# 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,

$ax^{n} + bx^{n-1} + ….. + rx + s = 0$

**If n is a natural number**, a^{n} – b^{n} = (a – b)(a^{n-1} + a^{n-2} +…+ b^{n-2}a + b^{n-1})

**If n is even** (n = 2k), a^{n} + b^{n} = (a + b)(a^{n-1} – a^{n-2}b +…+ b^{n-2}a – b^{n-1})

**If n is odd** (n = 2k + 1), a^{n} + b^{n} = (a + b)(a^{n-1} – a^{n-2}b +…- b^{n-2}a + b^{n-1})

(a + b + c + …)^{2} = a^{2} + b^{2} + c^{2} + … + 2(ab + ac + bc + ….

### Solved Examples

**Question 1:**What are the factors of the equation x

^{2}– 10x + 5 ?

**Solution:**

x

= x

^{2}– 10x + 5= x

^{2}– 2(5x) + 5^{2 }= x^{2}– 2(5)(x) + 5^{2 }= (x – 5)^{2 }More topics in Polynomial Formula | |

Perfect Square Trinomial Formula | Cubic Equation Formula |

Vieta’s Formula |