This chapter explains in detail polynomials and their various types, namely, linear polynomial, quadratic polynomial and cubic polynomial, followed by the concept of the zeroes of a polynomial. Finally, a brief mention of the degrees of a polynomial helps the students understand the basic essence of this chapter.
A linear polynomial is a polynomial of degree 1. For example, 2x-3 is a linear polynomial. Similarly, a polynomial of degree 2 is called a quadratic polynomial, for example, 2x2-3x+2; and a polynomial with degree 3 is called a cubic polynomial. For example, x3-2x2+3x-4 is a cubic polynomial.
Chapter 2: Polynomials also talks about the geometrical meaning of the zeroes of a polynomial. This is done by explaining the concept of the zeroes of a polynomial with the help of graphs, as pictorial representations are often easier to grasp. The zeros of the polynomial mean the values of x for which the value of the polynomial converts to zero.
It then sheds light on the relationship between the roots of a polynomial and its coefficients. This is a direct method to find out the zeroes of a given polynomial based on its coefficients.
If α and β are the roots of a polynomial, ax2+bx+c, where a, b, c are real numbers with a≠0,
α + β = -b/a; αβ = c/a.
An important topic discussed in this chapter is the 'Division Algorithm for Polynomials. This Algorithm is similar to Euclid's Division Algorithm, which we encountered in the first chapter. It states that "if p(x) and g(x) are two given polynomials such that g(x)≠0, then we can find polynomials, q(x) and r(x) by the following-
P(x) = g(x) * q(x)+r(x)”.
Where, r(x)=0 or the degree of r(x)
The above-given method is also known as the remainder theorem