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Question
Check whether 7 + 3x is a factor of 3x3 + 7x.
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Solution 1
7 + 3x will be a factor of 3x3 + 7x only if 7 + 3x divides 3x3 + 7x leaving no remainder.
Let p(x) = 3x3 + 7x
7 + 3x = 0
⇒ 3x = −7
⇒ x = `-7/3`
∴ Required remainder
`f(7/3) = 3(-7/3)^3 + 7(-7/3)`
= `3(-343/27) - 49/3`
= `-343/9-49/3`
= `-490/9`
Since `p(-7/3)` ≠ 0
∴ 7 + 3x is not a factor of 3x3 + 7x.
Solution 2
Let us divide (3x3 + 7x) by (7 + 3x). If the remainder obtained is 0, then 7 + 3x will be a factor of 3x3 + 7x.
By long division,
As the remainder is not zero, therefore, 7 + 3x is not a factor of 3x3 + 7x.
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