Question

check whether 7+3x is a factor of 3x³+7x​

Answer 1

Answer:

Assume 7+3x is a factor of  3x³+7x

7+3x=0

3x=-7

x=-7/3

substituting x=-7/3 in the expression we get ,

3(-7/3)³+7(-7/3)=  -490/9

there for it is not a factor (since g(-7/3) is not zero)

hope it helps...

Answer 2

$\huge\underline\mathfrak{Answer\::-}$

g(x) = 0

7 + 3x = 0

3x = -7

$\bold{x=}$$\sf\dfrac{-7}{3}$

$\star$ $\sf\underline{\:\:Put\: x=}$ $\sf\dfrac{-7}{3}$ $\sf\underline{in\:\:p(x)}$

$\implies \sf \: 3 \bigg( \frac{ - 7}{3} \bigg) {}^{ 3} + 7 \bigg( \frac{ - 7}{3} \bigg) \\ \\ \\ \implies \sf \: 3 \bigg( \frac{ - 343}{27} \bigg) + \bigg( \frac{ - 49}{3} \bigg) \\ \\ \\ \implies \sf \frac{ - 343}{9} - \frac{49}{3} \\ \\ \\ \implies \sf \blue{ \frac{ - 490}{9} }$

_____________________

$\therefore$ 7 + 3x is not the factor of 3x² + 7x as the remainder is not zero.