$$Question: Find the cubic polynomial $ h(x) $ such that $ h(1) = 3 $, $ h(2) = 12 $, $ h(3) = 27 $, and $ h(4) = 48 $.

Thu, 30 Apr 2026 05:05:20 +0000

**Find the cubic polynomial $ h(x) $ such that $ h(1) = 3 $, $ h(2) = 12 $, $ h(3) = 27 $, and $ h(4) = 48 $.** Curious minds often search for patterns hidden beneath everyday numbers—patterns that reveal deeper logic in data, trends, or growth. The equation $ h(1) = 3 $, $ h(2) = 12 $, $ h(3) = 27 $, $ h(4) = 48 $ is more than a math problem—it’s a gateway to understanding how cubic relationships model real-world change. This cubic polynomial reflects how values scale nonlinearly in complex systems, offering insight that’s increasingly relevant in analytics, finance, and technology sectors across the US. Why is this equation trending now? In an era shaped by data-driven decisions, understanding growth patterns helps industries forecast performance, optimize models, and innovate. New approaches to algorithmic scaling and predictive modeling are fueling interest in polynomials that capture nuanced change across discrete points—exactly what this cubic encapsulates. While simple in form, its structure reveals deeper principles of interpolation and polynomial behavior. To determine $ h(x) = ax^3 + bx^2 + cx + d $, we begin by substituting $ x = 1, 2, 3, 4 $ into the general cubic equation, yielding a system of four linear equations. Using known values: