Question

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

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

Answer Choices:

A.) n2 + 3n + 40 = (n – 8)(n – 5)

B.) n2 + 13n + 40 = (n + 8)(n + 5)

C.) n2 + 40n + 13 = (n + 8)(n + 5)

D.) n2 + 40n + 3 = (n – 8)(n – 5)

Answer:

B.) n2 + 13n + 40 = (n + 8)(n + 5)

Step-by-step explanation:

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Answer 2

Answer: Choice B)

Here's why:

Focus on right side only. We have (n+8)(n+5).

Let's use FOIL to expand that out

F = first means we multiply the first terms n and n to get n^2
O = outer tells us to multiply the outer terms n and 5 to get n*5 or 5n
I = inner tells us to multiply the inner expressions 8 and n to get 8n
L = last meaning we multiply 8 and 5 to get 8*5 = 40

Add up those results: n^2+5n+8n+40 = n^2+13n+40

Notice how the like terms (5n and 8n) combine to have the expression simplify a bit.

This shows how (n+8)(n+5) turns into n^2+13n+40, which is why choice B is the answer. The other choices aren't true equations for all values of n.