Given:
[tex]y=x+2\mleft(x^2+4x+3\mright)[/tex]The point where the graph crosses the x-axis is the x-intercept. At x-intercept, the y-coordinate is always zero.
Set y = 0 and solve for x, to find the x-intercept.
Therefore, the x-intercept of the graph is the following:
[tex]0=(x+2)(x^2+4x+3)[/tex][tex]\begin{gathered} 0=x+2 \\ x\text{ = -2} \\ (-2,\text{ 0)} \end{gathered}[/tex][tex]\begin{gathered} 0=x^2+4x+3 \\ \text{Factorize:} \\ 0\text{ = }x^2+x+3x+3 \\ 0\text{ = (x+1)(x+3)} \\ \\ 0\text{ = x+1} \\ x\text{ = -1} \\ (-1,\text{ 0)} \\ \\ 0\text{ = x + 3} \\ x\text{ = -3} \\ (-3,\text{ 0)} \end{gathered}[/tex]The x-intercepts are:
(-2, 0), (-1, 0), and (-3, 0)
The option that corresponds here is choice A.
ANSWER:
a. (-3, 0)
