 0 = -2*t + o + 6. Solve -t*h**2 + 0 + 3*h**3 - 1/2*h**4 + 4*h = 0.
0, 2
Let p be 4 + 237/21 - 8 - 7. Determine b so that 10/7*b**3 - 10/7*b + 6/7*b**2 + p - 8/7*b**4 = 0.
-1, 1/4, 1
Let t be (9/(-12))/(6/(-8))*5. Let i(v) be the second derivative of -2/5*v**2 - 2/15*v**3 - 4*v + 0 + 1/150*v**6 + 1/25*v**t + 1/20*v**4. Factor i(u).
(u - 1)*(u + 1)*(u + 2)**2/5
Let k(o) be the third derivative of o**9/100800 + o**8/11200 + o**7/2800 + o**6/1200 + o**5/30 + 21*o**2. Let r(a) be the third derivative of k(a). Factor r(b).
3*(b + 1)**3/5
Let n be (-18)/8*274/(-1233). Find r such that -1/3*r + 1/6 - n*r**2 = 0.
-1, 1/3
Let d = 3865/8 - 483. Let k(p) be the first derivative of -1/2*p**3 - 9/8*p**2 - 3/4*p + 3/8*p**4 - 2 + 9/20*p**5 + d*p**6. Find q, given that k(q) = 0.
-1, 1
Let s(c) = -c**4 - 35*c**3 - 45*c**2 + 41*c + 46. Let q(r) = -5*r**4 - 210*r**3 - 270*r**2 + 245*r + 275. Let n(u) = -6*q(u) + 35*s(u). Factor n(y).
-5*(y - 8)*(y - 1)*(y + 1)**2
Let y(t) be the third derivative of t**8/4200 + t**7/1050 - t**6/900 - t**5/150 + 11*t**3/3 + 21*t**2. Let d(z) be the first derivative of y(z). Factor d(w).
2*w*(w - 1)*(w + 1)*(w + 2)/5
Solve 18/5*k**4 + 12/5*k + 36/5*k**2 + 39/5*k**3 + 0 + 3/5*k**5 = 0 for k.
-2, -1, 0
Factor 900*u + 1119 + 66381 - 3*u**2 - 10*u**2 + 22*u**2 - 6*u**2.
3*(u + 150)**2
Let t(z) = -z**2 + 16*z - 26. Let c be t(14). Suppose n + 2 = 2*j, c*n + n = -2*j + 10. Factor 8/3*l + 1/3*l**3 + 5/3*l**n + 4/3.
(l + 1)*(l + 2)**2/3
Let a(n) = -9*n**3 - 4*n**2 + 80*n + 75. Let u(w) = -8*w**3 - 6*w**2 + 80*w + 78. Let l(b) = -6*a(b) + 7*u(b). Solve l(g) = 0.
-12, -1, 4
Let h(o) = -4*o - 2. Let y be h(-2). Let r = y + -3. Factor 2 + l**3 + 8*l**r - 21*l**2 + 10.
3*(l - 2)*(l - 1)*(3*l + 2)
Let f(s) be the first derivative of -4 + 4/5*s**5 + 0*s + 0*s**2 + 4*s**4 + 16/3*s**3. Factor f(w).
4*w**2*(w + 2)**2
Let b be (-24)/(15/5) + 11. Let a(g) be the first derivative of -7 + 1/10*g**4 - 4/15*g**b + 0*g + 0*g**2. Factor a(f).
2*f**2*(f - 2)/5
Let d = -98 + 100. Suppose -d*p + p - 8*p = 0. Find v, given that 1/2*v**2 + 1/2*v + p = 0.
-1, 0
Let x = -13 + 19. Suppose x = 5*s - 2*s. Suppose d**s - 2*d**2 - 2*d**3 - 5*d - d**3 + 8*d**2 + 1 = 0. Calculate d.
1/3, 1
Let n(s) = -6*s**3 - 59*s**2 + 22. Let l(i) = 2*i**3 + 20*i**2 - 8. Let q(b) = -11*l(b) - 4*n(b). Factor q(k).
2*k**2*(k + 8)
Factor -36/11*t**3 - 16/11*t**4 - 2/11*t**5 + 0 - 10/11*t - 32/11*t**2.
-2*t*(t + 1)**3*(t + 5)/11
Let r(o) be the first derivative of -o**8/392 - 2*o**7/735 + o**6/420 - o**2 - 10. Let j(p) be the second derivative of r(p). Find u such that j(u) = 0.
-1, 0, 1/3
Find z such that -2/5*z**3 + 98/5 + 6*z**2 - 126/5*z = 0.
1, 7
Let f(h) be the third derivative of h**5/15 - 2*h**3/3 - 106*h**2. Solve f(r) = 0 for r.
