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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)

Verified Answer :

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 n5 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 85 = 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.

Only option b is the correct, n^2 + 13n + 40 = (n + 8)(n + 5) equation is represented by Ms. Wilson’s model.

What are polynomials?

Polynomials are those algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.

a. n^2 + 3n + 40 = (n – 8)(n – 5)

from right side

(n – 8)(n – 5) = n^2 -5n -8n + 40

                     = n^2 -13n + 40

Thus, the right side is not equal to left side.

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

from right side

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

                     = n^2 + 13n + 40

Thus, the right side is equal to left side.

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

from right side

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

= n^2 + 13n + 40

Thus, the right side is not equal to left side.

d. n^2 + 40n + 3 = (n – 8)(n – 5)

from right side

(n – 8)(n – 5) = n^2 -5n -8n + 40

                     = n^2 -13n + 40

Thus, the right side is not equal to left side.

Therefore, only option b is correct which shows how (n+8)(n+5) turns into n^2+13n+40, The other choices aren't true equations for all values of n.

Learn more about polynomials;

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