
Let z(t) = -5*t**2 - 121*t + 1530. Let b(m) = -5*m**2 - 125*m + 1525. Let c(v) = 4*b(v) - 5*z(v). Factor c(l).
5*(l - 10)*(l + 31)
Let w(s) be the first derivative of -7/2*s**2 - 49*s - 28 - 1/12*s**3. Factor w(v).
-(v + 14)**2/4
Let p(h) be the third derivative of -h**7/420 + h**6/180 + h**5/10 - 23*h**3/2 + 55*h**2. Let v(f) be the first derivative of p(f). Find b, given that v(b) = 0.
-2, 0, 3
Let b = -302 + 438. Let o be 17/b + (-30)/(-16). Find d such that -87*d**2 + 1 + 4 + 21*d**3 + 1 + 9*d + 51*d**o = 0.
-2/7, 1
Let i be (-12)/(-11 + -12 + (-11)/((-55)/(-15))). Factor 10/13 + i*o**2 - 2/13*o**3 + 18/13*o.
-2*(o - 5)*(o + 1)**2/13
Suppose 2*o + 409 + 1134 = 5*d, -3*d = 2*o - 913. What is y in 557 - 6*y**4 + 16*y + 2*y**4 - 16*y**3 - 298 + 52*y**2 - d = 0?
-6, -1, 1, 2
Let z(a) be the first derivative of 3*a**5/5 - 117*a**4/4 + 75*a**3 - 111*a**2/2 + 851. Factor z(i).
3*i*(i - 37)*(i - 1)**2
Let b(z) be the second derivative of 22188041*z**6/120 + 22661807*z**5/80 + 79523*z**4/8 + 845*z**3/6 + z**2 - 322*z. Solve b(j) = 0 for j.
-1, -2/281
Let i = 59 + -87. Let v = 30 + i. Determine f so that f**v + 32*f + 174 - 126 + 3*f**2 = 0.
-6, -2
Let i be (-54)/63*(7/2 + -7). Let m(q) be the third derivative of 0 - 1/1140*q**6 + 0*q + 1/570*q**5 + 0*q**i - 6*q**2 + 1/114*q**4. Factor m(o).
-2*o*(o - 2)*(o + 1)/19
Let n = 1789/15210 - 18/169. Let o(g) be the third derivative of 0*g**3 - 1/18*g**4 - 4*g**2 - n*g**5 + 0*g + 0. Factor o(x).
-2*x*(x + 2)/3
Let h(o) = -4*o**3 + 7*o**2 + 3*o - 12. Let p(j) be the first derivative of j**4/4 - j**3/3 - 2*j - 51. Let n(r) = h(r) + 3*p(r). What is g in n(g) = 0?
-2, 3
Determine i, given that 36*i**2 + 41*i - 26*i - 12*i**4 - 17909 + 3*i**3 + 17903 = 0.
-1, 1/4, 2
Suppose 79*d**3 + 16*d**4 - 10*d**4 + 151*d**2 + 92*d**2 - 7*d**4 + 245*d + 82 = 0. Calculate d.
-1, 82
Let d(i) = -i**2 + 29*i - 194. Let x be d(18). Let s(g) be the third derivative of 34*g**2 + 0*g**3 + 1/8*g**x - 1/10*g**5 + 0*g + 1/40*g**6 + 0. Factor s(j).
3*j*(j - 1)**2
Solve 946*a**2 - 455*a**2 - 1463*a**3 - 64*a**4 - 937*a**3 + 36*a + 721*a**2 - 188*a = 0 for a.
-38, 0, 1/4
Let s(b) be the third derivative of 1/27*b**6 - 13/30*b**5 - 1/945*b**7 + 8*b**2 + 3/2*b**4 + 0*b - 5 + 0*b**3. Find q such that s(q) = 0.
0, 2, 9
Let u be (((-12)/10)/((143/242)/13))/(252/(-120)). Suppose u*j + 48/7 + 10/7*j**3 - 76/7*j**2 = 0. Calculate j.
-2/5, 2, 6
Determine c, given that 2/3*c**2 + 440/3 - 118/3*c = 0.
4, 55
Let v(b) be the third derivative of 25*b**7/504 - b**6/72 + b**5/600 - b**4/24 + b**2 - 35*b. Let g(f) be the second derivative of v(f). Factor g(t).
(25*t - 1)**2/5
Let b(w) be the second derivative of -w**4/18 - 46*w**3 + 2*w - 451. Factor b(q).
-2*q*(q + 414)/3
Let v be (13/(156/(-8)))/(4/18). Let r be (-9)/(-15) - (16/(-5) - v). Factor r - 2/5*g + 2/5*g**3 - 4/5*g**2.
