More about polynomials- (4.4-4.5)

Understand the concepts of the greatest common divisor and the least common multiple of polynomials

  • Theory
  • Examples
    Find the H.C.F. and L.C.M. of \({a^3}bc\) and \({b^2}{c^4}\).
  • Solutions

    \({\rm{H}}{\rm{.C}}{\rm{.F}}{\rm{.}} = \underline{\underline {bc}} \)

    \({\rm{L}}{\rm{.C}}{\rm{.M}}{\rm{.}} = \underline{\underline {{a^3}{b^2}{c^4}}} \)

Perform addition, subtraction, multiplication and division of rational functions

  • Theory
  • Examples
    Simplify \(\frac{{4{x^2} - 3x}}{{{x^2} + 4x - 12}} \div \frac{{4{x^2} + 5x - 6}}{{{x^2} + 8x + 12}}\).
  • Solutions

    \(\begin{array}{c}\frac{{4{x^2} - 3x}}{{{x^2} + 4x - 12}} \div \frac{{4{x^2} + 5x - 6}}{{{x^2} + 8x + 12}}\\ \\ = \frac{{4{x^2} - 3x}}{{{x^2} + 4x - 12}} \times \frac{{{x^2} + 8x + 12}}{{4{x^2} + 5x - 6}}\\ \\= \frac{{x(4x - 3)(x + 2)(x + 6)}}{{(x + 6)(x - 2)(x + 2)(4x - 3)}}\\\\ = \underline{\underline {\frac{x}{{x - 2}}}} \end{array}\)