Polynomials are algebraic expressions with variables like x and y. They involve various powers of the variable that are multiplied by specific numbers and added or subtracted, along with the potential addition or subtraction of a number. The highest power used determines the degree of the polynomial, such as a first degree polynomial involving the highest power of x being 1, a second degree polynomial having the highest power of x as 2, and so on. Examples are provided of polynomials up to the third degree.
11. We can summarise their general characters as follows .
power of x
the exponents of x are natural number
powers of x are multiplied by certain numbers.
the sum or difference of these products is found
with this a certain number is added or subtracted.
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13. Various powers of the number denoted by
x are multiplied by specific numbers and
these are added or subtracted along with
addition or subtraction of a specific
number including zero. Such algebraic
expressions are called polynomials .
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14. In a polynomial ,we take powers of variables .
The largest power used is called the
Degree of the polynomial .
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15. In the polynomials ,the largest power of x is 1 ,
it is called a first degree polynomials .
Eg:4x+2,11x-8
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16. In the polynomial, the largest power of
x is 2 ,
it is called a second degree
polynomials
Eg: 12x²+3x-9 ,x²-10x-6
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17. In the polynomial, the largest power of x is 3 ,
it is called a third degree polynomials
Eg: x³+7x²-8x+3
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18. General forms of polynomials
1st degree polynomial: ax+b
2nd degree polynomial: ax²+bx+c
3rd degree polynomial:ax³+bx²+cx+d
In all these a,b,c,d etc represents some
numbers .They can be natural numbers or
fractions or numbers which are not fractions
or negative numbers. They are called the
coefficients in a polynomial .
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