Chapter 2 of CBSE NCERT Class 9 Math covers polynomials. Concepts covered in chapter 2 include polynomials in one variable, long division of polynomials, finding zeroes of a polynomial, Remainder Theorem, factorization of polynomials, and useful algebraic identities. The extra questions given below include questions akin to HOTS (Higher Order Thinking Skills) questions and exemplar questions of NCERT.
Here is a quick recap of the key concepts that are covered in the Polynomials Chapter in the CBSE NCERT Class 9 Math text book.
A polynomial p(x) is an algebraic expression in a variable x of the form
p(x) = anxn + an - 1xn - 1 + ....... + a1x1 + a0x0, where an ≠ 0
a0, a1, .... an - 1, and an (an ≠ 0) are coefficients of x0, x1, ..... xn - 1, and xn respectively.
'n' is called the degree of the polynomial.
Each of a0x0, a0x0, ..... a0x0, and a0x0 where an ≠ 0 is called a term of the polynomial.
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.
If p(x) is a polynomial whose degree is greater than or equal to 1 and if p(x) is divided by (x - a), the remainder of the division is p(a).
If a polynomial p(x) is divided by (x - a) and p(a) = 0, then (x - a) is a factor of p(x).
Conversely, if (x - a) is a factor of a polynomial p(x), then p(a) = 0