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Mathematics > Course Model Algebra II (Traditional Pathway) > Arithmetic with Polynomials and Rational Expressions
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Mathematics | Course : Model Algebra II (Traditional Pathway)

Domain - Arithmetic with Polynomials and Rational Expressions

Cluster - Rewrite rational expressions.

[AII.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.

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.
  • Rational expression
    A quotient of two polynomials with a non-zero denominator.

Predecessor Standards:

  • 8.NS.A.1
    Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • AI.N-RN.B.3
    Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
  • AI.A-SSE.A.2
    Use the structure of an expression to identify ways to rewrite it. For example, see (x + 2)2 – 9 as a difference of squares that can be factored as ((x + 2) + 3)((x + 2 ) – 3).
  • AII.A-SSE.B.4
    Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.* For example, calculate mortgage payments.
  • AII.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).
  • AII.A-APR.D.7
    (+) 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.
  • PC.A-APR.D.7
    (+) 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.