How do you factor # 4x^5 - 9x^3#?

2 Answers
Apr 24, 2017

Answer:

#= x^3(2x+3)(2x-3)#

Explanation:

Always take out a common factor first if there is one.

#4x^5-9x^3#

#= x^3(4x^2 -9)" "larr# difference of squares

#= x^3(2x+3)(2x-3)#

To recognise Difference of squares:

  • 2 terms
  • minus sign
  • perfect squares
  • even indices

#x^2 =y^2 = (x+y)(x-y)#

Apr 24, 2017

Answer:

#x^3(2x+3)(2x-3)#

Explanation:

#4x^5-9x^3#

Factor out #x^3#

#x^3(4x^2-9)#

Here we realize that both #4x^2# and #9# are perfect squares. So, we factor them as.

#color(red)((sqrtA+sqrtB) (sqrtA-sqrtB))#
I this case #color(red)A=4x^2# and #color(red)B=9#

So,
#x^3(sqrt(4x^2)+sqrt9)(sqrt(4x^2)-sqrt9)#

Complete the square roots to get your final answer

#x^3(2x+3)(2x-3)#