Fundamentals of Polynomials

Fundamentals of Polynomials
Types of polynomials depending upon degree :
1.    Constant polynomial: A polynomial with ‘0’ as degree is known as constant polynomial. 
Ex: P(x) = 6
2.    Linear polynomial : A polynomial with ‘1’ as degree is known as linear polynomial.
Ex:  p(x) = 3x+1
3.    Quadratic polynomial: A polynomial with ‘2’ as degree is known as quadratic polynomial.
Ex:     p(x) = 4x²+x+1 
4.    Cubic polynomial: A polynomial with ‘3’ as degree is known as cubic polynomial.
Ex:     p(x) = 6x³+4x²+3x+1
5.    Biquadratic polynomial: A polynomial with ‘4’ as degree is known as biquadratic polynomial.
Ex:     8x⁴+3x³+4x²+2x+1
Zero Polynomial : If all the coefficients in a polynomial are zeroes, then it is called a zero polynomial
  \(O = 0.{x^n} + 0.{x^{n - 1}} + 0.{x^{n - 2}} + ................\)  
clearly all coefficients are zeroes and also degree is not defined as we can’t say value of ‘n’.
Zero of the polynomial :- The number for which the value of a polynomial is zero is called zero of the polynomial.
Ex:     Find the zero of the polynomial 4x-8
Sol:  Put zero on the R.H.S on the R.H.S
      \(\therefore 4x - 8 = 0\)
    \(\begin{gathered} 4x = 8 \hfill \\ x = \frac{8}{4} = 2 \hfill \\ \end{gathered} \)
 zero of the given polynomial x = 2
Substitutions: The method of replacing numerical values in the place of variables is called  substitution.
    EX:- The value 7z at z = -1 is 7(-1) = -7