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

Let q = 3991 + -³¹⁹²⁷⁄₈. Let p(a) be the first derivative of -10 - q*a2 + ¹⁄₁₆*a4 + 0*a + ¹⁄₁₂*a3 - ¹⁄₂₀*a5. Factor p(f).

-f*(f - 1)*2(f + 1)/4

Suppose 81*u3 + ²¹⁸⁷⁄₂ + 567*u2 - ³⁄₂*u5 - ⁹⁄₂*u4 + ²⁶⁷³⁄₂*u = 0. What is u?

-3, 9

Let 30*n2 - 8*n4 - 3510*n3 + 5*n - 3506*n3 - 22*n4 + 7011*n3 = 0. Calculate n.

-1, -¹⁄₆, 0, 1

Let p(v) = v + 40. Let h be p(13). Let s(u) = -u + 8. Let l be s(6). Determine i, given that h*il + 2 - 16*i5 + 23*i3 + 24*i4 - 68*i**2 - 2 + 2*i = 0.

-1, 0, ¹⁄₄, 2

Let w(q) be the first derivative of 3*q⁵⁄₃₅ + 15*q⁴⁄₁₄ + 3*q3 - 6*q²⁄₇ - 12*q + 383. Solve w(y) = 0 for y.

-7, -2, 1

Let b(y) be the third derivative of y⁶⁄₉₀ + y⁵⁄₆ + y4 - 20*y³⁄₃ + 46*y**2. Let a(u) be the first derivative of b(u). Let a(q) = 0. What is q?

-3, -2

Let z(h) = -h2 + 8*h - 11. Let l be z(4). Let b be 4 + (64/l)/(-4). Suppose -¹²⁄₅ - b*v4 + ²⁴⁄₅*v3 + 8*v - ⁴⁸⁄₅*v2 = 0. What is v?

1, 3

Let c(q) be the first derivative of 2*q³⁄₉ + 278*q2 + 115926*q - 1145. Suppose c(w) = 0. What is w?

-417

Let g(q) be the second derivative of -q⁴⁄₁₆ - 17*q³⁄₄ + 333*q**²⁄₈ - 232*q. Factor g(w).

-3(w - 3)(w + 37)/4

Let c(z) be the second derivative of 0*z2 - 10*z + ¹⁄₂*z3 + 0*z4 + 0 + ¹⁄₂₁₀*z5 - ¹⁄₁₂₆₀*z**6. Let i(x) be the second derivative of c(x). Factor i(g).

-2g(g - 2)/7