Question

given that m-2 is a positive number and a factor of 3m^2 -2m +10 .find the sum of all value of m​

Answer 1

Given data (corrected):

$(m-2)$ is a positive number and a factor of the polynomial $3m^{2}-2m-8$

To find:

The sum of all the values of $m$

Step-by-step explanation:

Now, $3m^{2}-2m-8$

$=3m^{2}-6m+4m-8$

$=3m(m-2)+4(m-2)$

$=(m-2)(3m+4)$

This shows that the factors of $3m^{2}-2m-8$ are $(m-2)$ and $(3m+4)$

$\Rightarrow m=2,-\dfrac{4}{3}$

Therefore the sum of all the values of $m$ is

$=2+(-\dfrac{4}{3})$

$=2-\dfrac{4}{3}$

$=\dfrac{6-4}{3}$

$=\dfrac{2}{3}$

Answer:

The sum of all the values of $m$ is $\dfrac{2}{3}$.