How do you factor completely 5x^4 +10x^2 -155x4+10x2−15?
2 Answers
=5(x^2+3)(x-1)(x+1)=5(x2+3)(x−1)(x+1)
=5(x-sqrt(3)i)(x+sqrt(3)i)(x-1)(x+1)=5(x−√3i)(x+√3i)(x−1)(x+1)
Explanation:
-
Separate out the common scalar factor
55 . -
Factor as a quadratic in
x^2x2 . -
Use the difference of squares identity:
a^2-b^2 = (a-b)(a+b)a2−b2=(a−b)(a+b)
as follows:
5x^4+10x^2-155x4+10x2−15
=5(x^4+2x^2-3)=5(x4+2x2−3)
=5((x^2)^2+2(x^2)-3)=5((x2)2+2(x2)−3)
=5(x^2+3)(x^2-1)=5(x2+3)(x2−1)
=5(x^2+3)(x-1)(x+1)=5(x2+3)(x−1)(x+1)
Then if we allow Complex coefficients...
=5(x^2-(sqrt(3)i)^2)(x-1)(x+1)=5(x2−(√3i)2)(x−1)(x+1)
=5(x-sqrt(3)i)(x+sqrt(3)i)(x-1)(x+1)=5(x−√3i)(x+√3i)(x−1)(x+1)
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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