Factor x^4+3x^2-40

Problem

x4+3*x2−40

Solution

1. Identify the expression as a trinomial in quadratic form, where the variable is x2

2. Substitute a temporary variable u=x2 to rewrite the expression as u2+3*u−40

3. Find two numbers that multiply to −40 and add to 3 These numbers are 8 and −5

4. Factor the quadratic expression in terms of u as (u+8)*(u−5)

5. Substitute x2 back in for u to get the final factored form.

Final Answer

x4+3*x2−40=(x2+8)*(x2−5)

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