```Question 185351
Question #1: "The product of the page numbers on two facing pages of a book is 132. Find the page number?"

Note: consecutive numbers are of the form x, x+1, x+2, etc...

So "The product of the page numbers on two facing pages of a book is 132" translates to {{{x(x+1)=132}}}

{{{x^2+x=132}}} Distribute

{{{x^2+x-132=0}}} Subtract 132 from both sides.

{{{(x+12)(x-11)=0}}} Factor the left side

{{{x+12=0}}} or {{{x-11=0}}} Use the zero product property to break up the equation

{{{x=-12}}} or {{{x=11}}} Solve for "x"

Now ignoring the negative solution {{{x=-12}}} (you can't have a negative page number), this means that the only answer is {{{x=11}}}

So the page numbers are 11 and 12

Note: 11*12=132

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Question #2: "There are n teams in a league and the number of games played is given by the polynomial n2 -n =N. A woman softball leagues has 11 teams. what is the total numbers of games to be played? "

Note: since "n" is the number of teams and there are 11 softball teams, this means that in this case {{{n=11}}}

{{{11^2-11=N}}} Plug in {{{n=11}}} (see above)

{{{121-11=N}}} Square 11 to get 11*11=121

{{{110=N}}} Subtract

So there are 110 games played.```