-1, 1
Let u(p) be the first derivative of p**5/5 + 9*p**4/4 + 8*p**3/3 + 38. Determine o, given that u(o) = 0.
-8, -1, 0
Suppose -q = w - 3, -w - 4*q + 9 = 3. Factor 4*r**4 + 9*r**2 - 25*r**w + 0 + 16*r + 0 - 4*r**3.
4*r*(r - 2)*(r - 1)*(r + 2)
Suppose 7*j - 1357 = -1343. Find w such that 2/17*w**j + 4/17*w + 2/17 = 0.
-1
Factor -85*l**3 + 124*l**3 - 74*l**3 - 30*l**2 - 5*l**4.
-5*l**2*(l + 1)*(l + 6)
Factor -15451 - 205*k + 925*k - 2818 + 2186 - 9837 - 5*k**2.
-5*(k - 72)**2
Suppose 83*m - 35 = 78*m, 3*m - 11 = 5*v. Factor 1/2*h**v + 2*h**3 - 2*h + 0 - 1/2*h**4.
-h*(h - 4)*(h - 1)*(h + 1)/2
Let s(w) = w**3 - 4*w**2 + 21*w - 196. Let a be s(6). Let -1/8*z**a + 1/2 + 0*z = 0. Calculate z.
-2, 2
Find o, given that -57*o**2 + 81*o + 687*o**2 - 108*o + 607*o - 125*o**4 - 225*o**3 + 120 = 0.
-3, -2/5, 2
Factor -214326/13*r + 13502538/13 + 1134/13*r**2 - 2/13*r**3.
-2*(r - 189)**3/13
Let l = -538 - -1618/3. Factor -l*f**5 + 4*f - 8/3*f**3 - 4*f**4 + 4/3 + 8/3*f**2.
-4*(f - 1)*(f + 1)**4/3
Let o(t) be the third derivative of t**8/420 + 8*t**7/525 - t**6/25 - 4*t**5/75 + t**4/6 - 109*t**2. Determine a, given that o(a) = 0.
-5, -1, 0, 1
Let v(c) be the first derivative of -c**7/105 - c**6/20 - c**5/30 + c**4/4 + 2*c**3/3 + 17*c**2/2 + 23. Let r(b) be the second derivative of v(b). Factor r(s).
-2*(s - 1)*(s + 1)**2*(s + 2)
Suppose -71*l**2 - 2*l**5 + 42*l**2 + 24*l**4 + 53*l**2 + 126*l - 76*l**3 = 0. What is l?
-1, 0, 3, 7
Let m(l) be the third derivative of l**7/42 + l**6/12 - l**5/4 - 5*l**4/3 - 10*l**3/3 - 30*l**2 - 1. Factor m(i).
5*(i - 2)*(i + 1)**2*(i + 2)
Let a(z) be the first derivative of -z**6/150 + z**5/50 - z**4/60 + 2*z - 7. Let s(k) be the first derivative of a(k). Factor s(w).
-w**2*(w - 1)**2/5
Let h(t) = t**3 + 8*t**2 - t - 5. Let f = -53 + 45. Let a be h(f). Factor 2/7*i**a + 2/7*i**4 - 2/7*i + 4/7 - 6/7*i**2.
2*(i - 1)**2*(i + 1)*(i + 2)/7
Let r(f) be the third derivative of f**8/84 + 2*f**7/15 + 76*f**2. Determine i so that r(i) = 0.
-7, 0
Suppose 5*m = w - 25, w - 3*m - 17 = -2. Factor 1/2*o**3 + w*o**2 + 0 + 0*o.
o**3/2
Let a = 1341 - 6701/5. Factor 4/5*r**2 - 1/5*r**5 + a*r**4 + 0 - 1/5*r - 6/5*r**3.
-r*(r - 1)**4/5
Let z be (-44)/(-6) + 378/(-162). What is f in -2/9*f + 2/9*f**4 + 4/9*f**3 + 2/9 - 4/9*f**2 - 2/9*f**z = 0?
-1, 1
Let w(k) be the second derivative of 9*k**2 + 39/8*k**4 + 22*k + 27/40*k**5 + 0 + 10*k**3. Suppose w(y) = 0. Calculate y.
-3, -2/3
Suppose -4*w - 4*f = -52, 4*w - 3*f = 3*w + 9. Suppose 4*k = 4*g - w, 4*k = -3*g + 10 + 6. Find c such that 2*c**2 + 4*c**g - 2*c**4 - 4*c**4 = 0.
-1, 0, 1
Let t(v) = v**3 + 35*v**2 - 167*v - 427. Let l be t(-39). Suppose -12/11*p + 6/11*p**l + 6/11 = 0. Calculate p.
1
Let l be (2/5)/(((-504)/(-35))/6). Let d(k) be the first derivative of -2/9*k**3 + 1/3*k**2 - 10 + 2/3*k - l*k**4. Let d(b) = 0. What is b?
