36x² - 97x + 36 Multiply the 36 by 36, disregarding signs, getting 1296. Write down a list of all the ways to factor 1296 using two positive integers: 1296*1 648*2 432*3 324*4 216*6 162*8 144*9 108*12 81*16 72*18 54*24 48*27 36*36 Now look at the sign of the last term to see whether we add or subtract those pairs of numbers. The last term is +36, which has a + sign, so we add those same pairs of numbers that we multiplied above to get 1296. (when the last term has a - sign, we subtract, but since it has a +, we add): 1296+1 = 1297 648+2 = 650 432+3 = 435 324+4 = 328 216+6 = 222 162+8 = 170 144+9 = 243 108+12 = 120 81+16 = 97 72+18 = 90 54+24 = 78 48+27 = 75 36+36 = 72 Next we look down that list to find the coefficient of the middle term of 36x² - 97x + 36, in absolute value, which is 97 and we find it as 81+16 = 97 So we substitute (81+16) in place of 97 36x² - 97x + 36 36x² - (81+16)x + 36 and remove the parentheses: 36x² - 81x - 16x + 36 Next we factor only the FIRST two terms by factoring out 9x: 9x(4x - 9) - 16x + 36 Next we factor only the LAST two terms by factoring out -4: 9x(4x - 9) - 4(4x - 9) Notice that the two parentheses are the same. I'll color them red: 9x(4x - 9) - 4(4x - 9) So factor out the red factor, leaving the black factors as terms in parentheses: (4x - 9)(9x - 4) Edwin