Explanation:
To find the zeros of the quadratic function g(x) = x(x + 10) + 16 by factoring, we need to set g(x) equal to zero and solve for x.
Setting g(x) = 0:
x(x + 10) + 16 = 0
Expanding and rearranging:
x^2 + 10x + 16 = 0
Now, we can factor the quadratic expression:
(x + 2)(x + 8) = 0
To find the zeros, we set each factor equal to zero and solve for x:
x + 2 = 0 => x = -2
x + 8 = 0 => x = -8
Therefore, the zeros of the quadratic function g(x) are x = -2 and x = -8. These are also the x-intercepts of the graph of the function.