+ 27054. Let c be s(-6). Factor -2/3*i**4 - 2/9*i**5 + c - 2/3*i**3 - 2/9*i**2 + 0*i.
-2*i**2*(i + 1)**3/9
Let n = -18117 - -18122. Let v(y) be the first derivative of 8*y - y**4 + 2*y**2 - n - 8/3*y**3. Factor v(j).
-4*(j - 1)*(j + 1)*(j + 2)
Let v(a) be the second derivative of -32/7*a**2 + 5/7*a**3 + 1/84*a**4 + a + 18. Determine b so that v(b) = 0.
-32, 2
Suppose -5*q = -174 + 154. Suppose 3*t - 26 + 14 = 0. Factor y**5 - 77*y**3 + 3*y**2 + y**2 + y**q + t*y**4 + 85*y**3.
y**2*(y + 1)*(y + 2)**2
Factor -17/5 - 1/5*p**2 + 18/5*p.
-(p - 17)*(p - 1)/5
Suppose -2*i = 4*r - 64, 2*r - 266 = 2*i - 258. Factor 5/3*j**5 - 18 + 74/3*j**3 + r*j**2 - 45*j - 38/3*j**4.
(j - 3)**3*(j + 1)*(5*j + 2)/3
Factor 40/3 - 1/3*b**2 + 6*b.
-(b - 20)*(b + 2)/3
Suppose 12*g = r + 29 - 113, -2*g = 14. Let k(j) be the third derivative of -10*j**2 + 0*j + r + 1/60*j**5 - 2/3*j**3 + 1/8*j**4. Find v, given that k(v) = 0.
-4, 1
Let v(u) be the first derivative of -u**4/16 + u**2/8 + 1719. Factor v(g).
-g*(g - 1)*(g + 1)/4
Let 20*s**3 - 465*s**2 - 41*s**3 + 14*s**3 - 5160 + 3070*s + 12*s**3 = 0. What is s?
3, 4, 86
Factor -45/2*a**2 + 3/4*a**3 + 93/2 - 99/4*a.
3*(a - 31)*(a - 1)*(a + 2)/4
Suppose 52 - 8782*t**5 + 104*t**3 - 4*t**2 - 102*t + 2929*t**5 + 2925*t**5 + 2926*t**5 - 48*t**4 = 0. What is t?
-26, -1, 1
Let 19/7*z**2 + 40/7*z - 12/7 - z**4 - 40/7*z**3 = 0. Calculate z.
-6, -1, 2/7, 1
Let d = 9817 + -9817. Let p(y) be the first derivative of 1/5*y**5 + 0*y + 0*y**3 - 20 + 1/3*y**4 + d*y**2 - 1/18*y**6. Let p(h) = 0. Calculate h.
-1, 0, 4
Let i(m) be the second derivative of -10*m + 1 + 35/6*m**3 - 5/3*m**4 + 25*m**2 - 1/4*m**5. Factor i(s).
-5*(s - 2)*(s + 1)*(s + 5)
Let f(x) be the first derivative of -x**4/20 + 337*x**3/15 - 2788*x**2 - 17340*x + 1757. Factor f(i).
-(i - 170)**2*(i + 3)/5
Let z = 1474314 + -1474311. Determine w so that 18*w + 93/7*w**2 + 20/7*w**z + 1/7*w**4 + 0 = 0.
-14, -3, 0
Factor 44/5*h + 2/5*h**3 + 0 - 46/5*h**2.
2*h*(h - 22)*(h - 1)/5
Let v(h) = -17*h**4 + 139*h**3 + 27*h**2 - 425*h - 296. Let p(w) = -15*w**4 + 140*w**3 + 25*w**2 - 425*w - 295. Let x(d) = 6*p(d) - 5*v(d). Factor x(z).
-5*(z - 29)*(z - 2)*(z + 1)**2
Let w be 1/22*(-3 + 11). Let y = -3379 + 37171/11. Factor -w*z + 2/11 + y*z**2.
2*(z - 1)**2/11
Let g(b) be the third derivative of b**7/840 + 7*b**6/480 - 7*b**5/60 + 5*b**4/24 - 2199*b**2. Factor g(k).
k*(k - 2)*(k - 1)*(k + 10)/4
Let z(t) be the first derivative of t**4/3 + 44*t**3/9 + 68*t**2/3 + 32*t - 486. Suppose z(m) = 0. What is m?
-6, -4, -1
Suppose 5*y - 60 = -45. Suppose 6*b**4 - 3*b**5 + 115*b**3 - 118*b**y + 0*b**4 = 0. Calculate b.
0, 1
Suppose -2 = -f + 1. Suppose 72*g + 323 = 323. Factor -3*m**f + g*m**3 - 3*m**2 + 38 - 29 - 21*m + 18*m**2.
