, 1
Let s = -168 + 173. Determine p so that 8*p - s*p**2 - 2*p**2 - 36*p + 3*p**2 - 48 = 0.
-4, -3
Let i be (-60)/(-175) - (-4)/5. Let q = -4427 - -4429. Factor -4/7*z**q + 4/7*z + i.
-4*(z - 2)*(z + 1)/7
Let n(i) = 8*i**2 + 3*i - 2. Let d be n(1). Suppose 2*o + d = -3*b, o + 3*b = 6*o - 30. Factor 41*k**3 - 40*k**o + 2*k**2 + 11*k + 5*k**2 + 5.
(k + 1)**2*(k + 5)
Suppose 2*n = -b - 15, -b - 74*n + 48 = -79*n. Suppose 2/23*v**b - 8/23*v + 0 + 0*v**2 = 0. Calculate v.
-2, 0, 2
Let x(m) = m**3 - 5*m**2 + 43*m + 149. Let f(k) = -8*k**2 + 44*k + 148. Let g(s) = -5*f(s) + 4*x(s). Factor g(t).
4*(t - 3)*(t + 2)*(t + 6)
Let o(l) = 12*l**2 - 5*l - 4. Let c be o(-1). Factor 11 + 20 + 6*y - 40 + c - 4*y**2.
-2*(y - 2)*(2*y + 1)
Let m(y) = 2*y**2 - 124*y + 845. Suppose -4*c - 4*c = -16. Let z(w) = 3*w**2 - 126*w + 845. Let b(o) = c*m(o) - 3*z(o). Factor b(r).
-5*(r - 13)**2
Let t(j) be the first derivative of j**8/840 + j**7/105 + j**6/45 + j**3 - 11. Let k(z) be the third derivative of t(z). Factor k(i).
2*i**2*(i + 2)**2
Factor 0*w**2 + 384/5 + 3/5*w**3 - 144/5*w.
3*(w - 4)**2*(w + 8)/5
Let o be (207 - 207)/(-2 - 1). Let v(l) be the second derivative of -1/12*l**3 - 1/84*l**7 + 1/20*l**5 - 1/12*l**4 + l + 1/60*l**6 + 1/4*l**2 + o. Factor v(p).
-(p - 1)**3*(p + 1)**2/2
Let f(t) be the third derivative of 169*t**5/180 - 39*t**4/2 + 162*t**3 + 2*t**2 + 223. Factor f(w).
(13*w - 54)**2/3
Let a(o) be the third derivative of 0*o**3 + 1/8*o**4 + 2 - 1/10*o**5 + 1/32*o**6 - 1/280*o**7 + 0*o + 13*o**2. Suppose a(b) = 0. Calculate b.
0, 1, 2
Let j = -119065/42 + 19871/7. Factor 7/3*l + 1/6*l**4 + 0 + j*l**2 + 5/3*l**3.
l*(l + 1)*(l + 2)*(l + 7)/6
Let y(k) be the first derivative of 3*k**5/10 + 7*k**4/8 - 17*k**3/3 - 10*k**2 + 32*k - 281. Let y(t) = 0. What is t?
-4, -2, 1, 8/3
Let h(p) be the third derivative of -1/600*p**6 + 0 - 9/10*p**3 + 3/40*p**4 + 33*p**2 + 0*p + 1/100*p**5. Find a, given that h(a) = 0.
-3, 3
Let b(k) = 3*k**3 - 6*k - 4*k**3 - 10*k**2 + 3 + 11*k**2 - 8*k**2. Let o(m) = 2*m**3 + 15*m**2 + 13*m - 5. Let s(t) = 5*b(t) + 3*o(t). What is i in s(i) = 0?
-9, -1, 0
Let h(s) = -3*s**3 - 27*s**2 + 75*s - 21. Let n(v) = 2*v**3 + v**2 - 14*v - 1. Let a(o) = h(o) + 2*n(o). Find q, given that a(q) = 0.
1, 23
Let f(b) be the first derivative of -b**6/120 + b**5/6 - 17*b**4/24 + 4*b**3/3 - b**2 - 44*b - 1. Let a(c) be the second derivative of f(c). Solve a(z) = 0.
1, 8
Let a(u) be the third derivative of u**9/90720 + u**8/10080 + u**7/3780 - 89*u**5/60 + u**2 + 57. Let l(s) be the third derivative of a(s). Factor l(q).
2*q*(q + 1)*(q + 2)/3
Suppose -5*l + 2*i = -131 + 128, 9*l = 3*i + 9. Factor 69/2*u - 3/2*u**l + 18 + 15*u**2.
-3*(u - 12)*(u + 1)**2/2
Let x(i) be the second derivative of -i**4/3 + 346*i**3 + 100*i + 8. Determine t so that x(t) = 0.
