Last week, Emily and Stephanie decided to see how fast they could sprint 300 meters. They asked their friend Kevin to time them
with a stopwatch. After 3.29 minutes, Kevin agreed to time the runners. Emily sprinted first and ran 300 meters in 58.81 seconds. When it was Stephanie's turn, she sped off and completed the run in 50.61 seconds. How much faster was Stephanie than Emily in seconds?
Let denote a constant (a number, rather than a variable like .)
Let denote an expression about (for example,
By the factor theorem, if is a factor of , then . In other words, if all mentions of in the expression are replaced with , then the expression should evaluate to zero.
is equivalent to . That is: .
Replace all mentions of in by to get:
.
That should evaluate to zero. Therefore: . Solve for to get .