Notes On Polynomials in One Variable - CBSE Class 9 Maths

Polynomial
The algebraic expression of the form p(x) = an xn + an-1 xn-1 +........+ a1 x1 + a0, where an, an-1, a1, a0 are real numbers and an≠ 0 is called a polynomial. The exponent of each term of a polynomial is a non-negative integer.

Monomial
A polynomial with only one term is called a monomial.

Binomial
A polynomial with only two terms is called a binomial.

Trinomial
A polynomial with only three terms is called a trinomial.

Zero Polynomial
The polynomial with all the coefficients as zeros is called a zero polynomial.

Constant Polynomial
A polynomial with a single term of a real number is called a constant polynomial.

Degree of a Polynomial
The exponent of the term with the highest power is called the degree of the polynomial. The degree of a non-zero constant polynomial is zero. The degree of the zero polynomial is not defined.

A polynomial is named according to the degree of the polynomial.

Linear Polynomial
A polynomial of degree one is called a first-degree or linear polynomial. The general form of a linear polynomial is ax + b, where a ≠ 0. Maximum number of terms of a linear polynomial is two.

Quadratic Polynomial
A polynomial of degree two is called a second degree or quadratic polynomial. The general form of a quadratic polynomial is ax2 + bx + c, where a ≠ 0. Maximum number of terms of a quadratic polynomial is three.

Cubic Polynomial
A polynomial of degree three is called a third-degree or cubic polynomial. The general form of a cubic polynomial is ax3 + bx2 + cx + d, where a ≠ 0. Maximum number of terms of a cubic polynomial is four.

Zero / Root of a Polynomial
A number 'a' is said to be a zero of a polynomial p(x), if p(a) = 0. It is a solution to the polynomial equation p(x) = 0. If we draw the graph of p(x) = 0, the values where the curve cuts the x-axis are called the zeros of the polynomial.
A non-zero constant polynomial has no zero. Every real number is a zero of the zero polynomial.

Zero of a polynomial can be found by 'trial and error' method or by 'equating the polynomial to zero' method. In 'equating polynomial to zero' method, the zero of the polynomial can be found by making 'x' as the subject.

Summary

Polynomial
The algebraic expression of the form p(x) = an xn + an-1 xn-1 +........+ a1 x1 + a0, where an, an-1, a1, a0 are real numbers and an≠ 0 is called a polynomial. The exponent of each term of a polynomial is a non-negative integer.

Monomial
A polynomial with only one term is called a monomial.

Binomial
A polynomial with only two terms is called a binomial.

Trinomial
A polynomial with only three terms is called a trinomial.

Zero Polynomial
The polynomial with all the coefficients as zeros is called a zero polynomial.

Constant Polynomial
A polynomial with a single term of a real number is called a constant polynomial.

Degree of a Polynomial
The exponent of the term with the highest power is called the degree of the polynomial. The degree of a non-zero constant polynomial is zero. The degree of the zero polynomial is not defined.

A polynomial is named according to the degree of the polynomial.

Linear Polynomial
A polynomial of degree one is called a first-degree or linear polynomial. The general form of a linear polynomial is ax + b, where a ≠ 0. Maximum number of terms of a linear polynomial is two.

Quadratic Polynomial
A polynomial of degree two is called a second degree or quadratic polynomial. The general form of a quadratic polynomial is ax2 + bx + c, where a ≠ 0. Maximum number of terms of a quadratic polynomial is three.

Cubic Polynomial
A polynomial of degree three is called a third-degree or cubic polynomial. The general form of a cubic polynomial is ax3 + bx2 + cx + d, where a ≠ 0. Maximum number of terms of a cubic polynomial is four.

Zero / Root of a Polynomial
A number 'a' is said to be a zero of a polynomial p(x), if p(a) = 0. It is a solution to the polynomial equation p(x) = 0. If we draw the graph of p(x) = 0, the values where the curve cuts the x-axis are called the zeros of the polynomial.
A non-zero constant polynomial has no zero. Every real number is a zero of the zero polynomial.

Zero of a polynomial can be found by 'trial and error' method or by 'equating the polynomial to zero' method. In 'equating polynomial to zero' method, the zero of the polynomial can be found by making 'x' as the subject.

Videos

References

Previous