How do you factor #6p ^ { 2} - 54p + 84#?

Question

642 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-13T03:47:17

# 6( p - 7) xx ( 1p xx -2) = 6p^2 - 54p + 84 #

#84# can be factored as #42 xx 2, 21 xx 4, 3 xx 28 #

#6# can be factored as #6 xx 1, 3 xx 2#

The sum of these factors multiplied must be 54

# 42 xx 1 = 42#

# 6 xx 2 = 12#

#42 + 12 = 54#

so the answer is #( 6p - 42) xx ( p - 2) #
But there is a common factor of #6# in the first factor:

#=6(p-7)(p-2)#

Answer 2 · 2017-03-13T03:54:52

#6 (p - 7) (p- 2)#

First you find a common factor in each term.

#6(p^2 - 9p + 14)#

Then you factor the bracket by looking for factors of #14# that give #-9# when summed .

1 -7
1 -2

#-7 and -2# are factors of #14# that add to give #-9#
(Both signs will be negative.)

#6 (p - 7) (p- 2)#

You cannot forget the 6 from step 1.