**Important Concepts and Formulas**

1. A polynomial p(x) in one variable x
is an algebraic expression in x of the form

*p(x) = a*_{n}x^{n}+ a_{n – 1}x^{n – 1}+ . . . + a_{2}x^{2}+ a_{1}x + a_{0}.
where

*a*are constants and a_{0}, a_{1}, a_{2}, . . ., a_{n}_{n}≠ 0.*a*are respectively the coefficient of

_{0}, a_{1}, a_{2}, . . ., a_{n }*x*, and n is called the degree of the polynomial. Each of

^{0}, x, x^{2}, . . ., x^{n}*a*, with a

_{n}x^{n}+ a_{n – 1}x^{n – 1}+ . . . + a_{2}x^{2}+ a_{1}x + a_{0 }_{n}≠ 0, is called a term of the polynomial p(x).

2. A polynomial with one, two and three
terms are called monomial, binomial and trinomial, respectively.

3. A polynomial of degree one is called
a linear polynomial, a polynomial of degree two is called a quadratic
polynomial and polynomial of degree three is called a cubic polynomial.

4. A real number ‘a’ is a

**zero of a polynomial**p(x) if p(a) = 0. In this case, a is also called a**root of the equation**p(x) = 0.
5. Every linear polynomial in one
variable has unique zero, a non-zero constant polynomial has no zero, and every
real number is a zero of the zero polynomial.

6.

**Remainder Theorem:**If p(x) is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial (x – a), then the remainder is p(a).
7.

**Factor Theorem: (**x – a) is a factor of the polynomial p(x), if p(a) = 0. Also, if**(**x – a) is a factor of p(x), then p(a) = 0.
8.

*(x + y + z)*^{2}= x^{2}+ y^{2}+ z^{2}+ 2xy + 2yz + 2zx

9.

*(x + y)*^{3}= x^{3}+ y^{3}+ 3xy(x + y)

10.

*(x – y)*^{3}= x^{3}– y^{3}– 3xy(x – y)

11.

*x*^{3}+ y^{3}+ z^{3}– 3xyz = (x + y + z) (x^{2}+ y^{2}+ z^{2}– xy – yz – zx)
nice post.

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