**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****Find a quadratic 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**

### 1. What are Polynomials?

A polynomial is an algebraic expression of the form p(x) = + +……..+ + , where , , , are real numbers and ≠ 0 is called a 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 + 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 + + 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 + + + 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.

### 6. Polynomial in one variable – Concept and Examples

### 7. Polynomial coefficients – **Polynomials Class 10 Maths**

### 8. Zeroes of Polynomial Examples

### 9. Division of Polynomial with monomial

### 10. Zeroes of Polynomials and Geometry – **Polynomials Class 10 Maths**

### 11. Relationship between zeros and coefficient of a polynomial

### 12. Find a quadratic polynomial

### 13. Division of a cubic polynomial by monomial

### 14. If a given polynomial is a factor of another polynomial

### 15. Finding all zeroes of biquadratic polynomial

### 16. Verification of zeroes of cubic polynomials

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

Suppose a cubical equation is ++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

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