How do you factor #12v ^ { 5} + 40v ^ { 4} - 32v ^ { 3}# completely?

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Answer 1 · 2017-04-18T22:08:23

#4v^3(3v-2)(v+4)#

Always take out any common factor first.

#12v^5 +40v^4 -32v^3#

#= 4v^3(3v^2 +10v-8)#

Find factors of 3 and 8 which combine and subtract to give 10.

# 3" "2" "1 xx 2 rarr 2#
# 1" "4" "3 xx 4 rarr ul12#
#color(white)(.................................)10#

Consider the signs: it must be +10

# 3" "-2" "1 xx -2 rarr -2#
# 1" "+4" "3 xx +4 rarr ul(+12)#
#color(white)(...........................................)+10#

The factors are :#" "4v^3(3v-2)(v+4)#