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ICSE Class 10 Answered

I can't understand that why x-a=0 in remainder theorem
Asked by 21janhvi.verma | 29 May, 2018, 02:55: PM
answered-by-expert Expert Answer
begin mathsize 16px style To space find space the space factors space of space straight x squared plus 5 straight x plus 6 space we space equate space it space to space zero straight x squared plus 5 straight x plus 6 equals 0 so space by space spitting space middle space term straight x squared plus 3 straight x plus 2 straight x plus 6 equals 0 left parenthesis straight x plus 2 right parenthesis left parenthesis straight x plus 3 right parenthesis equals 0 so space now straight a cross times straight b equals 0 either space straight a equals 0 space or space straight b equals 0 so space straight x plus 2 equals 0 space or space straight x plus 3 equals 0 so straight x equals negative 2 space and space straight y equals negative 3 end style
similarly if 
f(x)=(x-a)(q(x))
putting x=a
we get 
f(a)=0
 
or in other words
if f(a)=0
ie x=a
subtract a on both sides
x-a=a-a
x-a=0
Answered by Arun | 29 May, 2018, 05:30: PM

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