POLYNOMIALS

.                                                                                                                                                   POLYNOMIALS

SOME IMPORTANT POINTS TO REMEMBER

·         An algebraic expression p(x) of the form p(x) =0ₒ+ ax²+ax+....ax

where aₒ,a, a----a are the real numbers and all the indices of x are non-negative integers is called a polynomial in x and the highest index n is called the degree of the polynomial, if a ≠ 0. here aₒ,a x, a---ax  are called the terms of the polynomial and aₒ, a,a----a are called various coeddicients of the polynomial p(x) .A polynomial in x is said to be in standard form when terms are written either in increasing order or decreasing order of the indices of x in various terms.

·         A  polynomial with one term is called a monomial.

·         A  polynomial  with two terms is called a binomial.

·         A polynomial with three terms is called a trinomial.

·         A  polynomial of degree one is called a linear polynomial.

·         A polynomial of degree two is called a quadratic polynomial.

·         A polynomial of degree three is called a cubic polynomial.

·         Every linear polynomial in one variable has a unique zero, a constant polynomial has no zero, and every real number is a zero of the zero polynomial.

·         If p(x) be any polynomial of degree greater than or equal to 1 and a be any real number , then is p(x) is divided by the linear polynomial x-a, the remainder is p(a).

·         x-a is a factor of the polynomial p(x),if p(a)=0 and conversely, if x-a is a factor of p(x), then p(a)=0.

·         (x+y+z)² = x² +y² +z²+2xy+2yz+2zx.

·         (x+y)³=x³+y³+3xy(x+y).

·         (x-y)³=x³-y³-3xy(x-y).

·         x³+y³+z³-3xyz=(x+y+z)(x²+y²+z²-xy-yz-zx).