29*t. Let c(u) be the first derivative of -5 + 0*u**5 - 1/18*u**6 + 0*u + 1/12*u**4 + 0*u**t + 0*u**2. Find v, given that c(v) = 0.
-1, 0, 1
Let x = -439 + 443. Find z such that -28*z**3 - 531*z + 222*z**2 + 2 - 319*z**4 + 320*z**x + 167*z + 167 = 0.
1, 13
Suppose 5*b - 459 = 2*j, -2*b + 0*j - 2*j + 192 = 0. Let o = 97 - b. Determine t, given that -o*t**3 + 4*t - 12 - 18*t**3 + 12*t**2 + 18*t**3 = 0.
-1, 1, 3
Let p(n) = -2*n**2 - n - 1. Let v(l) = -11*l**2 - 19*l - 22. Let w(q) = 4*p(q) - v(q). Factor w(s).
3*(s + 2)*(s + 3)
Let f(h) = 5*h**2 + 436*h - 420. Let v(j) = 2*j**2 + 4*j + 1. Let u(k) = 4*f(k) - 12*v(k). Determine s so that u(s) = 0.
1, 423
Let j(v) be the first derivative of 1 + 0*v**3 + 1/60*v**5 + 1/8*v**4 - 1/2*v**2 + 0*v. Let f(y) be the second derivative of j(y). Solve f(o) = 0.
-3, 0
Suppose -425*f - 210*f + 1254 = -8*f. Let 16 + 46/3*v**f - 1/3*v**3 + 95/3*v = 0. Calculate v.
-1, 48
Let t(o) = -o**2 + o + 2. Let n(i) = -i**3 - 870*i**2 - 875*i - 6. Let f(c) = 4*n(c) + 12*t(c). Factor f(b).
-4*b*(b + 1)*(b + 872)
Let v = -2333/30 + -1669/10. Let o = v - -246. Factor -o*d + 0 - 4/9*d**2.
-4*d*(d + 3)/9
Factor -282*k + 1/2*k**2 + 0.
k*(k - 564)/2
Let i be (43 - 4 - 39)/(0 + -1). Let 4/3*u**3 + i*u + 0 - 4/3*u**2 = 0. What is u?
0, 1
Let k = -7 - -39. Solve -84*j**3 + 36*j + 8 - 5*j**2 - k*j**4 + 9*j**2 + 68*j**4 = 0 for j.
-1/3, 1, 2
Let k(w) be the first derivative of -3*w**5/5 - 15*w**4/4 + 7*w**3 + 15*w**2/2 - 18*w + 1556. Factor k(g).
-3*(g - 1)**2*(g + 1)*(g + 6)
Determine s so that -2/7*s**5 + 12/7*s**3 - 8/7*s**4 + 0 + 8/7*s**2 - 10/7*s = 0.
-5, -1, 0, 1
Suppose 9*q = 5*w + 7*q - 16, -12 = -5*w + 4*q. Determine b so that -93*b**2 - b**5 + 30*b + 46*b**2 + 12*b**4 + 3*b**w + 3*b**3 = 0.
-2, 0, 1, 15
Let 1/3*i**4 + 248/3 + 59/3*i**3 - 62*i**2 + 4/3*i = 0. Calculate i.
-62, -1, 2
Suppose 5*o - 2*m - 301 = -3*m, -4*m = 4*o - 244. Let v = o + -58. Find n, given that -3*n**v - 25 - 2*n**2 + 17*n - 100 + 33*n = 0.
5
Let u(p) be the second derivative of -32*p**7/105 - 8944*p**6/75 - 15489*p**5/25 - 1816*p**4/3 + 15448*p**3/15 - 2208*p**2/5 - 279*p + 5. What is y in u(y) = 0?
-276, -2, 1/4
Let m be 1*8/(-36) - 356/18. Let v(k) = -k**2 - 21*k - 17. Let a be v(m). Factor -4*d + 0*d**3 - 6*d**3 + 4*d**a - 5*d**2 - 1.
-(d + 1)**2*(2*d + 1)
Let f be (-340)/(-80) + ((-55)/(-20) - 2). Let j(i) be the second derivative of 0 + 1/20*i**6 + 12*i + i**3 + 3/4*i**4 + 3/10*i**f + 3/4*i**2. Factor j(v).
3*(v + 1)**4/2
Suppose 20 = 2*t - 3*c, -5*t - 14*c + 5*c + 50 = 0. Suppose 0 = 13*l - 8*l - t. What is j in -2*j - 1/2*j**l - 2 = 0?
-2
Let x(i) be the second derivative of i**7/630 + 29*i**3/3 - i - 46. Let q(v) be the second derivative of x(v). Suppose q(f) = 0. What is f?
