Answer :
[tex] (x-p)(2x^2+9x+10)=(x^2-4)(2x+q)\\
(x-p)(2x^2+4x+5x+10)=(x-2)(x+2)(2x+q)\\
(x-p)(2x(x+2)+5(x+2))=(x-2)(x+2)(2x+q)\\
(x-p)(2x+5)(x+2)=(x-2)(x+2)(2x+q)\\
(x-p)(x+2)(2x+5)=(x-2)(x+2)(2x+q)\\
\Downarrow\\
p=2\\
q=5[/tex]
(x - p)(2x² + 9x + 10) = (x² - 4)(2x + q)
2x³ + 9x² + 10x - 2px² - 9px - 10p = 2x³ + qx² - 8x - 4q
-2x³ -2x³
9x² + 10x - 2px² - 9px - 10p = qx² - 8x - 4q
+8x +8x
9x² + 18x - 2px² - 9px = qx² - 4q
2x³ + 9x² + 10x - 2px² - 9px - 10p = 2x³ + qx² - 8x - 4q
-2x³ -2x³
9x² + 10x - 2px² - 9px - 10p = qx² - 8x - 4q
+8x +8x
9x² + 18x - 2px² - 9px = qx² - 4q