Question

Ms. Wilson draws a model of the factorization of a polynomial with integer factors. Her model is partially complete.

A 2-column table with 2 rows. First column is labeled n with entries n squared, 5 n. Second column is not labeled with entries blank, 40. First row is not labeled with entries n squared, blank. Second row is labeled 5 with entries 5 n, 40.

Which equation is represented by Ms. Wilson’s model?

n2 + 3n + 40 = (n – 8)(n – 5)
n2 + 13n + 40 = (n + 8)(n + 5)
n2 + 40n + 13 = (n + 8)(n + 5)
n2 + 40n + 3 = (n – 8)(n – 5)

Answer 1

The model shows factors n and 5, and the missing column label must be 8 since 5·8 = 40. The middle term is 5n + 8n = 13n. So the equation is

n^2 + 13n + 40 = (n + 8)(n + 5).