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To prove that the nested form is equivalent to the original polynomial, we can work backward from the innermost part. Let's start with a simpler case: a quadratic polynomial P(x) = ax² + bx + c. Using Horner's Scheme, we rewrite it as P(x) = (ax + b)x + c. If we substitute x = c, we get P(c) = (ac + b)c + c. Expanding this, we get ac² + bc + c, which is exactly the same as evaluating the original polynomial at x = c. So, the nested form gives the same result.
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* **Internet of Things (IoT):** Connect devices and sensors to collect data and automate processes. From smart thermostats to connected vehicles, IoT is transforming how we interact with the physical world.
