Ex

  Mathematics (NTSE/Olympiad)  

Polynomial

Factors and coffieients

What is a Factor :
Each combination of the constants and variables, which form a term, is called a factor.

For examples :
(i) 7, x and 7x are factors of 7x, in which  7 is constant (numerical) factor and x is variable (literal) factor.
(ii) In –5x2y, the numerical factor is –5 and literal factors are : x, y, xy, x2 and x2y.

What is a Coefficient : 
Any factor of a term is called the coefficient of the remaining term.

For example :
(i) In 7x ; 7 is coefficient of x
(ii) In –5x2y; 5 is coefficient of ­–x2y or we can also say –5 is coefficient of x2y.

Example: Write the coefficient of :
(i) x2 in 3x3 – 5x2 + 7

(ii) xy in 8xyz
(iii) –y in 2y2 – 6y + 2
(iv) x0 in 3x + 7

Solution:
(i) –5
(ii) 8z
(iii) 6
(iv) Since x0 = 1, Therefore 3x + 7 = 3x + 7x0. Therefore, the coefficient of x0 is 7


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