Algebra and Co-ordinate Geometry
In this chapter, we will learn about polynomials, linear equations in two variables and co-ordinate geometry.
Polynomials
Polynomials are those algebraic expressions in which the variables involved have only non-negative integral powers. In other words, a polynomial p(x) in one variable x is an algebraic expression in x of the form,
\[P(x)={{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+......+{{a}_{3}}{{x}^{3}}+{{a}_{2}}{{x}^{2}}+{{a}_{1}}x+{{a}_{0}}.\]
Where \[{{a}_{n}}\],\[{{a}_{n-1}}\],…..\[{{a}_{3}},{{a}_{2}},{{a}_{1}},{{a}_{0}}\]are \[{{a}_{n}}\]\[\ne \]0.
Here, \[{{a}_{n}}\],\[{{a}_{n-1}}\],….,\[{{a}_{3}},{{a}_{2}},{{a}_{1}},{{a}_{0}}\] are respectively the coefficients of \[{{x}^{n}},{{x}^{n-1}}\],….,\[{{x}^{3}},{{x}^{2}},x,{{x}^{0}}\] and n is called the degree of the polynomial.
Each of \[{{a}_{n}}{{x}^{n}},{{a}_{n-1}},{{x}^{n-1}}\],…..,\[{{a}_{3}}{{x}^{3}},{{a}_{2}}{{x}^{2}},ax,{{a}_{0}}\],is called a term of the polynomial p(x). The degree of the polynomial in one variable is the highest index of the variable in that polynomial.
Note:
(i) A non zero constant polynomial is a polynomial of degree 0. For example \[-3,\frac{2}{3,}\sqrt{5}\] etc are constant polynomials.
(ii) Constant polynomial 0 is called the zero polynomial. In such a polynomial all the constants
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