To find factor pairs and sums of factor pairs

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In order to find factor pairs of a number, consider the following method on the TI-83/84 calculator:

  • Press the [Y=] button and enter the number which you would like to factor divided by x. For example, suppose you were going to factor the expression . One of the first steps in this factorization would be to find the factor pairs which have a product of 336 (which is calculated by multiplying the coefficient of the quadratic (first) term times the constant (last) term) and a sum of 37 (as given by the coefficient of the linear (middle) term). By entering the equation Y1 =336/x and then looking at the table, you will be able to pick out any factor pairs as those which yield an integral value; any decimal number would mean that the value of x in the table does not divide evenly into 336.

  • To include a separate column in the table for the sum of the factors, you will need to add the value of x to the calculated value of the corresponding factor in Y1. To set up this column, first press the [Y=] button and use the down arrow keys to move the cursor to Y2=. In order to use the calculated value of the factor in Y1, complete the following steps:

  • Press the button labeled [VARS].

  • Use the right arrow key to highlight the option “Y-VARS” at the top of the screen. Once highlighted, you will see another menu with option 1, FUNCTION highlighted. Do not change anything on this menu - just press the enter button.

  • You will see a menu labeled FUNCTION with option 1 for Y1 highlighted. Do not change anything on this menu - just hit the enter button again.

  • At this point, you will be returned to the [Y=] screen and you will see that Y1 has now been entered as part of the expression for Y2.

  • Add x to Y1 by pressing the + key and then x. The equation for Y2 should now look like:

Y2 = Y1 + X.

  • Go to the Table Set menu and enter a starting value of 1 and increments of 1.

  • View the table by pressing [2nd][TABLE]. You will see three columns in the table. The first column, labeled x, represents one of the factors. The second column, labeled Y1 represents the corresponding factor which when multiplied by x would give you the desired product. And in the third column, labeled Y2, you will see the sum of the factors listed in columns 1 and 2. As you scroll through the table, you will be able to easily identify the factor pair whose product and sum meet the criteria of the factoring problem. In the case of the example shown above, the factor pair which has a product of 336 and a sum of 37 would be 16 and 21.

  • Complete the factoring by rewriting the linear term and then factor by grouping:

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