2*(g - 2)*(g - 1)*(g + 1)/5
Let v(l) be the first derivative of l**4/8 - 97*l**3/3 - 98*l**2 - 2969. Suppose v(h) = 0. Calculate h.
-2, 0, 196
Let q be (-26)/(-2) - (332/21 - 3). Factor 0*y**2 + 0*y + 0 - 2/21*y**4 + 2/21*y**5 - q*y**3.
2*y**3*(y - 2)*(y + 1)/21
Let u(a) be the second derivative of 3*a**5/140 + 15*a**4/28 + 22*a**3/7 - 90*a**2/7 + 2343*a. Determine z, given that u(z) = 0.
-10, -6, 1
Let k(q) = 13*q**4 - 326*q**3 - 375*q**2 - 6*q. Let a(v) = 37*v**4 - 980*v**3 - 1119*v**2 - 17*v. Let o(z) = 6*a(z) - 17*k(z). Suppose o(p) = 0. What is p?
-1, 0, 339
Let x be 606/1212*0/(-2). Let a(y) be the third derivative of 35*y**2 + 0*y + 0 + 0*y**3 + 1/60*y**6 + x*y**4 + 1/15*y**5. Factor a(p).
2*p**2*(p + 2)
Let h = 1485 - 773. Let c = -697 + h. Find g such that -75 - 3/4*g**2 + c*g = 0.
10
Let i = 17326 - 17326. Let h(t) be the third derivative of 7*t**2 + i*t + 0*t**3 + 0 - 1/6*t**5 + 1/2*t**4 - 1/60*t**6. Solve h(r) = 0 for r.
-6, 0, 1
Let t be -6*(7 - 114/12). Let q be (23/3795*t)/(2/20). Find c such that q + 8/11*c - 2/11*c**2 = 0.
-1, 5
Factor -2/7*y**5 + 2992900/7*y**2 + 0*y - 1503370/7*y**3 + 3464/7*y**4 + 0.
-2*y**2*(y - 865)**2*(y - 2)/7
Suppose b + 7 = -1. Let q be b/(-14)*35/10. Factor -14 - 35*a**2 + q + 2 - 45*a.
-5*(a + 1)*(7*a + 2)
Suppose -229*p + 66 = -223*p. Suppose -b**4 + p*b**2 + 0*b**4 + 2*b**3 - 8*b**2 = 0. What is b?
-1, 0, 3
Let i be (-290)/(-188) - 197/((-361101)/(-78)). Find x such that -15/2*x**2 - 6*x - 3*x**3 - i = 0.
-1, -1/2
Let m be (-13113)/(-4185) + ((-8)/30)/2. Let d be 5 - (-5 + 3 + 61/9). Factor 8/9*c + 0 + 2/3*c**2 - d*c**m.
-2*c*(c - 4)*(c + 1)/9
Let l(s) be the second derivative of -2*s**6/45 + s**5/6 - 5*s**3/9 + 2*s**2/3 + 5848*s + 2. Determine g, given that l(g) = 0.
-1, 1/2, 1, 2
Let x be (2/50)/((-254)/(-3810)). Let 21/5*c + 0 - x*c**2 = 0. What is c?
0, 7
Let y(h) = -7*h - 49. Let p be y(-17). Factor -143*u**2 - 26*u - 56 + p*u**2 + 74*u**2.
(u - 28)*(u + 2)
Let y be (-31*110/1705)/(-1*4). Suppose n**2 + 0 + y*n**3 - 3/2*n = 0. Calculate n.
-3, 0, 1
Let m(l) = 12*l**3 + 95*l**2 + 22*l - 66. Let p(j) = j**3 + j**2 + 2*j - 6. Let d(h) = 2*m(h) - 22*p(h). Factor d(k).
2*k**2*(k + 84)
Suppose -2*f - 2*x = -34, -4*f = -0*f - 5*x - 23. Let m be 58/204 + f/(-918)*9. Suppose 0 - m*a**2 + 5/6*a = 0. What is a?
0, 5
Find z such that -2205 - 1731*z**2 - 83501*z**3 + 83332*z**3 + 340*z**2 - 3171*z = 0.
-5, -21/13
Let i(d) be the first derivative of d**6/9 + 548*d**5/15 - 278*d**4 + 6704*d**3/9 - 2240*d**2/3 + 5439. Factor i(f).
2*f*(f - 2)**3*(f + 280)/3
Let q = 3032312/7 + -433187. Solve -q*b**2 + 258/7*b - 5547/7 = 0.
43
Let r be 38*407/8436 + 10/(-6). Factor 1/6*g**2 + 1/2*g**3 - r*g + 0 - 5/6*g**4 + 1/3*g**5.
g*(g - 1)**3*(2*g + 1)/6
Let k = 369/31 + -952/93. Solve -k*m + 2*m**2 + 1/3 = 0 for m.
