More about polynomials (4.44.5)
Understand the concepts of the greatest common divisor and the least common multiple of polynomials

Theory

ExamplesFind 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

ExamplesSimplify \(\frac{{4{x^2}  3x}}{{{x^2} + 4x  12}} \div \frac{{4{x^2} + 5x  6}}{{{x^2} + 8x + 12}}\).

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