- Algebraic expressions in which the variables involved have only non-negative
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
- 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.
1. (a+b)2 = a2+2ab+b2
2. (a-b)2 = a2-2ab+b2
3. (a+b)(a-b) = a2-b2
4. (a+b)(a2-ab+b2) = a3+b3
5. (a-b)(a2+ab+b2) = a3-b3
6. (a+b)3 = a3+3a2b+3ab2+b3
7. (a-b)3 = a3-3a2b+3ab2-b3
8. (a+b+c)2 = a2+b2+c2+2ab+2bc+2ac
9. (a+b+c) (a2+b2+c2-ab-bc-ca)= a3+b3+c3-3abc
10. (x+a)(x+b) = x2+x(a+b)+a.b
11. (ax+b)(cx+d) = acx2+x(ad+bc)+b.d
12. (x+a)(x+b)(x+c) = x3+x2(a+b+c)+x(ab+bc+ca)+abc
Directions: Memorize the formulas and write all the formulas on a sheet of paper.