Factor x^4+x^2-12

Problem

x^4+x^2−12

Solution

1. Identify the expression as a trinomial in quadratic form, where the variable is x^2

2. Substitute u=x^2 to rewrite the expression as a standard quadratic: u^2+u−12

3. Find two numbers that multiply to −12 and add to 1 which are 4 and −3

4. Factor the quadratic expression in terms of u (u+4)*(u−3)

5. Substitute x^2 back in for u to get the factors: (x^2+4)*(x^2−3)

Final Answer

x^4+x^2−12=(x^2+4)*(x^2−3)

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