Question 156593
Given:
{{{(p^3-4p)/(p^2-49)}}}
Find the values of p for which the given expression is undefined.
An expression is "undefined" if its denominator is zero, so you want to find which values of p will make the denominator zero. You can leave the numerator as is and concentrate on the denominator:
{{{(p^3-4p)/(p^2-49)}}} Factor the denominator.  You have done this correctly!
{{{(p^3-4p)/(p-7)(p+7)}}}
Now look at the factors in the denominator to see what values of p will make either factor zero.
{{{p-7 = 0}}}, so {{{p = 7}}} is an "excluded" value.
{{{p+7 = 0}}}, so {{{p = -7}}} is an "excluded" value.
So that p = 7 and p = -7 are the values of p that will render the expression "undefined"