derivative of s**8/3360 + s**7/630 - s**6/45 - s**4/2 - s**3/2 - 34*s**2. Let z(j) be the second derivative of r(j). Factor z(m).
2*m*(m - 2)*(m + 4)
Determine q, given that -1778*q**5 - 80*q + 864*q**5 - 20*q**2 + 919*q**5 + 35*q**4 + 60*q**3 = 0.
-4, -2, 0, 1
Let b(o) be the second derivative of -o**6/45 + 11*o**5/5 - 697*o**4/18 - 532*o**3/3 - 832*o**2/3 + 26*o + 36. Suppose b(d) = 0. What is d?
-1, 16, 52
Let c(j) be the third derivative of -j**7/42 - 247*j**6/8 - 185*j**5/3 + 63*j**2 + 32*j. Let c(l) = 0. What is l?
-740, -1, 0
Let h(c) be the third derivative of 43/240*c**5 + 0*c**3 - 26*c**2 + 17/840*c**7 + 0 + 3/32*c**6 + 7/48*c**4 + 1/1344*c**8 + 0*c. Factor h(y).
y*(y + 1)**3*(y + 14)/4
Let c(f) be the third derivative of f**6/40 + 7*f**5/5 + 75*f**4/8 + f**2 + 199*f. Let c(s) = 0. Calculate s.
-25, -3, 0
Suppose 8*l - 5544 - 1008 = 0. Let g = l - 819. Factor -3/7*z**2 - 3*z + g.
-3*z*(z + 7)/7
Let l be 3509/348 - (-4 - -14). Let w(f) be the third derivative of 7*f**2 + 0*f - 1/120*f**5 + 0 + l*f**3 - 1/48*f**4 + 1/240*f**6. Factor w(r).
(r - 1)**2*(r + 1)/2
Let -3/2*q**4 + 45*q - 93/2*q**2 + 0 + 15*q**3 = 0. Calculate q.
0, 2, 3, 5
Let o(m) be the first derivative of 189 + 80*m - 42*m**2 + 4/3*m**3. Determine n, given that o(n) = 0.
1, 20
Let q(l) be the third derivative of l**6/180 - 2059*l**5/30 + 4239481*l**4/12 - 8729091379*l**3/9 + 4599*l**2. Find h such that q(h) = 0.
2059
Let m(v) be the first derivative of -7*v**5/4 - 20*v**4/3 - 10*v**3/3 + 35*v + 60. Let n(i) be the first derivative of m(i). Solve n(x) = 0.
-2, -2/7, 0
Let c(p) be the second derivative of 14*p + 3/20*p**5 + 3/4*p**4 - 18*p**2 + 0 - 2*p**3. Factor c(i).
3*(i - 2)*(i + 2)*(i + 3)
Factor 3/7*v**2 - 3*v + 0.
3*v*(v - 7)/7
Let -2/7*u**4 + 2/7*u**2 + 0 - 150/7*u**3 + 150/7*u = 0. Calculate u.
-75, -1, 0, 1
Factor -314*q + 1/6*q**2 + 147894.
(q - 942)**2/6
Let x(q) be the first derivative of 0*q**4 + 0*q**2 + 0*q + 1/45*q**6 - 2/75*q**5 + 0*q**3 - 107. Factor x(r).
2*r**4*(r - 1)/15
Let d = 77 - 75. Factor 4*o + 4*o**3 + 14*o - 3*o**2 + 36*o**d + 5*o**3.
3*o*(o + 3)*(3*o + 2)
Let l(x) = -2*x**3 + 158*x**2 + 452*x + 280. Let o(w) = w**3 - 2*w**2 - w + 6. Let f(y) = l(y) + 3*o(y). Find p, given that f(p) = 0.
-149, -2, -1
Let z = -2/677 + -8795/2031. Let b = 29/6 + z. Factor 0*g + 2 + b*g**3 - 3/2*g**2.
(g - 2)**2*(g + 1)/2
Let b be (-48)/(-21) - 6/21. Suppose -3*k + b - 2 = 0. Suppose k*r**2 - 3*r**2 + 28*r + r**3 - 27*r + r**2 = 0. Calculate r.
0, 1
Let q(l) be the first derivative of l**4/20 + l**3/5 - 2*l**2/5 - 12*l/5 - 9. Factor q(y).
(y - 2)*(y + 2)*(y + 3)/5
Let z(c) be the first derivative of -c**4/2 + 242*c**3/3 - 120*c**2 - 11685. Suppose z(x) = 0. Calculate x.
0, 1, 120
Let f be ((-14)/6)/((-224)/96). Let g be (15/(-60))/(-5 + 2 + f). Determine y so that 1/2*y + g*y**2 + 0 = 0.
