Question

Check whether 7 + 3x is a factor of 3x~ + 7x.​

Answer 1

$\huge\underline\mathbb\blue{ANSWER}$

$Let \: p(x) = 3 {x}^{3} + 7x \\ Divisor \: is \: 7 + 3x \\ So \: take, \: 7 + 3x = 0 \\ = > x = - \frac{7}{3}$

$Put \: \: \: x = - \frac{7}{3} \: \: \: in \: \: p(x), \: we \: get:$

$p( - \frac{7}{3} ) = 3{( - \frac{7}{3} ) }^{3} + 7( - \frac{7}{3} ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3 \times \frac{ - 343}{27} - \frac{49}{3} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - \frac{ 343}{9} - \frac{49}{3} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ - 343 - 147}{9} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ - 490}{9} ≠ 0$

$Since \: remainder \: is \: not \: zero, \: so, \: 7 + 3x \: is \: not\: the \: factor \: of \: 3 {x}^{3} + 7x$

Hope it's helpful ✅✅✅

Answer 2

Step-by-step explanation:

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