/3 + 1/3*m**o.
(m - 1)*(m + 4)/3
Let g(s) be the second derivative of s**6/135 + 113*s**5/90 - 463*s**4/54 + 583*s**3/27 - 26*s**2 + 324*s. Solve g(f) = 0 for f.
-117, 1, 2
Let d(u) be the first derivative of 3/11*u**4 - 2/5*u**5 - 40/11*u**2 + 8/3*u**3 + 0*u + 186 + 1/33*u**6. Find c, given that d(c) = 0.
-2, 0, 1, 2, 10
Let a be ((-80)/(-6) + 0)/(2/3). Suppose 23*p = a*p + 36. Suppose -15*d**3 + 8*d - p*d**4 + 20*d**2 - d**4 + 3*d**4 + 12*d + 5*d**5 = 0. Calculate d.
-1, 0, 2
Let k = 6 - 4. Let s be 280/45 + (-29736)/4779. Let -3/4 - 3/2*p**k + s*p**3 + 2*p + 1/4*p**4 = 0. Calculate p.
-3, 1
Let z(x) be the first derivative of -3*x**4/16 + 2007*x**3/4 - 4028049*x**2/8 + 898254927*x/4 + 2136. Determine r so that z(r) = 0.
669
Let q(s) be the first derivative of -s**5/40 - 3*s**4/2 - 36*s**3 - 432*s**2 - 16*s - 72. Let z(u) be the first derivative of q(u). Factor z(r).
-(r + 12)**3/2
Find n such that -186*n**2 - 1 + 1 + 3492*n + n**3 + 7551*n - 2394*n = 0.
0, 93
Let k be (0 - -1)/(((-11)/2)/(-11)). Let y be k + (-24)/(-4) + 3/(-1). Factor 13*s**4 + 30*s**2 + y*s + 7*s**4 + 4*s**3 + 41*s**3.
5*s*(s + 1)**2*(4*s + 1)
Let l be (10 + -8)*(2 - 0). Suppose -t + l*u + 17 = -6, 13 = t - 2*u. Factor 6*w - t*w**3 + 3*w**3 + 2*w**3 - 8*w.
2*w*(w - 1)*(w + 1)
Solve 19384 + 4*s**4 + 44*s - 19504 + 31*s**3 - 75*s**3 + 116*s**2 = 0.
-1, 1, 5, 6
Suppose -10*y + 4*y = 54. Let n(f) = -f**3 - 5*f**2 + 38*f + 18. Let a be n(y). Factor a - g + 1/4*g**3 - 1/4*g**4 + g**2.
-g*(g - 2)*(g - 1)*(g + 2)/4
Suppose -4*c - 5*j = 2, -c + 10 = 3*c - j. Let i be (4 - 1)*2/3. Determine d, given that i*d**3 + d**3 + d**4 - 3*d**2 - 3*d**5 + c*d**4 = 0.
-1, 0, 1
Let u(q) = 67*q + 10990. Let x be u(-164). Find l, given that -20/3 + 38/3*l - 6*l**x = 0.
1, 10/9
Suppose 382 = 496*q - 495*q. Let z = q + -380. Factor 0*n + 0 + 2/11*n**4 + 0*n**3 - 2/11*n**z.
2*n**2*(n - 1)*(n + 1)/11
Let s(m) be the first derivative of 3*m**5/20 + 39*m**4/8 + 133*m**3/4 + 719. Suppose s(o) = 0. Calculate o.
-19, -7, 0
Let x be (1/6*-2)/((-6)/36). Suppose -o + 0*o = x*h + 8, -h = -5*o + 15. Factor -1/5*q**4 + 1/10*q**5 + 0*q**o + 0*q + 0 + 1/10*q**3.
q**3*(q - 1)**2/10
Let u be (-8 + (-104)/26)/((-5)/2). Let o be (-8)/(-6) - (-6)/9. Let -4 + u*f - 4/5*f**o = 0. What is f?
1, 5
Let f(c) be the second derivative of c**7/70 + 101*c**6/90 - 17*c**5/15 - 58*c**3/3 + 53*c. Let b(d) be the second derivative of f(d). Factor b(o).
4*o*(o + 34)*(3*o - 1)
Let l(p) = 13*p + 226. Let w be l(-16). Let r be 10 - (-1 - w/(-2)). What is u in -32/5*u - 48/5*u**r + 0 - 2/5*u**5 - 2/5*u**3 + 12/5*u**4 = 0?
-1, 0, 4
Let j(w) be the second derivative of -9*w**3 + 0 + 0*w**2 + 39/20*w**5 - 24*w + 1/14*w**7 - 7/10*w**6 + 3/4*w**4. Find k, given that j(k) = 0.