0
Factor -780 - 3/5*n**2 + 51*n.
-3*(n - 65)*(n - 20)/5
Let p(d) be the second derivative of d**6/120 + d**5/10 - 11*d**4/16 + d**3/6 + 11*d**2/2 - 1146*d. Find u such that p(u) = 0.
-11, -1, 2
Let o(g) be the first derivative of -4/3*g**3 - 2*g**4 - 2/5*g**5 + 4*g**2 + 6*g - 73. Factor o(v).
-2*(v - 1)*(v + 1)**2*(v + 3)
Let i be 306 + 6/(12 - 6). Determine k, given that i*k**4 + 309*k**2 - 24*k**3 - 147*k - 632*k**4 + 18 + 277*k**4 = 0.
-3, 1/4, 2
Let h(j) be the second derivative of -5*j**4/12 - 85*j**3 - 500*j**2 + 55*j + 9. Let h(f) = 0. What is f?
-100, -2
Let w = -95289/14 - -13619/2. What is d in -2/7*d**4 + 0 - 12/7*d**3 - w*d**2 - 12/7*d = 0?
-3, -2, -1, 0
Let b = 5140186/5 - 1027548. Solve b*d**3 + 18/5*d**5 - 968/5 - 82*d**4 - 4664/5*d - 822/5*d**2 = 0.
-1, -2/9, 2, 11
Let n(d) be the third derivative of -d**6/540 - 23*d**5/135 - 89*d**4/108 - 44*d**3/27 - 373*d**2 - 3*d. Factor n(x).
-2*(x + 1)**2*(x + 44)/9
Let j(n) be the second derivative of -3*n + 1/4*n**4 - 11 + 2187/2*n**2 - 27*n**3. Solve j(f) = 0.
27
Let s(i) = -i**3 + i**2 + 1. Suppose -11*t + 25 = -6*t. Suppose 5*p - 13 = -8. Let q(l) = 10*l**3 - 10*l**2 - 5*l. Let u(h) = p*q(h) + t*s(h). Factor u(a).
5*(a - 1)**2*(a + 1)
Let t = -155476 + 155478. Find o, given that -8/11*o**5 + 26/11*o**4 + 4/11*o**2 + 0*o - t*o**3 + 0 = 0.
0, 1/4, 1, 2
Let h be (96/(-14))/(2 - (-32)/(-14)). Let w be (4/h)/((-2)/(-18)). Solve -g**4 - 1/4*g**5 + 0 - w*g**3 - g**2 - 1/4*g = 0.
-1, 0
Let a = 31800 + -31798. Factor -6/7*y + 10/7*y**a - 2/7*y**4 - 2/7*y**3 + 0.
-2*y*(y - 1)**2*(y + 3)/7
Determine z, given that -299418309*z - 144*z**4 + 284*z**4 + 896*z**3 - 139*z**4 - 2903*z**3 + 1342683*z**2 = 0.
0, 669
Let x(u) = 8*u**5 + 32*u**4 + 12*u**3 + 4*u + 4. Let h(k) = -9*k**5 - 36*k**4 - 12*k**3 - 5*k - 5. Let l(o) = -4*h(o) - 5*x(o). Factor l(q).
-4*q**3*(q + 1)*(q + 3)
Let m be ((-456)/798)/(-9*2/14). Let r(o) be the second derivative of 20*o + 0 + 1/54*o**4 + m*o**2 + 4/27*o**3. Factor r(q).
2*(q + 2)**2/9
Let a(w) be the first derivative of -w**5/5 - 13*w**4/4 - 20*w**3/3 + 50*w**2 + 6328. Solve a(l) = 0.
-10, -5, 0, 2
Let l(p) = 8*p**3 - 11*p**3 + 2*p**3 - 2*p**2 - 2*p + 9. Let z be l(0). Determine c so that 1 - 21*c + z*c**2 - 4*c**4 + 3 + 21*c**3 - 11*c**4 + 2 = 0.
-1, 2/5, 1
Let a = 577845 + -1733471/3. What is w in 512/9*w + a*w**2 + 2/9*w**4 + 512/9 + 32/9*w**3 = 0?
-4
Let p(o) = 6*o**2 - 504*o + 21189. Let r(g) = -7*g**2 + 504*g - 21196. Let c(w) = -4*p(w) - 3*r(w). Factor c(n).
-3*(n - 84)**2
Find l, given that 12/5*l**2 + 142/5*l + 236/5 = 0.
-59/6, -2
Let z(b) = 27*b + 20459 - 20459. Let v be z(0). Factor 0 + v*c**2 - 1/3*c**5 + 0*c - 2/3*c**4 - 1/3*c**3.
