Let us find the points where the graph of [tex]\( y = (x + 2)(x^2 + 4x + 3) \)[/tex] crosses the x-axis. These are the points where [tex]\( y = 0 \)[/tex].
1. Start with the equation:
[tex]\[
y = (x + 2)(x^2 + 4x + 3)
\][/tex]
2. Set [tex]\( y \)[/tex] to 0, as we are looking for the x-intercepts:
[tex]\[
0 = (x + 2)(x^2 + 4x + 3)
\][/tex]
3. Now, solve the equation by finding the roots of each factor.
4. The first factor [tex]\( (x + 2) \)[/tex]:
[tex]\[
x + 2 = 0 \implies x = -2
\][/tex]
5. The second factor [tex]\( (x^2 + 4x + 3) \)[/tex]:
[tex]\[
x^2 + 4x + 3 = 0
\][/tex]
This can be factored further:
[tex]\[
(x + 3)(x + 1) = 0
\][/tex]
6. Solve each factor:
[tex]\[
x + 3 = 0 \implies x = -3
\][/tex]
[tex]\[
x + 1 = 0 \implies x = -1
\][/tex]
So, the x-intercepts for the equation [tex]\( y = (x + 2)(x^2 + 4x + 3) \)[/tex] are [tex]\( x = -3, x = -2, \)[/tex] and [tex]\( x = -1 \)[/tex]. Therefore, the points where the graph crosses the x-axis are [tex]\((-3, 0)\)[/tex], [tex]\((-2, 0)\)[/tex], and [tex]\((-1, 0)\)[/tex].
Given the choices:
A. [tex]\((-3, 0)\)[/tex]
B. [tex]\((2, 0)\)[/tex]
C. [tex]\((1, 0)\)[/tex]
D. [tex]\((3, 0)\)[/tex]
The correct point where the graph crosses the x-axis is:
[tex]\[
\boxed{(-3, 0)}
\][/tex]
