Factor x^4-5x^2+4

Problem

x^4−5*x^2+4

Solution

1. Substitute a new variable to treat the expression as a quadratic. Let u=x^2

u^2−5*u+4

2. Factor the quadratic expression in terms of u by finding two numbers that multiply to 4 and add to −5 These numbers are −1 and −4

(u−1)*(u−4)

3. Substitute back x^2 for u to return to the original variable.

(x^2−1)*(x^2−4)

4. Apply the difference of squares formula, a^2−b^2=(a−b)*(a+b) to both factors.

(x−1)*(x+1)*(x−2)*(x+2)

Final Answer

x^4−5*x^2+4=(x−1)*(x+1)*(x−2)*(x+2)

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