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The numbers $-4$ and $-1$ satisfy these conditions since $(-4) \times (-1) = 4$ and $(-4) + (-1) = -5$.
Thus, $u^2 - 5u + 4$ factors as $(u - 4)(u - 1)$.
Substitute back $u = x^2$:
Both $x^2 - 4$ and $x^2 - 1$ are differences of squares:
x^2 - 4 = (x - 2)(x + 2)
Therefore, the complete factorization is:
The final factored form is:
\boxed{(x - 2)(x + 2)(x - 1)(x + 1)}
An interdisciplinary researcher is analyzing a system where the variables $q$ and $r$ are related by the equation $2q + 3r = 12$. If $q = 3$, determine the value of $5r - q$.
Given the equation $2q + 3r = 12$ and $q = 3$, substitute $q = 3$ into the equation: