Question

разложение многочлена на множители

Answer 1

4-29
$\frac{1}{3}{x}^{5} - 9{x}^{2} - \frac{4}{27}{x}^{3} + 4 = \\ = \frac{1}{3}{x}^{2}({x}^{3} - 27) - \frac{4}{27}( {x}^{3} - 27) = \\ = ( {x}^{3} - 27)( \frac{1}{3} {x}^{2} - \frac{4}{27}) = \\ = ( {x}^{3} - {3}^{3})( \frac{1}{3} {x}^{2} - \frac{4}{27} ) = \\ = (x - 3)( {x}^{2} + 3x + 9)( \frac{1}{3} {x}^{2} - \frac{4}{27)}$
4-30
$= 8 {x}^{5} - 8 {x}^{3} + 1 - {x}^{2} = \\ = 8 {x}^{3}( {x}^{2} - 1) - ( {x}^{2} - 1) = \\ = (8 {x}^{3} - 1)( {x}^{2} - 1) = \\ = (8 {x}^{3} - 1)(x - 1)(x + 1)$