# Polynomial Formula

A polynomial expression is the one which has more than two algebraic terms. As the name suggests, Polynomial is a repetitive addition of a monomial or a binomial.

The general Polynomial Formula is written as,

$ax^{n} + bx^{n-1} + ….. + rx + s$

If n is a natural number, an – bn = (a – b)(an-1 + an-2b+…+ bn-2a + bn-1)

If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)

If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)

(a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….)

### Solved Example

Question: What are the factors of the polynomial x2 – 10x + 25?
Solution:

x2 – 10x + 25
= x2 – 2(5x) + 52
= x2 – 2(5)(x) + 52
= (x – 5)2
Hence, the factors are (x – 5) and (x – 5).
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