Question

check whether 7 + 3 X is a factor of 3 x cube + 7 x

Answer 1

Hello dear friend.....

Here is Ur answer .
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Sol.

The zero of 7 + 3x is -7/3
by remainder theorem,
when 3x³+7x is divided by 7+3x,
the remainder is -7/3

$= > p(x) = {3x}^{2} + 7x \\ \\ = > p( \frac{ - 7}{3} ) = 3( { \frac{ - 7}{3}) }^{3} + 7( \frac{ - 7}{3} ) \\ \\ = > \frac{ - 1029}{27} + \frac{ - 49}{3} \\ \\ = > \frac{( - 1029) + ( - 441)}{27} \\ \\ = > \frac{1470}{27} \\ \\ the \: \: required \: \: remainder \: is \: not \: zero$
so, 3x³+7x is not a factor of 7+3x .

Hope it's helps you.
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