Answer:
f(3) = 1
Step-by-step 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.
