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18
Jul
Index
  1. Divisor
  2. H.C.F.  of  Polynomials
  3. L.C.M.
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18
Jul
Examples

(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)

…

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18
Jul
L.C.M.

☼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….

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18
Jul
H.C.F.  of  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…

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17
Jul
Index
  1. formulae
  2. Factor  Theorem
  3. Remainder Theorem
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17
Jul
Examples 7 to 8

 (7) If   x  +  y = – z ,  then find the value of 

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17
Jul
Examples 4 to 6

(4) If  m  =  – 28,   and  n  =  20,  find the value of  9m2 +  24mn  +  16n2.

Soln. 9m2  +  24mn  +  16n2  =  ( 3m  +  4n )2  =  ( – 84 + 80 )2  =  16.

…

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17
Jul
Examples 1 to 3

(1) If  a + b  =  9  and  a – b  =  5,  find   a2 +  b2   and  ab.

Soln. 2( a2+b2 ) =  (a + b) 2 +  (a – b) 2

=    (9) 2 +  (5) 2

=    1…

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17
Jul
Remainder Theorem

☼ Remainder Theorem  :   If an expression  f(x)  is divided by (x – a), then the remainder  is  f(a).

 e.g. Is  x + 2  a factor of   5x2 –  3x  –  14  ?

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17
Jul
Factor  Theorem

☼ Factor  Theorem  :   If  f(x)  is completely divisible by (x – a), then  f(a)  =  0.

Thus,  (x – a) is a factor of   f(x)

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