A.APR.2 Know and apply the Remainder Theorem: For a polynomial Make sense of p(x) and a number a, the remainder on division by x a is p(a), so problems and – p(a) = 0 if and only if (x a) is a factor of p(x). persevere in solving – them. Essential Skills and Knowledge Ability to make connections between factors, roots and Reason abstractly evaluating functions and Ability to use both long division and synthetic division quantitatively. Ability to use the graph of a polynomial to assist in the efficiency of the process for complicated cases Construct viable arguments and critique the reasoning of others. A.APR.3 Identify of polynomials when suitable factorizations are Model with available, and use the zeros to construct a rough graph of the mathematics. function defined by the polynomial. Use appropriate Understand the Essential Skills and Knowledge relationship tools Knowledge of the differences in the end behavior of the between strategically. graphs as dictated by the leading coefficient and whether zeros and factors the function is even or odd of polynomials. Attend to precision. Ability to capture the graphical behavior of polynomial functions which have roots with multiplicity greater than Look for and make one use of structure. Look for and express regularity in repeated reasoning.
Understand the relationship between zeros and factors of polynomials. A.APR.2 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). Essential Skills and Knowledge Ability to make connections between factors, roots and evaluating functions Ability to use both long division and synthetic division Ability to use the graph of a polynomial to assist in the efficiency of the process for complicated cases A.APR.3 Identify of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Essential Skills and Knowledge Knowledge of the differences in the end behavior of the graphs as dictated by the leading coefficient and whether the function is even or odd Ability to capture the graphical behavior of polynomial functions which have roots with multiplicity greater than one Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.
AlgebraIIFramework.docx