Answer: The correct option is (a) [tex]2x^2+3x-5.[/tex]
Step-by-step explanation: We are given to find the quotient in the following division :
[tex]Q=\dfrac{2x^3-3x^2-14x+15}{x-3}.[/tex]
To find the quotient, first we will try to factorize the numerator and then we will try to divide by the denominator.
We have
[tex]Q\\\\\\=\dfrac{2x^3-3x^2-14x+15}{x-3}\\\\\\=\dfrac{2x(x-3)+3x(x-3)-5(x-3)}{x-3}\\\\\\=\dfrac{(x-3)(2x^2+3x-5)}{(x-3)}\\\\=2x^2+3x-5.[/tex]
Thus, the required coefficient is [tex]2x^2+3x-5.[/tex]
Option (a) is CORRECT.
