Answer:
Question #1:
f(x) = c(x - 5)(x + 5)/((x + 3)(x - 4))
f(0) = 25c/12 = 7
25c = 84
c = 84/25
f(x) = 84(x² - 25)/(x² - x - 12)
Question #2:
f(x) = (10(x - a)² + c)/((x + 4)(x - 5))
f(-3) = (10(-3 - a)² + c)/-8 = 0
f(-1) = (10(-1 - a)²) + c)/-18 = 0
10(3 + a)² + c = 0
10(1 + a)² + c = 0
9 + 6a + a² - 1 - 2a - a² = 0
8 + 4a = 0
a = -2
10 + c = 0
c = -10
f(x) = (10(x + 2)² - 10)/(x² - x - 20)
f(x) = 10(x² + 4x + 3)/(x² - x - 20)