#### Mathematics (NTSE/Olympiad)

# Polynomial

__Value of a Polynomial__

**How to calculate of find the value of a Polynomial Equation: **

For a polynomial f(x) = 3x^{2} – 4x + 2.

To find its value at x = 3; replace x by 3 everywhere. So, the value of f(x) = 3x^{2} – 4x + 2 at x = 3 is given by

f(3) = 3 × 3^{2} – 4 × 3 + 2 = 27 – 12 + 2 = 17.

Similarly, the value of polynomial f(x) = 3x^{2} – 4x + 2,

(i) at x = –2 is f(–2) = 3(–2)^{2} –4(–2) + 2 = 12 + 8 + 2 = 22

(ii) at x = 0 is f(0) = 3(0)^{2} – 4(0) + 2 = 0 – 0 + 2 = 2

(iii) at x = 1/2 is f(1/2) = 3(1/2)^{2}– 4(1/2) + 2 = 3/4 – 2 + 2 = 3/4

**Example: Find the value of the polynomial 5x – 4x**^{2} + 3 at: **(i) x = 0 (ii) x = –1**

**Solution:** Let p(x) = 5x – 4x^{2} + 3.

(i) At x = 0, p(0) = 5 × 0 – 4 × (0)^{2} + 3 = 0 – 0 + 3 = 3

(ii) At x = –1, p(–1) = 5(–1) – 4(–1)^{2} + 3 = –5 – 4 + 3 = – 6