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Home » \[ b^2 - 4ac = 16 + 48 \] - Appfinity Technologies

\[ b^2 - 4ac = 16 + 48 \] - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 The expression $x^4 - 5x^2 + 4$ is a quadratic in terms of $x^2$. Let $u = x^2$. The expression becomes $u^2 - 5u + 4$. We need to factor this quadratic.

📌 Find two numbers that multiply to $4$ (the constant term) and add to $-5$ (the coefficient of the linear term).

📌 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:

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