How do you factor #56x^3+70x^2-280x-350#?

1 Answer
George C.
Apr 26, 2016

#56x^3+70x^2-280x-350=14(x-sqrt(5))(x+sqrt(5))(4x+5)#

Explanation:

Separate out the common scalar factor #14#, factor by grouping and finally use the difference of squares identity:

#a^2-b^2=(a-b)(a+b)#

with #a=x# and #b=sqrt(5)# as follows:

#56x^3+70x^2-280x-350#

#=14(4x^3+5x^2-20x-25)#

#=14((4x^3+5x^2)-(20x+25))#

#=14(x^2(4x+5)-5(4x+5))#

#=14(x^2-5)(4x+5)#

#=14(x^2-(sqrt(5))^2)(4x+5)#

#=14(x-sqrt(5))(x+sqrt(5))(4x+5)#

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