-3. Let d be (1 + 0 - 1)*(-17 + m). Suppose d*w**3 + 1/2*w**4 - w**2 + 0*w + 1/2 = 0. Calculate w.
-1, 1
Let w(c) be the third derivative of 1/9*c**4 + 4/27*c**3 - 20*c**2 + 1/90*c**6 + 0*c + 1/945*c**7 + 13/270*c**5 + 0. Suppose w(p) = 0. Calculate p.
-2, -1
Let f = -7820644/5 + 1564130. Factor -4/5 + 2/5*p**4 + 6/5*p + 2/5*p**2 - f*p**3.
2*(p - 2)*(p - 1)**2*(p + 1)/5
Suppose 4 = -2*u + 3*u. Let s = -1186 - -2034. Factor -848*v + s*v - v**u - v**3.
-v**3*(v + 1)
Let z = -61703/18 - -3428. Let h(q) be the first derivative of 0*q + 4/27*q**3 - z*q**4 - 6 + 0*q**2. Factor h(c).
-2*c**2*(c - 2)/9
Determine l, given that 1687500 + 449/2*l**3 + 1653750*l - 1/2*l**4 - 33525*l**2 = 0.
-1, 150
Let o(t) be the second derivative of 1/4*t**4 + 0 - 9/2*t**3 - 158*t + 21*t**2. Factor o(g).
3*(g - 7)*(g - 2)
Let p = -1973 - -41437/21. Let g(b) be the first derivative of p*b**3 - 10/7*b**2 + 24/7*b - 15. Factor g(q).
4*(q - 3)*(q - 2)/7
Let c(t) be the second derivative of 0*t**2 - 8 - 1/4*t**5 + 0*t**4 + 5/14*t**7 + 0*t**3 - 3*t - 1/3*t**6. Factor c(w).
5*w**3*(w - 1)*(3*w + 1)
Suppose 210 = 12*v - 3*c, -206*v + 207*v - 5*c = 8. Determine q, given that 138*q + v - 1587/2*q**3 - 600*q**5 + 315/2*q**2 - 1620*q**4 = 0.
-2, -3/5, -1/4, 2/5
Suppose 18 = -34*m + 36*m. Let q be ((-17)/((-153)/24))/(26/m). Determine g so that -8/13*g**2 + 2/13*g**4 + 0 + 2/13*g**5 + 16/13*g - q*g**3 = 0.
-2, 0, 1, 2
Suppose -551*t + 553*t - h = -8, 2*t = -h + 8. Factor t + 1/2*l**3 - 2/3*l - 2/3*l**2 + 1/3*l**4 - 1/6*l**5.
-l*(l - 2)**2*(l + 1)**2/6
Let r be (-30)/4*3/((-27)/6). Let a = -12 + 15. Solve -16*x**4 + 2*x**3 + 15*x**5 + 8*x**2 + 2*x**a - 4*x**5 - 23*x**r = 0.
-1, 0, 2/3
Let s be 4101/39 + 4/(-26). Let g be s/14*12/15. Factor 0*d**3 + 3 - d**3 - 6*d - 5*d**3 - g*d + 15*d**2.
-3*(d - 1)**2*(2*d - 1)
Let j(z) = 3*z - 12. Let k be j(12). Factor 4*c**2 - 6 + 12*c + 6 - k - 16.
4*(c - 2)*(c + 5)
Let m = -161600 + 484844/3. Determine g, given that 70/3*g**2 + 4*g**4 + m*g**3 + 14/3 + 1/3*g**5 + 17*g = 0.
-7, -2, -1
Let f be 8 + 66/(-18) + 1/((-12)/16). Let m(y) be the second derivative of 1/48*y**4 + 0*y**2 - 1/8*y**f + 9*y + 0. Solve m(w) = 0 for w.
0, 3
Let l = 120 - 36. Let j = l + -78. Solve 2*w**3 + 9*w**2 + 7*w - j*w**2 + 9*w + 8 + 7*w**2 = 0 for w.
-2, -1
Suppose -29*o**2 - 364/3 + 120*o - 1/3*o**3 = 0. What is o?
-91, 2
Suppose -16*i**2 + 29093*i**4 - 17*i**3 + 25*i**2 + 140*i + 23*i**2 - 29092*i**4 = 0. Calculate i.
-2, 0, 5, 14
Let u = -392696/7 + 56102. Suppose -32/7 - u*j**2 + 48/7*j = 0. What is j?
4/3
Solve -21115*k**2 + 5*k**5 - 7440*k + 1000*k**4 + 7435*k**3 - 2688*k**4 + 21780 + 1023*k**4 = 0.
-1, 1, 6, 121
Let s = 10/30129 - -240902/391677. Factor 2*o**2 - 56/13*o + s + 252/13*o**3 + 162/13*o**4.
