H.C.F. & L.C.M. Of Polynomials

(1) Find  the  H.C.F. and L.C.M. of 

(i)    8x² + 2x – 21   and  10x² – 11x – 6     (ii)    8 ( x³ + x² + x )  and  28 ( x⁵ – x² )

Soln. (i)

…

☼L.C.M.  :   A  polynomial  p(x)  is called the L.C.M. of  two or more given  polynomials, if it is a polynomial of  smallest degree which is divided by each one of  the given polynomials….

☼ H.C.F.  of  Polynomials  :   A polynomial  h(x) is  called the H.C.F. or  G.C.D. of  two or more given polynomials, if  h(x)  is a polynomial of  highest degree dividing each one of  the given polynomials.

The coefficient of  hi…

☼ Divisor  :   A polynomial  p(x) is called a divisor of  another polynomial  f(x),  if

f(x)  =  p(x) . h(x) for some polynomial  h(x)….