0, 519
Let f(m) = -9*m**4 - 64*m**3 - 318*m**2 - 444*m + 814. Let x(q) = 8*q**4 + 62*q**3 + 318*q**2 + 442*q - 812. Let u(c) = -6*f(c) - 7*x(c). Factor u(v).
-2*(v - 1)*(v + 5)**2*(v + 16)
Let f(r) be the first derivative of r**6/1080 + 43*r**5/360 + 7*r**4/12 - 5*r**3/3 + 24*r + 144. Let x(l) be the third derivative of f(l). Factor x(u).
(u + 1)*(u + 42)/3
Let o be 4 + (-68)/16 - (-10)/8. Suppose b + o = 3. Let 13*z**3 - 11*z**3 - 5*z**2 + 9*z**b = 0. What is z?
-2, 0
Let h = 185198 + -925968/5. Factor h*t - 24/5 + 2/5*t**2.
2*(t - 1)*(t + 12)/5
Let s(d) be the second derivative of -27/8*d**4 - 81/8*d**3 + 1/20*d**6 + 81/4*d**2 - 3/80*d**5 + 2*d - 55. Let s(n) = 0. What is n?
-3, 1/2, 6
Let m(f) be the third derivative of -f**6/120 + 29*f**5/20 + 91*f**4/6 + 2*f**2 + 458*f + 5. Factor m(g).
-g*(g - 91)*(g + 4)
Let t(l) = -177*l + 7614. Let x be t(43). Solve 2/3*q**2 + x*q - 1/3*q**3 - 6 = 0.
-3, 2, 3
Suppose 7*c = 4*s - 50, 2*c - 235*s + 236*s = 20. Factor -50/11*z - 12/11 + 18/11*z**c.
2*(z - 3)*(9*z + 2)/11
Let c(v) be the third derivative of -1/60*v**5 - 1/16*v**4 - 1/720*v**6 + 0*v + 0*v**3 + 4*v**2 - 3. Factor c(b).
-b*(b + 3)**2/6
Let f(g) be the first derivative of 3*g**3/4 - 31*g**2/8 + 786. Factor f(y).
y*(9*y - 31)/4
Let u = 1664/249 - 278/83. Let 1/3*i**2 - 11/3*i + u = 0. Calculate i.
1, 10
Suppose -x + 3*y + 34 = 0, 22*y = -4*x - 210 + 6. Factor -g**x + 3 + 1/2*g**5 + 10*g**2 - 19/2*g - 3*g**3.
(g - 2)*(g - 1)**3*(g + 3)/2
Let x(n) = 2*n**2 - 2. Let f(i) = 10*i**2 - 832*i - 282. Let r(l) = f(l) - 2*x(l). What is d in r(d) = 0?
-1/3, 139
Let o = 299419 - 299377. Factor o*f**2 + 9/2*f**4 - 27*f**3 - 76/3*f + 16/3.
(f - 4)*(3*f - 2)**3/6
Suppose -5*k + 5*n = -25 + 5, -4*n = -20. Let -k + 3*z + 2*z**2 - 4*z**2 + 4*z**2 + 4 = 0. What is z?
-5/2, 1
Let n = 501 - 556. Let o be 44/n*((-8)/(-6) + -3). Suppose -o - 5/3*h**2 + 1/3*h**3 + 8/3*h = 0. What is h?
1, 2
Let k(u) be the third derivative of u**5/30 - 293*u**4/12 - 98*u**3 + 1531*u**2. Factor k(w).
2*(w - 294)*(w + 1)
Let t be ((13 + -29)/(-8))/((-2)/(-3)). Let x(i) be the third derivative of 1/6*i**5 + 0 - t*i**2 - 1/24*i**6 + 0*i**3 - 5/24*i**4 + 0*i. Factor x(p).
-5*p*(p - 1)**2
Determine o so that -3206*o**2 + 3202*o**2 - 190*o + 76*o + 432*o + 730*o = 0.
0, 262
Let k(b) = -b**3 - 5*b**2 + 22*b - 4. Let p be k(-8). Factor -p*z**3 + 9*z**3 + 7*z**3 + 70*z**2 + z**3 + 65*z.
5*z*(z + 1)*(z + 13)
Let i = -260 - -263. Factor 3*r**i - 637*r + 0*r**2 + 625*r + 7*r**2 + 2*r**2.
3*r*(r - 1)*(r + 4)
Let v(b) = -4*b + 28. Suppose -3*x + 8*x + 10 = 5*y, 0 = 3*y - 5*x + 4. Let a be v(y). What is n in 0*n**2 + a*n**2 - 2*n**2 - 115*n + 121*n = 0?