-4, 0
Let q be (-2)/15*-1 - 15041/195. Let t = q + 80. What is s in 14*s**4 - 14*s**t - 3*s**5 + 8*s**2 + 8*s**2 - 4*s - 9*s**3 = 0?
0, 2/3, 1, 2
Let p(g) be the second derivative of -g**4/78 + 16*g**3/39 + 80*g**2/13 + g - 170. What is h in p(h) = 0?
-4, 20
Let k be (-28)/(2*(-1)/(-24)) + -5. Let i = k - -344. Factor -5/4*w**i + 0 + 3/2*w - 13/4*w**2.
-w*(w + 3)*(5*w - 2)/4
Let a(g) be the second derivative of -g**6/50 - 3*g**5/10 + 67*g**4/20 + 16*g**3 + 126*g**2/5 - 2*g + 7841. Find p such that a(p) = 0.
-14, -1, 6
Let h = -16750 + 16750. Let y(g) be the second derivative of -3/14*g**3 + 41*g - 1/28*g**4 + h + 0*g**2. Factor y(r).
-3*r*(r + 3)/7
Let w(n) be the third derivative of n**7/210 + 11*n**6/120 - n**5/2 - 68*n**4/3 - 448*n**3/3 + 2*n**2 + 14*n + 14. Determine l, given that w(l) = 0.
-8, -2, 7
Let d(w) = 4*w. Let y(p) = 2*p**2 - 86*p. Let v be (-30)/45 - 7/3. Let k(o) = v*d(o) - y(o). What is c in k(c) = 0?
0, 37
Factor 1320 + 404/3*u - 4/3*u**2.
-4*(u - 110)*(u + 9)/3
Suppose 2*s - 18 = 0, 3*r + 5*s + 82 = 139. Let d(u) be the third derivative of -8*u**2 + 25/2*u**3 + 1/20*u**5 + 0*u + 5/4*u**r + 0. Factor d(g).
3*(g + 5)**2
Suppose 0 = -4*v + 6*w + 24, -4*v + w + 0*w + 14 = 0. Let t(s) be the first derivative of 19 - 12/11*s**2 + 32/11*s + 1/22*s**4 + 0*s**v. Factor t(k).
2*(k - 2)**2*(k + 4)/11
Let f(q) be the first derivative of -q**6/6 + 14*q**5/5 - 77*q**4/4 + 208*q**3/3 - 138*q**2 + 144*q + 1663. Factor f(a).
-(a - 4)*(a - 3)**2*(a - 2)**2
Suppose -2*u + 25 = 3*u. Let o be (-306)/(-90) + (-2)/u. Factor -4*v**5 - 12*v**o - 9*v**3 - 11*v**3 + 16*v**3 + 20*v**4.
-4*v**3*(v - 4)*(v - 1)
Let v(l) = 6*l + 200. Let o be v(-33). Let h(q) be the second derivative of 14*q + 0 + 19/60*q**5 - 2/9*q**3 + 0*q**o + 7/90*q**6 + 2/9*q**4. Factor h(z).
z*(z + 1)*(z + 2)*(7*z - 2)/3
Factor -138/17*q + 36 - 28/17*q**2 + 2/17*q**3.
2*(q - 17)*(q - 3)*(q + 6)/17
Let t(d) be the third derivative of -1/210*d**5 + 8/21*d**3 + 1/42*d**4 + 0*d - 11*d**2 + 3. Find r such that t(r) = 0.
-2, 4
Let x(t) be the first derivative of -t**4/12 - 38*t**3/9 - 37*t**2/6 + 1012. Factor x(h).
-h*(h + 1)*(h + 37)/3
Let w be ((-7)/33)/(161772/936 + -173). What is p in -2/11*p**3 - 8/11*p + w*p**2 - 24/11 = 0?
-1, 2, 6
Let x(k) = -k**3 - 6*k**2 - 84*k - 1238. Let i be x(-10). Suppose -2/5*b**i + 22/5 - 4*b = 0. What is b?
-11, 1
Suppose 121801/2 - 349*w + 1/2*w**2 = 0. Calculate w.
349
Let h be 1344975/(-600) + 3/(-8). Let k = h - -2245. Let 0*l**2 + 7/8*l + 3/8*l**5 - 5/4*l**k + 1/4 - 1/4*l**4 = 0. What is l?
-1, -1/3, 1, 2
Suppose 1962*k = 3702*k - 1905*k. Factor 1/2*a**2 + k - 8*a.
a*(a - 16)/2
Let g(x) = -35*x**2 + 14*x - 6. Let y(n) = -385*n**2 - 485 + 172 - 35*n + 140 + 190*n + 108. Let t be 23/4 - 3/(-12). Let s(o) = t*y(o) - 65*g(o). Factor s(u).
