Elementary Algebra

$\frac{-30x^{5}+20x^{4} -10x^{3}}{-5x^{2}}$ = 6$x^{3}$ - 4$x^{2}$ + 2x To check if this is true or not, we simplify the left side. RECALL: $\frac{b^{n}}{b^{m}}$ = $b^{n-m}$ So, $\frac{-30x^{5}+20x^{4} -10x^{3}}{-5x^{2}}$ = $\frac{-30x^{5}}{-5x^{2}}$ + $\frac{20x^{4}}{-5x^{2}}$ + $\frac{-10x^{3}}{-5x^{2}}$ = $\frac{-30}{-5}$$x^{5-2} + \frac{20}{-5}$$x^{4-2}$ + $\frac{-10}{-5}$$x^{3-2}$ = 6$x^{3}$ - 4$x^{2}$ + 2x Because 6$x^{3}$ - 4$x^{2}$ + 2x is equal to 6$x^{3}$ - 4$x^{2}$ + 2x, this statement is true.