Factoring Method for Quadratic Polynomials
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Then, you would multiply the first term  by the last term  to get 120. So, your w is 120--making your equation xy=120.
Next, take your first equation (x+y=23) and transform it into slope-intercept, which can be done simply by subtracting x from both sides. This gives you y=23-x. Since now you have an expression equaling y, you can substitute it back into the second equation. This will leave you with x(-x+23)=120. When you distribute, you should get -x2+23x+0=120. Then, subtract 120 from each side, simply giving you -x2+23x-120=0. You can then plug into your quadratic formula program, and you will get your two magic numbers. You may then proceed with your factoring. For additional help on factoring, consult your algebra professor (or teacher).
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