How do you factor #2x^2 - 5x - 3#?

1 Answer
Dean R.
May 7, 2018

#2x^2 - 5x - 3 = (2x + 1)(x - 3)#

Explanation:

#2# only factors one way, #2=2 times 1#. So if there is a possible factorization, it looks like

# (2x + text{constant})(x + text{constant})#

The two constants multiply to #-3# and similarly, #-3=3 times -1 = -3 times 1# are the only possibilities for that. So we get four possibilities for a factorization (the first constant can be #-3, -1,quad 1, or 3#) and we quickly find

#2x^2 - 5x - 3 = (2x + 1)(x - 3)#

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