-3*(m - 3)*(m - 1)**2
Let g(c) be the first derivative of -c**2 + 1/3*c**3 - 4*c + 34 + 1/8*c**4. Factor g(l).
(l - 2)*(l + 2)**2/2
Solve -37*k**2 + 75 - 77/2*k + 1/2*k**3 = 0 for k.
-2, 1, 75
Let i(x) = 2*x**2 - x - 3. Let u(q) = 1101*q**2 - 7989*q + 14673. Let p(j) = 9*i(j) - u(j). Suppose p(w) = 0. What is w?
70/19
Let l(u) = 23*u - 3. Let i be l(3). Suppose i = -r + 66. Factor 0 + 4/3*c**5 + r*c**4 + 0*c - 4/3*c**3 + 0*c**2.
4*c**3*(c - 1)*(c + 1)/3
Let j = 2772/989 - 42/23. Let x = 175/129 + j. Factor -4/9*r**2 + x*r - 5/9.
-(r - 5)*(4*r - 1)/9
Let l(k) = -k**3 - 25*k**2 + 32*k - 21. Let c(r) = -12*r**2 + 16*r - 10. Let s(j) = -5*c(j) + 2*l(j). Determine g so that s(g) = 0.
1, 2
Let l = -36 + 31. Let z(q) = q**2 + 5*q + 4. Let n be z(l). Factor -n*w**3 - 100*w - 13*w**2 + 0*w**3 - 27*w**2.
-4*w*(w + 5)**2
Let a be ((-410)/(-7))/((-1859)/(-182)) + (-30)/65. Factor 8/11*t**2 + 48/11 - a*t + 2/11*t**3.
2*(t - 3)*(t - 1)*(t + 8)/11
Let s = 78385 - 78382. Solve 24/7 + 12/7*y - 3/7*y**s + 12/7*y**4 - 30/7*y**2 - 3/7*y**5 = 0 for y.
-1, 2
Let m(d) be the first derivative of 2*d**3/27 + 46*d**2 + 9522*d + 387. Factor m(t).
2*(t + 207)**2/9
Factor -18 + 51/4*z**2 - 3/2*z**3 - 15/4*z.
-3*(z - 8)*(z + 1)*(2*z - 3)/4
Let q be 64/(-48)*3/1 + -4. Let b be q/(-2)*(12 - 13) + 6. Factor -1/2*h**3 + 0 - 9/2*h + 3*h**b.
-h*(h - 3)**2/2
Let s(x) be the first derivative of -x**4/12 + 23*x**3/9 + 85*x**2/6 - 3179*x/3 - 1306. Factor s(b).
-(b - 17)**2*(b + 11)/3
Let c be 4 - (-1 + 0 - 1). Suppose -5*o + w = c*w, 3*w + 10 = 2*o. Factor 442 - 66*h**2 + o*h**3 - 1027 - 2077 + 726*h.
2*(h - 11)**3
Let y(u) be the first derivative of -u**7/4620 + 9*u**5/220 + 9*u**4/22 + 4*u**3/3 - 25. Let q(z) be the third derivative of y(z). Factor q(r).
-2*(r - 6)*(r + 3)**2/11
Suppose -3*v - 12 + 21 = 0. Factor -24*n**2 + 13*n**2 + 4*n**3 - 96 - n**v + 29*n**2.
3*(n - 2)*(n + 4)**2
Factor -100 - 7*z**2 - 5*z**2 + 8*z**2 + 0*z**2 - 40*z.
-4*(z + 5)**2
Find d, given that -273/8*d**4 - 150*d + 111*d**3 - 168 + 9/4*d**5 + 1323/8*d**2 = 0.
-1, 7/6, 8
Factor 40*g**2 - 57*g**2 - 56 - 19 + 491 + 16*g - 87*g**2 - 4*g**3.
-4*(g - 2)*(g + 2)*(g + 26)
Let q be (112464/(-710))/(-36) - (0 - 1). Suppose q - 27/5*g - 1/5*g**3 + 9/5*g**2 = 0. What is g?
3
Let v(a) be the second derivative of a**6/12 - 1271*a**5/40 + 2533*a**4/40 - 759*a**3/20 - a + 343. Solve v(z) = 0 for z.
0, 3/5, 253
Let c(z) be the second derivative of -14*z - 1/10*z**5 + 3 + 0*z**4 - 1/30*z**6 + 1/42*z**7 + 0*z**3 + 0*z**2. Suppose c(j) = 0. Calculate j.
-1, 0, 2
Let 215/2*y + 1/2*y**3 - 33/2*y**2 - 375/2 = 0. What is y?
3, 5, 25
Let p(v) be the third derivative of -1/2205*v**7 + 1/7*v**4 + 0*v - 4/105*v**5 - 11/1260*v**6 + 0 + 0*v**3 + 92*v**2. Let p(o) = 0. Calculate o.
