*(n - 1)*(n + 1)**2/6
Let b(n) be the second derivative of n**5/130 + 5*n**4/26 - 16*n**3/39 - 1684*n. Factor b(m).
2*m*(m - 1)*(m + 16)/13
Let t = -150 + 152. Let z be 1 - 1 - 1*(-3 - -1). Determine f so that 39*f**z - 4*f**t + 5*f**3 + 12*f - 80 + 28*f = 0.
-4, 1
Let t(l) be the second derivative of l**9/3780 + l**8/280 + l**7/126 - 5*l**4/6 - 108*l. Let o(n) be the third derivative of t(n). Factor o(v).
4*v**2*(v + 1)*(v + 5)
Suppose 5*z + 27 = 4*r, 2*r - 36 = -5*z - 45. Let s = 5 - 2. Find o, given that 3*o**4 + 0*o**r - 2*o**2 + 2*o**2 - 3*o**s = 0.
0, 1
Let h = -1169 - -1174. Let m(u) be the first derivative of 2/3*u**3 - 1/2*u**2 + 0*u**4 + 1/6*u**6 - 2/5*u**h + 0*u + 15. Factor m(d).
d*(d - 1)**3*(d + 1)
Let o(w) be the first derivative of 3*w**5/20 + 2*w**4 + 26*w**3/3 + 16*w**2 + 12*w - 4573. Factor o(r).
(r + 2)**2*(r + 6)*(3*r + 2)/4
Let d(p) be the first derivative of 6 + 3/55*p**5 + 21/22*p**2 - 10/33*p**3 - 9/11*p - 3/22*p**4 + 1/66*p**6. Factor d(v).
(v - 1)**3*(v + 3)**2/11
Let x be ((-86)/(-387))/(((-4)/3)/(-4)). Factor 4/3*r**3 - 2/3 + x*r**4 + 0*r**2 - 4/3*r.
2*(r - 1)*(r + 1)**3/3
Let o be ((-1548)/(-32))/9 + 65 + -70. Factor 0*p + 0*p**4 + 9/8*p**3 + 0 + 3/4*p**2 - o*p**5.
-3*p**2*(p - 2)*(p + 1)**2/8
Let t(s) be the second derivative of -s**5/24 + 70*s**4/9 + 1135*s**3/36 + 95*s**2/2 + 67*s - 8. Determine r, given that t(r) = 0.
-1, 114
Let x(j) be the first derivative of -j**4/36 - 2*j**3/9 + 8*j**2/9 - 658. Suppose x(y) = 0. Calculate y.
-8, 0, 2
Let 5*c**2 - c**2 - 8243*c + 8963*c + 716 = 0. Calculate c.
-179, -1
Let t be 3 + -2 + 7 - (-1 + 3). Suppose -4*y = -2*x - 22, 0 = 2*y + 3*y - 2*x - 26. Factor -2 - 19*c + y*c + 5 - 6*c**2 + t.
-3*(c + 3)*(2*c - 1)
Let r(j) = -5*j - 5. Let m be r(-4). Suppose w = -k + 1, -m - 1 = -4*w + 2*k. Let 2*d**2 + 11*d**w - 4*d**2 + 2 + 9*d**3 - 18*d**3 - 2*d = 0. What is d?
-1, 1
Let w = -1135 + 1140. Let f(a) be the third derivative of -1/80*a**6 - 1/20*a**w + 0*a - 1/16*a**4 + 0*a**3 - 13*a**2 + 0. Factor f(s).
-3*s*(s + 1)**2/2
Let 24/5*n**2 - 4/5*n**4 - 16/5*n**3 + 144/5*n + 108/5 = 0. Calculate n.
-3, -1, 3
Let y = -277229/30 + 9241. Let g(j) be the third derivative of -y*j**5 - 26*j**2 + 0 + 0*j + 1/24*j**4 + 0*j**3 + 1/120*j**6. Determine l, given that g(l) = 0.
0, 1
Let f = 3923 - 3918. Let v(n) be the third derivative of 0*n - 1/102*n**4 - 7*n**2 + 0 - 1/510*n**f - 1/51*n**3. Factor v(g).
-2*(g + 1)**2/17
Solve 1/2*n**2 - 157/2 + 78*n = 0.
-157, 1
Let u(j) be the first derivative of 0*j**2 - 1/5*j**4 - 1/25*j**5 - 67 + 0*j - 4/15*j**3. Factor u(i).
-i**2*(i + 2)**2/5
Let o(h) = h**4 - 12*h**3 + 48*h**2 + 16*h - 51. Let c(v) = -v**4 + 11*v**3 - 48*v**2 - 17*v + 52. Let t(g) = -2*c(g) - 3*o(g). Factor t(d).
