Checkpoint: Finding Unknowns in Polynomial Equations Solution

Find the missing value when P is a whole number.
$(P x - 2) (8 x + P) = 24 x^{2} - 7 x - 6$

$8 P x^{2} + P^{2} x - 16 x - 2 P = 24 x^{2} - 7 x - 6$
$\begin{array}{rcl} \begin{matrix} 8 P x^{2} = 24 x & P^{2} x - 16 x = - 7 x & - 2 p = - 6 & Check \\ 8 P = 24 & P^{2} - 16 = - 7 & P = 3 & (3 x - 2) (8 x + 3) \\ P = 3 & P^{2} = 9 & 24 x^{2} + 9 x - 16 x - 6 \\ P = \pm 3 & 24 x^{2} - 7 x - 6 ✓ \\ P = 3 \end{matrix} \end{array}$

Note

You can solve for P using any degree of the terms. They will all result in the same solution, though some may be found in fewer steps.

If you solve for P using the degree 2 terms, remember the square root would be ± 3. However, because the directions specify a whole number, 3 is the only solution.

Q: What step will you take first to solve for P ? Explain.
A: Sample: First, I will distribute all terms so that I can decide what to compare to solve for P.