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$\"\"$

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The polynomial function is $\"\"$ and Hint : $\"\"$ is a one factor of f.

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Rewrite the expression in long division form $\"\"$ .

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The number zero is included for missing term x in the divisor.

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$\"\"$ $\"\"$

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The remainder is the last entry in the last row.There fore, $\"\"$ .

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The number along the bottom row are the coefficients of the quotient.

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By the division algorithm theorem, the result of the division is $\"\"$ .

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The factorization (factors are irreducible over the rationals) of f(x) is $\"\"$ . $\"\"$

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The factorization (factors are irreducible over the rationals) of f(x) is $\"\"$ .

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$\"\"$

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$\"\"$

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The polynomial function is $\"\"$ and Hint : $\"\"$ is a one factor of f.

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Rewrite the expression in long division form $\"\"$ .

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The zero is included for missing term x in the divisor.

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$\"\"$

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$\"\"$

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By the division algorithm theorem, the result of the division is $\"\"$ .

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The factorization of f(x) is $\"\"$ . $\"\"$

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Consider the quadratic factor $\"\"$ and solve by using quadratic formula.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The complete factorization of f(x) is $\"\"$ . $\"\"$

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The complete factorization of f(x) is $\"\"$ .