\"\"

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The function \"\".

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Identify Rational Zeros :

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Usually it is not practical to test all possible zeros of a polynomial function using only synthetic substitution. The Rational Zero Theorem can be used for finding the some possible zeros to test.

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Rational Root Theorem, if a rational number in simplest form p/q is a root of the polynomial equation \"\", then p is a factor of a0 and q is a factor if an.

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If p/q is a rational zero, then p is a factor of \"\" and q is a factor of \"\".

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The possible values of p are   ±0.

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The possible values for q are \"\".

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By the Rational Roots Theorem, the only possible rational roots are, \"\"

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Make a table for the synthetic division and test possible real zeros.

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p/q

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4 \ \

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-5

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1

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1

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- 1

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- 1

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1

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- 3

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2 \ \

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Since f(3) = 0, x = 3 is a zero. The depressed polynomial is  x3 + x2 – 4x + 6 = 0.

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