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

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#### Solution 1

7 + 3x will be a factor of 3x^{3} + 7x only if 7 + 3x divides 3x^{3} + 7x leaving no remainder.

Let p(x) = 3x^{3} + 7x

7 + 3x = 0

⇒ 3x = -7

`⇒ x = -7/3`

`therefore"Remainder "= 3(-7/3)^3+7(-7/3)`

`= -343/9-49/3`

`= -490/9`

`≠ 0`

∴ 7 + 3*x* is not a factor of 3*x*^{3} + 7*x*.

#### Solution 2

Let us divide (3*x*^{3} + 7*x*) by (7 + 3*x*). If the remainder obtained is 0, then 7 + 3*x *will be a factor of 3*x*^{3} + 7*x*.

By long division,

As the remainder is not zero, therefore, 7 + 3*x* is not a factor of 3*x*^{3} + 7*x*.

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