Answer and Explanation
The zeros of a factored polynomial function are the places where each factor is equal to zero, and this correlates to the x-coordinates of the function's x-intercepts.
We are given the function:
[tex]g(x)=(x+4)(x-7)[/tex]
To find its zeros, we can:
- set the function equal to zero (as this will give us the x-values when the function output is 0 ... i.e. the x-intercepts)
- split it into two equations using the zero product property
- solve for x
↓↓↓
1. [tex](x+4)(x-7)=0[/tex]
2. [tex]x+4=0[/tex] or [tex]x-7=0[/tex]
3. [tex]x=-4[/tex] or [tex]x=7[/tex]
So, we can make the following statements about g(x):
- g(x) = 0 when x = -4 and when x = 7.
- The graph of g(x) intercepts the x-axis at x = -4 and x = 7.
- The zeros of g are -4 and 7.
