 Algebraic expressions in which the variables involved have only nonnegative
integral exponents are called polynomials.
 A polynomial that involves only one variable is called a polynomial in one variable.
 The highest exponent of the variable in various terms of a polynomial in one
variable is called its degree.
 A constant is a polynomial of degree zero.
 The standard form of a polynomial in one variable is that in which the terms of the
polynomial are written in the decreasing order of the exponents of the variable.
 The coefficient in the quotient of two monomials is equal to the quotient of their
coefficients.
 The variable part in the quotient of two monomials is equal to the quotient of the
variable parts in the given monomials.
 If on dividing a polynomial (dividend) by a polynomial (divisor), a zero remainder
is obtained, then the divisor is a factor of the dividend. In such cases, quotient is
also a factor of the dividend. Further,
Dividend = Divisor × Quotient
 In general,
Dividend = Divisor × Quotient + Remainder
 The degree of the remainder is always less than the degree of the divisor.
 Before performing long division, the divisor and the dividend must be written in
the standard form.
 While performing long division, like terms are written one below the other, leaving
gaps wherever necessary.
Important Formulas
1. (a+b)^{2} = a^{2}+2ab+b^{2}
2. (ab)^{2} = a^{2}2ab+b^{2}
3. (a+b)(ab) = a^{2}b^{2}
4. (a+b)(a^{2}ab+b^{2}) = a^{3}+b^{3}
5. (ab)(a^{2}+ab+b^{2}) = a^{3}b^{3}
6. (a+b)^{3} = a^{3}+3a^{2}b+3ab^{2}+b^{3}
7. (ab)^{3} = a^{3}3a^{2}b+3ab^{2}b^{3}
8. (a+b+c)^{2} = a^{2}+b^{2}+c^{2}+2ab+2bc+2ac
9. (a+b+c) (a^{2}+b^{2}+c^{2}abbcca)= a^{3}+b^{3}+c^{3}3abc
10. (x+a)(x+b) = x^{2}+x(a+b)+a.b
11. (ax+b)(cx+d) = acx^{2}+x(ad+bc)+b.d
12. (x+a)(x+b)(x+c) = x^{3}+x^{2}(a+b+c)+x(ab+bc+ca)+abc
Directions: Memorize the formulas and write all the formulas on a sheet of paper.
