting rational expressions: like denominators
- Adding rational expression: unlike denominators
- Dividing rational expressions
- Dividing rational expressions
- Dividing rational expressions: unknown expression
- Intro to adding & subtracting rational expressions
- Intro to adding rational expressions with unlike denominators
- Multiply & divide rational expressions
- Multiply & divide rational expressions (advanced)
- Multiply & divide rational expressions (basic)
- Multiplying & dividing rational expressions: monomials
- Multiplying rational expressions
- Multiplying rational expressions
- Multiplying rational expressions: multiple variables
- Nested fractions
- Nested fractions
- Subtracting rational expressions
- Subtracting rational expressions: factored denominators
- Subtracting rational expressions: unlike denominators