Factor x^4-3x^2-4

Problem

x^4−3*x^2−4

Solution

1. Substitute a new variable to treat the expression as a quadratic. Let u=x^2 which implies u^2=x^4

u^2−3*u−4

2. Factor the quadratic expression in terms of u by finding two numbers that multiply to −4 and add to −3 These numbers are −4 and 1

(u−4)*(u+1)

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

(x^2−4)*(x^2+1)

4. Identify the difference of squares in the first factor, x^2−4 which can be written as x^2−2^2

(x−2)*(x+2)*(x^2+1)

Final Answer

x^4−3*x^2−4=(x−2)*(x+2)*(x^2+1)

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