Factor x^4+x^2-6

Problem

x4+x2−6

Solution

1. Identify the expression as a trinomial in quadratic form by letting u=x2

2. Rewrite the expression in terms of u to make it easier to factor.

u2+u−6

3. Find two numbers that multiply to −6 and add to 1 These numbers are 3 and −2

4. Factor the quadratic expression using these numbers.

(u+3)*(u−2)

5. Substitute x2 back in for u to return to the original variable.

(x2+3)*(x2−2)

Final Answer

x4+x2−6=(x2+3)*(x2−2)

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