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(3x²-x-2) (x+2) -first choice

Step-by-step explanation:

First we notice that when x → - ∞ the y or f(x) → -∞ because the graph goes on the negative side of the y-axis (down) as we move on the left ( where x is negative)

Second we notice that the graph touches the x-axis at x= -2 so one of the roots is -2

The equation (3x²-x-2) (x+2) has a root at -2 because x+2= 0 will give x=-2

d.) yes, because the volume of the cone is greater than the volume of the sphere

step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.