| Solved by pluggable solver: Factoring using the AC method (Factor by Grouping) | |||||||||||||||||||||||||||
Looking at the expression Now multiply the first coefficient Now the question is: what two whole numbers multiply to To find these two numbers, we need to list all of the factors of Factors of 1,2,3,6,7,14,21,42 -1,-2,-3,-6,-7,-14,-21,-42 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to 1*42 = 42 2*21 = 42 3*14 = 42 6*7 = 42 (-1)*(-42) = 42 (-2)*(-21) = 42 (-3)*(-14) = 42 (-6)*(-7) = 42 Now let's add up each pair of factors to see if one pair adds to the middle coefficient
From the table, we can see that the two numbers So the two numbers Now replace the middle term =============================================================== Answer: So In other words, Note: you can check the answer by expanding |