Let l be (-38)/(-20) + 1/2. Solve 2/5*x**u + 18/5 - l*x = 0 for x.
3
Let n(q) be the third derivative of q**7/525 + 43*q**6/300 + 217*q**5/75 - 187*q**4/15 - 968*q**3/5 - 2*q**2 - 57*q. Find s, given that n(s) = 0.
-22, -2, 3
Let v(c) be the third derivative of c**6/420 - 47*c**5/210 + 85*c**4/28 - 123*c**3/7 + 7*c**2 + 73. Factor v(b).
2*(b - 41)*(b - 3)**2/7
Let l = 395 + -392. Factor -13*i**l - 10*i**2 + 12*i**3 + 7*i**2.
-i**2*(i + 3)
Suppose 30*v = 43 + 77. Let c(b) = b**2 - 16*b - 31. Let p be c(18). Suppose -2*a**v + 4/5 + 26/5*a - 8/5*a**p + 22/5*a**3 + 46/5*a**2 = 0. What is a?
-1, -1/4, 2
Let c = 4189/20 + -11207/60. Determine x, given that c*x + 1156/3 + 1/3*x**2 = 0.
-34
Let q = -17054 - -17054. Let l(i) be the first derivative of 5/6*i**6 + 5/3*i**3 + q*i**2 + 10 + 3*i**5 + 0*i + 15/4*i**4. Solve l(d) = 0 for d.
-1, 0
Suppose 0 = 2*o - 0*y + 5*y - 51, o = -5*y + 23. Suppose 0*r - 7*r + o = 0. Determine z, given that 2*z**2 + r*z**3 + 10*z - 12*z - 2*z**4 - z - z = 0.
-1, 0, 1, 2
Let z = -1488106 + 1488129. Factor z*h + 0 + 1/2*h**3 + 25/2*h**2.
h*(h + 2)*(h + 23)/2
Let -2604 - 942 - 4*r**2 - 3260*r + 290 = 0. What is r?
-814, -1
Find n, given that -70 - 278/3*n - 202/9*n**2 + 2/9*n**3 = 0.
-3, -1, 105
Suppose 99*s = 17*s + 656. Let u be ((-858)/(-676))/(6/s). Determine t, given that -4/13*t - u*t**4 + 6/13*t**5 + 22/13*t**3 + 0 - 2/13*t**2 = 0.
-1/3, 0, 1, 2
Let m(t) = 4*t**2 - 50*t + 359. Let o be m(28). Let d = 2097 - o. Factor 3/5*n**d + 3/5*n**3 - 12/5*n - 12/5.
3*(n - 2)*(n + 1)*(n + 2)/5
Suppose 5202/11*g + 0 - 204/11*g**2 + 2/11*g**3 = 0. What is g?
0, 51
Let a = -6223 + 6226. Suppose 0*h + 3/8*h**2 + 9/8*h**a + 9/8*h**4 + 0 + 3/8*h**5 = 0. What is h?
-1, 0
Let y(d) = 3*d**3 - 172*d**2 + 67*d - 566. Let u be y(57). Factor x - 3/2*x**2 + 0 - 1/4*x**3 + 3/8*x**u.
x*(x - 2)*(x + 2)*(3*x - 2)/8
Let d(t) be the third derivative of -10*t**7/21 - 11*t**6/2 - 57*t**5/5 + 361*t**4/6 - 4*t**2 - t + 3. Factor d(q).
-4*q*(q - 1)*(5*q + 19)**2
Suppose -128 + 18*z**2 - 63*z**3 - 16*z + 2*z**2 + 61*z**3 = 0. Calculate z.
-2, 4, 8
Let v(c) = 8*c**4 - 114*c**3 + 2164*c**2 - 5658*c + 3600. Let y(b) = -7*b**4 + 116*b**3 - 2164*b**2 + 5655*b - 3600. Let j(k) = 5*v(k) + 6*y(k). Factor j(r).
-2*(r - 30)**2*(r - 2)*(r - 1)
Let c(g) = 245*g - 9 - 5 + 2 - 3*g**2 + 2 - 222*g. Let r be c(7). Factor 0 + 2/3*j - 2/3*j**r - 2/3*j**3 + 2/3*j**2.
-2*j*(j - 1)*(j + 1)**2/3
Let j be (56870/(-66))/47*5/(-5). Factor 1/6*v**2 + j*v + 3025/6.
(v + 55)**2/6
Let o(h) be the second derivative of 1/4*h**5 - 34*h + 0*h**2 - 5/42*h**7 + 0*h**3 + 5/6*h**6 + 0 - 25/12*h**4. Suppose o(w) = 0. Calculate w.
-1, 0, 1, 5
Suppose 3*b - 570 = 3*f, -30*f - 574 = -3*b - 31*f. Factor -b*j + 12 + 181*j - 4*j**2 + 5*j**3 - 3*j**3.
