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You need a pair of factors of 18 that add up to 11.
\n" ); document.write( "The pairs of factors for 18 are ;
\n" ); document.write( "1 and 18 (adding to 19),
\n" ); document.write( "2 and 9 (adding to 11),
\n" ); document.write( "3 and 6 (adding to 9).
\n" ); document.write( "So, your pair of factors is 2 and 9.
\n" ); document.write( "
\n" ); document.write( "Next, you could re-write the polynomial uswing 2 and 9 as coefficients for a split middle term as
\n" ); document.write( "6(p-5)^2+2(p-5)+9(p-5)+3 ,
\n" ); document.write( "and then factor by parts
\n" ); document.write( "6(p-5)^2+11(p-5)+3 = 6(p-5)^2+2(p-5)+9(p-5)+3 = [6(p-5)^2+2(p-5)]+[9(p-5)+3]
\n" ); document.write( "= 2(p-5)[3(p-5)+1] + 3[3(p-5)+1] = [2(p-5)+3][3(p-5)+1]
\n" ); document.write( "= (2p-10+3)(3p-15+1) = (2p-7)(3p-14)
\n" ); document.write( "
\n" ); document.write( "It looks complicated, and looks like it would be easy to make some mistake.
\n" ); document.write( "An easier option would be to start by making a cahnge of variable,
\n" ); document.write( "with y = p-5 , and factor 6y^2+11y+3.
\n" ); document.write( "6y^2+11y+3 = 6y^2+2y+9y+3 = (6y^2+2y) + (9y+3) = 2y(3y+1) + 3(3y+1)
\n" ); document.write( "= (2y+3)(3y+1)
\n" ); document.write( "At that point, you can change back to p as a variable, rplacing p-5 for y:
\n" ); document.write( "[2(p-5)+3] [3(p-5)+1] = (2p-10+3)(3p-15+1) = (2p-7)(3p-14) \n" ); document.write( "