Polynomials are expressions in algebraic mathematics which is comprised of variables and their coefficients containing operations like addition, subtraction, or exponents. Class 10 Maths Chapter 2 - Polynomials deals with these algebraic expressions or polynomials of various degrees. If p(x) is a polynomial of x, then the highest power of x in p(x) is the degree of the polynomial. If the degree is 1, 2, and 3, it is called linear, quadratic, and cubic polynomials, respectively. When x is replaced by any integer k, it is known as the value of p(x) at k and is denoted by p(k). In linear polynomials, the zero value of the polynomial px+q can be found by -q/p (coefficients). But in the case of higher-degree polynomials, it is harder to find where zeros would be obtained.
A quadratic polynomial has almost 2 zeros which are found with the help of the graphical method. It can also be done by using the factorization method. Equate each factor of a polynomial to zero and find the value of x. The polynomial would be zero at these values of x. In the case of cubic polynomials, there are almost 3 zeros (factors).
The chapter further discusses the relationship between the zeros and coefficients of a polynomial. In the case of an equation like ax2+bx+c, the sum of two values of x is equal to (-b/a), and the product of the two values of x is equal to (c/a).
Maths Chapter 2 Polynomials further discusses the division of polynomials. For example, if you are given one factor, the remaining two factors can be found by the Division algorithm for a polynomial. The division method of polynomials says that if p(x) and g(x) are two polynomials with g(x) not equal to zero, then the p(x)=g(x).q(x) + r(x). The value of r(x) is zero, or it has a lower degree than g(x). This method is also known as the remainder theorem.
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