check whether 3x+7 is a factor of 3x³+7x
Answers
Step-by-step explanation:
To find whether
f(x) = 7+ 3xf(x)=7+3x
is a factor of
\begin{lgathered}g(x) = 3 {x}^{3} + 7x \\ \\\end{lgathered}
g(x)=3x
3
+7x
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{lgathered}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{lgathered}
f(x)=>7+3x
3x+7=0
x=
3
−7
g(x)=3x
3
+7x
g(
3
−7
)=3(
3
−7
)
3
+7(
3
−7
)
\begin{lgathered}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{lgathered}
g(
3
−7
)=3(
27
−343
)−
3
49
=−
9
343
−
3
49
=−
9
490
g(-7/3) is not zero,hence f(x) is not a factor of g(x)
Hope it helps you.
Answer:
it is not the factor of this
you can check by long division or by factorisation method!