Let o(f) be the third derivative of f**5/30 - 3*f**4/2 + 24*f**3 - 1246*f**2 + 2. What is c in o(c) = 0?

Determine q so that 8 + ¹⁷⁄₃*q + ¹⁄₂*q2 - ¹⁄₆*q3 = 0.

-3, -2, 8

Let k(f) = -f3 + 13*f2 - 10*f - 20. Let c be k(12). Factor -4*j - c*j + 2*j - 2*j3 + 15*j2 - 4*j**3.

-3j(j - 2)*(2*j - 1)

Factor 5*s3 - 6*s2 - 10 - 3*s3 - 304*s + 10 + 154*s2.

2s(s - 2)*(s + 76)

Let d® be the first derivative of r⁶⁄₈₄₀ - 13*r⁵⁄₁₄₀ + 169*r⁴⁄₅₆ - r3 - 20*r + 74. Let n(m) be the third derivative of d(m). What is z in n(z) = 0?

13

Suppose 4*k - 562 = 5*g, 5*g + 435 + 130 = 5*k. Let a = -108 - g. Suppose -⁸⁄₃ + ²⁄₃*v**a - 2*v = 0. Calculate v.

-1, 4

Let l(x) be the third derivative of 49*x⁵⁄₂₅ - 293*x⁴⁄₃₀ - 4*x³⁄₁₅ - 848*x2 - x. Suppose l© = 0. Calculate c.

-¹⁄₁₄₇, 2

Let q be (12 - (1 + 5)) + 33. Solve 14*a3 - 9 - 6 - q*a + a3 + 6*a**2 + 33 = 0 for a.

-2, ³⁄₅, 1

Let r(b) be the third derivative of -b⁶⁄₄₂₀ - b⁵⁄₁₅ + 31*b⁴⁄₈₄ - 16*b³⁄₂₁ + b**2 + 1060*b. Solve r(p) = 0.

-16, 1

Let a(n) be the second derivative of -n⁶⁄₂₁₆₀ - n⁵⁄₁₂₀ - n⁴⁄₁₆ + 10*n³⁄₃ + 6*n + 1. Let z(j) be the second derivative of a(j). Factor z(t).

-(t + 3)**²⁄₆

Suppose -³⁄₈*r4 - ⁸⁷⁄₈*r3 + 0*r + ⁴⁵⁄₄*r**2 + 0 = 0. What is r?

-30, 0, 1