A manufacturer of calculators found that the number of calculators sold at a price of \( p \) dollars is given by the polynomial \( 32,000-200 \mathrm{p} \). Write \( 32,000-200 \mathrm{p} \) in factored form.

To factor the polynomial \( 32,000 - 200p \), we can first take out the greatest common factor (GCF). The GCF of \( 32,000 \) and \( 200 \) is \( 200 \). So, we factor it out: \( 32,000 - 200p = 200(160 - p) \). Thus, the factored form is \( 200(160 - p) \). --- You might find it interesting that this linear expression tells us a lot about market dynamics. Specifically, the term \( 160 - p \) suggests that as the price increases, sales will decrease, demonstrating the law of demand in economics. This simple polynomial can guide manufacturers in setting prices to optimize their sales! Another fun fact is that understanding these mathematical concepts can help in developing better strategies for pricing and inventory management. If a manufacturer knows the relationship between price and sales volume, they can adjust prices strategically to maximize profits or move excess inventory more efficiently. It’s like having a secret weapon for business success!