Question

Which point is a point where the graph of y= (x + 2)(x2 + 4x + 3) crosses the x-axis?O A. (-3,0)OB. (2,0)O C. (1,0)OD.(3,0)

Answer 1

Given:

`y=x+2\mleft(x^2+4x+3\mright)`

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:

`0=(x+2)(x^2+4x+3)`
`\begin{gathered} 0=x+2 \\ x\text{ = -2} \\ (-2,\text{ 0)} \end{gathered}`
`\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}`

The x-intercepts are:

(-2, 0), (-1, 0), and (-3, 0)

The option that corresponds here is choice A.

ANSWER:

a. (-3, 0)