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Use the remainder theorem and synthetic division

to find the value of f(3) if f(x) = x^3 - 6x^2 + 13x - 11

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Show the steps of the synthetic division!

Use the remainder theorem and synthetic division to find the value of f(3) if f(x-example-1
User Mingle Li
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1 Answer

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22 votes

Answer:

f(3) = 1

Explanation:

The value of f(3) is told by the remainder theorem to be the remainder from division of f(x) by (x -3). That division is shown in the attachment. The remainder is 1, so ...

f(3) = 1

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The number at upper left in the synthetic division table is the value of x for which we are evaluating f(x).

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Additional comment

When the polynomial is written in Horner Form:

f(x) = ((x -6)x +13)x -11

the coefficient of x at each point in the evaluation is the same as the number on the bottom row of the synthetic division. The result of the evaluation is the same as the remainder from the division.

Use the remainder theorem and synthetic division to find the value of f(3) if f(x-example-1
User Haem
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