If ( x

Asked by digantverma08 | 23rd May, 2015, 01:11: PM

Expert Answer:

Factorisation of x2+2x-3 gives
x squared plus 2 x minus 3 equals x squared plus 3 x minus x minus 3 equals x open parentheses x plus 3 close parentheses minus 1 open parentheses x plus 3 close parentheses equals open parentheses x plus 3 close parentheses open parentheses x minus 1 close parentheses
If the given polynomial (x3-3x2-13x+15) is divisible by (x2+2x-3), then 
it must be divisible by its factors (x+3) and (x-1).
 
Now, by remainder theorem, if (x+3) is a factor of (x3-3x2-13x+15), then substituting x=-3
in the polynomial will give a value of zero.
open parentheses negative 3 close parentheses cubed minus 3 open parentheses negative 3 close parentheses squared minus 13 open parentheses negative 3 close parentheses plus 15 equals negative 27 minus 27 plus 39 plus 15 equals negative 54 plus 54 equals 0
Hence, (x+3) is a factor of (x3-3x2-13x+15).....(1)
 
Similarly, by remainder theorem, if (x-1) is a factor of (x3-3x2-13x+15), then substituting x=1
in the polynomial will give a value of zero.
1 cubed minus 3 cross times 1 squared minus 13 cross times 1 plus 15 equals 1 minus 3 minus 13 plus 15 equals 1 minus 16 plus 15 equals 0
 
Hence, (x-1) is also a factor of (x3-3x2-13x+15).....(2)
 
From (1) and (2), the given polynomial (x3-3x2-13x+15) is divisible by (x2+2x-3).

Answered by satyajit samal | 24th May, 2015, 08:23: AM