-1, 0, 2, 3
Let f = 981116/7 + -140159. Factor -f*i**4 - 48/7 - 72/7*i**2 - 24/7*i**3 - 96/7*i.
-3*(i + 2)**4/7
Let a(u) = u**3 + 3*u**2 + u + 10. Let j be a(-3). Let i be 2 + (-3)/63*-3*j. What is h in -4/5*h + 16/5*h**i + 12/5*h**2 + 0 = 0?
-1, 0, 1/4
Let r(o) be the third derivative of 40*o**2 - 13/12*o**6 + 0 + 37/12*o**5 - 35/12*o**4 + 0*o**3 + 0*o + 1/14*o**7. Factor r(p).
5*p*(p - 7)*(p - 1)*(3*p - 2)
Let o(a) be the third derivative of 0 - 1/70*a**5 - 3*a**2 + 6/7*a**3 + 2*a + 11/56*a**4 - 1/280*a**6. Factor o(u).
-3*(u - 3)*(u + 1)*(u + 4)/7
Let h be (30/60)/(-2 + 73/36). Let l be (3/h)/(2/84). Solve -8*u - 2*u**2 - 266 + 216 - l*u - 5*u = 0 for u.
-5
Let t be ((-1 + 0)*-1)/((-1)/(-17)). Solve 6 + 5*b - 35 + 8*b - b**2 + 10 - t = 0.
4, 9
Let u(o) be the first derivative of 0*o**2 + 0*o - 8/5*o**5 - 4/3*o**3 + 9/2*o**4 - 215. Suppose u(b) = 0. Calculate b.
0, 1/4, 2
Determine s so that 6316*s**3 + 426 + 186*s**2 + 234*s**2 - 6319*s**3 + 849*s = 0.
-1, 142
Let f(v) be the first derivative of -2/9*v**3 - 2/45*v**5 + 0*v - 5/36*v**4 - 1/180*v**6 + 9*v**2 - 23. Let y(h) be the second derivative of f(h). Factor y(w).
-2*(w + 1)**2*(w + 2)/3
Let g be 6228/1730*(-10)/(-18). Suppose -5 + g*o - 1/5*o**2 = 0. What is o?
5
Let i(u) = -u**4 - 7*u**3 - 14*u**2 + 32*u - 64. Let l(o) = o**3 + 4*o - 8. Let h(r) = -5*i(r) + 40*l(r). Factor h(j).
5*j**2*(j + 1)*(j + 14)
Let v(s) be the second derivative of s**6/180 - s**5/12 - s**4/2 + 49*s**3/3 - 83*s. Let j(x) be the second derivative of v(x). Factor j(u).
2*(u - 6)*(u + 1)
Let x = -1 - -5. Let u = -660 + 663. Factor -7*i**3 - x*i**2 - 10*i + 24*i - 4 + i**u.
-2*(i - 1)*(i + 2)*(3*i - 1)
Suppose -16*f + 60 = -4*f. Factor 39*x**2 + f*x**5 - 1079*x**3 - 15*x**4 - 2*x**5 + 8*x + 22*x + 1070*x**3.
3*x*(x - 5)*(x - 2)*(x + 1)**2
Let p = 148553 - 1336927/9. Factor -56/9*b + 76/9*b**2 + 16/9*b**4 - 2/9*b**5 - p*b**3 + 16/9.
-2*(b - 2)**3*(b - 1)**2/9
Solve 267/2*n - 3*n**4 - 99/8*n**3 + 3/8*n**5 + 69/2*n**2 + 90 = 0.
-3, -2, -1, 4, 10
Let x be 0/((-66 - -70) + 2 + 1*-8). Let w(j) be the second derivative of 5/24*j**4 - 1/8*j**5 + 0 + 0*j**2 + x*j**3 - 9*j. Let w(t) = 0. What is t?
0, 1
Let u = -69633 + 1183769/17. Find d, given that u*d**2 + 12/17 - 22/17*d + 2/17*d**3 = 0.
-6, 1
Let d = 38/6333 + 62684/107661. Find f such that 0 - 16/17*f**2 - 56/17*f**3 - d*f**5 + 0*f - 44/17*f**4 = 0.
-2, -2/5, 0
Let t(y) be the first derivative of -15/2*y**2 + 12/5*y**5 - 3/4*y**4 + 6*y - 12*y**3 - 31. Determine c, given that t(c) = 0.
-1, 1/4, 2
Let x(d) be the second derivative of -d**5/60 - d**4/6 - 5*d**3/18 + 108*d - 36. Factor x(a).
-a*(a + 1)*(a + 5)/3
Let r(k) be the third derivative of -2*k**5/75 + 649*k**4/60 - 54*k**3/5 + 158*k**2. Factor r(s).
