Question 211249
Remeber the "zero product" rule?
If {{{a*b = 0}}} the either {{{a = 0}}} or {{{b = 0}}} or both.
Your work so far is immpecable. When you get to the line:
{{{0 = 4(2+x)(2-x)}}} Apply the zero product rule:
{{{4 = 0}}} Clearly not true.
{{{2+x = 0}}} thus {{{ x = -2}}}
{{{2-x = 0}}} thus {{{x = 2}}}
You can ignore the 4 as it is not pertinent to the x-intercepts.
Another way to look at doing this problem (if the 4 still bothers you) is:
{{{-4x^2+16 = 0}}} Divide both sides by -4.
{{{x^2-4 = 0}}} Factor.
{{{(x-2)(x+2) = 0}}} Apply the zero product rule.
{{{x-2 = 0}}} or {{{x+2)= 0}}} so...
{{{x = 2}}} or {{{x = -2}}} and these are the x-intercepts.
{{{graph(400,400,-5,5,-5,20,-4x^2+16)}}}