Synthetic Substitution

Synthetic Substitution

How to use the synthetic substitution to find the function value: examples and their solutions.

Example 1

If f(x) = x^4 - 9x^3 + 15x^2 + 3x - 62, find f(7).

Instead of putting 7 into f(x),
use the synthetic division.
(divisor's zero: 7)

The remainder is 8.

Then, by the remainder theorem,
f(7) = 8.

Example 2

If f(x) = x^5 - 4x^4 + 5x^3 - 20x + 7, find f(3).

Instead of putting 3 into f(x),
use the synthetic division
(divisor's zero: 3)

The remainder is 1.

Then, by the remainder theorem,
f(3) = 1.