Factor x^4+x^2-20

Problem

x^4+x^2−20

Solution

1. Identify the expression as a trinomial in quadratic form by letting u=x^2 which transforms the expression into u^2+u−20

2. Find two numbers that multiply to −20 and add to 1 (the coefficient of the middle term).

3. Determine that the numbers are 5 and −4 since 5⋅(−4)=−20 and $5 + (-4) = 1$.

4. Rewrite the expression as a product of two binomials using these factors: (x^2+5)*(x^2−4)

5. Recognize that x^2−4 is a difference of squares, which can be factored further into (x−2)*(x+2)

6. Combine all factors to reach the final factored form.

Final Answer

x^4+x^2−20=(x^2+5)*(x−2)*(x+2)

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