
Let h(a) be the first derivative of a**3 + 1083*a**2/2 - 1086*a - 5284. Let h(d) = 0. Calculate d.
-362, 1
Let p = 98589 + -695558/7. Let m = p - -781. Solve m + 4/7*z**2 - 36/7*z = 0.
1, 8
Suppose 2*n - 119 = 25. Let w be n/5 + (-4)/10. Find r, given that w + 20*r**2 + 15 - 11 - 42*r - r**5 - r**5 + 12*r**3 - 6*r**4 = 0.
-3, 1
Let r(k) be the first derivative of k**4/22 + 336*k**3/11 + 1005*k**2/11 + 1004*k/11 + 1900. Factor r(h).
2*(h + 1)**2*(h + 502)/11
Let x(d) = -4*d**5 + 4*d**4 + 10*d**3 + 14*d**2 - 6*d - 6. Let h(r) = -2*r**4 - r**3 - r**2 + r + 1. Let j(w) = 6*h(w) + x(w). Determine g so that j(g) = 0.
-2, -1, 0, 1
Let h(x) be the first derivative of -4*x**5/5 + 611*x**4 - 124844*x**3 + 183610*x**2 + 744200*x - 607. Find f, given that h(f) = 0.
-1, 2, 305
Let q = -6397/10 - -641. Let v = q + 61/30. Find c, given that v*c**2 + 5/6*c**3 + 25/6*c + 5/3 = 0.
-2, -1
Suppose 9*i - 15*i + 12 = 0. Let z be i - 710/1425 - (-4)/(-30). Factor z*w**4 + 0 + 4/19*w - 10/19*w**5 - 18/19*w**3 - 2/19*w**2.
-2*w*(w - 1)**3*(5*w + 2)/19
Factor -3518*d**2 + 5941*d**2 - 25*d**4 + 1476*d**2 + 2385*d**3 + 194 - 1845*d.
-(d - 97)*(d + 2)*(5*d - 1)**2
Suppose -5*m = -2*g - 36, 9*g + 2*m - 6 = 14*g. Let q(h) be the first derivative of -1/6*h**3 - 5/16*h**g + 4 + 1/32*h**4 + 0*h. Factor q(x).
x*(x - 5)*(x + 1)/8
Let w(n) be the third derivative of 1/1365*n**7 + 2/39*n**4 + 0*n**6 + 0 - 1/13*n**3 + 85*n**2 - 1/65*n**5 + 0*n. Factor w(z).
2*(z - 1)**3*(z + 3)/13
Suppose 36/5*a**3 - 405 - 414/5*a**2 - 1/5*a**4 + 324*a = 0. What is a?
3, 15
Let v(n) = n**2 + 49*n + 184. Let w(a) = -4*a + 59. Let g be w(26). Let p be v(g). Factor 9/5*f**2 + 12/5*f**3 + 4/5*f**p + 0 + 2/5*f.
f*(f + 2)*(2*f + 1)**2/5
Let s(n) be the third derivative of 256/15*n**3 - 66*n**2 + 7/75*n**6 - 16/5*n**4 + 0 + 6/175*n**7 + 1/420*n**8 + 0*n - 56/75*n**5. Factor s(j).
4*(j - 2)*(j - 1)*(j + 4)**3/5
Let a(y) be the second derivative of -3*y**5/20 + 117*y**4/4 - 231*y**3/2 + 345*y**2/2 - 3775*y. Factor a(v).
-3*(v - 115)*(v - 1)**2
Let d(h) be the third derivative of -h**5/30 + 202*h**4/3 - 269*h**3 + 25*h**2 + 6*h. Find y such that d(y) = 0.
1, 807
Let o be (-4)/(-5) + (-3806)/(-1730). Let x(k) be the first derivative of k + 2/15*k**5 + 11 - 5/9*k**o - 5/6*k**2 + 5/12*k**4. Let x(d) = 0. Calculate d.
-3, -1, 1/2, 1
Let v = 21473 - 64391/3. Let t(d) be the first derivative of 8 + 6/5*d**5 - 24*d**2 - 18*d + v*d**3 + 8*d**4. Factor t(l).
2*(l - 1)*(l + 3)**2*(3*l + 1)
Suppose 2 = -w + 6. Let 19*s**5 - 12*s**4 + 4*s**2 - 12*s**5 + 35*s**w + 20*s**3 = 0. Calculate s.
-2, -1, -2/7, 0
Let z(g) be the second derivative of -5*g**7/42 - 4*g**6 + g**5/2 + 20*g**4 - 5*g**3/6 - 60*g**2 - 835*g. Determine r so that z(r) = 0.
-24, -1, 1
Factor 154*j**4 - 138701*j**3 + 3833*j**2 + 134165*j**3 + 7831*j**2 - 28*j**4 - 3*j**5 + 99*j**4.
