How do you factor #50x^2-90x+16#?

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Answer 1 · 2017-03-20T06:12:17

#2(5x-1)(5x-8)#

Factor out the common constant #2#: #2(25x^2-45x+8)#

Find two #x#-terms that multiply to #25x^2#:

Possible choices:
#5x * 5x = 25x^2#
#25x * x = 25x^2#

Find two numbers that multiply to #8# and sum to #-45#. Since they must sum to a negative number, both numbers must be negative to multiply to #+8#.

Possible choices:
#-1 * -8 = 8#
#-2 * -4 = 8#

#2(25x^2-45x+8) = 2(5x -1) (5x -8)#

The #x#-term is found by multiplying the "insides" and "outsides" and summing: #-1*5x + 5x *-8 = -5x + (-40x) = -45x#

Therefore the solution is: #2(5x-1)(5x-8)#