How do you factor completely #5x^4 +10x^2 -15#?
2 Answers
May 10, 2016
#=5(x^2+3)(x-1)(x+1)#
#=5(x-sqrt(3)i)(x+sqrt(3)i)(x-1)(x+1)#
Explanation:
-
Separate out the common scalar factor
#5# . -
Factor as a quadratic in
#x^2# . -
Use the difference of squares identity:
#a^2-b^2 = (a-b)(a+b)#
as follows:
#5x^4+10x^2-15#
#=5(x^4+2x^2-3)#
#=5((x^2)^2+2(x^2)-3)#
#=5(x^2+3)(x^2-1)#
#=5(x^2+3)(x-1)(x+1)#
Then if we allow Complex coefficients...
#=5(x^2-(sqrt(3)i)^2)(x-1)(x+1)#
#=5(x-sqrt(3)i)(x+sqrt(3)i)(x-1)(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.
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