To find the equivalent expression, we need to put the equation in the form:
[tex]a(x-x_1)(x-x_2)[/tex]Where x1 and x2 are the roots of the equation.
So the first step is to find those roots, using the quadratic formula:
[tex]\begin{gathered} -3x^2-24x-36 \\ a=-3,b=-24,c=-36 \\ x_1=\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{24+\sqrt{576-4\cdot(-3)\cdot(-36)}}{-6} \\ x_1=\frac{24+\sqrt{576-432}}{-6}=\frac{24+\sqrt{144}}{-6}=\frac{24+12}{-6}=\frac{36}{-6}=-6 \\ x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}=\frac{24-\sqrt{144}}{-6}=\frac{24-12}{-6}=\frac{12}{-6}=-2 \end{gathered}[/tex]So now we have the values of a, x1 and x2, so our equation will be:
[tex]-3x^2-24x-36=-3(x+6)(x+2)=-3(x+2)(x+6)[/tex]So the options to select are -3, 2 and 6.
