The trinomial x2 + bx – c has factors of (x + m)(x – n), where m, n, and b are positive. What is the relationship between the values of m and n? Explain.

Answer:

Since the trinomial is $x^2 + bx - c$ and its factors are $(x + m)(x - n)$, we know that $m + (-n) = b$ and $m(-n) = -c$. Because $b$ is positive, the sum of $m$ and $-n$ must be positive. This means the positive value, $m$, must have a greater absolute value than the negative value, $n$. Therefore, $m$ must be greater than $n$.