PSAT #2, Section 3, #16

OK, so you’re told that 3x+4 is a factor of 12x^2+ax-20. You need to find a. To do so, you’ll need to set up a classic FOIL scenario. I’m going to use p and r for the unknowns in the second factor.


Now remember what happens when you FOIL. The 3x and the px will combine to make the 12x^2, and the 4 will combine with the second r to make -20. Therefore, it must be true that p=4 and r=-5. We can use that information to solve for a.


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