Question

Check whether 7+3x is factor of 3xpower 3 +7x

Answer 1

To find whether

f(x) = 7+ 3x is a factor of

$\begin{gathered}g(x) = 3 {x}^{3} + 7x \\ \\ \end{gathered}$

find the value of x from f(x) and put to g(x) ,if expression becomes zero than f(x) is a factor of g(x),otherwise not

$\begin{gathered}f(x)= > 7+3x\\\\3x+7=0\\\\x=\frac{-7}{3} \\\\g(x)=3 {x}^{3} + 7x\\\\g(\frac{-7}{3})=3\Big({\frac{-7}{3}}\Big)^3 + 7 \Big(\frac{-7}{3}\Big)\\\end{gathered}$

$\begin{gathered}g\Big(\frac{-7}{3}\Big)=3\Big(\frac{-343}{27}\Big)-\frac{49}{3}\\\\=-\frac{343}{9}-\frac{49}{3}\\\\= -\frac{490}{9}\\\\\end{gathered}$

g(-7/3) is not zero,hence f(x) is not a factor of g(x)