What are the roots of (3x^3 + 8x^2 + 4x)(x^2 + 3x – 4)?

Let f(x) = (3x^3 + 8x^2 + 4x)(x^2 + 3x –
4).

We need to find the roots of the function
f(x).

First we will factor and simplify the
function.

We notice that f(x) is a product of two
terms.

Let us simplify each
term.

==> (3x^3 + 8x^2 +
4x)

We will factor x from all
terms.

==> 3x^3 + 8x^2 + 4x = x( 3x^2 + 8x +
4).

Now we will factor between
brackets.

==> (3x^3 + 8x^2 + 4x = x(
3x+2)(x+2)

Now we will factor the second
term.

(x^2 + 3x - 4) = (
x+4)(x-1).

Now we will rewrite the function
f(x).

f(x) =
x(3x+2)(x+2)(x+4)(x-1).

Now we have 5 roots for the
function.

x1= 0, x2= -2/3, x3=-2, x4= -4 ,and x5=
1

==> x= { 0, -2/3, -2, -4,
1}