WEBVTT

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Here is the problem: x squared plus 1.

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Factor a polynomial over the rational numbers.

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Write the polynomial in standard form.

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Check the discriminant. b squared minus 4ac equals negative 4. It is negative, so there are no real roots and the quadratic does not factor over the rational numbers.

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The polynomial is prime over the rationals.

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So the answer is x squared plus 1.

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x squared plus 1 has no factors with rational coefficients other than constants, so it is already fully factored over the rationals.

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Expanding x squared plus 1 gives back x squared plus 1.