How do you factor the quadratic expression completely? #2x^2 - 13x + 20#

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Answer 1 · 2018-06-10T16:35:42

#(x-4)(2x-5)#

#2x^{2}-13x+20#

Factors of #20 * 2# which add up to -13 are -5 and -8

so you can replace -13 with -5 and -8 such that:

#2x^{2}-5x-8x+20#
which goes to:
#x(2x-5)-4(2x-5)#

Take the expressions not in the brackets together to get:
#(x-4)(2x-5)#

Answer 2 · 2018-06-10T16:36:29

#(x-4)(x-5/2)#

#2x^2-13x+20#

The simplest way to do this is using the quadratic equation:

#x=(-b+-sqrt(b^2-4ac))/(2a)#

Where,
#a=2#
#b=-13#
#c=20#

#x=(-(-13)+-sqrt((-13)^2-4*2*20))/(2*2)#

#x=((13)+-sqrt(169-160))/(4)#
#x=((13)+-sqrt(9))/(4)#
#x=4# and #x=5/2#

#x-4=0#
#x-5/2=0#

Therefore,

#2x^2-13x+20= (x-4)(x-5/2)#