et l(m) be the first derivative of -m**3/12 + 251*m**2/8 + 63*m - 2394. Factor l(r).
-(r - 252)*(r + 1)/4
Factor -1047/2*h - 15/2*h**2 + 105.
-3*(h + 70)*(5*h - 1)/2
Let a(g) be the first derivative of g**6/15 + g**5/10 - g**4/6 - g**3/3 + 75*g + 36. Let j(f) be the first derivative of a(f). Factor j(q).
2*q*(q - 1)*(q + 1)**2
Let f(k) be the second derivative of 0*k**3 + 10*k - 1/15*k**6 + 0 + 0*k**2 + 7/6*k**4 + 3/5*k**5. Factor f(j).
-2*j**2*(j - 7)*(j + 1)
Let 2/7*z**3 + 276/7*z**2 + 0 + 9522/7*z = 0. Calculate z.
-69, 0
Suppose 7*t - 95 = 465. Factor 0*l**2 - t*l**2 + 60*l**3 + 6*l**5 + 4*l**5 - 15*l**5.
-5*l**2*(l - 2)**2*(l + 4)
Let f(c) = -c**3 + 20*c**2 - 19*c + 2. Let o be f(19). Factor 30 - 46 - 12*w + 4*w**2 + 28 - w**o.
3*(w - 2)**2
Let h(k) be the third derivative of 0*k**3 + 7*k**2 + 3*k + 0 + 3/4*k**4 - 3/40*k**6 - 7/20*k**5. Find p such that h(p) = 0.
-3, 0, 2/3
Let l be 1079/52 - (-1)/4. Suppose 6*t = -t + l. Factor 119*z**2 + 5*z**t - 59*z**2 - 2*z**4 - 62*z**2.
-z**2*(z - 2)*(2*z - 1)
Let l(u) be the second derivative of -4*u**6/15 - u**5/5 + u**4 + 2*u**3/3 - 2*u**2 + 1105*u - 3. Determine j so that l(j) = 0.
-1, 1/2, 1
Let t(u) be the third derivative of -u**6/780 - u**5/130 - u**4/78 - 59*u**2 - 6. Find o, given that t(o) = 0.
-2, -1, 0
Let z = 12140 + -12119. Let s(j) be the second derivative of 1/48*j**4 + 1/6*j**3 - 2 + 3/8*j**2 + z*j. Factor s(y).
(y + 1)*(y + 3)/4
Let k be (-23)/230 - (3 - (-266)/(-60)). Let t(n) be the first derivative of k*n**3 - 1/3*n**6 + n**2 - 4/5*n**5 + 0*n + 0*n**4 + 18. Solve t(m) = 0 for m.
-1, 0, 1
Let y = -66 + 65. Let b(m) = 0 + 26*m**3 + 28*m**2 - 2 + 7 - 28*m**3. Let i(q) = -q**3 - q**2 + 1. Let n(a) = y*b(a) + 5*i(a). Factor n(z).
-3*z**2*(z + 11)
Let m be (-1763)/860 + (-1)/(-20). Let v be -128*(m + (-19)/9 - -4). Factor -v - 32/9*z - 2/9*z**2.
-2*(z + 8)**2/9
Suppose 29*d - 22320 = 9*d. Let t be (d/(-2170))/(6/(-14)). Find m, given that 0 + 3/5*m**2 - t*m = 0.
0, 2
Let a(w) be the first derivative of 11*w**6/90 + 2*w**5/15 + 8*w**3/3 + 3*w + 102. Let j(n) be the third derivative of a(n). Factor j(h).
4*h*(11*h + 4)
Let m = 112579/15 - 112259/15. Determine w, given that 1/6*w**4 - 7/3*w**3 + 16/3*w**2 + m*w + 0 = 0.
-2, 0, 8
Let j(r) be the first derivative of 9*r**5/40 - 5*r**4/8 + r**3/2 + 35*r - 17. Let f(y) be the first derivative of j(y). Let f(w) = 0. What is w?
0, 2/3, 1
Let y = 47 - 43. Suppose -5*f + 755 = -4*x, -3*f = y*x + 140 - 561. Factor 16*l**3 - 152*l**4 - l**3 - 10*l**2 + f*l**4.
-5*l**2*(l - 2)*(l - 1)
Suppose d = 3*o - 12, 10 = -4*d + 2*d - o. Let k be d/(-7)*(-301)/(-129). What is y in 2/11 + 4/11*y + 2/11*y**k = 0?
-1
Let q(p) be the second derivative of p**4 + 24*p + 1/42*p**7 + 2/3*p**3 + 1/5*p**6 + 0*p**2 + 0 + 13/20*p**5. Suppose q(c) = 0. Calculate c.
