Class 9 Maths Polynomials Degree of Polynomial

Degree of Polynomial

Highest power of variable in a polynomial is called degree of polynomial. E.g. p(x)=9x3 - 3x2 +8x – 2, the highest power is 3. For p(x)= 3x2 +8x – 2 , highest power is 2

Classification of Polynomials based on degree

  1. Linear Polynomial: Degree is 1.                 g.  p(x)=8x – 2
  2. Quadratic Polynomial: Degree is 2. g.   p(x)= 3x2 +8x – 2
  3. Cubic Polynomial: Degree is 3. g.   p(x)=9x3 - 3x2 +8x – 2

Note that linear polynomial can have at most 2 terms, Quadratic polynomials can have at most 3 terms, and Cubic polynomials can have at most 4 terms.

General form of polynomials of various degrees.

  1. Linear Polynomial.                 p(x) = ax + b  , where a≠ 0
  2. Quadratic Polynomial. p(y) = ay2 + by + c , where a≠ 0
  3. Cubic Polynomial. p(x) = ax3 + bx2 + cx + d  , where a≠ 0

 

Note: Degree of Zero polynomial is not defined. It can have any degree.

P(x) = 0 can be written as P(x) =0 * xn     where n can be any number.

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