2*(o + 1)**2*(9*o - 2)**2/13
Let u(r) be the first derivative of 3*r**5/10 - 21*r**4/2 - 30*r**3 + 566. Solve u(c) = 0 for c.
-2, 0, 30
Let p be (-40)/(-30)*-2*-1*3. Let 965*u**2 + 4 - 962*u**2 - u + p*u = 0. What is u?
-4/3, -1
Suppose 52775 = -37*k + 19105. Let h = k + 4561/5. Factor -1/5*g**3 + 6/5 - h*g + 6/5*g**2.
-(g - 3)*(g - 2)*(g - 1)/5
Let d(f) = -10*f**3 + 339*f**2 - 692*f + 363. Let n(a) = -8*a**3 + 271*a**2 - 554*a + 291. Let j(t) = -9*d(t) + 11*n(t). Factor j(l).
2*(l - 33)*(l - 1)**2
What is o in -38/5 + 78/5*o**2 + 36/5*o + 4/5*o**3 = 0?
-19, -1, 1/2
Let k(u) be the second derivative of 249*u + 17/12*u**4 + 0 - 1/120*u**5 - 289/3*u**3 + 9826/3*u**2. Factor k(b).
-(b - 34)**3/6
Suppose -41/2*i + 1/2*i**4 - 39/2*i**2 - 7 - 11/2*i**3 = 0. Calculate i.
-1, 14
Factor -246/13*w + 238/13*w**2 + 8/13.
2*(w - 1)*(119*w - 4)/13
Let g(n) = -78*n + 322. Let s be g(4). Let x be (6/s)/(-15 - 783/(-45)). Factor -1/2*d**2 - x*d**3 + 1/2 + 1/4*d.
-(d - 1)*(d + 1)*(d + 2)/4
Suppose 32*r - 52 + 18 = 8 + 22. Suppose 3/5*q**r + 12*q + 57/5 = 0. What is q?
-19, -1
Let s(l) be the first derivative of l**5/20 + 5*l**4/8 + 3*l**3 + 27*l**2/4 + 27*l/4 + 211. Suppose s(j) = 0. What is j?
-3, -1
Let l(j) be the third derivative of -51/4*j**4 + 0*j - 198*j**2 + 1/20*j**5 + 2601/2*j**3 + 0. Suppose l(n) = 0. What is n?
51
Let a(g) be the third derivative of -238*g**2 - 1/6*g**5 + 0*g + 5/3*g**3 - 1/24*g**4 + 1/120*g**6 + 0. Solve a(n) = 0.
-1, 1, 10
Let u = 550 + -252. Let c = u - 294. Determine m so that -2/3*m**3 - c*m + 10/3*m**2 + 0 = 0.
0, 2, 3
Let t(v) = v**3 + 250*v**2 + 3086*v + 1187. Let c be t(-237). Let -1/2*b**5 + 0*b + 0 + 1/6*b**4 + 0*b**c + 0*b**3 = 0. What is b?
0, 1/3
Let y(d) be the third derivative of -d**5/20 - 85*d**4/8 + 2*d**2 - 195. Suppose y(c) = 0. Calculate c.
-85, 0
Let j(o) = 2*o**3 + 26*o**2 + 11*o - 66. Let g be j(-2). Factor g + 57/4*m - 3/4*m**2.
-3*m*(m - 19)/4
Let k(s) = -s**3 + 6*s**2 + 7*s + 4. Let t be k(7). Suppose -2*w - 20 - 23 = -b, t*b - 4*w - 168 = 0. Factor -5*z**3 + 77*z**5 - b*z**5 - 31*z**5.
5*z**3*(z - 1)*(z + 1)
Let t(r) be the second derivative of 4/21*r**4 + 6/7*r**2 - 4*r + 13 - 1/70*r**5 - 13/21*r**3. Factor t(z).
-2*(z - 6)*(z - 1)**2/7
Factor -44224704*m**2 + 43096*m**3 + 482288149*m + 4852172858*m + 9798809169*m - 14*m**4 - 4320182304.
-2*(m - 1026)**3*(7*m - 2)
Let w(j) = -2*j**2 - 404*j + 1712. Let m(z) = z**2 + 405*z - 1684. Let b(f) = -4*m(f) - 3*w(f). Suppose b(s) = 0. Calculate s.
4, 200
Let p be (-328)/902 - (-80518)/(-66). Let w = p + 1223. Determine m, given that 0*m + 4/3*m**3 - w*m**2 + 0 + 20/3*m**5 + 32/3*m**4 = 0.
-1, 0, 2/5
Let -15/2 + 7/8*v**4 + 1/8*v**5 - 55/8*v**2 + 3/8*v**3 - 14*v = 0. Calculate v.
