NCERT Class 9 Mathematics Textbook for Blind and Visually Impaired Students made Screen Readable by Professor T K bansal.

In this chapter, you have studied the following points:

1. A polynomial p(x) in one variable x is an algebraic expression in x of the form
p(x) = an x^n+ an−1 x^(n−1) + . . . + a2 x^2 + a1 x + a0,
where a0, a1, a2, . . ., an are constants and an ≠0.
a0, a1, a2, . . ., an are respectively the coefficients of x^0, x^1, x^2, . . ., x^n, and n is called the degree of the polynomial. Each of an x^n, a(n−1) x^(n−1), ..., a0, with an ≠0, is called a term of the polynomial p(x).

2. A polynomial of one term is called a monomial.

3. A polynomial of two terms is called a binomial.

4. A polynomial of three terms is called a trinomial.

5. A polynomial of degree one is called a linear polynomial.

6. A polynomial of degree two is called a quadratic polynomial.

7. A polynomial of degree three is called a cubic polynomial.

8. A real number ‘a’ is a zero of a polynomial p(x) if p(a) = 0. In this case, a is also called a root of the equation p(x) = 0.

9. Every linear polynomial in one variable has a unique zero, a non−zero constant polynomial has no zero, and every real number is a zero of the zero polynomial.

10. Remainder Theorem : If p(x) is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial x − a, then the remainder is p(a).

11. Factor Theorem : x − a is a factor of the polynomial p(x), if p(a) = 0. Also, if x − a is a factor of p(x), then p(a) = 0.

12. (x + y + z)^2 = x^2 + y^2 + z^2 + 2 x y + 2 y z + 2 z x

13. (x + y)^3 = x^3 + y^3 + 3 x y × (x + y)

14. (x − y)^3 = x^3 − y^3 − 3 x y × (x − y)

15. x^3 + y^3 + z^3 − 3 x y z = (x + y + z) × (x^2 + y^2 + z^2 − x y − y z − z x)

I, Dr. T K Bansal, is thankful to you for studying this chapter with me, with so much of patience. I am sure that if you study this lesson time and again you will really enjoy this chapter, and will become a master of the subject. In case you have any suggestions, or find any mistakes, which in any case there will be, please do write to me at Blind2Visionary@Gmail.com, your efforts will be highly appreciated.

End of Chapter 2