Polynomials Class 10 Maths

Polynomials Class 10 Maths, deals with various concepts which are as under:-

• What are Polynomials?
• Degree of Polynomial
• Types of Polynomials
• Value of a polynomial
• Zero of a polynomial
• Polynomial in one variable – Concept and Examples
• Polynomial coefficients
• Zeroes of Polynomial Examples
• Division of Polynomial with monomial
• Zeroes of Polynomials and Geometry
• Relationship between zeros and coefficient of a polynomial
• Division of a cubic polynomial by monomial
• If a given polynomial is a factor of another polynomial
• Finding all zeroes of biquadratic polynomial
• Finding all zeroes of biquadratic polynomial
• Verification of zeroes of cubic polynomials
• Relation of factors and coefficients of cubic equations
• Finding Zeroes of a Cubic Polynomial

2. Degree of Polynomial

The exponent of the highest power of the variable of a polynomial is called the degree of the polynomial.

If”x” is a variable in a polynomial (x), highest power of the variable x in a polynomial is called the degree of the polynomial.

3. Types of Polynomials – Polynomials Class 10 Maths

• The polynomial with all the coefficients as zero is called a zero polynomial.
• A polynomial with a single term of a real number is called a constant 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 and b are real numbers and a≠0.
• 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, b and c are real numbers and a≠0.
• 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, b, c and d are real numbers and a≠0.
• A polynomial of degree four is called a fourth-degree or biquadratic polynomial. the general form of a biquadratic polynomial is a(x^4) + bx³ + cx² + dx + e, where a, b, c, d and e are real numbers and a≠0.

4. Value of a polynomial

The value of a polynomial p(x) when x = k (k is a real number) is the value obtained by substituting x as k.

It is denoted by p(k).

5. Zero of a polynomial – Polynomials Class 10 Maths

The zero of the polynomial is defined as any real value of x, for which the value of the polynomial becomes zero.

17. Relation of factors and coefficients of cubic equations – Polynomials Class 10 Maths

Suppose a cubical equation is ax³+bx²+cx+d=0 have 3 zeroes α,β and γ. Then

Sum of the zeroes = α+β+γ=-b/a
Sum of the product taking 2 at a time = αβ+βγ+γα=c/a
Product of the zeroes = αβγ=-d/a