Teacher2Teacher |
Q&A #104 |
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Actually, the most effective way I have found is to use the TIC-TAC-TOE method. Create a 9 square board. a---c---ac Row one takes the a coefficient in square 1, c in the second square and the product ac in the third. Next do column 3. What do you multiply to get ac but add to equal "b"? (Note that we haven't used b yet). Place those factors along column 3 in rows 2 and 3. Let me take you through an example: 6x^2-7x-3 6 -3 -18 What multiplies to equal -18 and adds to equal = -7 ? -9 and +2. Put them in position. 6 -3 -18 -9 2 (Either order is fine.) Now, what are two factors of -9, such that one divides evenly into the 6 located in row 1 and the other into the -3, also in row 1? 3 and -3. Position them. 6 -3 -18 3 -3 -9 You can repeat the same thing for factors of 2 or just 2 1 2 divide the 3 into 6 and get 2, -3 into -3 and get +1. Now look at the square in the lower left 3 -3 2 1 The diagonals of these form the factored trinomial (3x+1)(2x-3). It is somewhat difficult to illustrate this on the computer... I hope this makes sense!
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