An algebraic expression is the combination of constants and variable connected by the four basic operations (+, –, ×, ÷). For example : 2x , x2y , xy/3, 3 etc. Types of Algebraic expression : • Polynomial in one variable : An algebraic expression is of the form are constants and n is non – negative integer. • Degree of polynomial : largest exponent of the variable is called the degree of the polynomial. Types of polynomial based on degree • If deg = 0, then polynomial is called non – zero constant polynomial . • If deg = 1, then polynomial is called linear polynomial. • If deg = 2, then polynomial is called quadratic polynomial. • If deg = 3, then polynomial is called cubic polynomial . • 0 is called zero polynomial and its deg is not defined . • Value of a polynomial : Let P(x) be a polynomial, then value of P(x) at x = a is given by P(a) . i.e. by putting x = a. • Zero of a polynomial : (i) Let P(x) be a polynomial, then x = a is said to be zero of P(x) if P(a) = 0. (ii) To find zero of P(x), put P(x) = 0 and get the value of x . • Factor theorem : Let P(x) be a polynomial of deg ≥ 1 and q be any real number then , (i) If P(a) = 0, then (x-a) is factor of P(x) (ii) If (x-a) is factor of P(x), then P(a) = 0. • Remainder theorem : Let P(x) be a polynomial of deg ≥ 1 and a be any real number. If we divide P(x) by (x-a) then a remainder is given by remainder = P(a) • Algebraic Identities : (i) (a+b)2 = a2 + 2ab + b2 (ii) (a-b)2 = a2 – 2ab + b2 (iii) (a2 – b2) = (a – b) (a+b) (iv) (x+a) (x+b) = x2 + (a+b)x + ab (v) (a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca (vi) (a+b)3 = a3 + b3 + 3ab (a+b) (vii) (a-b)3 = a3 – b3 – 3ab(a-b) (viii) a3 + b3 = (a+b) (a2 – ab + b2) (ix) a3 – b3 = (a-b) (a2 + ab + b2) (x) a3 + b3 + c3 – 3abc = (a+b+c)(a2+b2+c2-ab – bc – ca)