Access Point #: MAFS.912.A-APR.2.AP.2b (Archived Access Point)


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Understand that a is a root of a polynomial function if and only if x-a is a factor of the function.

Clarifications:

Essential Understandings

Concrete:

  • Use a tool to determine whether the polynomial function crosses the x-axis. Click Here
  • Use a graphing tool or graphing software to find the roots (where the function intersects the x-axis) of a function.
  • Match the polynomial function with its corresponding graph.
  • Match the graph of the polynomial function with its roots (zeros).
Representation:
  • Understand the following concepts and vocabulary: root, factor, quadratic, integer, real number, quadratic equation, quadratic formula, polynomial, degree, exponent, square root, solution, terms, coefficient, intercept, intersect, zero.
  • Understand that a function that intersects the x-axis has real roots (zeros)

    Example graphs for statement •	Understand that a function that intersects the x-axis has real roots (zeros).
  • Understand that a root is where a function crosses the x-axis.

    Example graph for statement •	Understand that a root is where a function crosses the x-axis.
  • Understand that the degree (largest exponent) of a polynomial determines the type and shape of the graph.

    Sample Constant, Linear, Quadratic, and Cubic graphs
  • For example:

    Example f(x) = x to the 3rd power plus 2 times x to the 2nd power - 3x with steps and solutions.
  • Teacher tools:
    LearnZillion Lessons: Click Here
    LearnZillion Factor Theorem: Click Here

Number: MAFS.912.A-APR.2.AP.2b Category: Access Points
Date Adopted or Revised: 07/14 Cluster: Understand the relationship between zeros and factors of polynomials. (Algebra 1 - Supporting Cluster) (Algebra 2 - Major Cluster)

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Related Standards

Name Description
MAFS.912.A-APR.2.2: 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).



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