Given that

(x-p)(2x²+9x+10)=(x²-4)(2x+q)

for all values of x, find the constants p and q.

\((x-p)(2x^2+9x+10)=(x^2-4)(2x+q)\\ (x-p)(2x^2+4x+5x+10)=(x-2)(x+2)(2x+q)\\ (x-p)(2x(x+2)+5(x+2))=(x-2)(x+2)(2x+q)\\ (x-p)(2x+5)(x+2)=(x-2)(x+2)(2x+q)\\ (x-p)(x+2)(2x+5)=(x-2)(x+2)(2x+q)\\ \Downarrow\\ p=2\\ q=5\)

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Panoyin Panoyin · Answer 2 · 2015-03-19T19:53:30-04:00

(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

Given that(x-p)(2x²+9x+10)=(x²-4)(2x+q)for all values of x, find the constants p and q.

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Given that

(x-p)(2x²+9x+10)=(x²-4)(2x+q)

for all values of x, find the constants p and q.