NCERT Notes for Class 10 Maths Chapter 2 Polynomials
![NCERT Notes for Class 10 Maths Chapter 2 Polynomials NCERT Notes for Class 10 Maths Chapter 2 Polynomials](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVAn9CHlOqgEQIEhbE0QsCRSNIzixgjTcyamdDLDy0d9Nsw_SXRyOQCnACvf04UbOSjrnFNKb9uX2lycpBZajemPGwc6XVu89RvKa4_joLhQWFKW2PjYAHrhCd6XjGwPDyQ0igGIms1ydp9rv_wk4PUacBFZEB2N261W6NtRwXz1YS38_pUfn97Xx3-TYM/s16000/chapter2-polynomials-revision-notes-class10-maths.jpg)
Class 10 Maths Chapter 2 Polynomials Notes
Chapter Name | Polynomials Notes |
Class | CBSE Class 10 |
Textbook Name | NCERT Mathematics Class 10 |
Related Readings |
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- “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: 3x3 + 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
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGmR1EFbzUR6pTg0GDWeB3QOre04XLueij8pdnFkAKT4xXnb7ezkrZz7tt8o8QPJiw0CkNfh9B2y_-OWHNH8gUdQBCx51gW3DrQZMRXsuHbNfLZkAGunJTIJnnx9QtEXrc0A0K2B90tq9tvkahwfuQ6YLxiBLMooNLwTU7ixRRS62kSGbipF8jYjouv9E/w451-h73/Class%2010%20ncert%20notes%20chapter%201%20polynomials%20img%201.png)
If α, β, γ are the zeroes of the cubic polynomial ax3 + bx2 + cx + d = 0, then
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMrgw3NiJvNt9ghFJ30Pv1jTDOW3EQzbUDcuTgGRasBtiW_cZuhTk-7FoPueaNKRtRuBG9kQGNBnIjF87RnmPPk__jMrpFe0m0lotS4O_66MVyOEW0ktnMODT1XfRJSUKOFnyyGy0_V21h4qFylCZYKfx25wTdAFDvd5B9C8LwbfQOhf8Bg83Wj9-oOIk/w399-h130/Class%2010%20ncert%20notes%20chapter%201%20polynomials%20img%202.png)
Zeroes (α, β, γ) follow the rules of algebraic identities, i.e.,
(α + β)² = α² + β² + 2αβ
∴ (α² + β²) = (α + β)² – 2αβ
Divisional 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 × 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).