Factor x^4-13x^2+36

Problem

x^4−13*x^2+36

Solution

1. Identify the expression as a trinomial in quadratic form by substituting u=x^2

u^2−13*u+36

2. Find two numbers that multiply to 36 and add to −13

−9⋅−4=36

−9+(−4)=−13

3. Factor the quadratic trinomial using these numbers.

(u−9)*(u−4)

4. Substitute x^2 back in for u

(x^2−9)*(x^2−4)

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

x^2−9=(x−3)*(x+3)

x^2−4=(x−2)*(x+2)

Final Answer

x^4−13*x^2+36=(x−3)*(x+3)*(x−2)*(x+2)

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