-6, 0, 1
Let t = 1159 + -28974/25. Let j(i) be the first derivative of -t*i**5 - 1/10*i**2 + 17 + 0*i + 1/15*i**3 + 1/20*i**4. Factor j(w).
-w*(w - 1)**2*(w + 1)/5
Let r(j) be the first derivative of -1/4*j**4 - 70 - 3/2*j**2 + 4/3*j**3 + 0*j. Factor r(d).
-d*(d - 3)*(d - 1)
Let s(v) be the third derivative of v**6/210 + 139*v**5/105 - 71*v**4/21 - 80*v**3/3 - 571*v**2. Solve s(j) = 0 for j.
-140, -1, 2
Suppose 6*x = 10*x. Suppose 4*c + 2*w = 0, -4*w - 6 = 5*c - 0*w. Factor t**4 + x*t - 5*t - 6*t**3 - 12*t**2 - c*t**4 - 3*t.
-t*(t + 2)**3
Let d(a) be the first derivative of -1/5*a**5 - 23/6*a**3 + 0*a + 0*a**2 - 53 + 47/8*a**4. Determine f, given that d(f) = 0.
0, 1/2, 23
Determine t so that 6/11*t**3 - 1110/11 + 2226/11*t - 102*t**2 = 0.
1, 185
Let o(u) be the third derivative of u**5/45 - 13*u**4/6 - 80*u**3/9 + 1151*u**2. Factor o(d).
4*(d - 40)*(d + 1)/3
Let v(d) be the first derivative of 5/4*d**2 + 1/16*d**4 - 17 + 0*d - 11/12*d**3. Factor v(a).
a*(a - 10)*(a - 1)/4
Let l(y) be the third derivative of -y**6/540 - y**5/10 + 70*y**4/27 + 3*y**2 - 6*y + 3. Find j such that l(j) = 0.
-35, 0, 8
Let g(f) = -11*f**2 + 52*f + 5 + 1 + 51*f + 3*f**2 - 106*f - 7*f**3. Let u(c) = c**3 + c**2 + c - 1. Let y(h) = g(h) + 6*u(h). Factor y(o).
-o*(o - 1)*(o + 3)
Suppose -2*q + 3*a + 71 = 0, -2*a = 3*q - 19 - 55. Suppose q*d = -0*d + 112. Factor 4*c**2 - 22/3*c - 2/3*c**3 + d.
-2*(c - 3)*(c - 2)*(c - 1)/3
Factor 3/5*o**3 + 96 - 228/5*o - 12/5*o**2.
3*(o - 10)*(o - 2)*(o + 8)/5
Let c(t) = t**3 - 5*t**2 + 8*t - 4. Let s be c(3). Suppose s*p + 26 = 36. Let -12/5*v**3 + 4/5*v**p + 4/5*v**4 - 8/5*v - 4*v**2 + 0 = 0. What is v?
-1, 0, 2
Let y be ((-24)/330)/((-432)/(-2808) + -4*(-9)/(-65)). Factor 0*l + 2/11 - y*l**2.
-2*(l - 1)*(l + 1)/11
Suppose 2*n + 1 + 9 = 2*i, 0 = -2*i + 5*n + 25. Let v(g) = g**3 + g**2 - 2*g + 17. Let a be v(i). Factor a - 10*m - m**2 + m**2 - 2 - 5*m**2.
-5*(m - 1)*(m + 3)
Let x(w) be the second derivative of -w**4/30 - 327*w**3/5 + 982*w**2/5 - 4*w - 858. Factor x(a).
-2*(a - 1)*(a + 982)/5
Determine s, given that -10108/3 - 68/3*s**3 - 1/3*s**4 - 281*s**2 + 11020/3*s = 0.
-38, 1, 7
Solve -2933*r - 9*r**3 + 208*r + 2720*r**2 + 14*r**3 = 0.
-545, 0, 1
Let q be (12/7)/(-3)*20124/16. Let o = 719 + q. Factor -2/7 - 2/7*r**3 + o*r + 2/7*r**2.
-2*(r - 1)**2*(r + 1)/7
Suppose 8*v - 2 = 2*k, 5*k = -2*v - 895 + 912. Let 0 + b**4 + 0*b**k + 1/2*b - b**2 - 1/2*b**5 = 0. Calculate b.
-1, 0, 1
Factor 101*l**2 + 2*l**3 - 2*l**2 + 33*l**2.
2*l**2*(l + 66)
Solve -317435*o - 2*o**2 + 317415*o - 2*o**2 = 0.
-5, 0
Suppose -185*u = -220*u. Let d(n) be the third derivative of 0*n**4 + 0*n - 17*n**2 + 0*n**5 + 0 + u*n**3 + 1/504*n**8 - 1/180*n**6 + 0*n**7. Factor d(z).
2*z**3*(z - 1)*(z + 1)/3
Det