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Home » $ 5a \cdot 7b = 35ab $, - Deep Underground Poetry

$ 5a \cdot 7b = 35ab $, - Deep Underground Poetry

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Solution: By the Remainder Theorem, the remainder when a polynomial \( f(x) \) is divided by \( x - c \) is \( f(c) \). Here, \( f(x) = x^3 - 4x + 1 \) and \( c = 2 \).

📌 Calculate \( f(2) \):

📌 f(2) = 2^3 - 4(2) + 1 = 8 - 8 + 1 = 1.

📌 \(\boxed{1}\)**Question:

📌 A quantum biologist is modeling the interaction between quantum states and genetic mutations. Given the expression $x^4 - 5x^2 + 4$, factor it completely.

📌 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 $(-4) + (-1) = -5$.

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