0, 3
Let s(r) = -19*r**2 - 21766*r - 29724307. Let n(o) = 5*o**2 - 14*o + 1. Let z(j) = -3*n(j) - s(j). Determine t, given that z(t) = 0.
-2726
Let u(f) be the first derivative of f**5/7 + 43*f**4/21 + 44*f**3/21 - 32*f**2/7 + 61*f - 34. Let o(c) be the first derivative of u(c). Factor o(v).
4*(v + 1)*(v + 8)*(5*v - 2)/7
Let x be 993/99 + (-150)/15. Let t(k) be the second derivative of -1/165*k**6 + 1/66*k**4 + 18*k + 0 + 1/110*k**5 - x*k**3 + 0*k**2. Factor t(f).
-2*f*(f - 1)**2*(f + 1)/11
Suppose -11 = -z + 26. Let p = z - 35. Factor 7*w**2 + w**p - 7*w**2.
w**2
Suppose -10*q + 11*q - 5 = 0. Suppose 0 = -3*s - 2*c + 17, -q*s - 8*c = -4*c - 29. What is k in s*k**3 - 3*k**3 - 4*k**3 + 2*k = 0?
-1, 0, 1
Let w(d) be the first derivative of d**5 + 35*d**4 + 115*d**3/3 - 280*d**2 - 540*d + 2900. Find c, given that w(c) = 0.
-27, -2, -1, 2
Let n be ((2 - 34)/(-1))/(-45 + 77 + -29). Let u(c) be the first derivative of -2*c**3 - 30 - n*c + 1/6*c**4 + 8*c**2. Determine q so that u(q) = 0.
1, 4
Factor 3925/3*w - 5/3*w**3 + 3375 + 355/3*w**2.
-5*(w - 81)*(w + 5)**2/3
Suppose 8*b = 10*b - 3*n + 5, 0 = -n + 3. Suppose -6 = -19*j + 15*j - b*f, -3*f = 3*j. Factor -2/11*m**j + 2/11*m**4 + 2/11*m**5 + 0*m - 2/11*m**2 + 0.
2*m**2*(m - 1)*(m + 1)**2/11
Let w = 4/15629 + 62480/140661. Let d(s) be the first derivative of w*s**3 + 484/3*s - 44/3*s**2 + 42. Factor d(u).
4*(u - 11)**2/3
Let r(g) be the second derivative of -g**4/84 - 25*g**3/42 - 68*g**2/7 - 1095*g. What is b in r(b) = 0?
-17, -8
Let w be 124/(-3)*(-5331)/55087. Let -5/3*a - 1/3*a**w - 5/3*a**5 + 10/3*a**3 - 1/3 + 2/3*a**2 = 0. Calculate a.
-1, -1/5, 1
Let q(t) = -t**2 + 24*t + 321. Let d be q(29). Let u be (26 - -4)/5 - d/30. Find s, given that 4/5*s**3 + 0*s + 0*s**2 - u*s**4 + 0 - 2/15*s**5 = 0.
-3, 0, 2
Let p(t) be the third derivative of t**6/210 + 519*t**5/35 + 269361*t**4/14 + 93198906*t**3/7 - 854*t**2 + 2*t. Find h such that p(h) = 0.
-519
Factor 909 - 80*x**2 - 1232*x - 2677 + 4*x**3 - 526*x - 94*x.
4*(x - 34)*(x + 1)*(x + 13)
Factor 2/7*k**2 + 1124/7 + 566/7*k.
2*(k + 2)*(k + 281)/7
Let l(f) be the first derivative of -5*f**4/4 - 565*f**3/3 - 7540*f**2 + 50460*f + 349. Find w such that l(w) = 0.
-58, 3
Let z(d) be the first derivative of -4/21*d**3 + 48 + 48/7*d - 16/7*d**2 + 1/7*d**4. Factor z(n).
4*(n - 2)**2*(n + 3)/7
Let j(z) be the first derivative of 15*z**4/4 - 2035*z**3/3 + 5305*z**2/2 + 1995*z - 3914. Suppose j(i) = 0. Calculate i.
-1/3, 3, 133
Let t = 665 - 810. Let f = t - -731/5. Let -4/5*j**4 - 12/5*j**3 + f*j + 8/5*j**2 + 6/5*j**5 - 4/5 = 0. Calculate j.
-1, 2/3, 1
Let a(l) = 43*l**4 + 14*l**3 + 151*l**2 + 96*l + 6. Let y(b) = 51*b**4 + 13*b**3 + 152*b**2 + 92*b + 7. Let r(t) = 7*a(t) - 6*y(t). What is o in r(o) = 0?
-3, -1, 0, 8
Factor -1/4*u