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Mathematics > Course Model Mathematics III (Integrated Pathway) > Arithmetic with Polynomials and Rational Expressions
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Mathematics | Course : Model Mathematics III (Integrated Pathway)

Domain - Arithmetic with Polynomials and Rational Expressions

Cluster - Understand the relationship between zeros and factors of polynomials.

[MIII.A-APR.B.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).

Resources:


  • Polynomial
    The sum or difference of terms which have variables raised to positive integer powers and which have coefficients that may be real or complex. The following are all polynomials: 5x3 – 2x2 + x – 13, x2y3 + xy, and (1 + i)a2 + ib2.
  • Remainder Theorem
    If f(x) is a polynomial in x then the remainder on dividing f (x) by x − a is f (a).

Predecessor Standards:

No Predecessor Standards found.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • MII.A-SSE.B.3.a
    Factor a quadratic expression to reveal the zeros of the function it defines.
  • MII.A-APR.A.1.a
    Perform operations on polynomial expressions (addition, subtraction, multiplication), and compare the system of polynomials to the system of integers when performing operations.
  • MII.A-APR.A.1.b
    Factor and/or expand polynomial expressions; identify and combine like terms; and apply the Distributive property.
  • MIII.N-CN.C.9
    (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
  • MIII.A-APR.B.3
    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.
  • MIII.A-APR.D.6
    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.
  • PC.N-CN.C.9
    (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.