-2, -1, 0
Let v be (-1 + 1)/(-11 - (29 - 19 - 15)). Suppose -2/5*c**4 + 2/5*c**2 + 4/5*c + v - 4/5*c**3 = 0. What is c?
-2, -1, 0, 1
Let b(k) = -30*k**4 + 96*k**3 - 367*k**2 + 104. Let p(v) = -23*v**4 + 72*v**3 - 275*v**2 + 80. Let w(f) = 10*b(f) - 13*p(f). Factor w(a).
-a**2*(a - 19)*(a - 5)
Suppose 177/2*y - 15/2*y**2 - 66 = 0. Calculate y.
4/5, 11
Let x(a) be the second derivative of a**7/42 + 71*a**6/30 + 207*a**5/20 + 205*a**4/12 + 34*a**3/3 + 5421*a + 2. Determine f so that x(f) = 0.
-68, -1, 0
Factor 927408/5 - 3336/5*p + 3/5*p**2.
3*(p - 556)**2/5
Let v be 1 - -7 - (21 - 1). Let r be (-2)/15*-2 - 4/v. Let 4/5*h + 1/5*h**2 + r = 0. What is h?
-3, -1
Let g(s) be the third derivative of -s**5/90 - 77*s**4/12 + s**2 - 1108. Factor g(n).
-2*n*(n + 231)/3
Let l(y) be the second derivative of 27/20*y**5 + 0 + 2/3*y**4 - 3/2*y**2 + 13/84*y**7 - 11/12*y**3 + 224*y + 23/30*y**6. Suppose l(q) = 0. What is q?
-1, 6/13
Suppose 0 = 28*i - 29*i + 2. Factor 0*w**i + 12*w**2 + 3*w**3 + 15*w + 17 - 11.
3*(w + 1)**2*(w + 2)
Let q(w) be the third derivative of w**6/630 + 8*w**5/105 + 2*w**4/3 + 179*w**3/6 - 40*w**2 + 1. Let s(b) be the first derivative of q(b). Factor s(l).
4*(l + 2)*(l + 14)/7
Let k(h) be the first derivative of -h**3/12 - 26*h**2 - 103*h + 343. Factor k(j).
-(j + 2)*(j + 206)/4
Let l(c) = 5*c**2 - 5 + 39*c**3 - 49*c**3 + 5*c + 0*c**2. Let o(r) = r**3 + r + 1. Let k(m) = -l(m) - 5*o(m). Factor k(t).
5*t*(t - 2)*(t + 1)
Let w = -428/5 - -86. Let k be (42/(-1785))/(10/(-170)). Let 2/5*y**2 - 2/5 + k*y**3 - w*y = 0. Calculate y.
-1, 1
Let s(y) be the second derivative of y**5/10 - 137*y**4/6 + 664*y**3/3 - 528*y**2 + 7804*y. Let s(o) = 0. Calculate o.
1, 4, 132
Suppose -3*h - h = 4*b - 152, 0 = 2*b + 5*h - 70. Let v be 2*-7*(-8)/b. Determine u, given that 4/5*u**2 + 0 - 22/5*u**3 + 0*u + 32/5*u**4 - v*u**5 = 0.
0, 2/7, 1
Suppose 0 = -4*g + 4*v + 104, -3*v - 7 = -g + 29. Suppose -g*j + 60 = -6*j. Factor 0*r**2 + 1/2*r**j + 0*r + 0 - 1/2*r**3.
r**3*(r - 1)/2
Let r(t) be the first derivative of 2*t**5/65 - 17*t**4/26 - 212*t**3/39 - 88*t**2/13 + 62. What is j in r(j) = 0?
-4, -1, 0, 22
Let f(z) be the second derivative of -z**4/3 + 118*z**3/27 + 56*z**2/9 - 192*z. Find c, given that f(c) = 0.
-4/9, 7
Let x be 12/7*539/231. Let z(i) be the first derivative of -7*i**2 + 32/5*i**3 - 11 + 12/5*i + 9/10*i**x. Suppose z(s) = 0. What is s?
-6, 1/3
Let i(f) be the second derivative of 3/5*f**5 + 0*f**2 + 16/3*f**3 + 0 - 10/3*f**4 + 239*f. Factor i(k).
4*k*(k - 2)*(3*k - 4)
Suppose -2 = 5*a + 13*p - 12*p, -3*a = 5*p + 10. Let z(f) be the second derivative of -1/6*f**3 + a*f**2 - 1/24*f**4 + 0 - 13*f + 3/40*f**5. Solve z(w) = 0.