-(d - 7)**2*(d - 1)*(d + 1)
Let k = -13475/6 + 2246. Let a(i) be the third derivative of 0*i + 1/15*i**5 + 0 - 13*i**2 + k*i**4 - 4/3*i**3. Factor a(o).
4*(o - 1)*(o + 2)
Let a be (1104/60 - 18)/(4/10). Suppose -14*r + 11*r = 3, -5*y + r + a = 0. Find l, given that -1/10*l**3 - 1/5*l + y + 3/10*l**2 = 0.
0, 1, 2
Let s be (-274)/18 - ((-195)/27 + 7). Let z be (2/(-2))/(s/60). Factor -14 + 14 + 4*w**4 - z*w**2 - 2*w**4 - 2*w**3.
2*w**2*(w - 2)*(w + 1)
Let y = 226 + -209. Factor 3 + 10 - y + 4*o**2.
4*(o - 1)*(o + 1)
Let j(k) = 3*k**2 + 32*k + 82. Let n be j(-4). Let v(g) be the first derivative of -1/8*g**4 + 1/4*g**n - 2/3*g**3 - 2 + 2*g. Factor v(d).
-(d - 1)*(d + 1)*(d + 4)/2
Let h be 6/4*(-32)/24 + 2. Let l(t) be the first derivative of h*t - 1/15*t**3 - 15 + 0*t**2. Solve l(d) = 0.
0
Let a(n) be the second derivative of -n**5/270 + n**3/27 - 55*n**2 - 59*n. Let f(d) be the first derivative of a(d). Factor f(o).
-2*(o - 1)*(o + 1)/9
Suppose -9684 = 8*o + 6860. Let r = 2070 + o. Factor 3/2*n**r - 27*n + 243/2.
3*(n - 9)**2/2
Let r(u) be the second derivative of -u**4/3 - 1676*u**3/3 - 1674*u**2 + 176*u + 1. Solve r(n) = 0.
-837, -1
Let r(h) = 14456*h**2 + 686*h + 2. Suppose 15 = 5*i + 3*v, -5*i + i + 29 = -v. Let l(k) = -14457*k**2 - 687*k - 1. Let q(b) = i*l(b) + 7*r(b). Factor q(g).
2*(85*g + 2)**2
Let u = -12345 - -12345. Let v(y) be the third derivative of 0*y - 5/336*y**8 + u + 5/24*y**4 + 0*y**6 + 1/6*y**5 - 1/21*y**7 + 0*y**3 - 11*y**2. Factor v(w).
-5*w*(w - 1)*(w + 1)**3
Let l = 17092 - 17090. Let o(n) be the second derivative of 4/9*n**l - 1/54*n**4 + 9 + 0*n**3 + n. Find d such that o(d) = 0.
-2, 2
Suppose 0 = -152*v + 41*v + 44*v. Let k(b) be the second derivative of 0*b**3 + 0*b**4 + 1/75*b**6 + 0*b**2 + v*b**5 + 0 + 1/30*b**7 + 8*b. Factor k(w).
w**4*(7*w + 2)/5
Suppose -6 = -3*b, -18*o + 3*b = -19*o + 486. Let n be (o/45)/(-16) + (-20)/(-3). Factor 9/2*g**2 + 9*g + 3/4*g**3 + n.
3*(g + 2)**3/4
Let f = -70323 - -70325. Factor -432/5*h - 3/5*h**3 + 0 + 72/5*h**f.
-3*h*(h - 12)**2/5
Let u(q) be the third derivative of -1/120*q**6 + 0*q - 1/210*q**7 + 0*q**3 + 188*q**2 + 1/60*q**5 - 1 + 1/24*q**4. What is g in u(g) = 0?
-1, 0, 1
Suppose -q**3 + 4*q - q + 41 + q - 2130*q**2 + 2089*q**2 - 3*q = 0. What is q?
-41, -1, 1
Let -322/9*v - 154/3*v**3 - 6 + 16/9*v**4 + 274/3*v**2 = 0. What is v?
-1/8, 1, 27
Let x(m) = 4*m**2 + 28*m. Suppose -14 + 8 = 2*p. Let w(c) = -28*c**2 - 196*c. Let j(y) = p*w(y) - 20*x(y). Find s, given that j(s) = 0.
-7, 0
Suppose 4691*b = 4545*b + 1168. Suppose 5*c - 2*f - 3 = 2, 0 = -5*f + 25. Factor -1/2*r**4 + b - 14*r + 1/2*r**c + 6*r**2.
-(r - 2)**2*(r - 1)*(r + 4)/2
Solve -7/3*q**2 + 40/3 - 2/3*q - 1/3*q**3 = 0 for q.
-5, -4, 2
Factor y**2 - 3*y**2 + 94 - 396 + 3637*y - 3333*y.
