Problem $3-$ Asymptotic Notation Properties $(6$pts$)$ Prove the following statements

$(3$pts$)$ If f$1($x$)$ is O$($g$1($x$))$ and f$2($x$)$ is O$($g$2($x$)),$ then f$1($x$)$ f$2($x$)$ is O$($g$1($x$)$ g$2($x$))$

$(1$pts$)$ f $($x$)$ is O$($g$($x$))$ implies g$($x$)$ is $($f $($x$)).$

$(2$pts$)$ f $($x$)=5$x$3+6$x$2$ is O$($x$3)$