 derivative of c**8/1176 + 2*c**7/245 - c**6/28 + 4*c**5/105 + c**2 + 51*c. Determine h, given that l(h) = 0.
-8, 0, 1
Suppose 5*o + 8*z = 4*z - 517, 4*o = -z - 418. Let s be (40/o)/(((-30)/9)/5). Let -4/7*n**4 + s + 8/7*n + 0*n**2 - 8/7*n**3 = 0. What is n?
-1, 1
Let z = -294 - -591/2. Let o(s) be the first derivative of 3*s**2 - z*s**4 - 4*s + 4/3*s**3 + 2. Factor o(l).
-2*(l - 1)*(l + 1)*(3*l - 2)
Let z = -131 + 134. Suppose 3*p = 11 - 2. Find f, given that 40*f**3 + 6*f - z*f**4 - 17*f**3 - 29*f**p + 3 = 0.
-1, 1
Let p = 212 + -212. Let y(r) be the first derivative of 0*r - 2 + 1/12*r**4 + p*r**2 - 5/36*r**6 + 0*r**3 + 1/10*r**5. Factor y(f).
-f**3*(f - 1)*(5*f + 2)/6
Let f = 1/938 + 3617/938. Solve -6/7*q - f*q**3 - 3*q**2 + 0 - 3/7*q**5 - 15/7*q**4 = 0 for q.
-2, -1, 0
Suppose 6*g - 9 - 9 = 0. Let i(n) = n**3 + 3*n**2 - 5*n - 2. Let p be i(-4). Factor -9*a**2 + 88*a**g - 85*a**3 + 3*a + 3*a**p.
3*a*(a - 1)**2
Find q, given that 7*q**5 - 28*q**3 - 8*q**2 - 4*q**2 - 20*q**4 + 3*q**5 - 14*q**5 = 0.
-3, -1, 0
Let k(s) be the first derivative of -5*s**4/4 - 5*s**3 + 25*s**2 + 81. Solve k(a) = 0 for a.
-5, 0, 2
Let t(h) be the third derivative of 1/30*h**5 + 0*h**7 - 6*h**2 + 0*h**3 + 0*h**4 + 1/40*h**6 + 0*h + 0 - 1/336*h**8. Factor t(s).
-s**2*(s - 2)*(s + 1)**2
Let m(z) be the first derivative of -2/3*z + 16 - 5/9*z**2 + 4/27*z**3. Factor m(n).
2*(n - 3)*(2*n + 1)/9
Let y(a) be the third derivative of a**6/240 + a**5/40 - 3*a**4/16 - 9*a**3/4 + 300*a**2. Factor y(s).
(s - 3)*(s + 3)**2/2
Determine i so that 18 + 14*i**2 - 13*i**3 - 15*i**3 + 36*i**3 - 30*i - 10*i**3 = 0.
1, 3
Let i(p) be the first derivative of p**3/27 + 31*p**2/18 + 58*p/9 - 174. Factor i(f).
(f + 2)*(f + 29)/9
Let x(i) be the second derivative of 20*i**3 + 15/4*i**4 + 1/4*i**5 - 2*i + 0 + 40*i**2. Factor x(l).
5*(l + 1)*(l + 4)**2
Factor 2/7*d**2 + 40/7 - 18/7*d.
2*(d - 5)*(d - 4)/7
Let q(o) be the third derivative of o**10/529200 - o**8/70560 + o**5/30 - 4*o**2. Let s(h) be the third derivative of q(h). Suppose s(k) = 0. What is k?
-1, 0, 1
Factor 0 + 5/3*v**2 + 5/3*v.
5*v*(v + 1)/3
Let -4/5 - 11/5*x**2 + 13/5*x**3 - 28/5*x = 0. Calculate x.
-1, -2/13, 2
Factor 2/3*w**3 - 40/3 + 16*w - 6*w**2.
2*(w - 5)*(w - 2)**2/3
Determine i so that 5893*i**5 + i**3 + 4*i**3 - 5894*i**5 - 4*i = 0.
-2, -1, 0, 1, 2
Let l(d) = d**2 - 13*d - 28. Let p be (-206)/(-14) + 5/(140/8). Let t be l(p). Factor -8/5 + 24/5*x + 18/5*x**t - 14/5*x**3.
-2*(x - 2)*(x + 1)*(7*x - 2)/5
Let r(y) = y**3 - 6*y**2 - y + 1. Let u be r(6). Let k be (3/(-3))/(u/50). Factor k*b - 2*b**2 - 15*b**3 - 19*b**3 - 6 + 32*b**3.
-2*(b - 1)**2*(b + 3)
Let h be (-1 - 1/(25/(-30)))*(-28)/(-7). Factor 8/5*u**2 - 8/5*u**3 - h*u**4 + 4/5*u + 4/5*u**5 - 4/5.
