Question 2.4.5: Using the Remainder Theorem to Evaluate a Polynomial Functio...
Using the Remainder Theorem to Evaluate a Polynomial Function
Given f(x) = x³ – 4x² + 5x + 3, use the Remainder Theorem to find f(2).
By the Remainder Theorem, if f(x) is divided by x – 2, then the remainder is f(2). We’ll use synthetic division to divide.
The remainder, 5, is the value of f(2). Thus, f(2) = 5. We can verify that this is correct by evaluating f(2) directly. Using f(x) = x³ – 4x² + 5x + 3, we obtain
f(2)=2^3-4 \cdot 2^2+5 \cdot 2+3=8-16+10+3=5.
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