Question

Which statement best describes the graph of -x3 - x2 + 4x + 4?

t starts down on the left and goes up on the right and intersects the x-axis at x = -2, 2, and 4.

It starts down on the left and goes up on the right and intersects the x-axis at x = -2, -1, and 2.

It starts up on the left and goes down on the right and intersects the x-axis at x = -2, -1, and 2.

It starts up on the left and goes down on the right and intersects the x-axis at x = -2, 2, and 4.

Answer 1

firstly factorise -x3-x2+4x+4 to find the x intercepts.
Let f(x) = -x3-x2+4x+4
By trial and error, f(-1)=-(-1)^3-2(-1)+4(-1)+4)=0
Hence, (x+1) is a factor of f(x)

By long division/inspection/synthetic division (whichever you're more comfortable with but I'm gonna use synthetic),
f(x)÷(x+1)