-5, -2, -1, 3
Suppose 3*u + 49*j = 47*j - 1643, -2*u = -2*j + 1092. Let n = u - -550. Factor -3*p + 147/4*p**n + 0 + 1029/8*p**4 - 21/2*p**2.
3*p*(7*p - 2)*(7*p + 2)**2/8
Let s(i) = 62*i**2 - 3614*i + 3568. Let c(w) = -35*w**2 + 2065*w - 2039. Let q(g) = -16*c(g) - 9*s(g). Factor q(r).
2*(r - 256)*(r - 1)
Let t(c) be the second derivative of -1/30*c**6 + 2 + 2/5*c**5 + 0*c**2 + 5/3*c**3 + c + 19/12*c**4. Determine b so that t(b) = 0.
-1, 0, 10
Suppose 7*v + 34 = 24*v. Factor 430*a**3 - 881*a**3 + 426*a**3 - 30*a**v - 5*a**4.
-5*a**2*(a + 2)*(a + 3)
Let t(u) = 30*u**2 + 2*u - 1. Let l(g) = 483*g**2 + 236*g + 2369. Let b(x) = l(x) - 16*t(x). Factor b(o).
3*(o + 15)*(o + 53)
Let f(u) be the first derivative of 49*u**4 - 116144*u**3/3 + 33160*u**2 - 9472*u - 5346. Factor f(o).
4*(o - 592)*(7*o - 2)**2
Let s(m) be the first derivative of -2*m**3/9 - 389*m**2/3 - 776*m/3 - 276. Factor s(c).
-2*(c + 1)*(c + 388)/3
Let n(y) = 2*y + 1. Let g(u) = 5*u**3 + 55*u**2 - 194*u + 143. Let a(t) = g(t) - 3*n(t). Factor a(p).
5*(p - 2)*(p - 1)*(p + 14)
Let p(v) be the second derivative of v**4/84 - 50*v**3/21 - 102*v**2/7 - v - 162. Determine u, given that p(u) = 0.
-2, 102
What is j in 1335*j**2 + 7863*j**2 - 9261 - 1323*j + 1322*j**3 + 65*j**4 - 2*j**4 + j**5 = 0?
-21, -1, 1
Let 13*b**2 + 9*b**2 + 1984*b + 3*b**2 - 28*b**2 + 7*b**2 = 0. Calculate b.
-496, 0
Let y(k) = -1 - 8*k - 2*k**2 - k**2 - 17 + 4*k**2. Let s be y(10). Determine a, given that -7*a - a - 64*a**2 - s - 40*a - 7 = 0.
-3/8
Solve 2274*n**5 - 15444 + 12852*n + 2286*n**5 + 2281*n**5 + 60*n**4 - 184*n**3 - 2664*n**2 - 6837*n**5 = 0.
-13, -11, 3
Let b = 58 + -60. Let f(m) = -900*m**2 - 242*m - 16. Let y(v) = 900*v**2 + 243*v + 16. Let h(r) = b*y(r) - 3*f(r). Factor h(o).
4*(15*o + 2)**2
Let v be ((-6)/(-4))/(-10*(-5)/100). Suppose v = 2*x + l, -l + 17 = 5*x + 8. Find r such that 10/11*r - 10/11*r**3 + 4/11*r**x - 4/11 = 0.
-1, 2/5, 1
Let f(c) be the first derivative of -2*c**3/51 - 72*c**2/17 + 936*c/17 - 6617. Find y such that f(y) = 0.
-78, 6
Let o(b) = 18*b**3 - 75*b**2 - 339*b + 9. Let q(m) = 35*m**3 - 148*m**2 - 679*m + 15. Let x(r) = 5*o(r) - 3*q(r). Suppose x(t) = 0. What is t?
-3, 0, 38/5
Let l(h) be the first derivative of h**4/20 - h**2/10 + 1599. Factor l(s).
s*(s - 1)*(s + 1)/5
Let s(z) be the second derivative of -2*z**6/15 + 2*z**5 - 16*z**4/3 + 300*z - 1. Find h, given that s(h) = 0.
0, 2, 8
Let o be (-11 + -3 + 11)/((-90)/11996). Let q = 400 - o. Let 4/15*i**2 - 2/15*i**4 - 2/15 - 2/15*i + 4/15*i**3 - q*i**5 = 0. Calculate i.
-1, 1
Find f, given that -438/7 + 6/7*f**2 + 1312/7*f = 0.
-219, 1/3
Let n = -1512672 + 12101379/8. Factor -69/8*x + n*x**2 + 63/4.
3*(x - 21)*(x - 2)/8
Let w(c) be the first derivative of c**7/21 + c**6/15 - 27*c - 29. Let