Question 252544
{{{15x^2-22x+8}}}
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It's a trial and error thing.  The 1st term, 15, can be:
1*15 or 3*5
The last term, 8, can be 1*8 or 2*4.  It's +8, so the signs are the same.
Start with 1 and 15, ignore the sign but try to get 22 for the middle term:
(x - 1)*(15x - 8) --> 23x NG
(3x - 1)*(5x - 8) --> 29x NG
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(x - 2)*(15x - 4) --> 34x NG
(3x - 2)*(5x - 4) --> 22x  That's it. The 22x is negative, so it's factored.
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The best approach is to use the quadratic equation, but students are usually subjected to factoring before learning the quadratic equation.