1.

If the polynomials f(x) `=x^(2)+5x-pandg(x)=x^(2)-2x+6p` have a common factor , then find the common factor .A. `x+2`B. xC. `x+4`D. Either (b) or (c )

Answer» Given , `f(x)=x^(2)+5x-pandg(x)=x^(2)-2x+6p`
Let ` x- k` be the common factor of `f (x) and g(x)`.
`:.f(x)=0andg(k)=0`
`rArrk^(2)+5k-p=0` (1)
`k^(2)=2k+6p=0` (2)
From Eqs . (1) and (2) , we get
`k=p`
substitute k = p in Eq . (1) , we have
`p^(2)+5p-p=0`
`p^(2)+4p=0rArrp=0`
or `p=-4`
`:.xorx+4` is a common factor of f(x) and g(x).


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