Select the correct answer.
Which point is a point where the graph of crosses the -axis?
A.
B.
C.
D.

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Mar 30,2025

Question

Select the correct answer. Which point is a point where the graph of $$ y=(x+2)\left(x^{2}+4 x+3\right) $$ crosses the $$ x $$-axis? A. $$ (-3,0) $$ B. $$ (2,0) $$ C. $$ (1,0) $$ D. $$ (3,0) $$

UpStudy AI · Accepted Answer

1. Write the equation $$ y=(x+2)\left(x^2+4x+3\right) $$.

2. Factor the quadratic term:
   $$
   x^2+4x+3 = (x+1)(x+3)
   $$

3. The factored form of the equation is:
   $$
   y=(x+2)(x+1)(x+3)
   $$

4. For the graph to cross the $$ x $$-axis, set $$ y=0 $$:
   $$
   (x+2)(x+1)(x+3)=0
   $$

5. Set each factor equal to 0 and solve for $$ x $$:
   $$
   x+2=0 \quad \Rightarrow \quad x=-2
   $$
   $$
   x+1=0 \quad \Rightarrow \quad x=-1
   $$
   $$
   x+3=0 \quad \Rightarrow \quad x=-3
   $$

6. The zeros of the function are at $$ x=-2 $$, $$ x=-1 $$, and $$ x=-3 $$. Among the given choices, the point corresponding to a zero is:
   $$
   (-3,0)
   $$

7. Therefore, the correct answer is:
   
   A. $$ (-3,0) $$
The correct answer is $$ (-3,0) $$, choice A.

Select the correct answer.
Which point is a point where the graph of crosses the -axis?
A.
B.
C.
D.

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Select the correct answer. Which point is a point where the graph of crosses the -axis? A. B. C. D.