Factoring by the Bottoms Up! to the front method using the calculator:

Factor completely: 42x² + 17x - 15

Analysis: Is the polynomial in descending order? Yes.
Identify a (a = 42), b (b = 17), and c (c = —15). Is a negative? No. Is there a GCF of a, b, and c? No.
Find a•c:



What factors multiply to —630 and subtract to +17?
Turn on calculator and push the [Y =] button. Enter a•c/X for Y1 and a•c/X + X for Y2. For our example you should have:



Now press [2^nd][WINDOW] for TBLSET.
Here is what you want:
  TABLE SETUP
  TblStart = 1
  
  Indpnt:   Auto Ask
  Depend: Auto Ask

Now push [2^nd][GRAPH] for TABLE.

You want to find the row where b is the value in the Y2 column, so scroll until you find +17 in Y2.

 X   Y1   Y2
35  -18    17

Now write your binomials as

For our example, you’ll write

Simplify the fractions to get

Now Bottoms Up! Take the denominator and write it in front of x in each binomial.
. Check by FOIL.



Solving a quadratic equation such as 42x² + 17x - 15 = 0 using this method is even easier because you do not make as many steps. Once you have simplified the fractions in your binomials, , you merely change the sign of the constant in each binomial to find your solutions. You change the sign because you are looking for each value for x, and the value for x is what you add to the and the to get zero. In our example, the solutions are x = or x = .





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