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
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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