How do I factor this expression completely?

#4x^2(x^2+1)(x+2)^3+36(x^2+1)^2(x+2)^4#

Answer 1

#4x^2(x^2+1)(x+2)^2+36(x^2+1)^2(x+2)^4=4(x^2+1)(x+2)^2(9x^4+36x^3+46x^2+36x+36)#

It is observed that #4x^2(x^2+1)(x+2)^2# and #36(x^2+1)^2(x+2)^4# have common factors

#4#, #(x^2+1)# and #(x+2)^2#.

Note that for #(x^2+1)# and #(x+2)#, we have selected the minimal power of these among two expressions. Similarly between #4# and #36#, #4# is common factor.

Hence taking out these common factors, we get

#4x^2(x^2+1)(x+2)^2+36(x^2+1)^2(x+2)^4#

= #4(x^2+1)(x+2)^2[x^2+9(x^2+1)(x+2)^2]#

= #4(x^2+1)(x+2)^2[x^2+9(x^2+1)(x^2+4x+4)]#

= #4(x^2+1)(x+2)^2[x^2+9(x^4+4x^3+4x^2+x^2+4x+4)]#

= #4(x^2+1)(x+2)^2(9x^4+36x^3+46x^2+36x+36)#

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Answer 2

Ethan Adkins

Sure, please provide the expression you'd like factored.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.