Question

Evaluate the function at the given value using synthetic division.

f(x)=-4^3+3x^2+7 at x=-1
f(x)=

Answer 1

14

Explanation:

You want the value of f(-1) when f(x) = -4x³ +3x² +7.

Synthetic division

Finding the value of f(-1) is the same as finding the remainder from division by (x+1). The attached synthetic division tableau shows the result is 14.

f(-1) = 14

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Additional comment

The "entry in the left part of the table" is the value of x for which you want f(x).

This process is equivalent to evaluating the function written in Horner form:

f(x) = ((-4x +3)x)x +7

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