How do you use synthetic substitution to evaluate f(2) for f(x)=x44x3+2x23?

1 Answer
Jul 9, 2015

f(2)=11 (using synthetic substitution, below)

Explanation:

Rewrite f(x) so all powers of x are represented (in descending power sequence).
XXXXf(x)=x44x3+2x2+0x3

[A]XXXXWrite the substitution value (2) separated by a vertical bar from a row of the from the coefficients as noted above.
XXXXXXDraw a vertical line below the coefficients, allowing enough space to write another row of numbers between the coefficients and the line.

[B]XXXXCopy the first coefficient to a position below the line.

[C]XXXXMultiply the substitution value and the number just written below the line and record the product above the line under the second coefficient.

[D]XXXXAdd the product just developed and the second coefficient and write the sum below the line.

[E]XXXXMultiply the substitution value and the number just written below the line and record the product below the line.

[F] to [I]XXXXContinue this process until all coefficients have been processed.

[I]The solution is the last value written below the line.

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