(px+q)(2x+5)=6x^2+11x+r
2px² + (5p + 2q)x + 5q = 6x² + 11x + r
Start with the x² coefficients:
2px² = 6x²
2p = 6
p = 3
Next, the x coefficients:
(5p + 2q)x = 11x
( (5)(3) + 2q) = 11
15 + 2q = 11
2q = -4
q = -2
Next, the constant terms:
5q = r
5(-2) = r
r = -10
Thus,
p = 3, q = -2, r = -10