-1, 1
Let q(d) be the third derivative of -d**8/112 + 7*d**7/10 - 102*d**6/5 + 1216*d**5/5 - 512*d**4 - 5*d**2 - 4*d. Factor q(b).
-3*b*(b - 16)**3*(b - 1)
Let w = -25668 - -76085/3. Let m = -303 - w. Factor 0 - 2/3*b**3 - 2/3*b**2 + 0*b - 2*b**5 + m*b**4.
-2*b**2*(b - 1)**2*(3*b + 1)/3
Determine w, given that -2*w**4 - 101 + 36*w + 197 - 112 + 104*w**2 + 36*w**3 - 14*w**4 = 0.
-1, 1/4, 4
Let n(p) = 7*p**5 - 6*p**4 - 15*p**3 - 2*p**2 - 18*p + 18. Let z(a) = -3*a**5 + 3*a**4 + 7*a**3 + a**2 + 8*a - 8. Let f(o) = -4*n(o) - 9*z(o). Factor f(c).
-c**2*(c + 1)**3
Let g be 17/((-204)/168) + 17. Factor 9/4*i**4 - 7/4*i + 7/4*i**g + 1/2 - 11/4*i**2.
(i - 1)*(i + 1)**2*(9*i - 2)/4
Suppose 156*w - 4*w**5 - 456*w + 500 - 377*w**2 - 42*w**2 - 6*w**5 - 135*w**4 - 636*w**2 - 620*w**3 = 0. Calculate w.
-5, -2, 1/2
Determine o, given that 12/5 + 2*o + 2/5*o**4 - 2*o**3 - 14/5*o**2 = 0.
-1, 1, 6
Let r(m) = -70*m**2 - 1 - 2*m**3 + m**3 + 71*m**2 - m. Let b(c) = c**3 + 9*c**2 + 6*c + 6. Let o(a) = -b(a) - 6*r(a). Factor o(t).
5*t**2*(t - 3)
Suppose -5*w = n + 33, -n + 2*w = 2*n + 14. Let o(m) = m**3 + 9*m**2 + 10*m + 16. Let j be o(n). Factor -1/2 + 1/2*u**4 + u**3 + j*u**2 - u.
(u - 1)*(u + 1)**3/2
Let x = -5726/3 - -1910. Factor 2/3*u + x - 2/3*u**2.
-2*(u - 2)*(u + 1)/3
Let p(y) be the third derivative of -y**6/600 + 3*y**5/50 - 11*y**4/40 + 8*y**3/15 - 682*y**2. Factor p(x).
-(x - 16)*(x - 1)**2/5
Let j(b) be the third derivative of b**8/84 - 8*b**7/189 + 2*b**6/135 + 393*b**2. Factor j(s).
4*s**3*(s - 2)*(9*s - 2)/9
Let n be (-8)/(-2) - (-13507)/(-156). Let t = n - -268/3. Factor 3/4*m**4 + t*m**2 - 15/4*m**3 + 3/2 - 21/4*m.
3*(m - 2)*(m - 1)**3/4
Determine y so that -2*y**3 + 79*y**2 - 173*y**2 + 61*y**2 + 105507 - 441*y**2 - 37446*y - 1091585 = 0.
-79
Let q = 28 - 11. Suppose -g + q*g = g. Solve 2/7*d**4 + 0*d + 0*d**2 + 1/7*d**5 + 0 + g*d**3 = 0 for d.
-2, 0
Let f(k) be the second derivative of k**5/20 - 5*k**4/6 - k**3/6 + 5*k**2 - 2*k + 17. Factor f(b).
(b - 10)*(b - 1)*(b + 1)
Suppose -4*b = -3*b + 2, 3*d - b = 11. Suppose 5*i + 5 = -3*f - 6, d*f = 3*i + 21. Find o such that 8*o**3 - o**2 - 3*o**2 + 2*o**2 - 4*o**f - 2*o**4 = 0.
0, 1
Let z = 18855/14806 - 1/1346. Suppose -4/11*n + 0 - z*n**2 = 0. What is n?
-2/7, 0
Let v(d) be the first derivative of -d**4/4 - 2*d**3/3 + 9*d**2/2 + 18*d + 161. Let v(w) = 0. What is w?
-3, -2, 3
Let z be ((-1)/10)/(66/(-396)) - (-46)/90. Find a, given that 0*a - z*a**3 + 4/9*a**2 - 44/9*a**4 - 10/3*a**5 + 0 = 0.
-1, -2/3, 0, 1/5
Determine j, given that 0 + 6*j**5 - 8*j**4 - 4/3*j**3 + 2/3*j + 8/3*j**2 = 0.
-1/3, 0, 1
Determine u, given that -5*u**4 + 2*u**