WEBVTT

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Here is the problem: (x squared plus 1)(x minus 1).

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Expand and simplify the polynomial into standard form.

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Distribute every product and power. Multiply each term of one factor by each term of the other; expand powers by repeated multiplication.

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Combine like terms and order by degree.

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Read off the key features. degree 3, leading coefficient 1, constant term negative 1.

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So the answer is x cubed minus x squared plus x minus 1.

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In standard form the polynomial is x cubed minus x squared plus x minus 1 (degree 3, leading coefficient 1, constant term negative 1).

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Spot check at x equals 2: original and expanded form both give 5.