Polynomials - Class 9 Maths

Constant - The symbol which has a fixed numerical value is called a constant

Variable - The symbol which assumes different values in different situations is called a variable

Coefficient - A numerical or constant quantity before the variable

Operator - The symbol of a mathematical operation

Exponent - A number or a value or letter written above and to the right of a mathematical expression

Algebraic Expression - The combination of constants and variables by the use of some or all operations as x²+5y-7

Terms - The various parts of an algebraic expression seperated by operators are called terms of the algebraic expression

Polynomial - An algebraic expression is called a polynomial if the variable involved have only non-negative integral powers as 7x³-5x²+6x-9

Degree of a Polynomial

(i)When the polynomial is in one variable - In this case, the highest power of the variable is called the degree of the polynomial.
  Example - 7x²+x is a polynomial in x whose degree is 2
  7y³+y is a polynomial in y whose degree is 3
 (ii)When the polynomial is in two variable - In this case, the sum of the powers of the variables in each term is taken up and the highest sum, so obtained, is called the degree of the polynomial.
  Example - 5x²y³-5x⁴y³-3x²y², Note carefully for the first expression the sum of the powers is 5, for the second expression the sum of the powers is 7 and for the third it is 4, as 7 is the highest sum so the degree of x and y is 7
  For multiple variables, we follow the above step.

Types of Polynomials

Zero Polynomial - A polynomial which consists of 0 only is called a zero polynomial. The degree of a zero polynomial is not defined.
Constant Polynomial - A polynomial which consists of only one constant term is called a constant polynomial. The degree of a constant polynomial is zero. Each real number is a constant polynomial. Example 5, -7/8, -3 are constant polynomials
Linear Polynomial - A polynomial of degree one is called a linear polynomial. Example 5x+7 is a linear polynomial in x, 5x + 7y + 6 is a linear polynomial in x and y
Quadratic Polynomial - A polynomial of degree two is called a quadratic polynomial. Example 5y²+7 is a quadratic polynomialin y, xy + x + 2 is a quadratic polynomial in x and y
Cubic Polynomial - A polynomial of degree three is called a cubic polynomial. Example 5x³+2x²+6 is a cubic polynomial in x, 5x²y+4xy²+5 is a cubic polynomial in x and y
Biquadratic Polynomial - A polynomial of degree four is called a biquadratic polynomial. Example 5x⁴+8 is a biquadratic polynomial in x, 5x³y+6xy³+7 is a biquadratic polynomial in x and y

Number of terms in a Polynomial

Monomial - A polynomial which has only one non-zero term. Example 5, -7
Binomial - A polynomial which has only two non-zero terms. Example 5 + 7x, x - 7y, 3x²y+2xy has
Trinomial - A polynomial which has only three non-zero terms. Example 5+7x+x², xy+yz+zx

Tuition Notes