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Harder Trinomials - Undoing FOIL

Since 5 is prime, our only choice is

1 * 5 = 5 gives us ( x ) ( 5x ) ... the last guys will have to give us a 3 ...

Since 3 is prime, our only choice is

1 * 3

BUT, which guy goes in which spot?

graphic showing the uncertainty of how 1 * 3 will fit into ( x ) ( 5x )

Well, let's just see which works!

We need the middle term to be -8x.

( x 3 ) ( 5x 1 ) ... the inner terms give 15x and the outer terms give x ... we cannot get a -8x using x and 15xvertical line
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vertical line		( x 1 ) ( 5x 3 ) ... the inner terms give 5x and the outer terms give 3x ... -3x - 5x = -8x

So,

5x^2 - 8x + 3 = ( x - 1 ) ( 5x - 3 ) ... always double check this last term! does it give a +3 ?