# IMPORTANT TERMS, DEFINITIONS AND RESULTS

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1. An expression of the form

where is called a polynomial in of degree ,
Here, are real numbers and each power of is a non – negative interger.
2. The exponent of the highest degree term in a polynomial is known as its degree. A polynomial of degree 0 is called a constant polynomial.
3. A polynomial of degree 1 is called a linear polynomial. A linear polynomial is of the form where ,
4. A polynomial of degree 2 is called a quadratic polynomial. A quadratic polynomial is of the form where .
5. A polynomial of degree 3 is called a cubic polynomial. A cubic polynomial is of the form where .
6. A polynomial of degree 4 is called a biquadratic polynomial. A biquadratic polynomial is of the form where ,
7. If is a polynomial in and if is any real number, then the value obtained by putting in is called the value of at . The value of at is denoted by .
8. A real number is called a zero of the polynomial , if .
9. A polynomial of degree n can have at most n real zeroes.
10. Geometrically the zeroes of a polynomial are the x-coordinates of the points, where the graph of , intersects x-axis.
11. Zero of the linear polynomial is
12. If and are the zeroes of a quadratic polynomial then
13. If and are the zeroes of a cubic polynomial then
14. A quadratic polynomial whose zeroes are is given by – (sum of the zeroes) + product of the zeroes.
15. A cubic polynomial whose zeroes are is given by – (sum of the zeroes) + (sum of the products of the zeroes taken two at a time) – product of the zeroes.
16. The division algorithm states that given any polynomial and any non-zero polynomial , there are polynomial and such that , where or degree degree .

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