Let l(f) be the second derivative of f**7/735 + f**6/140 + f**5/105 - 23*f**2 + 25*f. Let d(p) be the first derivative of l(p). Suppose d(g) = 0. Calculate g.

Suppose 3*w + 19*w - 109 = 111. Let a(p) be the first derivative of 9 + ³⁵⁄₃*p3 - ⁴⁵⁄₂*p2 + w*p. Determine t, given that a(t) = 0.

²⁄₇, 1

Let c(u) be the second derivative of -u⁵⁄₆₀ + 8*u⁴⁄₃ + 1591*u. Factor c(w).

-w*2(w - 96)/3

Let q(s) be the third derivative of ¹⁄₈*s4 + 0 + 0*s3 - 7*s + 5*s2 - ¹⁄₈₀*s5. Factor q(o).

-3o(o - 4)/4

Let t(o) be the third derivative of -2*o2 - ¹⁄₁₀₅*o7 - ¹⁄₃*o4 + ¹⁄₂₀*o6 + 0 + 0*o5 + 0*o3 + 3*o. What is m in t(m) = 0?

-1, 0, 2

Let q(j) be the first derivative of -j⁴⁄₃₀ + 26*j³⁄₉ + 133*j**²⁄₁₅ + 134*j/15 + 1274. Factor q(m).

-2(m - 67)(m + 1)**²⁄₁₅

Let z(b) be the first derivative of 5*b5 + 155*b⁴⁄₄ + 38*b3 - 86*b2 + 40*b + 513. Factor z(f).

(f + 2)(f + 5)(5*f - 2)**2

Factor ¹⁄₆*n**2 - 17 + ⁴⁹⁄₆*n.

(n - 2)*(n + 51)/6

Factor -20*t**2 + 42*t + 30*t + 740 - 11*t + 24*t + 20*t.

-5(t + 4)(4*t - 37)

Let u(a) be the third derivative of 43*a⁵⁄₁₀ - 23*a⁴⁄₃ + 4*a³⁄₃ - a2 + 684*a. Factor u(p).

2*(3p - 2)(43*p - 2)

Let x be ⁶⁄₁₆39/(-18)(-16)/52. Let c(a) be the second derivative of ¹⁄₂*a3 + 0 - x*a4 + 0*a**2 + 18*a. Factor c(i).

-3i(i - 1)