1/3, 1/2
Let a(f) = -18*f - 13. Let q be a(-4). Suppose -j - 56 = -q. Suppose -65*v - 4 - 18*v**2 - 8*v**3 + 0*v**4 - 2*v**4 - 2*v**j + 51*v = 0. Calculate v.
-2, -1
Let s(l) be the first derivative of -5*l**3/9 - 65*l**2/6 + 340*l/3 + 1528. Factor s(i).
-5*(i - 4)*(i + 17)/3
Factor -742/11*a + 8/11*a**2 - 186/11.
2*(a - 93)*(4*a + 1)/11
Let f(s) = 5*s + 34. Let g be f(-14). Let y = 28 - g. What is q in -2*q**5 + 16*q**5 + 8*q**2 + 2*q**5 + 12*q**5 + 44*q**3 + y*q**4 = 0?
-1, -2/7, 0
Let k(r) = -r**3 + 2*r**2 - 4*r - 3. Let d(a) = -2*a + 3*a - 1 + 2. Suppose 0 = 8*y - 149 + 117. Let n(g) = y*k(g) + 12*d(g). What is m in n(m) = 0?
0, 1
Suppose 721*i - 1500*i = -726*i - 212. Factor -116/7*c + 2/7*c**i - 24/7*c**3 + 90/7*c**2 + 48/7.
2*(c - 6)*(c - 4)*(c - 1)**2/7
Let w(j) = -j**4 + j**3 - 3*j**2 + 3*j + 3. Let m(b) = -4 + 7 - b**3 - 3*b**4 + 5 + 8*b + 3*b**3 - 8*b**2. Let f(p) = -3*m(p) + 8*w(p). Factor f(y).
y**3*(y + 2)
Let q = -4841 - -4845. Let c(d) be the third derivative of 0*d**3 + 0 + 0*d + 7/20*d**5 + 12*d**2 - 1/4*d**q. Suppose c(o) = 0. Calculate o.
0, 2/7
Let s = 4677800/11 - 425254. Let 54/11*t**3 + 50/11*t**2 + 12/11*t + 0 + s*t**4 - 10/11*t**5 = 0. What is t?
-1, -2/5, 0, 3
Let d(i) = -i**2 - 4. Let h(m) = -22*m**2 + 222*m - 936. Let j(o) = -20*d(o) + h(o). Factor j(f).
-2*(f - 107)*(f - 4)
Let z = -16 - -19. Suppose f - 69 = 2*t, 3*f - 4 = -z*t + 212. Find q, given that -2 - 70*q + 1 - q**3 + f*q - q**2 + 2*q**2 = 0.
-1, 1
Let d(t) be the second derivative of 5*t**5/48 - 65*t**4/96 - 5*t**3/4 - 101*t**2/2 + 14*t. Let b(w) be the first derivative of d(w). Let b(i) = 0. What is i?
-2/5, 3
Suppose -5*l = -2*s - 36 + 33, -3*s - 37 = -l. Let y be s + (-4920)/(-340) + 0/1. Factor 18/17*f - 4/17 - y*f**2.
-2*(f - 2)*(4*f - 1)/17
Factor -4/7 - 1909924/7*w**2 - 5528/7*w.
-4*(691*w + 1)**2/7
Factor 4575 + 5/3*g**2 - 13730/3*g.
5*(g - 2745)*(g - 1)/3
Suppose 234*n + 274*n - 3556 = 0. Let f(h) be the second derivative of -2*h + 0*h**2 + 2/15*h**3 - n - 1/30*h**4. Factor f(s).
-2*s*(s - 2)/5
Let w(v) be the second derivative of v**6/15 - 3*v**5/5 - 4*v**4 - 26*v**3/3 - 9*v**2 - v - 74. Factor w(h).
2*(h - 9)*(h + 1)**3
Let j(m) be the second derivative of -m**7/126 - 2*m**6/15 - m**5/6 + m**4/3 + 11*m**3/18 + 2*m - 374. What is d in j(d) = 0?
-11, -1, 0, 1
Let a(z) = -10*z**4 + 20*z**3 + 40*z**2 - 85*z + 35. Let h(l) = 15*l**4 - 30*l**3 - 60*l**2 + 127*l - 49. Let u(c) = 7*a(c) + 5*h(c). Factor u(i).
5*i*(i - 2)**2*(i + 2)
Suppose 4*r + m = 2, -m + 2175 - 2173 = 0. Let c(j) be the second derivative of -6*j**2 + r - 11/4*j**4 - 7*j**3 + 3