Apolynomial has been factored below, but some constants are missing.
3x^3+6x^2-24x=ax(x+b)(x+c)
what are the missing values of a, b, and c

a=3, b=4, and c=-2

Step-by-step explanation:

3x^3+6x^2-24x

Each of the three terms has a common factor of 3x.

3x(x^2+2x-8)

Now can you think of two numbers that multiply to be -8 and add to be 2?

How about 4 and -2? 4(-2)=-8 and 4+(-2)+2.

So the factored form of x^2+2x-8 is (x+4)(x-2).

We can check this by using foil.

First: x(x)=x^2

Outer: x(-2)=-2x

Inner:  4(x)=4x

Last: 4(-2)=-8

Add them up! This gives you x^2+2x-8 which is the desired result.

So the factored form of 3x^3+6x^2-24x is 3x(x+4)(x-2).

Comparing 3x(x+4)(x-2) to ax(x+b)(x+c) gives us  a=3, b=4, and c=-2

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

look at the picture i have filled out a table for it. hope this .