Question 107275
{{{The}}}{{{ Null}}}{{{ Factor}}}{{{ Law}}}

as we know, {{{3*0 = 0}}}, {{{x*0 = 0}}}, and so on....

From this we can conclude that:

If the {{{product}}} of any two numbers {{{is}}} {{{zero}}}, then {{{one}}} or {{{both}}} of the numbers {{{is}}}{{{ zero}}}.

In other words, if {{{xy= 0}}}, then {{{x = 0}}} or {{{y = 0}}}. We need also to include the possibility that {{{x = y = 0}}}.

This is called {{{the}}}{{{ Null}}}{{{ Factor}}}{{{ Law}}} and we use it often to solve quadratic equations.

here is one example:

{{{3x(x-5) = 0}}}

by the null factor law, either {{{3x}}} or {{{x-5}}} must be equal to {{{0}}}.

{{{3x}}} will be equal to {{{0}}} only if {{{x= 0}}}
{{{x - 5 }}} will be equal to {{{0}}} only if {{{x = 5}}}