Question

1. rei.c.7

find the point of intersection between the two following polynomial functions:
f(x)=(x-3)(x+2) g(x)=(x+2)

Explanation:

Step1: Set \( f(x) = g(x) \)

To find the intersection point of two functions \( f(x) \) and \( g(x) \), we set them equal: \( (x - 3)(x + 2)=(x + 2) \)

Step2: Move all terms to left side

Subtract \( (x + 2) \) from both sides: \( (x - 3)(x + 2)-(x + 2)=0 \)

Step3: Factor out \( (x + 2) \)

Using the distributive property (factoring), we get \( (x + 2)[(x - 3)-1]=0 \), which simplifies to \( (x + 2)(x - 4)=0 \)

Step4: Solve for \( x \)

Set each factor equal to zero:

• For \( x + 2 = 0 \), we have \( x=-2 \)
• For \( x - 4 = 0 \), we have \( x = 4 \)

Step5: Find corresponding \( y \)-values

Since \( g(x)=x + 2 \), when \( x=-2 \), \( y=g(-2)=-2 + 2=0 \); when \( x = 4 \), \( y=g(4)=4 + 2=6 \)

Answer:

The points of intersection are \( (-2,0) \) and \( (4,6) \)