ctor i(t).
3*t**2*(t + 1)*(t + 15)/2
Let l be (-4 + 25/4)/((-2)/(-4)). Factor 3/2*n**2 + l*n + 0.
3*n*(n + 3)/2
Suppose -510 = 39*a + 12*a. Let k be a*(-7 - 140/(-21)). What is q in 2/3*q**3 - k*q**2 + 14/3*q - 2 = 0?
1, 3
Let h(j) be the first derivative of -j**5/110 + j**3/33 - 137*j - 62. Let p(q) be the first derivative of h(q). Factor p(k).
-2*k*(k - 1)*(k + 1)/11
Let t be (-79664)/(-10725) - (-54)/2025. What is b in -12/11*b**2 - 200/11*b - 8/11*b**5 - 48/11 + 6/11*b**4 + t*b**3 = 0?
-2, -1/4, 2, 3
Suppose -3*s + b + 256 = 3*b, -s = 4*b - 92. Suppose s*r + 52 + 614 + 3*r**2 - 78 = 0. Calculate r.
-14
Suppose -2892*u = -2753*u - 278. Factor 0*k + 1/4*k**3 + 0 - 1/4*k**u.
k**2*(k - 1)/4
Let r be 120/(-75)*(9/(-4) + (-3)/(-3)). Let u(n) be the second derivative of -3 - 1/3*n**3 + 5*n + 1/6*n**4 - 6*n**r. Factor u(m).
2*(m - 3)*(m + 2)
Let r(f) be the third derivative of f**5/20 - 3*f**4/4 - 36*f**3 + 643*f**2. Determine n so that r(n) = 0.
-6, 12
Let f(u) = 222*u**2 - 911*u - 10. Let b(w) = 885*w**2 - 3645*w - 39. Let a(k) = -2*b(k) + 9*f(k). Factor a(c).
3*(c - 4)*(76*c + 1)
Let m = 33 - 20. Suppose -4 + 199 = m*g. Factor -5*h**4 - 25*h**3 - g*h + h**2 - 41*h**2 + 5*h**2.
-5*h*(h + 1)**2*(h + 3)
Let k(n) = -100*n**2 - 3690*n - 32895. Let h(b) = 11*b**2 + 410*b + 3654. Let l(j) = 55*h(j) + 6*k(j). Factor l(i).
5*(i + 10)*(i + 72)
Let u(i) be the first derivative of 285*i - 4 + 64 - i**4 - 24*i**2 + 8*i**3 - 253*i. Factor u(j).
-4*(j - 2)**3
Determine o, given that -8*o**4 + 108*o**2 - 288/5*o + 2/5*o**5 + 0 - 214/5*o**3 = 0.
-6, 0, 1, 24
Let b(m) = 3*m**3 - 2*m + 1. Let i be b(1). Suppose 423*x + 46 = 446*x. What is v in -i*v**x + 22*v**2 - 5*v**3 + 5 - 25*v + 5 = 0?
1, 2
Solve -250 + 510*r**2 + 83*r**4 - 745*r + 740*r**3 + 37*r**4 + 5*r**5 - 8 - 351 - 21 = 0 for r.
-14, -9, -1, 1
Factor 2/11*j**5 + 2*j**3 + 0 + 0*j + 34/11*j**4 - 110*j**2.
2*j**2*(j - 5)*(j + 11)**2/11
Let m(u) be the first derivative of -u**4/42 - 11*u**3/21 - 10*u**2/7 + 12*u - 118. Let s(b) be the first derivative of m(b). Suppose s(y) = 0. What is y?
-10, -1
Let h be ((-4)/14)/((-5145)/19208). Let b(c) be the first derivative of 8/5*c - 1 + 2*c**2 + 1/5*c**4 + h*c**3. Find o such that b(o) = 0.
-2, -1
Let i be 0 - 5/(-2) - 641207/256872. Let c(a) be the third derivative of 0 - i*a**4 - 1/660*a**5 + 0*a - 28*a**2 + 0*a**3. Factor c(h).
-h*(h + 1)/11
Let l(f) = -3*f**2 + 4. Let d(i) = 40*i**2 + 488*i + 435. Let o(p) = -d(p) - 13*l(p). Factor o(c).
-(c + 1)*(c + 487)
Let w = 189 + -150. Solve w*y + 56 - 3*y + 11*y**2 - 7*y**2 = 0.
-7, -2
Let j be (-5 + 612 + -3)*(-6)/4. Let b be (-755)/j - 2/(-4). Find v such that -2*v**4 + b*v + 0 + 2*v**2 - 2/3*v**3 - 2/3*v**5 = 0.
