Factor x^4-10x^2+9

Problem

x^4−10*x^2+9

Solution

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

u^2−10*u+9

2. Factor the quadratic expression in terms of u by finding two numbers that multiply to 9 and add to −10 These numbers are −9 and −1

(u−9)*(u−1)

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

(x^2−9)*(x^2−1)

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

(x−3)*(x+3)*(x−1)*(x+1)

Final Answer

x^4−10*x^2+9=(x−3)*(x+3)*(x−1)*(x+1)

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