Students write explicit polynomial expressions for sequences by investigating successive differences of those sequences.
Students explore the difference of two squares identity x2 − y2 = (x − y)(x + y) in the context of finding Pythagorean triples.
Students find solutions to polynomial equations where the polynomial expression is not factored into linear factors.
Students construct a polynomial function that has a specified set of zeros with stated multiplicity.
Students develop the distributive property for application to polynomial multiplication. Students connect multiplication of polynomials with multiplication of multi-digit integers.
Students develop a division algorithm for polynomials by recognizing that division is the inverse operation of multiplication.
Students perform arithmetic operations on polynomials and write them in standard form.
Students understand the structure of polynomial expressions by quickly determining the first and last terms if the polynomial were to be written in standard form.
Students work with polynomials with constant coefficients to prove polynomial identities.
Students perform arithmetic by using polynomial identities to describe numerical relationships.
Students apply polynomial identities to the detection of prime numbers.
Students understand that the sum of two square roots (or two cube roots) is not equal to the square root (or cube root) of their sum.
Students convert expressions to simplest radical form.
Students understand that the product of conjugate radicals can be viewed as the difference of two squares.
Students will factor certain forms of polynomial expressions by using the structure of the polynomials.
Students will use the structure of polynomials to identify factors.
Students will use the factored forms of polynomials to find zeros of a function.
Students will use the factored forms of polynomials to sketch the components of graphs between zeros.
Students graph polynomial functions and describe end behavior based upon the degree of the polynomial.
Students transition between verbal, numerical, algebraic, and graphical thinking in analyzing applied polynomial problems.
Students transition between verbal, numerical, algebraic, and graphical thinking in analyzing applied polynomial problems.
Students know and apply the Remainder Theorem and understand the role zeros play in the theorem.
Students learn to fit polynomial functions to data values.
Students model a cross-section of a riverbed with a polynomial function and estimate fluid flow with their algebraic model.
Students define rational expressions and write them in equivalent forms.