# Polynomials class 10 Notes Mathematics

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## CBSE Guide Polynomials class 10 Notes

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## 10 Mathematics notes Chapter 2 Polynomials

Download CBSE class 10th revision notes for Chapter 2 Polynomials in PDF format for free. Download revision notes for Polynomials class 10 Notes and score high in exams. These are the Polynomials class 10 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the the best tips recommended by teachers during exam days.

CBSE Class–10 Mathematics
Revision Notes
CHAPTER 02
POLYNOMIALS

1. Geometrical Meaning of the Zeroes of a Polynomial
2. Zeroes and Coefficients of a Polynomial
3. Division Algorithm for Polynomials
4. Monomials: Algebraic expression with one term is known as Monomial.
5. Binomial: Algebraic expression with two terms is called Binomial.
6. Trinomial: Algebraic expression with three terms is known as Trinomial.
7. Polynomials: All above mentioned algebraic expressions are called Polynomials.
8. Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.
9. A quadratic polynomial in x with real coefficient is of the form ${\text{a}}{{\text{x}}^2}{\text{ }} + {\text{ bx }} + {\text{ c}}$,where a, b, c are real numbers with ${\text{a }} \ne 0$.
10. 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 i.e. x = a is a zero of polynomial p(x) if p(a) = 0.
11. A polynomial can have at most the same number of zeros as the degree of polynomial.
12. For quadratic polynomial ${\text{a}}{{\text{x}}^2} + {\text{ bx }} + {\text{ c}}$$(a \ne 0)$

Sum of zeroes =$\; - \frac{b}{a}$

Product of zeroes = $\;\frac{c}{a}$

10. In a cubic polynomial $a{x^3} + b{x^2} + cx + d$, if $\alpha ,\beta ,\gamma$ are the zeroes of the polynomial, then

$\alpha + \beta + \gamma = {{ - b} \over a}$

$\alpha \beta + \beta \gamma + \gamma \alpha = {c \over a}$

$\alpha .\beta .\gamma = {d \over a}$

11. The division algorithm states that given any polynomial p(x) and polynomial g(x), there are polynomials q(x) and r(x) such that :

${\text{p}}\left( {\text{x}} \right){\text{ }} = \;{\text{g}}\left( {\text{x}} \right).{\text{q }}\left( {\text{x}} \right){\text{ }} + \;{\text{r}}\left( {\text{x}} \right),\;\;{\text{g}}\left( {\text{x}} \right){\text{ }} \ne 0$

where r(x) = 0 or degree of r(x) < degree of g(x).

Or          Dividend = Divisor x Quotient + Remainder

If r(x) = a zero polynomial, then p(x) is said to be completely divisible by g(x), i.e., g(x) is a factor of p(x).

## Polynomials class 10 Notes

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• Quick revision notes for CBSE board exams

## CBSE Class-10 Revision Notes and Key Points

Polynomials class 10 Notes. CBSE quick revision note for Class-10 Mathematics, Chemistry, Maths, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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