z - g. Let m = -167 - z. Solve 36/5*c + 18/5*c**3 + 39/5*c**2 + 12/5 + 3/5*c**m = 0 for c.
-2, -1
Let a(w) be the first derivative of -w**4/9 + 4*w**3/27 + 16*w**2/9 - 16*w/3 - 1136. Suppose a(b) = 0. Calculate b.
-3, 2
Let c(k) = 33*k**3 - 11519*k**2 - 28885*k - 11612. Let g(u) = -10*u**3 + 3840*u**2 + 9628*u + 3868. Let t(a) = 2*c(a) + 7*g(a). Factor t(w).
-2*(w - 963)*(w + 2)*(2*w + 1)
Suppose -z - 3 = 5*t, -t = -17*z + 15*z + 5. Let l(v) be the second derivative of -4/45*v**3 + 1/5*v**z + 0 + 1/90*v**4 - 8*v. Factor l(b).
2*(b - 3)*(b - 1)/15
Let l(d) be the first derivative of 25/3*d**3 + 20*d + 20*d**2 + 5/4*d**4 + 104. Determine k, given that l(k) = 0.
-2, -1
Let c(n) be the first derivative of -n**3 + 51*n**2/2 + 44. Let y(h) = -16*h**2 + 256*h. Let a(k) = 33*c(k) - 6*y(k). Let a(l) = 0. Calculate l.
0, 49
Suppose -2*o - 752*f + 748*f = 40, 5*o + 5*f = -50. Suppose -2/11*t**3 + 32/11*t**2 - 128/11*t + o = 0. Calculate t.
0, 8
Let n(x) = x**2 - 10*x - 21. Let w be n(12). Let t be w - 5/(-15)*0. Solve -231 + 4*r + 4*r**2 + 231 + r**t = 0 for r.
-2, 0
Let t(y) = 9*y**4 + 117*y**3 - 198*y**2 - 12*y + 12. Let r(h) = h**4 + 2*h**2 - h + 1. Let j(m) = -12*r(m) + t(m). Let j(i) = 0. Calculate i.
0, 2, 37
Let a = 3223 + -1807. Let o = 1416 - a. Factor o + 6/5*p - 2*p**2 + 2/5*p**3 + 2/5*p**4.
2*p*(p - 1)**2*(p + 3)/5
Suppose -16 = 3*x + 5*h, 3*x + 22 = -3*h + 16. Determine f, given that 0 - 12/5*f + 38/5*f**2 - 42/5*f**x - 2/5*f**5 + 18/5*f**4 = 0.
0, 1, 6
Let w(d) = -d**2 - 31*d. Let x(m) = -23*m**2 - 66*m - 3. Let l(n) = -4*w(n) + x(n). Factor l(u).
-(u - 3)*(19*u - 1)
Let l(d) be the second derivative of -5*d**7/42 - 2*d**6/3 + 25*d**5/4 + 35*d**4/3 - 1928*d. Determine h, given that l(h) = 0.
-7, -1, 0, 4
Suppose 45*l - 46*l + 3*a + 14 = 0, -7*a - 26 = l. Let v(d) be the first derivative of -12*d - 9/4*d**3 + 3/16*d**4 + 9*d**l + 17. Factor v(n).
3*(n - 4)**2*(n - 1)/4
Suppose -3*b + 12 = -3. Factor 3*r**3 + 3*r + 4*r - 9*r**3 + 5 - 2 + 2*r**2 - 5*r**4 - r**b.
-(r - 1)*(r + 1)**3*(r + 3)
Let f(v) be the first derivative of -27 - 32/7*v - 65/7*v**2 - 8/21*v**3. Factor f(o).
-2*(o + 16)*(4*o + 1)/7
Let w = 1 - -3. Let l be 0/(17/(-11) - ((-12615)/319 - -39)). Suppose 2*o**w - 3*o**3 - 1/2*o + l + 2*o**2 - 1/2*o**5 = 0. What is o?
0, 1
Let r = 28 - 16. Let o be (-16)/r*71/(-2)*3. Let o*w + 5*w**4 - 142*w - 25*w**3 + 20*w**2 = 0. What is w?
0, 1, 4
Let s(y) be the third derivative of 0*y**3 - 4/45*y**5 - 14/45*y**6 + 30*y**2 - 2 + 1/84*y**8 + 8/9*y**4 + 0*y - 2/63*y**7. Let s(h) = 0. What is h?
-2, -1, 0, 2/3, 4
Let w(z) be the third derivative of 5/2*z**3 - 82*z**2 - 1/2*z**5 + 0 + 0*z - 5/24*z**4 - 5/336*z**8 + 1/14*z**7 + 1/12*z**6. Suppose w(c) = 0. What is c?
