Question 961563

the area of a rectangle is given by a polynomial function 

{{{A(x)=a^2b^2-ab-6}}}....we know that the area of a rectangle is is {{{length* width}}}, so factor completely {{{A(x)=a^2b^2-ab-6}}} and see if the {{{ (ab-3)}}} is a factor; if it is a factor, then the other part will be the width


{{{A(x)=a^2b^2-ab-6}}}

{{{A(x)=(ab)^2-ab-6}}}....write {{{-ab}}} as {{{2ab-3ab}}}

{{{A(x)=(ab)^2+2ab-3ab-6}}}...group

{{{A(x)=((ab)^2+2ab)-(3ab+6)}}}

{{{A(x)=ab(ab+2)-3(ab+2)}}}

{{{A(x)=(ab-3)(ab+2)}}}

since given that {{{(ab-3)}}} is the length, then {{{highlight(ab+2)}}} is the width