Karnataka Secondary Education Examination BoardKarnataka SSLC
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Introduction to Polynomials

notes

Before we start with the introduction let us try to recall what we studied earlier about Polynomials.
1) Polynomials in one variable and their degrees. Eg `x^2+x^5+x^3+x` is polynomial in one variable i.e. variable x. And the degrees here are 2, 5, 3, 1.
2) If p(x) is a polynomial in x, highest power of x in p(x) is called degree of p(x). Take the example, here the degree of polynomial is 5, because 5 is the highest degree in p(x).
3) A polynomial of degree 1 is called a linear polynomial. Eg. x+4 is a linear polynomial as the highest degree here is 1.
4) A polynomial of degree 2 is called a quadratic polynomial. `x^2-9` is a example of Qadratic Polynomial, as 2 is the highest degree.
5) A polynomial of degree 3 is called a Cubic Polynomial. For example `x^3+5x+11` is Cubic Polynomial sicnce the highest degree is 3.
6) If p(x) is a polynomial in x, and if k is any real number, then the value obtained by replacing x by k is p(x), is called the value of p(x) at x=k, and is denoted by p(k). For example, `p(x)=x^3+1` if x=4 then `p(4)=4^3+1= 64+1= 65` 
7) A real number k is said to be a zero of a polynomial p(x), if p(k)=0. Let's take a example, if `p(x)=x^3-8`, and x=2 the `p(2)= 2^3-8= 8-8= 0`. Thus any value of x that makes p(x) as 0 that is called zeros of polynomial.
Now let us understand more about Polynomials through a real life example, Manav works at three differen places to earn more money in a day. The employer at the first place pays him 2x as salary where x is the number of hours he work. At the second place Manav is paid with `x^2` while at the third place he earns `x^3`. So the total amount of money is represented as p(x) and `p(x)= 2x+x^2+x^3`
Here in this example we have only one variable i.e x

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Polynomials part 1 (Introduction to polynomials) [00:10:47]
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