Question

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 1

Sample Response: The value of m must be greater than the value of n. When you multiply the binomials, the middle term is the result of combining the outside and inside products. So, bx = –nx + mx, or bx = (–n + m)x. This means that b = –n + m. When adding numbers with opposite signs, you subtract their absolute values, and keep the sign of the number having the larger absolute value. Since b is positive, m must have the larger absolute value

Answer 2

Answer:

The value of m must be greater than the value of n.

The coefficient of the middle term, b, is the sum of m and –n.

The factor with the greater absolute value has the sign of the middle term.

Since b is positive, m must have the larger absolute value.