4*(u - 1)**3*(u + 1)**2/5
Let l(t) be the second derivative of -t**4/24 + 145*t**3/6 - 21025*t**2/4 - 46*t - 5. Find c such that l(c) = 0.
145
Let t(b) be the third derivative of b**8/1064 - 11*b**7/1995 + b**6/76 - 3*b**5/190 + b**4/114 - 252*b**2. Solve t(s) = 0.
0, 2/3, 1
Let b(x) be the third derivative of 0 - 1/16*x**4 + 3/80*x**5 + 0*x + 0*x**6 + 0*x**3 - 12*x**2 - 1/280*x**7. Factor b(u).
-3*u*(u - 1)**2*(u + 2)/4
Suppose 2/9*q**2 + 68/9 - 38/9*q = 0. What is q?
2, 17
Let l(y) = y**3 + y**2 + y + 2. Let a be l(0). Let f be (a*1)/(28/42). Factor -f + 6 - 2 - r**2.
-(r - 1)*(r + 1)
Solve -3*r**4 + 174*r - 302*r + r**4 - 1156 + 170*r**2 - 548*r**2 - 1470*r + 62*r**3 = 0.
-2, -1, 17
Factor -153/4*q - 27 - 3/4*q**3 - 12*q**2.
-3*(q + 1)*(q + 3)*(q + 12)/4
Let m(s) = 2*s - 14. Let a be m(20). Let v = -125 - -128. Factor -8 - a*o**2 - 80/3*o - 6*o**v.
-2*(o + 3)*(3*o + 2)**2/3
Let y(l) be the third derivative of l**6/360 + 3*l**5/40 - 5*l**4/12 + l**3 - 39*l**2. Let x(v) be the first derivative of y(v). Factor x(b).
(b - 1)*(b + 10)
Let h = -9453 - -47271/5. Factor h*y + 3/5*y**2 - 6/5*y**3 - 3/5.
-3*(y - 1)*(y + 1)*(2*y - 1)/5
Suppose -5*a + 5*v + 325 = 0, a + 252 = 5*a + 4*v. Determine b, given that 3*b**3 - 91*b**4 + a*b**3 - 16*b**2 + 17*b**4 + 9*b**3 + 14*b**5 = 0.
0, 2/7, 1, 4
Suppose 12/7 + 15/7*i**2 - 24/7*i - 3/7*i**3 = 0. What is i?
1, 2
Let m(r) be the first derivative of -35/4*r**4 - 80/3*r**3 + 0*r + 23 - 10*r**2. Let m(c) = 0. What is c?
-2, -2/7, 0
Suppose -5*t + o - 1 = 0, -25*t - 3*o = -23*t - 3. Let g**3 - 3*g**2 + 4/5 + 3*g**4 + t*g - 9/5*g**5 = 0. Calculate g.
-2/3, 1
Let o = -27 - -29. Let -8*j**3 - 20*j**2 - 4*j**o + 36*j**2 - 16*j**4 - 6*j**5 + 14*j + 4 = 0. Calculate j.
-1, -2/3, 1
Let g(x) be the third derivative of 10*x**2 + 0*x**6 + 0*x**4 + 0*x + 0 - 1/105*x**5 + 1/21*x**3 + 1/735*x**7. Factor g(w).
2*(w - 1)**2*(w + 1)**2/7
Let x(b) be the second derivative of b**7/3360 - b**6/144 + 5*b**5/96 - 2*b**3/3 - 3*b. Let f(w) be the second derivative of x(w). Let f(l) = 0. Calculate l.
0, 5
Let n be (-13)/(-2) + 60/(-15). Let r(b) be the second derivative of -9/2*b**2 - 7/12*b**4 - 1/20*b**5 - 3*b + 0 - n*b**3. Factor r(f).
-(f + 1)*(f + 3)**2
Let r(l) = 22*l + 71. Let f be r(-3). Let h(t) be the first derivative of 1/6*t**3 + 7 - 1/10*t**f + 1/8*t**4 + 0*t - 1/4*t**2. Factor h(o).
-o*(o - 1)**2*(o + 1)/2
Let b(q) be the second derivative of -1/10*q**5 + 0*q**2 + 1/6*q**4 - 18*q + 0 + 0*q**3. Factor b(a).
-2*a**2*(a - 1)
Let y be 4 + -12 + 68/(-64)*-8. Factor 0 + 3/2*b - y*b**2.
-b*(b - 3)/2
Let v(u) = -2*u**2 + 3*u - 7. Let s be v(5). Let f be (s - -3)*10/(-15). Solve -20*b**2 + f*b**5 - 12*b**3 + 20*b**4 - 10*b**5 - 5*b + b = 0.
