Check whether $3x + 2$ is the factor of the polynomial $15x^2 + x - 6$.

Given :

$f(x) = 15x^2 + x - 6, g(x) =3x+2$ are the given polynomials.

To find :

We have to check g(x) is the factor of f(x).

Solution :

If g(x) is a factor of f(x) then $f(\frac{-2}{3}) = 0$.

 $f(\frac{-2}{3}) = 15 (\frac{-2}{3})^2+\frac{-2}{3}-6$

              $= 15\times \frac{4}{9} -\frac{-2}{3}-6$

              $= 5\times\frac{4}{9} -\frac{-2}{3}-6$

              $= \frac{20}{3} - \frac{-2}{3}-6$

              $= \frac{20-2-6\times3}{3}$

              $=\frac{(18-18)}{3}$

              = 0

 $f(\frac{-2}{3})=0$

Therefore, $3x+2$ is a factor of $15x^2 + x - 6$.

Tutorialspoint

Updated on: 10-Oct-2022

56 Views

Kickstart Your Career

Get certified by completing the course

Get Started