How do you factor completely #5x^4 +10x^2 -15#?

2 Answers
May 10, 2016

Answer:

#5x^4+10x^2-15#

#=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

Answer:

#5(x^2 + 3)(x + 1)(x - 1)#

Explanation:

Divide the common factor of 5 out first.

This is a disguised quadratic: #5((x^2)^2 + 2(x)^2 - 3)#

Find factors of 3 which subtract to give 2.

=#5(x^2 + 3)(x^2 - 1)#

=#5(x^2 + 3)(x + 1)(x - 1)#