document.write( "Question 206449: I am studying for the compass exam and I see that others have posted the same question: What is the rational expression when r is not equal to plus or minus 2, r^2-5r+6 / r^2-4. What I don't understand is why r^2-5r+6 factors to [(r-3)(r-2)]...please help! \n" ); document.write( "
Algebra.Com's Answer #155999 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
You first learn to multiply: 2*3=6
\n" ); document.write( "Then you learn to factor: 6=2*3
\n" ); document.write( "-----------------------------------------
\n" ); document.write( "Your problem:
\n" ); document.write( "What I don't understand is why r^2-5r+6 factors to [(r-3)(r-2)]...
\n" ); document.write( "You first learn FOIL:
\n" ); document.write( "(r-3)(r-2)
\n" ); document.write( "F: r*r = r^2
\n" ); document.write( "O: r*-2= -2r
\n" ); document.write( "I: -3*r= -3r
\n" ); document.write( "L: -2*-3= 6
\n" ); document.write( "---------------------------
\n" ); document.write( "Then you learn to factor:
\n" ); document.write( "r^2-5r+6
\n" ); document.write( "Think of two numbers whose product is 6 and whose sum is -5
\n" ); document.write( "The numbers are -2 and -3
\n" ); document.write( "Rewrite the problem replacing -5r by -3r-2r
\n" ); document.write( "r^2-3r-2r+6
\n" ); document.write( "Factor the 1st two and the last two terms separately:
\n" ); document.write( "r(r-3)-2(r-3)
\n" ); document.write( "Factor again to get the factored answer:
\n" ); document.write( "(r-3)(r-2)
\n" ); document.write( "=======================
\n" ); document.write( "Hope that helps.
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "
\n" );