Answer: The answer is (3x - 8).
Step-by-step explanation: The given algebraic expression is
[tex]E=\dfrac{6x^2-x-40}{5+2x}.[/tex]
We are given to find the quotient here. For that, first we will try to factorise the numerator and then we will try to cancel the common term with the denominator as follows:
[tex]E\\\\\\=\dfrac{6x^2-x-40}{5+2x}\\\\\\=\dfrac{6x^2-16x+15x-40}{5+2x}\\\\\\=\dfrac{2x(3x-8)+5(3x-8)}{5+2x}\\\\\\=\dfrac{(2x+5)(3x-8)}{5+2x}\\\\\\=3x-8.[/tex]
Thus, the quotient is (3x - 8).
