Mathematics

The core concept here is the Factor Theorem: if a number is a zero of a polynomial, then the corresponding linear expression is a factor. Since $5$ makes $p(x)$ equal to zero, you can "reverse engineer" which binomial must divide evenly into $p(x)$. Think about what linear factor, when set equal to zero, gives you $x = 5$.

The core concept here is the Factor Theorem: if a number is a zero of a polynomial, then the corresponding linear expression is a factor. Since $5$ makes $p(x)$ equal to zero, you can "reverse engineer" which binomial must divide evenly into $p(x)$. Think about what linear factor, when set equal to zero, gives you $x = 5$.