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. wilsons model?$\bigcirc$ $n^{2}+3n + 40=(n - 8)(n - 5)LXB0\bigcirc$ $n^{2}+40n + 13=(n + 8)(n + 5)$$\bigcirc$ $n^{2}+40n + 3=(n - 8)(n - 5)$

Explanation:

Step1: Identify total polynomial

Add all tile areas:
$n^2 + 5n + n + 40 + 5$

Step2: Simplify the polynomial

Combine like terms:
$n^2 + (5n + n) + (40 + 5) = n^2 + 6n + 45$
Correction: Re-identify side lengths from tiles

Step1: Find binomial factors

Left side: $n + 5$, Bottom side: $n + 8$

Step2: Expand the factors

Use distributive property:
$(n + 8)(n + 5) = n^2 + 5n + 8n + 40$

Step3: Combine like terms

Simplify the expanded form:
$n^2 + 13n + 40$

Answer:

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