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ICSE Class 10 Answered

Please can I get the proof for factor theorem along with its explanation
Asked by 21janhvi.verma | 28 May, 2018, 07:06: PM
answered-by-expert Expert Answer

Factor Theorem: Let f(x)  be a polynomial such that  for some constant x=a, f(a)=0. Then x-a  is a factor of f(x). Conversely, if x-a is a factor of f(x), then f(a)=0.

Proof:

Since f(a)=0 ,

by division algorithm,

we have f(x)=(x-a)q(x)+remainder,

put x=a in above

we get

remainder = zero,

so f(x)=(x-a)q(x).

Hence, (x-a) is a factor of f(x).

Answered by Arun | 29 May, 2018, 09:58: AM

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