Answer:
Option: D is the correct answer.
D. The quotient is 2x-6 with no remainder.
Step-by-step explanation:
We are given a polynomial as:
[tex]2x^2-2x-12[/tex]
We know that any polynomial equation p(x) may be represented as:
[tex]p(x)=q(x).s(x)+r(x)-----------(1)[/tex]
where q(x) is the quotient , s(x) is the divisor and r(x) is the remainder.
We may also represent this polynomial as follows:
[tex]2x^2-2x-12=2(x^2-x-6)\\\\\\2x^2-2x-12=2(x^2-3x+2x-6)\\\\\\2x^2-2x-12=2(x(x-3)+2(x-3))\\\\\\2x^2-2x-12=2(x+2)(x-3)\\\\\\2x^2-2x-12=(x+2)\cdot (2(x-3))\\\\\\2x^2-2x-12=(x+2)\cdot (2x-6)[/tex]
This means that on dividing the polynomial with (x+2); the quotient is: 2x-6 and remainder is zero.
( Since on comparing the equation with equation (1) )
