CBSE Class 10 Maths Notes Chapter 2 Polynomials Pdf free download is part of Class 10 Maths Notes for Quick Revision. Here we have given NCERT Class 10 Maths Notes Chapter 2 Polynomials. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.

## CBSE Class 10 Maths Notes Chapter 2 Polynomials

- “Polynomial” comes from the word ‘Poly’ (Meaning Many) and ‘nomial’ (in this case meaning Term)-so it means many terms.
- A polynomial is made up of terms that are only added, subtracted or multiplied.
- A quadratic polynomial in x with real coefficients is of the form ax² + bx + c, where a, b, c are real numbers with a ≠ 0.
- Degree – The highest exponent of the variable in the polynomial is called the degree of polynomial. Example: 3x
^{3}+ 4, here degree = 3. - Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomial respectively.
- A polynomial can have terms which have Constants like 3, -20, etc., Variables like x and y and Exponents like 2 in y².
- These can be combined using addition, subtraction and multiplication but NOT DIVISION.
- The zeroes of a polynomial p(x) are precisely the x-coordinates of the points, where the graph of y = p(x) intersects the x-axis.

If α and β are the zeroes of the quadratic polynomial ax² + bx + c, then

\(sum\quad of\quad zeros,\alpha +\beta =\frac { -b }{ a } =\frac { -coefficient\quad of\quad x }{ coefficient\quad of\quad { x }^{ 2 } } \)

\(product\quad of\quad zeros,\alpha \beta =\frac { c }{ a } =\frac { constant\quad term }{ coefficient\quad of\quad { x }^{ 2 } } \)

If α, β, γ are the zeroes of the cubic polynomial ax^{3} + bx^{2} + cx + d = 0, then

\(\alpha +\beta +\gamma =\frac { -b }{ a } =\frac { -coefficient\quad of\quad { x }^{ 2 } }{ coefficient\quad of\quad { x }^{ 3 } } \)

\(\alpha \beta +\beta \gamma +\gamma \alpha =\frac { c }{ a } =\frac { coefficient\quad of\quad { x } }{ coefficient\quad of\quad { x }^{ 3 } } \)

\(\alpha \beta \gamma =\frac { -d }{ a } =\frac { -constant\quad term }{ coefficient\quad of\quad { x }^{ 3 } } \)

Zeroes (α, β, γ) follow the rules of algebraic identities, i.e.,

(α + β)² = α² + β² + 2αβ

∴(α² + β²) = (α + β)² – 2αβ

**DIVISION ALGORITHM:**

If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then

p(x) = g(x) × q(x) + r(x)

Dividend = Divisor x Quotient + Remainder

**Remember this!**

- If r (x) = 0, then g (x) is a factor of p (x).
- If r (x) ≠ 0, then we can subtract r (x) from p (x) and then the new polynomial formed is a factor of g(x) and q(x).

### Class 10 Maths Notes

- Chapter 1 Real Numbers Class 10 Notes
- Chapter 2 Polynomials Class 10 Notes
- Chapter 3 Pair of Linear equations in Two Variables Class 10 Notes
- Chapter 4 Quadratic Equations Class 10 Notes
- Chapter 5 Arithmetic Progressions Class 10 Notes
- Chapter 6 Triangles Class 10 Notes
- Chapter 7 Coordinate Geometry Class 10 Notes
- Chapter 8 Introduction to Trigonometry Class 10 Notes
- Chapter 9 Some Applications of Trigonometry Class 10 Notes
- Chapter 10 Circles Class 10 Notes
- Chapter 11 Constructions Class 10 Notes
- Chapter 12 Areas related to Circles Class 10 Notes
- Chapter 13 Surface Areas and Volumes Class 10 Notes
- Chapter 14 Statistics Class 10 Notes
- Chapter 15 Probability Class 10 Notes