How do you factor completely #5x^4 +10x^2 15#?
2 Answers
May 10, 2016
#=5(x^2+3)(x1)(x+1)#
#=5(xsqrt(3)i)(x+sqrt(3)i)(x1)(x+1)#
Explanation:

Separate out the common scalar factor
#5# . 
Factor as a quadratic in
#x^2# . 
Use the difference of squares identity:
#a^2b^2 = (ab)(a+b)#
as follows:
#5x^4+10x^215#
#=5(x^4+2x^23)#
#=5((x^2)^2+2(x^2)3)#
#=5(x^2+3)(x^21)#
#=5(x^2+3)(x1)(x+1)#
Then if we allow Complex coefficients...
#=5(x^2(sqrt(3)i)^2)(x1)(x+1)#
#=5(xsqrt(3)i)(x+sqrt(3)i)(x1)(x+1)#
May 10, 2016
Explanation:
Divide the common factor of 5 out first.
This is a disguised quadratic:
Find factors of 3 which subtract to give 2.
=
=