Let s(v) be the third derivative of v**8/84 + 2*v**7/15 + 7*v**6/30 - 19*v**5/15 - 8*v**4/3 + 40*v**3/3 - 1414*v**2. Let s(y) = 0. Calculate y.

Let t(k) = k**2 - 6*k. Let a be 9 + 4/(-7) + (-21)/49. Let i(o) = -a*o + 12*o - 5*o. Let s(x) = 5*i(x) - t(x). Factor s(p).

-p*(p - 1)

Factor -325*z + 315 + 144*z2 + 5*z3 + 128*z2 - 267*z2.

5(z - 7)(z - 1)*(z + 9)

Suppose 18 = 11*t - 15. Let w(g) be the third derivative of ¹⁄₇₂*g4 + 0*gt - ¹⁄₃₆₀*g6 + ¹⁄₆₃₀*g7 + 0 - ¹⁄₁₈₀*g5 + 0*g - 17*g2. Factor w(v).

v*(v - 1)*2(v + 1)/3

Let v(l) be the second derivative of -l⁷⁄₃₅₇ + l⁶⁄₅₁ - 3*l⁵⁄₈₅ - 2*l⁴⁄₅₁ + 8*l**³⁄₅₁ - 3*l - 67. Let v(m) = 0. What is m?

-1, 0, 2

Determine r, given that -28896*r - ²³⁴⁶¹⁵⁄₇*r2 + ⁴⁸⁄₇*r5 - 4116 + ⁹³⁸⁴⁄₇*r4 + 65181*r3 = 0.

-98, -¹⁄₄, 1

Suppose -5*c + 15 = 5. Factor 139*j2 + 39*jc - 16 - 62*j**2 - 224*j.

4(j - 2)(29*j + 2)

Let i be (-364)/21*(-60)/260. Find n, given that -¹²⁄₅ + ⁴⁰²⁄₅*n3 + ¹⁶²⁄₅*n2 + ³⁵⁴⁄₅*ni + ¹⁰⁸⁄₅*n5 - ⁶⁄₅*n = 0.

-1, -¹⁄₂, ²⁄₉

Let i(l) be the first derivative of -10*l + 6*l2 + 1 - ²⁄₃*l3. Factor i(h).

-2(h - 5)(h - 1)

Let j(u) be the first derivative of -u5 - 55*u⁴⁄₄ - 70*u3 - 160*u2 - 160*u - 337. Factor j(h).

-5(h + 1)(h + 2)*(h + 4)**2

Let o(u) = u3 + u2 - u - 1. Suppose 1 = -5*d + q - 4*q, -3 = 5*d + 4*q. Let f(b) = -10*b3 + 47*b2 - 68*b + 19. Let j® = d*o® + f®. Factor j(s).

-3(s - 3)(s - 2)*(3*s - 1)