-5*u*(7*u - 4)
Let y(s) = -s + 1. Suppose 3*b - 7*b + 16 = 0, 2*d = -b - 6. Let g(n) = n**2 - 2*n + 3. Let c(u) = d*g(u) - 15*y(u). Find h such that c(h) = 0.
2, 3
Factor 25*y**2 + 40*y**3 + 75*y**2 + 8760*y - 5*y**4 - 8760*y.
-5*y**2*(y - 10)*(y + 2)
Let r(c) be the first derivative of -c**8/1260 - c**7/126 - 4*c**6/135 - 2*c**5/45 - 7*c**3 - 2*c - 132. Let a(w) be the third derivative of r(w). Factor a(h).
-4*h*(h + 1)*(h + 2)**2/3
Let r(t) = -7*t**4 - 47*t**3 + 3*t**2 - 6. Let j(h) = -25*h**4 - 189*h**3 + 11*h**2 - 22. Let d(s) = 3*j(s) - 11*r(s). Factor d(w).
2*w**3*(w - 25)
Solve -1068*d**2 - 11064*d + 355*d**2 - 15130 + 360*d**2 + 4062 + 357*d**2 = 0 for d.
-1, 2767
Let r(i) = -435*i + 3049. Let v be r(7). Let m(h) be the second derivative of 0 - 1/7*h**3 - 9/14*h**2 - 29*h + 1/28*h**v. Solve m(z) = 0.
-1, 3
Let n(r) be the third derivative of r**6/600 + 7*r**5/75 - 17*r**4/10 + 2*r**2 + 156*r - 5. Let n(x) = 0. What is x?
-34, 0, 6
Find j, given that 80/13*j**3 - 2/13*j**4 - 232/13*j**2 + 192/13*j + 0 - 2/13*j**5 = 0.
-8, 0, 2, 3
Suppose 552 = -12*j + 120*j + 30*j. What is o in 128/3*o - 512/3 + 184/3*o**2 - 28/3*o**3 - 14/3*o**j - 1/3*o**5 = 0?
-8, -2, 2
Let j = -6/122659 + 2575851/245318. Factor -19/2*d**4 + 0*d + j*d**3 - d**2 + 0.
-d**2*(d - 1)*(19*d - 2)/2
Let b(v) be the first derivative of 2*v**3/15 - 1372*v**2/5 + 941192*v/5 - 3555. Factor b(c).
2*(c - 686)**2/5
Suppose -581*o = -548*o. Let w(k) be the third derivative of 5*k**2 - 1/56*k**4 + 0*k + 1/21*k**3 + o + 1/420*k**5. Find m, given that w(m) = 0.
1, 2
Let s(n) be the third derivative of -12321*n**6/160 - 4551*n**5/80 - 19*n**4/4 - n**3/6 + 75*n**2. Let s(v) = 0. What is v?
-1/3, -2/111
Let r(s) = 4*s**2 - 1515*s + 142896. Let i(z) = z - 4. Let y(w) = 3*i(w) + r(w). Let y(u) = 0. What is u?
189
Suppose -19*g + 11 = 5*s - 15*g, -2 = 2*g. Suppose s*j = -2 - 10, j + 4 = -2*z. Solve -2/7*p**4 + 4/7*p + 22/7*p**2 + z - 8/7*p**5 + 24/7*p**3 = 0 for p.
-1, -1/4, 0, 2
Suppose 29*q - 322 = -3*g + 28*q, -3*q - 200 = -2*g. Suppose -g*k = -43*k - 189. Factor 1/5*j**5 + 0 - 1/5*j**k - 1/5*j**4 + 1/5*j**2 + 0*j.
j**2*(j - 1)**2*(j + 1)/5
Let m(d) be the second derivative of -d**6/60 + 29*d**5/40 - 13*d**4/4 - 882*d. Solve m(o) = 0.
0, 3, 26
Let f = 1272 + -1270. Suppose -i + 2 = -0*i. Factor b**i - 12 + 12 - 3*b + 2*b**f.
3*b*(b - 1)
Let q be 7/(6 + -48)*-2. Let x(g) be the first derivative of 4/3*g - q*g**2 - 16 - 2/9*g**3. Factor x(j).
-2*(j - 1)*(j + 2)/3
Let t(y) be the second derivative of y**7/231 - 4*y**6/165 - y**5/10 + 13*y**4/33 + 28*y**3/33 - 40*y**2/11 - 237*y + 3. Find p, given t