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Check whether 7+3xis a factor of 3x^3+7x...

Check whether `7+3x`is a factor of `3x^3+7x`.

Text Solution

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Let `p(x)=3x^(3)+7x and g(x)=7+3x`. Then,
`g(x)=0rArr7+3x=0rArr3x=-7rArrx=(-7)/(3)`.
By the remainder theorem , we know that when p (x) is divided by `(7+3x)` then the remainder is `p((-7)/(3))`.
Now , `p((-7)/(3))={3xx((-7)/(3))^(3)+7xx((-7)/(3))}={3xx((-343))/(27)-(49)/(3)}`
`=((-343)/(9)-(49)/(3))=((-343-147)/(9))=(-490)/(9)ne0`.
Thus , when p (x) is divided by g (x) , the remainder is divided by g (x) , the remainder is nonzero .
`therefore(7+3x)` is not a factor of `(3x^(3)+7x)`.
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