ALGRZ.MATH.4.C

Determine the quotient of a polynomial function of degree three and of degree four when divided by a polynomial function of degree one and of degree two when represented tabularly and symbolically.

Algebraic Reasoning · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
quotientpolynomial functiondegree threedegree fourdivided bypolynomial function of degree onepolynomial function of degree twotabular representationsymbolic representation
Skills
  • determine (the quotient of a cubic polynomial divided by a linear or quadratic polynomial, represented tabularly) #dok2
  • determine (the quotient of a quartic polynomial divided by a linear or quadratic polynomial, represented symbolically) #dok2
  • interpret (tabular and symbolic representations of polynomial division) #dok2
  • connect (tabular representation and symbolic procedure in polynomial division) #dok3
Learning Targets
  • I can identify the degree of polynomial functions in both the dividend and divisor. #dok1
  • I can recognize and match symbolic expressions representing polynomial division. #dok1
  • I can use a table to determine the result when dividing a cubic or quartic polynomial function by a linear or quadratic polynomial function. #dok2
  • I can perform division of polynomial functions of degree three or four by polynomials of degree one or two using symbolic methods. #dok2
  • I can analyze and connect the results of polynomial division from tabular and symbolic representations to verify solutions. #dok3
  • I can justify my process for determining the quotient by explaining my steps using mathematical language. #dok3
Big Ideas
  • Polynomial division connects symbolic manipulation with tabular data to reveal deeper function relationships.
  • Understanding polynomial division empowers students to solve complex real-world and mathematical problems involving higher-degree functions.
Essential Questions
  • How does the degree of the dividend and divisor affect the result when dividing polynomial functions?
  • In what ways can we use tables and symbolic representations to find and verify the quotient of two polynomials?
  • Why might it be helpful to represent polynomial division both symbolically and in a table?
  • How can accurately determining the quotient of polynomial functions help in solving real-world problems?