-2, -1, 0, 1
Let f(v) be the second derivative of -16*v**7/147 - 2*v**6/105 + 387*v**5/140 - 116*v**4/21 - 50*v**3/21 + 24*v**2/7 - 2158*v. What is i in f(i) = 0?
-4, -3/8, 1/4, 2
Let h(s) = s**3 + 12*s**2 - 1961*s - 15941. Let d be h(-8). Solve 0 - d*g**3 - 4*g - 1/2*g**4 - 6*g**2 = 0 for g.
-2, 0
Let a(c) be the second derivative of 8*c + 1/12*c**2 - 1/72*c**4 + 0*c**3 - 10. Solve a(h) = 0 for h.
-1, 1
Let f(a) be the third derivative of -a**5/210 - 15*a**4/14 - 24*a**3 + 29*a**2 + 14*a. Factor f(s).
-2*(s + 6)*(s + 84)/7
Let j(t) be the second derivative of -t**5/4 + 85*t**4/6 + 115*t**3/6 - 15870*t**2 - 2487*t. What is g in j(g) = 0?
-12, 23
Let o(p) = p**3 - 47*p**2 + 6*p + 18. Let v be o(47). Let s be (1 - 308/v)*40*-3. Find y such that 8/5*y**3 + s*y + 6/5 - 6*y**2 = 0.
-1/4, 1, 3
Let v(s) = 872*s - 111613. Let d be v(128). Factor 96/17*a**2 - 148/17*a**d + 6/17*a**4 + 0 + 0*a.
2*a**2*(a - 24)*(3*a - 2)/17
Let b = -637231 + 1912213/3. What is f in 16 - 594*f**3 + 588*f**2 - b*f = 0?
2/9, 6/11
Determine s, given that -180*s + 44*s**2 - 94*s - 49 - 39 - 164*s - 38*s = 0.
-2/11, 11
Let j be (-160)/6*(-90)/(-40). Let u be (-9)/(-12)*-10*16/j. Let 12/5 + 108/5*q + 243/5*q**u = 0. What is q?
-2/9
Suppose 155*n - 13 = 150*n + 2. Suppose 0*j - 1/4*j**5 + 0 + 0*j**4 + 3/4*j**n + 1/2*j**2 = 0. What is j?
-1, 0, 2
Let f(q) be the second derivative of -q**4/18 + 424*q**3/3 - 1271*q**2/3 + 13687*q. Suppose f(l) = 0. What is l?
1, 1271
Let c = 85020704 - 339827752168/3997. Let j = c - 1/571. Factor 6/7*i**3 - j*i**4 - 3/7*i**2 + 0*i + 0.
-3*i**2*(i - 1)**2/7
Let k(v) be the first derivative of -24*v**5/5 + 23*v**4 + 308*v**3/3 + 16*v**2 - 48*v - 2562. Let k(u) = 0. Calculate u.
-2, -1/2, 1/3, 6
Let w(a) be the third derivative of a**5/450 + 17*a**4/30 + 752*a**3/45 - 13107*a**2. Factor w(i).
2*(i + 8)*(i + 94)/15
Suppose -150*t = 293*t + 212*t - 1052 - 258. Factor -45 - 1/2*g**3 - 69/2*g - 8*g**t.
-(g + 3)**2*(g + 10)/2
Factor 173*q**2 + 1807*q - 5549*q - 2366*q - 9908*q - 177*q**2 - 16032016.
-4*(q + 2002)**2
Let r(q) = -q + 50. Let g be r(47). Let u be (735/(-28))/(-15) - (-1)/4. Factor 5/3*x**u + 10/3*x + 0 - 5/3*x**4 - 10/3*x**g.
-5*x*(x - 1)*(x + 1)*(x + 2)/3
Let v(q) = -10*q**3 + 13*q**2 - 40*q + 26. Let c(w) = w**3 + w**2 - w. Let p(r) = 22*c(r) + 2*v(r). Factor p(b).
2*(b - 1)**2*(b + 26)
Suppose 15*k + 18628 = -932. Let q = 1308 + k. Determine p, given that -25/6*p**3 + 5/2*p**q - 55/6*p**2 - 5/2*p + 0 = 0.
-1, -1/3, 0, 3
Let j = 310953/74 + -103827983/24753. Let z = -4/669 + j. Factor 9/2 + 15/2*w**3 - z*w - 9/2*w**2.
3*(w - 1)*(w + 1)*(5*w - 3)/2
Let y(n) be the first derivative of 1/40*n**5 + 1/16*n**4 - 1/2*n - 90 - 1/2*n**2 - 1/8*n**3. Suppose y(u) = 0. What is u?
-2, -1, 2
Let f(q) be the first derivative of -2*q**5 - 263*q**4/8 + 563*q**3/6 + 29*q**2 - 30*q - 2253. Suppose f(t) = 0. Calculate t.