-2/3, 0, 1
Let n = 137 + -137. Suppose n = 4*z - r - r - 8, 4*z - 4*r = 4. Factor 9*u - 12*u**2 + 2*u**z - 2*u + u + 10*u.
2*u*(u - 3)**2
Let v = -664 + 656. Let t be 3/6*(-143)/220*v. Factor -3/5*f**2 - 4/5 + t*f.
-(f - 4)*(3*f - 1)/5
Let m be (14*87/812)/2. Let 9/2*z**2 - 3/4*z + m*z**3 - 9/2 = 0. Calculate z.
-6, -1, 1
Suppose 0 = -4*l + 39 + 41. Suppose -3*k = 2*k + l, 8981 = 5*s + k. Factor -1800*h**3 + s*h**3 + h**2 + 5*h**2.
-3*h**2*(h - 2)
Suppose 0 = -260*m + 268*m - 72. Determine w, given that 73*w + m*w**3 + 19*w - 88*w**2 - 13*w**3 + 0*w**3 = 0.
-23, 0, 1
Let t = 41888897/48316 - 121492/141. Let x = 1/1028 + t. Let 8/3*r**2 - x*r + 5/3 + 2/3*r**5 + 14/3*r**3 - 13/3*r**4 = 0. What is r?
-1, 1/2, 1, 5
Let f be (-40)/(4 + -9) + -1*2 - 4224/792. Suppose 0 = -v + 2. Factor f*s**2 - 20/3 - v*s.
2*(s - 5)*(s + 2)/3
Let l(y) be the second derivative of -2*y**5/35 - y**4/2 + 36*y**3/7 + 160*y**2/7 + 49*y - 2. What is h in l(h) = 0?
-8, -5/4, 4
Let c(l) be the third derivative of 0*l**3 + 1/3*l**4 - 1/5*l**6 + 1/15*l**5 + 27*l**2 + 0*l + 0. Factor c(z).
-4*z*(2*z + 1)*(3*z - 2)
Let a(u) = -2*u**2 + u + 1. Let w(l) = 10*l**2 + 192*l + 190. Let j(m) = -4*a(m) - w(m). Suppose j(z) = 0. Calculate z.
-97, -1
Let x(c) be the first derivative of -15/2*c**4 + 0*c**2 + 0*c + 18/5*c**5 - 1/3*c**6 + 14/3*c**3 + 24. Factor x(a).
-2*a**2*(a - 7)*(a - 1)**2
Let a = -11665 - -11668. Find b such that 3/2 + 15/4*b**a - 3/2*b**2 - 15/4*b = 0.
-1, 2/5, 1
Let 1/5*i**2 + 335241/5 + 1158/5*i = 0. Calculate i.
-579
Find z such that 1503792/7 + 4507128/7*z + 4498635/7*z**2 + 1491057/7*z**3 - 4239/7*z**4 + 3/7*z**5 = 0.
-1, 708
Let c(d) be the first derivative of -6*d**5/35 - 51*d**4/14 - 30*d**3/7 + 1551*d**2/7 - 2904*d/7 + 3024. Suppose c(p) = 0. What is p?
-11, 1, 4
Let n(k) be the second derivative of -17*k**5/130 + 47*k**4/78 + 4*k**3/13 + 863*k. Factor n(x).
-2*x*(x - 3)*(17*x + 4)/13
Let o(t) be the third derivative of -t**5/30 + 187*t**4/72 - 61*t**3/9 + 6*t**2 - 73*t. What is p in o(p) = 0?
2/3, 61/2
Factor -111/8*h**3 + 392*h + 378*h**2 + 0 + 1/8*h**4.
h*(h - 56)**2*(h + 1)/8
Let v = -8433/44 - -2111/11. Let c(j) be the third derivative of 0*j + 26*j**2 + 1/42*j**7 + 0*j**3 + 0 + 5/12*j**4 - v*j**5 + 0*j**6. Let c(u) = 0. What is u?
-2, 0, 1
Let p(v) be the first derivative of -6*v**3 + 0*v - 9/40*v**5 + 0*v**2 - 1/4*v**4 - 27/320*v**6 + 16. Let q(d) be the third derivative of p(d). Factor q(j).
-3*(9*j + 4)**2/8
Let f(n) = -n**2 - 12*n - 12. Let v be f(-12). Let l be v/(6 + -2) - -11. Suppose -s + 7*s**3 + 5*s + 9*s**3 - 22*s**2 + 18*s**4 + l*s**3 = 0. Calculate s.
-2, 0, 1/3
Let w(p) be the first derivative of 1/15*p**5 + 0*p - 28 + 8/9*p**3 - 1/2*p**4 + 0*p**2. Solve w(y) = 0 for y.
0, 2, 4
Let a = 3