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.
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).
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 (LIMIT TO 1ST- AND 2ND-DEGREE POLYNOMIALS).
PROVE POLYNOMIAL IDENTITIES AND USE THEM TO DESCRIBE NUMERICAL RELATIONSHIPS. FOR EXAMPLE, THE POLYNOMIAL IDENTITY (X^2 + Y^2)^2 = (X^2 – Y^2)^2 + (2XY)^2 CAN BE USED TO GENERATE PYTHAGOREAN TRIPLES.
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.
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.
Mississippi: A-APR Math Standards