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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Consider the polynomial function P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, where $a$ is an unknown real number. If $(x - 2)$ is a factor of this polynomial, ...
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