-2*(y - 151)*(y - 1)
Let l be -205*3/9*(-24)/20. Let w be l*3*7/(-252) + 7. Let -1/2*a + w*a**2 + 1/3 = 0. Calculate a.
1, 2
Let w(n) be the first derivative of n**4/4 - 65*n**3 + 384*n**2 - 764*n - 267. Factor w(d).
(d - 191)*(d - 2)**2
Let q(j) be the first derivative of 6/55*j**5 - 327/11*j**2 + 222/11*j**3 + 1 + 216/11*j - 117/22*j**4. Solve q(o) = 0 for o.
1, 36
Let w(j) be the first derivative of -j**4/34 - 2*j**3/51 + 14*j**2/17 + 48*j/17 + 164. Factor w(a).
-2*(a - 4)*(a + 2)*(a + 3)/17
Let p be (4/25)/((-1715)/(-17150)). Find h such that -12/5*h**2 - 2/5 + p*h**3 - 2/5*h**4 + 8/5*h = 0.
1
Let y(x) be the second derivative of -67/16*x**4 + 21/16*x**5 + 0*x**2 - 1/40*x**6 + 33/8*x**3 - 23*x + 2. Solve y(f) = 0 for f.
0, 1, 33
Let s(g) be the third derivative of -3/20*g**6 + 0*g**3 - 1/70*g**7 - 37*g**2 + g**4 + 1/5*g**5 + 0*g + 1/112*g**8 + 2. Solve s(x) = 0.
-2, -1, 0, 2
Let r(i) be the second derivative of -9*i**5/5 + 13*i**4/4 + 6*i**3 - 39*i**2/2 - 1511*i. Factor r(f).
-3*(f - 1)*(f + 1)*(12*f - 13)
Let k(w) be the first derivative of -4/5*w**5 - 11/8*w**4 + 175 + 5/4*w**2 + 0*w + 1/3*w**3. Factor k(j).
-j*(j + 1)**2*(8*j - 5)/2
Suppose -14*z = 58*z - 216. Let s(b) be the first derivative of -2/3*b**z + 9 - b + 5/4*b**2 + 1/8*b**4. Factor s(t).
(t - 2)*(t - 1)**2/2
Find f such that -2*f**4 + 233561473 - 2243400973 - 2*f**4 + 2017423800*f - 7593840*f**2 + 9544*f**3 = 0.
1, 795
Suppose f = 19 - 43. Let q = 33 + f. Factor -r**2 + 18 + r + 2*r + q*r + 3*r**2.
2*(r + 3)**2
Solve 3/4*f**3 + 0 - 273/4*f - 135/2*f**2 = 0 for f.
-1, 0, 91
Factor -92 + 22/3*o**2 + 94/3*o.
2*(o - 2)*(11*o + 69)/3
Factor 3264*w - 39*w**3 - 2774*w**2 - 11560 + 123*w**3 + 3856*w**2 + 2*w**4.
2*(w - 2)*(w + 10)*(w + 17)**2
Let s(p) = 55*p**3 + 685*p**2 + 4225*p + 6025. Let a(j) = -9*j**3 - 114*j**2 - 704*j - 1004. Let b(i) = 25*a(i) + 4*s(i). Suppose b(m) = 0. Calculate m.
-10, -2
Suppose -5*n + 4*l = 36, 18*l - 36 = -5*n + 14*l. Factor 0 - 6/11*s**2 - 4/11*s + 2/11*s**4 + n*s**3.
2*s*(s - 2)*(s + 1)**2/11
Let r(m) be the first derivative of 3*m**2 + 70 - 1/6*m**3 - 10*m. Find s, given that r(s) = 0.
2, 10
Let d(b) be the third derivative of 0*b + 0*b**4 + 4*b**2 + 0 + 0*b**3 + 0*b**5 + 1/70*b**7 + 1/40*b**6. Determine k so that d(k) = 0.
-1, 0
Let i = 29104 + -29075. Let c(x) be the third derivative of 1/24*x**6 + 1/3*x**5 + 0*x**3 + 0 + 5/8*x**4 + 0*x + i*x**2. Factor c(z).
5*z*(z + 1)*(z + 3)
Let o(h) be the second derivative of -1/2*h**3 + 1/12*h**4 - 9*h**2 - 51*h + 0. Factor o(y).
(y - 6)*(y + 3)
Let v = 9 - 5. Suppose -4*d - 2*s + 8 = 0, d - s = v*s + 24. Find c, given that -3 + 21*c**3 + 36*c**d + 3 + 16*c**5 + 3*c**3 + 4*c**2 = 0.
-1, -1/4, 0
Suppose 876 - 55*v**2 - 22364*v +