2*(j - 3)*(j - 1)*(j + 2)
Solve 20*l**5 + 15837*l**2 + 752*l - 16893*l**2 + 393*l**3 - 192*l**4 + 275*l**3 - 192 = 0.
3/5, 1, 2, 4
Factor 3575 + 166*v + 2*v**2 - 3281 + 130*v.
2*(v + 1)*(v + 147)
Let n(v) be the third derivative of 5*v**2 - 1/15*v**6 + 0*v**3 + 0*v**4 + v + 0 + 1/84*v**8 + 2/105*v**7 + 0*v**5. Determine d so that n(d) = 0.
-2, 0, 1
Let p(q) be the third derivative of -268203*q**7/175 - 265811*q**6/100 + 716*q**5/15 - 4*q**4/15 - 2*q**2 + 303*q + 1. Factor p(m).
-2*m*(m + 1)*(897*m - 4)**2/5
Let l(m) be the first derivative of m**4/6 - 14*m**3/9 + 2*m**2 - 2589. Factor l(x).
2*x*(x - 6)*(x - 1)/3
Solve 12149*i**2 + 10350 - 2139*i**3 + 7630*i**2 - 4378*i + 27*i**4 - 46487*i = 0 for i.
2/9, 5, 69
Let l(a) = 10*a**4 - 348*a**3 - 118*a**2 + 224*a. Let x(j) = -9*j**4 + 346*j**3 + 118*j**2 - 225*j. Let c(h) = -3*l(h) - 4*x(h). Factor c(b).
2*b*(b - 57)*(b + 1)*(3*b - 2)
Let o(d) be the second derivative of 1/15*d**3 + 0*d**4 + 0*d**2 + 4*d - 1/50*d**5 - 1. Factor o(s).
-2*s*(s - 1)*(s + 1)/5
Let k(u) = u**3 - 23*u**2 + 43*u - 19. Let w(x) = -2*x**2 + 4*x + 21. Let o be w(0). Let z be k(o). Let -2480 + 2500 + 0*f**z - 5*f**2 = 0. Calculate f.
-2, 2
Let o(h) be the third derivative of -h**5/100 - 13*h**4/24 + 11*h**3/15 + 3643*h**2. Factor o(s).
-(s + 22)*(3*s - 1)/5
Let o(l) = -6152 - 40*l + 6107 - 2*l**2 - 69*l. Let h be o(-54). Determine u, given that -3*u**3 + 45/2*u**2 - h*u - 21/2 = 0.
-1/2, 1, 7
Let c(w) = -5*w + 195. Let v be c(38). Let m(o) be the first derivative of 3/5*o**2 + o**3 + 16 + 0*o + 9/20*o**4 - 1/10*o**6 - 3/25*o**v. Factor m(k).
-3*k*(k - 2)*(k + 1)**3/5
Let u be ((-140)/(-15) + -9)/(5/10). Let g(p) be the first derivative of 3*p**2 - 4*p - u*p**3 + 25. Determine h so that g(h) = 0.
1, 2
Let p(s) be the second derivative of 3*s**5/20 - 13*s**4/4 + 25*s**3 - 84*s**2 - 30*s + 17. Factor p(n).
3*(n - 7)*(n - 4)*(n - 2)
Let a = -482181 + 482183. Factor 2/9*x**a + 22/3 + 68/9*x.
2*(x + 1)*(x + 33)/9
Suppose -4*q + 478 = -2*q. Factor 4*y**3 + 58*y - 3*y - 261 - 60*y**2 - q + 245*y.
4*(y - 5)**3
Find b, given that 330*b**4 + 10890*b**3 + 0 + 0*b**2 + 5/2*b**5 + 0*b = 0.
-66, 0
Suppose 0 = -3*j + 2*i + 3*i - 60, -j + 3*i - 20 = 0. Let v be 5/j + 33/4 + 1. Let 4*r**2 - 8 + v + r**2 + 20*r + 19 = 0. Calculate r.
-2
Factor 30 + 27*c - 4/3*c**3 - 55/3*c**2.
-(c - 2)*(c + 15)*(4*c + 3)/3
Determine r so that 11*r**3 + 21*r**2 + 638*r**4 - 36*r**5 - 662*r**4 - 98*r + 64*r**3 + 56*r**3 = 0.
-2, -1, 0, 7/6
Suppose g**5 + 193*g**2 - 32*g**2 + 83*g**3 + 31*g + 185*g + 80 + 44*g**2 + 15*g**4 = 0. Calculate g.
-5, -4, -1
Suppose -1573*q = -1570*q - 24, -2*d + 2*q - 10 = 0. Solve 2/3*a**5 + 4*a**2 - 16/3*a**d + 14/3*a + 0 - 4*a**4 = 0.
