Question

For the rational expression do the following (a) write this ratio in quotient-remainder form.(b) is x-2 a factor of 2x^2+5x-14

Answer 1

Solution

For this case we have the following expression:

$\frac{2x^2+5x-14}{x-2}$

Part a

Then we can do this:

$2x+\frac{9x-14}{x-2}=2x+9+\frac{4}{x-2}$

Part b

x-2= 0

x=2

We can replace x= 2 into the function:

$f(2)=2(2)^2+5(2)-14=4$

Since f(2) is not equal to 0 then we can conclude that x-2 is not a factor of 2x^2 +5x-14