-2*(s - 162)*(4*s - 1)/5
Let g(v) = 9*v**2 - 196*v - 360. Let d(s) = s**2 - 4*s + 5. Let q(z) = -4*d(z) + g(z). Find x, given that q(x) = 0.
-2, 38
Let v = -220 + 220. Suppose -8*t + 4*t + 4 = v, 2*y = 2*t + 2. Factor y*f + 0 - 2/3*f**2.
-2*f*(f - 3)/3
Let l(u) be the first derivative of -u**4/8 - 64*u**3/3 + u**2/4 + 64*u - 16173. Solve l(g) = 0 for g.
-128, -1, 1
Let t(h) = -1852*h - 14816. Let u be t(-8). Factor 1/3*b**3 - 2*b**2 + u + 0*b.
b**2*(b - 6)/3
Let i(f) = -3*f**3 + 93*f**2 - 15*f + 469. Let k be i(31). What is t in -8/5*t**k + 16/5 - 84/5*t**2 - 46/5*t**3 - 8*t = 0?
-2, 1/4
Factor 1174 + 3*s**2 + 657 + 886 - 129*s + 718 - 2769.
3*(s - 37)*(s - 6)
Factor 4/7*g**2 - 2/7*g - 4/7*g**4 + 0*g**3 + 0 + 2/7*g**5.
2*g*(g - 1)**3*(g + 1)/7
Suppose -2919 = 11*m - 12225. Suppose 5*x + u - 500 = 565, 4*x + 2*u = m. Determine d, given that 42*d**2 - 12*d**2 - 118 + x - 3*d**3 - 96*d = 0.
2, 4
Let y(i) be the first derivative of i**5/20 - 15*i**4/4 + 283*i**3/12 - 111*i**2/2 + 55*i - 1792. Factor y(x).
(x - 55)*(x - 2)**2*(x - 1)/4
Suppose 4*g = 3*j + 42, -3*j = -14*g + 20*g + 42. Factor -1/8*i**2 + 0 - 1/8*i**4 - 1/4*i**3 + g*i.
-i**2*(i + 1)**2/8
Suppose 3*p = 5*y + 20 - 8, -3*y = 0. Factor 29*u**3 + 0*u**3 - p*u**5 - 7*u**2 - 17*u**3 - u**2.
-4*u**2*(u - 1)**2*(u + 2)
Factor 5/3*z**3 - 3840 + 640*z + 220/3*z**2.
5*(z - 4)*(z + 24)**2/3
Let i be -1 - 165/(-25) - 20/(-50). Let y(v) be the second derivative of 1/2*v**3 + 26*v + 0*v**2 + 0 - 1/20*v**i + 1/8*v**4 - 3/20*v**5. Factor y(k).
-3*k*(k - 1)*(k + 1)*(k + 2)/2
Let c(y) be the third derivative of -y**7/140 - y**6/40 + 3*y**5/8 + 9*y**4/4 + 2018*y**2. Determine d, given that c(d) = 0.
-3, 0, 4
Factor 129*u + 4440*u - 33913*u**3 + 707*u**2 + 33909*u**3 + 1098.
-(u - 183)*(u + 6)*(4*u + 1)
Let h(c) be the first derivative of c**3/27 - 23*c**2/18 + 14*c + 1374. Factor h(q).
(q - 14)*(q - 9)/9
Let i(n) = 6*n**2 - 3*n - 5. Let j be i(-2). Suppose 0 = 3*l - 31 + j. Factor 2/7*f**l + 0 + 2/7*f.
2*f*(f + 1)/7
Suppose 28 = -14*p - 518. Let t = 44 + p. Solve 3/2*s**t + 0*s**4 - 9/2*s**3 + 3*s**2 + 0*s + 0 = 0 for s.
-2, 0, 1
Suppose -23*c - 90 = 2. Let t = 26/5 + c. Factor 8/5 - 12/5*w + t*w**2 - 1/5*w**3.
-(w - 2)**3/5
Let t be 0*((-43 - -21) + 23). Suppose t*k + 2/3*k**4 + 0*k**3 + 0 + 0*k**2 = 0. Calculate k.
0
Let u(g) be the first derivative of -g**6/12 + 4*g**5/5 + 23*g**4/8 - 13*g**3/3 - 11*g**2 + 20*g - 1034. What is m in u(m) = 0?
-2, 1, 10
Let p(i) be the third derivative of -1/672*i**8 + 0*i + 0 + 244*i**2 - 1/48*i**4 + 0*i**3 + 1/120*i**6 + 0*i**5 + 0*i**7. Factor p(t).
-t*(t - 1)**2*(t + 1)**2/2
Suppose 0 = n - 3*i - 263, -2*i + 1230 = -26*n + 31*n. Let s be ((-31)/n)/((-3)/8). Factor h + 0 - s*h**2.
-h*(h - 3)/3
Let l = -523706 - -36