-1, 0, 1, 7
Let d(g) = -3*g + 86. Let f be d(28). Solve -4*o**5 + 8*o**4 + 6*o**2 - 22*o**f - 12*o**3 + 12*o**4 + 7*o**2 - 27*o**2 = 0.
-1, 0, 3
Suppose 28*x + 12 = 4*o + 30*x, 3*x - 26 = -10*o. Let l(j) be the second derivative of -3*j - 1/72*j**4 + 0*j**3 + 0 + 0*j**o + 1/120*j**5. Factor l(y).
y**2*(y - 1)/6
Suppose -388 + 298 - 134*y - 20*y + 45*y**2 - 241*y = 0. What is y?
-2/9, 9
Let h(y) be the second derivative of -92*y + 6*y**2 - 5/3*y**3 + 0 + 1/6*y**4. Find o, given that h(o) = 0.
2, 3
Let b(m) be the third derivative of m**5/450 + 83*m**4/90 + 161*m**3/9 + 4*m**2 + 577*m - 1. Solve b(v) = 0.
-161, -5
Let b be (-406)/(-4263) - 328/(-84). Factor -16/7*q + 2/7*q**b + 24/7*q**2 + 0 - 12/7*q**3.
2*q*(q - 2)**3/7
Determine g so that -222784/5*g**2 + 0 + 0*g - 944/5*g**3 - 1/5*g**4 = 0.
-472, 0
Solve -4012009/5 + 4006/5*w - 1/5*w**2 = 0 for w.
2003
Let v = 331847 + -2322925/7. Factor 0 - 2/7*s**2 + v*s.
-2*s*(s - 2)/7
Suppose 12 = -72*c + 75*c. Suppose c*r = 5*j + 18, -5*r - 4*j + 4 = -j. Factor 1/2 - 1/2*n**3 + 1/2*n - 1/2*n**r.
-(n - 1)*(n + 1)**2/2
Let y = 713 + -601. Factor 56*b**4 - 16*b - 4*b**3 - 4*b**4 - y*b**2 - 40*b**3.
4*b*(b - 2)*(b + 1)*(13*b + 2)
Solve -124/7*v + 22 + 10/7*v**2 = 0.
7/5, 11
Let q be 12/(-168)*(8 - (4 - -8)). Factor -10/7*r + 2/7*r**3 - q*r**2 - 6/7.
2*(r - 3)*(r + 1)**2/7
Let z = 219061/2 + -109512. Factor 11/2*w**3 + z*w - 1/4*w**4 + 18*w**2 + 25/4.
-(w - 25)*(w + 1)**3/4
Suppose 0 = -173*v + 177*v - 204. Let w be (-2)/5 - v/(-15). Determine i so that 6*i**2 + i - 14*i**2 + 6*i**2 + i**w = 0.
0, 1
Suppose 4*i = c + 1, 3 = 3*i + 9. Let q be (35/70)/((-1)/c). Find u such that 28*u**3 - q + 21*u - 8*u**4 - 73/2*u**2 = 0.
3/4, 1
Let o(a) = 3*a**3 - 10*a**2 - 7*a - 2. Let h(y) = -10*y**3 + 31*y**2 + 20*y + 7. Let g = -231 + 233. Let p(x) = g*h(x) + 7*o(x). Find i, given that p(i) = 0.
-1, 0, 9
Suppose 105*f - 20*f - 316 = -73*f. Let b = 276 - 1929/7. Factor -3/7*s**f + b*s + 6/7.
-3*(s - 2)*(s + 1)/7
Let x be (70/(-105))/((-3)/18). Factor -1099*d**4 - 82*d**3 - 18*d**3 + 4*d**5 + 1055*d**x - 52*d**2.
4*d**2*(d - 13)*(d + 1)**2
Let m = 1097461 - 1097457. Find p such that -99*p**2 - 31/3*p**3 + 2662/3 - 605/3*p - 1/3*p**m = 0.
-11, 2
Suppose -4*i + 3480 + 1768 = 0. Find w such that 934 + 2*w**2 - 116*w + i - 564 = 0.
29
Let q(k) be the second derivative of 25/2*k**3 + 45/2*k**2 + 1/4*k**5 - 88*k + 35/12*k**4 + 0. Find a, given that q(a) = 0.
-3, -1
Factor -1490 + 204*p**2 + 669 + 64*p + 757 - 54*p**3.
-2*(p - 4)*(3*p + 2)*(9*p - 4)
Solve -9/2*q**3 + 0*q + 11*q**2 - 1/2*q**4 + 0 = 0 for q.
-11, 0, 2
Let r(o) = -o**3 + 26*o + 46. Let f be r(-2). Let l(n) be the second derivative of -1/45*n**6 - 3*n - 1/6*n**5 + 0 - 4/9*n**4 - 4/9*n**3 + 0*n**f. Factor l(s).
-2*s*(s + 1)*(s + 2)**2/