Let g(v) = 9*v**4 - 42*v**3 + 173*v**2 - 196*v + 76. Let k(x) = -125*x**4 + 590*x**3 - 2420*x**2 + 2745*x - 1065. Let f(b) = -55*g(b) - 4*k(b). Factor f(w).

Let w(t) = -106*t + 534. Let c be w(5). Let d(i) be the first derivative of 9 + 0*i - ⁶⁄₇*i3 + ⁶⁄₇*ic - ²⁄₇*i5 + ²⁄₇*i2. Determine n so that d(n) = 0.

0, ²⁄₅, 1

Find v, given that ²¹⁄₁₀*v + 0 + ¹⁄₁₀*v**2 = 0.

-21, 0

Let o(l) be the third derivative of -l⁷⁄₄₂ - 2*l⁶⁄₃ - 41*l⁵⁄₁₂ - 65*l⁴⁄₁₂ - 4*l**2 + 66*l. Factor o(w).

-5w(w + 1)(w + 2)(w + 13)

Let p(t) be the second derivative of -t⁷⁄₃₉₉ - 16*t⁶⁄₂₈₅ - 27*t⁵⁄₁₉₀ + 8*t⁴⁄₅₇ + 28*t**³⁄₅₇ - 5*t - 41. Solve p(n) = 0.

-14, -2, -1, 0, 1

Let p = 802 - ¹⁵⁹⁵⁄₂. Let i(j) be the first derivative of -12*j + 9 + j3 + p*j2. Suppose i(o) = 0. Calculate o.

-4, 1

What is w in -11228*w2 + 5615*w2 + 5616*w**2 + 264*w = 0?

-88, 0

Suppose s - 5*s - 91 = -3*l, 2*l - 84 = -2*s. Factor 80*c2 - 12 - 38*c2 - 28*c - l*c**2.

(c - 6)*(5*c + 2)

Let g(x) = -7*x - 19. Let t(o) = 30*o + 75. Let l(w) = 15*g(w) + 4*t(w). Let z be l(-1). Factor -¹⁄₃*j5 + z*j + 0*j2 + 0 + 0*j4 + ¹⁄₃*j3.

-j*3(j - 1)*(j + 1)/3

Let v(s) be the second derivative of ³⁄₄*s3 + 2*s2 + 20*s + ¹⁄₂₄*s**4 + 2. Factor v(q).

(q + 1)*(q + 8)/2

Let i = 45177 + -45175. Factor -2 + ²⁄₃*u4 - ⁸⁄₃*u + ⁸⁄₃*u3 + ⁴⁄₃*u**i.

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