-3*j**2*(j - 36)**2*(j - 3)
Factor 362332*v**2 + 570*v**4 - 289744 + 422396*v**2 - 508642 + 36282*v**3 + 492161*v - 701896 + 186538*v + 3*v**5.
3*(v - 1)*(v + 2)*(v + 63)**3
Let s = 3027/32 + -2971/32. Find x such that -5/4*x + s*x**2 - 1/2*x**3 + 0 = 0.
0, 1, 5/2
Let p(j) be the third derivative of -j**3/6 + j**2. Let x(g) = -g**2 + 14*g - 54. Let y = -12748 + 12753. Let s(c) = y*p(c) - x(c). Solve s(d) = 0.
7
Let b be (-28 + 27)/((-1)/3). Let m(u) be the first derivative of -4/3*u**b + 2 - 9/2*u**4 + 9*u**2 + 4*u. Factor m(h).
-2*(h - 1)*(h + 1)*(9*h + 2)
Let i(t) be the first derivative of 1/2*t**4 - 127 - 35/6*t**2 - 2*t + 7/9*t**3. What is o in i(o) = 0?
-3, -1/6, 2
Find w such that 0 + 2/15*w**4 - 2*w**3 + 2*w - 2/15*w**2 = 0.
-1, 0, 1, 15
Let h(q) be the third derivative of q**5/180 + 19*q**4/36 - 42*q**2 - 3*q. Factor h(v).
v*(v + 38)/3
Let u = 388 + -379. Factor 15*h**3 - 21*h - 22*h**3 - 29*h + u*h**3 + 250 - 7*h**2 - 3*h**2.
2*(h - 5)**2*(h + 5)
Let x(n) = -n**4 + 75*n**3 + 121*n**2 - 471*n + 268. Let q(i) = -3*i**4 + 300*i**3 + 483*i**2 - 1884*i + 1074. Let m(f) = -4*q(f) + 15*x(f). Factor m(b).
-3*(b - 1)**2*(b + 4)*(b + 23)
Let q(l) be the second derivative of l**6/10 + 3*l**5/2 + 21*l**4/4 - 2*l**3 - 42*l**2 - 288*l. Factor q(t).
3*(t - 1)*(t + 2)**2*(t + 7)
Suppose -n - f = -0*f - 105, -3*n + 3*f + 327 = 0. Let t be -109 + n + (-2)/(12/(-13)). Factor t + 1/6*w**2 - 1/3*w.
(w - 1)**2/6
Let k be (-6)/4 - (-105)/30. Suppose 4*a - k*a + 4*f = 28, 2*a = 5*f - 17. Factor 10*u**4 + 3*u**4 + 10*u**3 - 5*u**a + 2*u**2.
2*u**2*(u + 1)*(4*u + 1)
Solve 7/3*q + 0 - 1/3*q**2 = 0.
0, 7
Determine l so that 234/7 - 87/7*l + 3/7*l**2 = 0.
3, 26
Factor 1/3*o**3 + 76/3 - 76/3*o**2 - 1/3*o.
(o - 76)*(o - 1)*(o + 1)/3
Let b = 580 + -836. Let d = b + 1312/5. Solve -18/5*i**2 - d + 2/5*i**3 + 48/5*i = 0.
1, 4
Determine u, given that -10691 + 4958*u - 1640*u**2 - 4*u**4 - 102*u**3 - 3889 + 294*u**3 - 21374*u = 0.
-5, -1, 27
Let x(r) = 7*r**3 - 13*r**2 + 55*r + 21. Let a(s) = -10*s**3 + 12*s**2 - 54*s - 22. Let o(l) = 5*a(l) + 6*x(l). Factor o(h).
-2*(h - 2)*(h + 4)*(4*h + 1)
Let r(m) be the second derivative of -5/2*m**3 - 1/48*m**4 - 225/2*m**2 + 63*m + 0. Factor r(o).
-(o + 30)**2/4
Suppose 4*d + 28*d + 13376 = 0. Let j be (38/d)/((-75)/24 + 3). Factor 2/11*i**2 - j + 8/11*i - 2/11*i**3.
-2*(i - 2)*(i - 1)*(i + 2)/11
Let f(z) be the second derivative of -7*z**6/10 - 2343*z**5/5 + 5373*z**4/4 - 673*z**3 - 1344*z**2 + 6745*z. Let f(c) = 0. Calculate c.
-448, -2/7, 1
Let v = -66 - -50. Let x be ((-6)/(-24))/((-2)/v). Find h such that x*h - 4*h**2 + 4*h**2 + 5*h**2 - 6*h**2 = 0.