-1, 1, 3
Suppose -1 + 2/3*k**5 + 11/3*k**4 + 8/3*k**2 + 6*k**3 - 4/3*k = 0. Calculate k.
-3, -1, 1/2
Let j be (-6 + (-164)/(-24))*6. Determine u so that -1121*u**3 + 13*u + 59*u - 38*u**2 + 6*u**4 + 72 + 1085*u**3 + 4*u**j = 0.
-3, -3/2, -1, 2
Let r(l) = -43*l**2 + 135*l + 91. Let c(b) = -11*b**2 + 34*b + 18. Let d(w) = 9*c(w) - 2*r(w). Factor d(z).
-(z - 2)*(13*z - 10)
Let d(v) = 2*v**2 - 4 + 4 + 2*v**3 + v**5 + v**4. Let y(r) = 3*r**5 + 4*r**4 + 7*r**3 + 6*r**2. Let j(p) = 8*d(p) - 3*y(p). Factor j(z).
-z**2*(z + 1)**2*(z + 2)
Factor -169932/5*s**3 + 0 - 167042/5*s - 46648/5*s**4 - 275128/5*s**2 - 4802/5*s**5.
-2*s*(7*s + 17)**4/5
Suppose 3*n = -67 + 19. Let i be -3 + (-9 - 476/n). Solve -i*f**3 + 5/2*f**2 + 7*f - 5*f**4 + 25/4*f**5 - 2 = 0 for f.
-1, 2/5, 2
Let n(s) = s**2 - 14*s - 13. Let o be n(15). Suppose m + o - 15 = 5*q, 2*q + 4 = 0. Find w such that 22/15*w**2 - 38/15*w - 2/15*w**m + 6/5 = 0.
1, 9
Let w(z) = -z**3 + z**2 + 16*z. Let m be w(0). Suppose m = -h - 4*f + 5, -3*f + 20 = 4*h. Factor 5/3*y**4 - y**3 - 1/3*y**2 + 0 + 1/3*y - 2/3*y**h.
-y*(y - 1)**3*(2*y + 1)/3
Let a(p) be the third derivative of -p**8/336 - p**7/15 - p**6/12 + 11*p**5/15 + 67*p**4/24 + 13*p**3/3 - 1632*p**2. Factor a(w).
-(w - 2)*(w + 1)**3*(w + 13)
Let y(o) be the second derivative of -o**5/5 - 5*o**4/9 + 16*o**3/3 - 32*o**2/3 + o - 229. Solve y(f) = 0 for f.
-4, 1, 4/3
Let p(q) be the first derivative of q**3/4 - 53*q**2/8 - 19*q - 2938. Factor p(v).
(v - 19)*(3*v + 4)/4
Let d(o) be the second derivative of 3*o**5/20 - 22*o**4 + 968*o**3 - 3387*o. Find c, given that d(c) = 0.
0, 44
Let h(r) = r + 1. Let j be (0 - 2)/(0 + -2)*3. Suppose 14 = -d - j*g, g = 4*g + 15. Let a(f) = -2*f**2 + 10*f + 12. Let w(x) = d*a(x) - 6*h(x). Factor w(t).
-2*(t - 3)*(t + 1)
Let p(v) be the second derivative of -v**6/1440 + v**5/96 - 7*v**3/3 + v**2 - 2*v + 7. Let r(s) be the second derivative of p(s). What is l in r(l) = 0?
0, 5
Let s = 27541/5 - 192707/35. Suppose -30/7*f**2 + s*f**3 - 52/7*f - 6/7 = 0. Calculate f.
-1, -1/8, 3
Factor 4/3*i**2 + 52/15 - 74/15*i + 2/15*i**3.
2*(i - 2)*(i - 1)*(i + 13)/15
Suppose 2*k - 16*l = -20*l - 8, -4*k + 3*l + 6 = 0. Let m(y) be the second derivative of 2*y + 5/2*y**3 + 0*y**2 + k - 5/12*y**4. Suppose m(u) = 0. Calculate u.
0, 3
Let t be (609/174*(-6)/7)/(3/(-4)). Let p(c) be the second derivative of -1/20*c**t - 24/5*c**2 + 6*c + 0 + 4/5*c**3. Factor p(a).
-3*(a - 4)**2/5
Let p(j) be the third derivative of -5*j**8/336 - 4*j**7/21 - j**6/6 + 20*j**5/3 + 40*j**4/3 - 640*j**3/3 - 2169*j**2 - 2. Factor p(m).
-5*(m - 2)**2*(m + 4)**3
Let h(u) be the first derivative of 4*u**3/3 + 196*u**2 - 1632*u + 2407. Factor h(q).
4*(q - 4)*(q + 102)
Suppose -2*w - 2 = -2*d, -5*w + 52 = 6*d - 9. Factor 0*v + d*v**2 + 0 + 2/5*v**3.