-15, -2/5, 1/4, 2
Let d be (-56)/(-35)*(-1)/(-5)*275/44. Find t such that 1/2*t**3 - 14 + d*t**2 - 25/2*t = 0.
-7, -1, 4
Let k(l) be the first derivative of 10*l**5/9 + 55*l**4/9 + 82*l**3/27 + 4*l**2/9 + 2476. Suppose k(a) = 0. Calculate a.
-4, -1/5, 0
Suppose 26 = 5*f + 4*y - 0, 3*f - 5*y = -14. What is r in -22*r - 18*r**3 + f*r**4 - 42*r**2 + 53492 - 53492 = 0?
-1, 0, 11
Let k(f) = 16*f**4 + 46*f**3 + 252*f**2 + 70*f + 8. Let s(z) = 3*z**4 + 3*z**2 + 2*z + 1. Let q(v) = -k(v) + 8*s(v). Factor q(n).
2*n*(n - 9)*(n + 3)*(4*n + 1)
Let i = -775 + 780. Let k be (6 - i/(-2)) + -8. Suppose 0 + k*v + 1/4*v**2 = 0. What is v?
-2, 0
Let s(b) be the second derivative of -b**5/80 - b**4/48 + b**3/4 + 2*b - 92. Factor s(g).
-g*(g - 2)*(g + 3)/4
Let 15*w + 1/2*w**5 - 11/2*w**4 - 61/2*w**2 + 41/2*w**3 + 0 = 0. What is w?
0, 1, 2, 3, 5
Let a(r) = -2*r**3 - 282*r**2 + 20187*r - 93851. Let z(p) = -3*p**3 - 563*p**2 + 40358*p - 187700. Let q(j) = -5*a(j) + 3*z(j). Solve q(s) = 0.
5, 137
Let y(i) be the third derivative of 0*i**3 - 1/90*i**5 + 0*i + 0 - 1/10*i**6 + 1/35*i**7 + 23*i**2 + 1/18*i**4. Solve y(t) = 0 for t.
-1/3, 0, 1/3, 2
Factor 20*d**5 - 12*d**5 - 7*d**5 - 187*d**4 - 1250*d + 573*d**3 - 725*d**2 + 236*d**4.
d*(d - 2)*(d + 1)*(d + 25)**2
Let 0 + 156*l - 3/5*l**2 = 0. What is l?
0, 260
Let k(p) be the third derivative of -207*p**2 + 0*p + 0 - 1/600*p**6 + 0*p**3 + 1/300*p**5 + 1/10*p**4. Factor k(s).
-s*(s - 4)*(s + 3)/5
Let g = 327 - 320. Solve -12*u**2 + 3*u**2 - 56 - 12*u**3 - 6*u - g*u**2 + 16*u**3 - 70*u = 0.
-2, -1, 7
Let a(s) = 35*s**3 + 945*s**2 - 9361*s - 11. Let p(n) = 22*n**3 + 630*n**2 - 6239*n - 7. Let c(z) = -7*a(z) + 11*p(z). Factor c(m).
-3*m*(m - 94)*(m - 11)
Let i(b) be the first derivative of -88 - 37/12*b**3 - 1/8*b**4 + 0*b - 9/4*b**2. Factor i(n).
-n*(n + 18)*(2*n + 1)/4
Determine y, given that 1440 + 4/9*y**3 - 16*y - 104/9*y**2 = 0.
-10, 18
Let u = 65106/13 - 568586/117. Let 560/9*q**5 + 158/9*q**2 - u*q**4 - 76/9*q + 8/9 + 371/9*q**3 = 0. What is q?
-2/5, 1/4, 2/7, 2
Let w be (-6324)/(-360) - 286/(-110). Factor -w*v**2 - 6 - 22*v.
-(11*v + 6)**2/6
Let h(s) be the second derivative of s**6/225 - 137*s**5/15 + 473317*s**4/90 - 186868*s**3/3 + 1395372*s**2/5 + 10947*s. Factor h(m).
2*(m - 682)**2*(m - 3)**2/15
Let w(g) be the second derivative of g**6/10 - 7*g**5/20 + g**4/3 - 220*g + 4. Factor w(y).
y**2*(y - 1)*(3*y - 4)
Let p(m) be the third derivative of -m**7/42 + m**6/8 + m**5/12 - 5*m**4/8 + 635*m**2 + 1. What is n in p(n) = 0?
-1, 0, 1, 3
Let j = 3373/751920 + -1/3133. Let x(k) be the third derivative of 0*k - 1/200*k**5 + 17*k**2 + 0*k**3 - j*k**4 + 0. Factor x(u).
-u*(3*u + 1)