-c**3*(c + 1)**2/3
Let p(k) be the first derivative of -3*k**4/20 - 21*k**3 - 2205*k**2/2 - 25725*k - 1648. Factor p(u).
-3*(u + 35)**3/5
Let u(o) be the third derivative of -o**8/1008 + o**7/63 + o**6/10 + 19*o**5/90 + 13*o**4/72 - 494*o**2. Factor u(b).
-b*(b - 13)*(b + 1)**3/3
Let u be (-6*8/(-15) - 1) + (91 - (-15279)/(-165)). Find c, given that 93/5 - u*c**2 - 18*c = 0.
-31, 1
Let g = -1/1588076 - -794041/4764228. Find k such that 0*k**2 - g*k**3 + 10/3 + 7/2*k = 0.
-4, -1, 5
Suppose -5/8*l**2 + 23/8*l + 5/4 = 0. Calculate l.
-2/5, 5
Factor -227/3*u + 30 + 5/3*u**2.
(u - 45)*(5*u - 2)/3
Let c(x) = 841*x**3 - 6493*x**2 - 1855*x - 131. Let d(q) = -1682*q**3 + 12987*q**2 + 3705*q + 261. Let f(v) = -5*c(v) - 3*d(v). Factor f(z).
(z - 8)*(29*z + 4)**2
Let y(x) = -x**3 + 33*x**2 + 11*x - 223. Let k be y(33). Let b be 28/k - (-74)/30. Find j, given that -b + 6*j - 4/3*j**2 = 0.
1/2, 4
Let n(b) be the first derivative of 45/2*b**4 - 76*b**2 - 4/3*b**6 + 40/3*b**3 - 96*b + 133 - 14/5*b**5. Solve n(l) = 0.
-4, -1, -3/4, 2
Factor 33/2*y**4 + 0*y + 1/2*y**5 + 63/2*y**3 + 31/2*y**2 + 0.
y**2*(y + 1)**2*(y + 31)/2
Let u(x) be the first derivative of -5*x**4/16 + 325*x**3/12 - 5115*x**2/8 - 5445*x/4 + 584. Factor u(l).
-5*(l - 33)**2*(l + 1)/4
Let j(u) = -9*u**3 + 375*u**2 + 375*u - 753. Let i(m) = 11*m**3 - 376*m**2 - 373*m + 754. Let w(l) = -3*i(l) - 4*j(l). Find b, given that w(b) = 0.
-2, 1, 125
Let z(p) be the first derivative of -2/15*p**3 + 0*p + 80 + 0*p**4 - 1/60*p**6 + 3/50*p**5 + 0*p**2. Factor z(k).
-k**2*(k - 2)**2*(k + 1)/10
Let b(k) be the first derivative of -k**6/3 - 24*k**5/5 - 22*k**4 - 140*k**3/3 - 51*k**2 - 28*k - 983. Let b(d) = 0. What is d?
-7, -2, -1
Let f(j) be the second derivative of -j**5/25 + 179*j**4/60 + 37*j**3/3 + 187*j**2/10 - 1374*j. Determine i so that f(i) = 0.
-1, 187/4
Let b(r) be the first derivative of 25*r**4/4 + 240*r**3 + 2355*r**2/2 - 500*r + 2957. What is n in b(n) = 0?
-25, -4, 1/5
Let r be (872/460 - 2)*(-350)/20. Let b = r + -355/207. Factor -4/9*s + 4/9*s**3 - 2/9*s**2 + 1/3 - b*s**4.
-(s - 3)*(s - 1)**2*(s + 1)/9
Let s(p) be the third derivative of -11*p**5/720 + 9*p**4/32 + 23*p**3/18 - 5827*p**2. Find w such that s(w) = 0.
-1, 92/11
Let j = -1331 - -1333. Let m(p) be the third derivative of 0*p + p**3 + 0 + 7/12*p**4 + 12*p**j + 1/60*p**6 + 1/6*p**5. Factor m(f).
2*(f + 1)**2*(f + 3)
Let t(c) be the second derivative of c**7/399 + 134*c**6/95 + 40801*c**5/190 + 13400*c**4/19 + 40000*c**3/57 + 20*c - 16. Suppose t(y) = 0. Calculate y.
-200, -1, 0
Factor 2/5*q**2 + 7352/5*q + 6756488/5.
2*(q + 1838)**2/5
Let y = -135838/5 - -27168. Suppose 0 = 3*j - 53 + 44. Determine q, given that 2/5*q**2 - 2/5 + y*q**j - 2/5*q = 0.
-1, 1
Let a(w) = w**3 + 460*w**2 + 2304*w + 13197. Let m be a(-455). Factor -54/5 + 3/5*k**m + 9/5*k.