0, 2
Let w be ((4/56)/(30/3600) - 12)/(20/(-42)). Let 5*u**4 - w*u**2 + 68/5*u - 16/5 - 19*u**3 = 0. What is u?
-1, 2/5, 4
Let z(g) be the first derivative of -g**3/12 - 374*g**2 - 559504*g + 2603. Find m, given that z(m) = 0.
-1496
Let c(l) = -2*l**2 + 744*l + 75532. Let d be c(455). Suppose 0 + 2*n - 1/4*n**d = 0. Calculate n.
0, 8
Let x(n) be the second derivative of n**5/15 + 2311*n**4/9 - 4624*n**3/9 + 2*n + 1860. Determine f, given that x(f) = 0.
-2312, 0, 1
Let p = 16786 + -16786. Determine f so that -4*f**5 + p + 12/7*f**3 - 4/7*f + 2*f**2 - 34/7*f**4 = 0.
-1, 0, 2/7, 1/2
Let x(m) = 17*m**2 + 7*m - 210. Let k(a) = 3*a**2 + 3*a. Let y(c) = -6*k(c) + 2*x(c). Let y(f) = 0. What is f?
-5, 21/4
Suppose 0*s = 2*s - 66. Let a = s + -24. Factor -9 + 6*y**3 - 4*y**2 - 11 + a*y**2 - y**3 - 20*y.
5*(y - 2)*(y + 1)*(y + 2)
Let -24/7 + 1/7*p**5 - 5/7*p**3 + 4/7*p - 6/7*p**4 + 30/7*p**2 = 0. What is p?
-2, -1, 1, 2, 6
Suppose 0 = -8*m - 46*m + 4*m. Factor m*b + 0 + 1/2*b**2 - 1/2*b**3.
-b**2*(b - 1)/2
Find c such that 58*c**2 + 70*c**2 + 650 - 126*c**2 - 454*c - 198*c = 0.
1, 325
Let q(o) = 25*o**2 - 109*o + 50. Let a(f) = 27*f**2 - 111*f + 51. Let u(l) = 4*a(l) - 3*q(l). Determine h, given that u(h) = 0.
6/11, 3
Let 0*o**4 + 0*o - 2/11*o**2 + 0 - 1/11*o**5 + 3/11*o**3 = 0. What is o?
-2, 0, 1
Let s(r) be the third derivative of r**7/70 + 11*r**6/40 + 3*r**5/2 - 4*r**4 - 80*r**3 + 736*r**2. Factor s(n).
3*(n - 2)*(n + 4)**2*(n + 5)
Suppose -2*a + 0 = -3*r - 21, -5*a + 40 = -5*r. Let u(i) be the first derivative of 14/9*i**2 + 98/9*i + 8 + 2/27*i**a. Find c such that u(c) = 0.
-7
Let o be 1 + -6 + (-1)/(-1). Let h(n) = -4*n - 16. Let q be h(o). Factor -12*c**4 - 32*c**3 + 10*c + q*c + 4*c**3 + 6*c.
-4*c*(c + 1)*(c + 2)*(3*c - 2)
Factor 76/3*f - 16/3*f**2 - 1/3*f**3 - 80/3.
-(f - 2)**2*(f + 20)/3
Let j(y) be the first derivative of y**4/44 + 19*y**3/33 + 39*y**2/11 - 1940. Factor j(i).
i*(i + 6)*(i + 13)/11
Let 2*t**2 + 16*t**2 + 108*t + 416 + 42*t**2 - 80*t**2 = 0. What is t?
-13/5, 8
Let r(q) = 8*q**2 + 1145*q + 2288. Let w(n) = 38*n**2 + 5726*n + 11440. Let x(k) = -28*r(k) + 6*w(k). What is j in x(j) = 0?
-572, -2
Let n(g) = g**2 - 35*g + 180. Let p be n(29). Determine l, given that 24*l - 9*l**2 - 25 + 5*l**2 - p*l**3 + 2*l**4 + 9 = 0.
-2, 1, 2
Let o(h) be the third derivative of -h**8/3192 + 23*h**7/1995 - 139*h**6/1140 - 9*h**5/38 + 162*h**4/19 + 972*h**3/19 - 5*h**2 - 24. Factor o(w).
-2*(w - 9)**3*(w + 2)**2/19
Let h = 1816 + -1746. Let v be 12/(40/h*7). Factor 0*b**2 + 3/2*b**v - 1/2*b**4 - 2*b + 0.
-b*(b - 2)**2*(b + 1)/2
Let w(l) be the third derivative of l**3 + 0 + 0*l + 1/60*l**6 - 11/60*l**5 + 7*l**2 - 7/24*l**4. Factor w(b).
(b - 6)*(b + 1)*(2*b - 1)
Let p = 48 - 48. Suppose -i = -5*v - 5*i + 3, p = -5