-1, -1/4, 0, 1
Let u(s) be the third derivative of -s**5/240 - 39*s**4/16 - 4563*s**3/8 - 104*s**2. Find l, given that u(l) = 0.
-117
Let y(c) = c**2 - 97*c - 74. Let f(o) = -2*o**2 + 287*o + 223. Let s(n) = 4*f(n) + 11*y(n). Suppose s(v) = 0. What is v?
-26, -1
Let f(s) be the first derivative of 25*s**3/3 + 70*s**2/3 - 20*s/3 - 91. Suppose f(d) = 0. What is d?
-2, 2/15
Suppose 3*m = -58*c + 61*c - 6, -4*c + 9 = -3*m. Factor 0 - 3/4*u**2 + 1/2*u + 1/4*u**c.
u*(u - 2)*(u - 1)/4
Let r be 322/8 + 2/(-8). Factor -r*k - 6*k**2 + 19*k + 7*k + 12.
-2*(k + 3)*(3*k - 2)
Let l(o) be the third derivative of -1/240*o**5 + 0 + 0*o - 21*o**2 + 1/4*o**3 + 5/96*o**4. Find p such that l(p) = 0.
-1, 6
Let a(t) = 20*t**5 - 24*t**4 - 12*t**3 + 16*t**2 + 32*t. Let p(r) = r**5 - r**4 + r. Let b(g) = -a(g) + 16*p(g). Find f such that b(f) = 0.
-1, 0, 2
Let x be (-6)/9 + (-89)/(-3). Factor -x*p**3 - p**5 - 43*p**2 - 9*p**4 - 17*p - 19*p + 6*p - 8.
-(p + 1)**3*(p + 2)*(p + 4)
Let w(d) be the third derivative of -d**7/7560 - d**6/2160 + d**5/180 + 7*d**4/12 - 9*d**2. Let p(q) be the second derivative of w(q). Let p(c) = 0. What is c?
-2, 1
Let m(h) be the second derivative of -h**9/3780 + h**8/240 - h**7/42 + h**6/20 - 4*h**4/3 - 9*h. Let w(t) be the third derivative of m(t). Factor w(q).
-4*q*(q - 3)**2*(q - 1)
Determine p so that -4*p**2 + 84*p - 5632 - 5897 + 3813 - 748 - 452*p = 0.
-46
Let s(f) = 7*f**2 + 24*f + 87. Suppose -39 = 3*p - t, 2*p + 28 = -3*t + 2. Let g(w) = -15*w**2 - 49*w - 175. Let c(x) = p*s(x) - 6*g(x). Factor c(l).
-(l + 9)**2
Solve 228 + 5*z**3 + 100*z**2 - 168*z + 433*z - 58 = 0 for z.
-17, -2, -1
Let q(v) be the second derivative of -1/36*v**6 - 35/24*v**4 - 10/3*v**2 + 23*v + 0 + 1/3*v**5 + 55/18*v**3. Let q(y) = 0. What is y?
1, 2, 4
Let v(p) be the second derivative of -5/6*p**3 + 0 + 1/2*p**6 + 15/2*p**2 - 7*p - 5/42*p**7 + 1/2*p**5 - 5/2*p**4. What is c in v(c) = 0?
-1, 1, 3
Let l(y) = y**3 + 13*y**2 - 29*y + 21. Let h be l(-15). Determine o, given that -4*o + 13*o - 16*o - h - o**2 = 0.
-6, -1
Factor -2*o**2 - 1/5*o + 0.
-o*(10*o + 1)/5
Factor -86/7 + 2/7*v - 2/7*v**3 + 86/7*v**2.
-2*(v - 43)*(v - 1)*(v + 1)/7
Let c = 2910 + -26158/9. Factor -14/9*t**2 + c + 2/9*t**3 + 16/9*t.
2*(t - 4)**2*(t + 1)/9
Factor -27*f**2 + 175 - 21*f**3 - 73 - 90 + 36*f.
-3*(f - 1)*(f + 2)*(7*f + 2)
Suppose -7*n - 20 = -12*n. Let c(z) = -3*z**3 - 43*z**2 + 17*z + 50. Let s(d) = -d**3 - 21*d**2 + 9*d + 25. Let u(w) = n*c(w) - 7*s(w). Factor u(q).
-5*(q - 1)*(q + 1)*(q + 5)
Let s(m) = 4*m**4 + 2*m**3 + 3*m**2 - 16*m. Let c(l) = 3*l**4 + 3*l**3 + 3*l**2 - 15*l. Let v(d) = 7*c(d) - 6*s(d). Suppose v(g) = 0. Calculate g.
-1, 0, 1, 3
Let q(m) be the second derivative of 1/12*m**3 + 0 + 1/10*m**2 + 1/30*m**4 + 14*m + 1/200*m**5. Factor q(d).
(