The polynomial function f is defined as f(c)=(c-k)(c^(2)-4c+4) where k is a constant. The value 2 is a zero of f. What is the remainder of f(c) when divided by (c-2) ? ◻

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The polynomial function  f is defined as  f(c)=(c-k)(c^(2)-4c+4) where  k is a constant. The value 2 is a zero of  f. What is the remainder of  f(c) when divided by  (c-2) ?  ◻

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Identify Given Information: Identify the given information and the question prompt. We are given that f(c) = (c-k)(c^2 - 4c + 4) and that 2 is a zero of f. We need to find the remainder when f(c) is divided by (c-2).Determine Value of k: Use the fact that 2 is a zero of f to determine the value of k. If 2 is a zero of f, then f(2) = 0. We can substitute c with 2 in the equation f(c) = (c-k)(c^2 - 4c + 4) to find k. f(2) = (2-k)(2^2 - 4*2 + 4) = 0Apply Remainder Theorem: Simplify the equation to find k. f(2) = (2-k)(4 - 8 + 4) = (2-k)(0) = 0 Since (2-k)(0) = 0 for any value of k, we cannot determine k from this equation. However, we do not need the value of k to find the remainder when f(c) is divided by (c-2).Substitute to Find Remainder: Apply the Remainder Theorem to find the remainder. The Remainder Theorem states that the remainder of a polynomial f(c) when divided by (c-a) is f(a). Since we want to divide f(c) by (c-2), we need to find f(2).Calculate Remainder: Substitute c with 2 in the polynomial f(c) to find the remainder. f(2) = (2-k)(2^2 - 4*2 + 4) Simplify the expression. f(2) = (2-k)(4 - 8 + 4) = (2-k)(0)Calculate the remainder. f(2) = (2-k)(0) = 0 The remainder of f(c) when divided by (c-2) is 0.

The polynomial function $f$ is defined as $f(c)=(c-k)(c^{2}-4c+4)$ where $k$ is a constant. The value $2$ is a zero of $f$ . What is the remainder of $f(c)$ when divided by $(c-2)?$ $\newline$ ◻

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The polynomial function $f$ is defined as $f(c)=(c-k)(c^{2}-4c+4)$ where $k$ is a constant. The value $2$ is a zero of $f$ . What is the remainder of $f(c)$ when divided by $(c-2)?$ $\newline$ ◻