2*v**2*(v + 15)/5
Let p(l) be the first derivative of 5*l**6/24 + 57*l**5/2 + 1125*l**4/16 + 140*l**3/3 - 2110. Factor p(c).
5*c**2*(c + 1)**2*(c + 112)/4
Let c = 2745 + -2742. Let f(i) be the first derivative of -22/5*i**5 + 0*i - i**4 + 0*i**c - 3*i**6 + 16 + 0*i**2. Factor f(k).
-2*k**3*(k + 1)*(9*k + 2)
Let j(u) = -7*u - 54. Let i be j(-8). Factor -16*q - 30*q**3 - 150*q**3 + 37*q**5 - 50*q**4 - 12*q**2 + 213*q**5 + 116*q**i.
2*q*(q + 1)*(5*q - 2)**3
Suppose -8 + 7 = o. Let a(z) = -2*z**2 - 53*z - 122. Let h(l) be the first derivative of -l**3/3 + l**2/2 - l - 7. Let q(u) = o*a(u) - 3*h(u). Factor q(g).
5*(g + 5)**2
Let p be (-2)/(68/20 + 1*(-1 - 4)). Let u(s) be the first derivative of 45/2*s**2 + 20*s + 10*s**3 + p*s**4 + 18. Find k, given that u(k) = 0.
-4, -1
Suppose t + f = 51, 5*f + 59 = t - 16. Factor 21*h**3 + 21*h**4 + 8*h**4 - t*h**4 + 11*h**4 + 36*h**2.
-3*h**2*(h + 1)*(5*h - 12)
Let y = -26923/10 - -13469/5. Factor -9*n + 3/2*n**4 + y*n**2 + 0 + 6*n**3.
3*n*(n - 1)*(n + 2)*(n + 3)/2
Let s = -3 - -5. Suppose 5*p + 30 = 0, 3*u + 16*p - 37 + 133 = 0. Factor -8*a**s + 2*a**2 + u*a**2 - 8*a + 2*a**3.
2*a*(a - 4)*(a + 1)
Let a = -333041 - -2331431/7. Suppose -a*j**2 - 136/7*j**3 + 108/7*j + 216/7 - 4/7*j**5 - 40/7*j**4 = 0. What is j?
-3, -2, 1
Let w(b) be the first derivative of -32*b + b**2 - 40 + 32/3*b**3 - 1/2*b**4. Determine u, given that w(u) = 0.
-1, 1, 16
Let j(w) be the second derivative of 5*w**4/48 + 1049*w**3/12 - 105*w**2 + 1190*w. Factor j(f).
(f + 420)*(5*f - 2)/4
Let s(j) be the first derivative of -j**4 - 624*j**3 - 109512*j**2 - 10588. Factor s(y).
-4*y*(y + 234)**2
Suppose -2*n = 10, n = 5*p - 3 - 17. Suppose 7 = 5*j + 2*u - 18, -10 = -2*j - p*u. Determine q so that j*q**3 - 18*q**2 - 10*q**2 - 8*q - 25*q**3 = 0.
-1, -2/5, 0
Let k(u) be the first derivative of 2*u**3/3 + 32*u**2 - 288*u + 205. Factor k(j).
2*(j - 4)*(j + 36)
Let y be 3/4 - 5203/8228. Suppose 14/17*w**2 - 12/17 - 2/17*w**4 + 2/17*w - y*w**3 = 0. What is w?
-3, -1, 1, 2
Let g(y) be the first derivative of -5*y**2/2 - 10*y + 5. Let v be g(-5). Factor 23*b**3 + v*b - 31*b - 7*b**4 + 16*b - 6*b**2.
-b**2*(b - 3)*(7*b - 2)
Factor -1/7*h**2 - 35*h + 246/7.
-(h - 1)*(h + 246)/7
Suppose 16 = -0*t + 2*t. Let i be (t/16)/((-1)/(-6)) + -1. Suppose 11*p**i + 9*p**3 + 9*p**3 - 15*p**3 + p**2 = 0. What is p?
-4, 0
Let v(c) = -2*c + 12. Let x be v(-7). Let 2*n + 3*n**4 - 3*n**5 - x*n + 8*n**4 + 10*n**4 - 54*n**3 + 60*n**2 = 0. What is n?
0, 1, 2
Factor -5006*y**4 + 5007*y**4 - 10*y**2 - 44*y**2 - 3*y**3.
y**2*(y - 9)*(y + 6)
Let r(s) = 88*s**3 + 1581*s**2 + 6093*s + 3719. Let u(i) = -8*i**3 - 144*i**2 - 554*i - 338. Let v(m) = 4*r(m) + 46*u(m). Let v(b) = 0. Calculate b.
-14, -4, -3/4