How do you factor the expression #x^2-10x+24#?

1 Answer
Dec 8, 2015

Answer:

#(x-6)(x-4)#

Explanation:

We attempt to generate factors in the form:
#color(white)("XXX")(x+a)(x+b)#

Since the constant term: #+24# is positive
we know that #a# and #b# have the same sign.

Since the middle term: #(-10x)# is negative
we know that #a# and #b# are negative.

All that remains is to find factors of #24#
that add up to #10#

Factors of #24#
#color(white)("XXX"){(1,24), (2,12), (3,8), (4,6)}#

Only the factors #(4,6)# add up to #10#