This math unit guides students through advanced techniques and concepts of polynomial and rational functions, beginning with synthetic division and building towards understanding rational functions and their asymptotes. Initially, students learn to set up and perform synthetic division, progressing from simple tasks such as finding appropriate divisors and arranging polynomial coefficients to more complex operations like completing the quotient row and determining the entire polynomial result from division. The unit then transitions to applying the Rational Root Theorem to identify possible rational roots of polynomials, augmenting their factoring skills and preparing them for manipulating algebraic expressions with greater complexity. Further, students explore the Factor Theorem as they solve for unknown coefficients and interpret remainders in polynomial division, fostering a deeper understanding of polynomial behaviors and relationships. The unit culminates with intensive practice on rational functions, where students analyze and graph these functions, identifying various types of asymptotes—vertical, horizontal, and slant—and understand how polynomial degrees in numerators and denominators influence these asymptotic behaviors. Overall, this unit equips students with critical skills in polynomial manipulation, division techniques, and comprehension of function behaviors, crucial for advanced algebra and calculus.Skills you will learn include:
Topics are small, focused areas which build towards the greater unit's goals.