MathDB
Polynomial Symmetry

Source: 2022 AMC 10A #16 / 2022 AMC 12A #15

November 11, 2022
algebraAMCAMC 102022 AMC2022 AMC 10a2022 AMC 12AAMC 12

Problem Statement

The roots of the polynomial 10x339x2+29x610x^3 - 39x^2 + 29x - 6 are the height, length, and width of a rectangular box (right rectangular prism. A new rectangular box is formed by lengthening each edge of the original box by 2 units. What is the volume of the new box?
<spanclass=latexbold>(A)</span>245<spanclass=latexbold>(B)</span>425<spanclass=latexbold>(C)</span>815<spanclass=latexbold>(D)</span>30<spanclass=latexbold>(E)</span>48<span class='latex-bold'>(A) </span>\frac{24}{5}\qquad<span class='latex-bold'>(B) </span>\frac{42}{5}\qquad<span class='latex-bold'>(C) </span>\frac{81}{5}\qquad<span class='latex-bold'>(D) </span>30\qquad<span class='latex-bold'>(E) </span>48