Q. 307 - Intermediate Algebra

Question

Solve the exercise

$16p^3=24p^2+9p$

Step-by-Step Solution

Answer

The equation has no solution, it is prime.

Step 1. Given information

The given equation is  $16p^3=24p^2+9p$

Step 2. Simplifying the equation

$$\begin{gathered} (a - b)(a + b) = 0 \\ a - b = 0 or a + b = 0 \\ \mathrm{a}=\mathrm{b} \mathrm{or} \mathrm{a}=-\mathrm{b} \\ \mathrm{Simplify} \mathrm{the} \mathrm{quadratic} \mathrm{expression}: \\ 1{\mathrm{p}}^3 = 24{\mathrm{p}}^2 + 9\mathrm{p} [\mathrm{Given} \mathrm{the} \mathrm{expression}] \\ 16{\mathrm{p}}^3- 24{\mathrm{p}}^2 - 9\mathrm{p} = 0 [\mathrm{Write} \mathrm{the} \mathrm{quadratic} \mathrm{equation} \mathrm{of} \mathrm{standard} \mathrm{form}] \\ 16{\mathrm{p}}^3 - 24{\mathrm{p}}^2 - 9\mathrm{p} = 0 [\mathrm{There} \mathrm{is} \mathrm{no} \mathrm{factor}] \\ \mathrm{Expression} \mathrm{has} \mathrm{not} \mathrm{factors} \mathrm{so}, \mathrm{it} \mathrm{is} \mathrm{prime} \end{gathered}$$