Let u(s) be the third derivative of 0 + 77*s**2 + 0*s + 2/525*s**7 + 8/15*s**3 - 1/30*s**6 - 1/15*s**5 + 2/15*s**4 + 1/420*s**8. Suppose u(g) = 0. What is g?

Factor -²¹³⁄₄*p + ¹⁵⁄₄*p**2 + ¹⁸³⁄₂.

3(p - 2)(5*p - 61)/4

Let f be ⁸¹⁄₁₈*(-4)/(-6). Factor 5*i4 - 24*i3 + 17*if + 7*i3 + 10*i3 - 5*i5.

-5*i*3(i - 2)*(i + 1)

Suppose 4*n + 5*o = 13, 29*o - 31*o = -2. Let d(s) be the first derivative of -²⁄₅*s + ²⁄₄₅*s3 + ²⁄₁₅*sn - 17. Factor d(y).

2(y - 1)(y + 3)/15

Let z(g) = -2*g2 - 3724*g + 861181. Let d(t) = -12*t2 - 18624*t + 4305904. Let f(b) = -3*d(b) + 16*z(b). Solve f(v) = 0 for v.

464

Let u© be the third derivative of c⁸⁄₄₈₀ + 13*c⁷⁄₄₂₀ - 59*c⁶⁄₁₂₀₀ - 17*c⁵⁄₁₂₀ + 13*c⁴⁄₆₀ + c³⁄₃ + 1274*c**2. Determine p, given that u(p) = 0.

-10, -1, -²⁄₇, 1

Let v = 57708 - 57706. Find u, given that ⁵⁄₁₂*uv + 0 + ¹⁄₃*u3 + ¹⁄₁₂*u**4 + ¹⁄₆*u = 0.

-2, -1, 0

Let m(t) be the second derivative of 5*t⁴⁄₁₂ - 890*t³⁄₃ + 79210*t**2 + 559*t. Factor m(z).

5*(z - 178)**2

Factor 30*o3 - 2674 - 2674 + 5348 - 120*o + 3*o4 - 12*o**2.

3o(o - 2)(o + 2)(o + 10)

Suppose 0 = -2*y - 2*y + 3*q - 1, y + 3*q = 11. Determine u so that -2 + 16*u2 - 41*uy - 10*u**3 + 12 - 2*u - 3*u = 0.

-2, -1, ¹⁄₂

Let n(b) = -b3 + b2. Let z(o) = -12*o4 + 192*o3 - 456*o**2 + 224*o. Let y(u) = -8*n(u) + z(u). Determine q so that y(q) = 0.

0, ²⁄₃, 2, 14