Question

Select the correct answer from each drop-down menu. Consider this expression. -3x^2-24x-36 what expression is equivalent to the given expression?

Answer 1

-3(x+2)(x+6)

Explanation:

PLATO

Answer 2

To find the equivalent expression, we need to put the equation in the form:

`a(x-x_1)(x-x_2)`

Where x1 and x2 are the roots of the equation.

So the first step is to find those roots, using the quadratic formula:

`\begin{gathered} -3x^2-24x-36 \\ a=-3,b=-24,c=-36 \\ x_1=(-b+√(b^2-4ac))/(2a)=(24+√(576-4\cdot(-3)\cdot(-36)))/(-6) \\ x_1=(24+√(576-432))/(-6)=(24+√(144))/(-6)=(24+12)/(-6)=(36)/(-6)=-6 \\ x_2=(-b-√(b^2-4ac))/(2a)=(24-√(144))/(-6)=(24-12)/(-6)=(12)/(-6)=-2 \end{gathered}`

So now we have the values of a, x1 and x2, so our equation will be:

`-3x^2-24x-36=-3(x+6)(x+2)=-3(x+2)(x+6)`

So the options to select are -3, 2 and 6.