**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?**

**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.

**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 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

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