Factor x^4-5x^2+4

Problem

x4−5*x2+4

Solution

1. Substitute a new variable to treat the expression as a quadratic. Let u=x2

u2−5*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 x2 for u to return to the original variable.

(x2−1)*(x2−4)

4. Apply the difference of squares formula, a2−b2=(a−b)*(a+b) to both factors.

(x−1)*(x+1)*(x−2)*(x+2)

Final Answer

x4−5*x2+4=(x−1)*(x+1)*(x−2)*(x+2)

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