Calculate x.
0, 1
Let p(a) be the third derivative of a**8/70560 - a**7/17640 + a**5/60 + a**2. Let s(d) be the third derivative of p(d). What is z in s(z) = 0?
0, 1
Suppose j = -3*j + 8. Factor -5 + 2*m**j - 3 - m + m.
2*(m - 2)*(m + 2)
Let d = 10484141/2017274 - 1004/1619. Let l = d + -1/178. Let l + 18/7*q**5 + 96/7*q - 30/7*q**4 + 48/7*q**2 - 64/7*q**3 = 0. What is q?
-1, -2/3, 2
Suppose -5*h + 13 = -2. Suppose 7*s**5 - 2*s**2 + 4*s**h + 2*s**4 + 0*s**2 - 11*s**3 = 0. What is s?
-1, -2/7, 0, 1
Let h(d) be the third derivative of 1/30*d**5 + 3*d**2 + 0*d + 1/180*d**6 + 1/9*d**3 + 0 + 1/12*d**4. Factor h(u).
2*(u + 1)**3/3
Let s be (-2)/10*(7/4 - 3). Let n be -1 - (0 + (-10)/8). Find a, given that s*a**2 - 1/2*a**3 + 0 + n*a**4 + 0*a = 0.
0, 1
Find w, given that 8/3*w**3 + 0*w + 0 - 4/3*w**4 + 0*w**2 + 1/6*w**5 = 0.
0, 4
Let b(p) = 4*p**5 - 14*p**4 + 22*p**3 - 6*p**2. Let a(f) = 4*f**5 - 13*f**4 + 23*f**3 - 5*f**2. Let t(x) = -2*a(x) + 3*b(x). What is o in t(o) = 0?
0, 1, 2
Suppose 0*c**2 - 1/4*c**3 + 0 + 1/4*c = 0. Calculate c.
-1, 0, 1
Suppose 4*x - g + 0*g - 38 = 0, -3*g + 30 = 4*x. Let w = 37/4 - x. Factor -1/4*r**2 + 0*r + w.
-(r - 1)*(r + 1)/4
Let z(j) = -j**2 - 7*j + 5. Let b be z(-7). Let c = b + -2. Factor 1/3*h**2 + 0 - 1/3*h**4 + 1/3*h - 1/3*h**c.
-h*(h - 1)*(h + 1)**2/3
Let r(o) be the first derivative of -2/3*o**3 - 2/5*o**5 + 0*o**2 - o**4 + 0*o - 3. Factor r(n).
-2*n**2*(n + 1)**2
Find q such that 84 - 156*q + 423/7*q**2 + 78/7*q**3 + 3/7*q**4 = 0.
-14, 1
Let -9*o**3 - 10*o**4 - 10*o**4 - 28*o**3 + 5*o**3 - 12*o**2 = 0. Calculate o.
-1, -3/5, 0
Let m = 109/3 - 36. Find z, given that -m*z**4 + 0 + 0*z + 1/3*z**2 + 0*z**3 = 0.
-1, 0, 1
Let h(r) be the second derivative of -r**10/50400 - r**9/25200 + r**8/11200 + r**7/4200 + r**4/12 - 4*r. Let p(y) be the third derivative of h(y). Factor p(d).
-3*d**2*(d - 1)*(d + 1)**2/5
Factor 4*o**2 - 14*o - 3*o + 11*o - 10*o - 20.
4*(o - 5)*(o + 1)
Let y = 215/146 + 2/73. Let 3/4 - 3/4*g**4 + 0*g**2 + y*g**3 - 3/2*g = 0. Calculate g.
-1, 1
Find u such that -4*u**3 + u**4 + 833*u + 3*u**4 - 833*u - 8*u**2 = 0.
-1, 0, 2
Let i(l) = 4*l - 1. Let n(y) = y**3 + 6*y**2 - 6*y + 8. Let s be n(-7). Let v be i(s). Factor -4/7*d**2 + 2/7*d + 0 + 2/7*d**v.
2*d*(d - 1)**2/7
Let c(l) be the third derivative of l**10/151200 - l**9/30240 + l**8/20160 - l**5/60 - 2*l**2. Let o(n) be the third derivative of c(n). Factor o(m).
m**2*(m - 1)**2
Let f = 69/70 - 13/70. Let b = -5/13 - -51/65. Let 0 + f*g**2 + b*g + 2/5*g**3 = 0. What is g?
-1, 0
Let o(k) = 10*k**3 - 3*k**2 - k. Let a(w) = -w + 20*w**3 + 0*w - 5*w**2 + 0*w. Let y(r) = -3*a(r) + 7*o(r). Solve y(f) = 0.
-2/5, 0, 1
Suppose -3*f + f = -p - 4, 5*p + 5*f - 25 = 0. Let b be ((-1)/14)/(p/(-8)). Suppose 4/7*r - b*r**2 - 2/7 = 0. Calculate r.
1
Let l(p) be the second derivative of p**4/42 + 5*p**3/21 + 4*p**2/7 + 6*p. Factor l(i).
2*(i + 1)*(i + 4)/7
Factor 30*o**4 - 25*o**4 - 5*o**3 - 20*o**3 + 45*o + 15*o**2.
5*o*(o - 3)**2*(o + 1)
Let x(v) be the first derivative of 0*v**3 - 3 - 4/5*v**5 + 0*v**2 + 1/2*v**4 + 1/3*v**6 + 0*v. Factor x(n).
2*n**3*(n - 1)**2
Let w(z) be the first derivative of 28*z**5/5 - 6*z**4 - 32*z**3/3 + 12*z**2 + 4*z - 55. Let w(k) = 0. Calculate k.
-1, -1/7, 1
Let g(n) = -2*n + 2. Let v(d) = -d - 3. Let q be v(-4). Let b be g(q). Factor -3*w**3 + 0 + 3/2*w**2 + b*w + 3/2*w**4.
3*w**2*(w - 1)**2/2
Let x = -61 - -551/9. Factor -2/9*l + 0 + x*l**2.
2*l*(l - 1)/9
Let n(y) = y**3 + 2*y**2 + 3*y + 2. Let t = 5 - 2. Let c(b) = 6*b + 9 + 4*b**t - 2 + 4*b + 7*b**2. Let v(o) = -2*c(o) + 7*n(o). Factor v(j).
-j*(j - 1)*(j + 1)
Let m be -2*(-2)/((-8)/(-10)). Suppose -m*d + 24 = 2*l, 2 = d - l - 0. Factor -q**2 - 5*q**4 + 2*q**3 + 4*q**d - 4*q**3.
-q**2*(q + 1)**2
Let a(g) be the third derivative of g**7/70 - g**6/20 + g**4/4 - g**3/2 + g**2. Find u such that a(u) = 0.
-1, 1
Suppose -2 - 14*s - 40*s**3 - 19*s**2 - 14*s**2 - 16*s**4 - 3*s**2 = 0. Calculate s.
-1, -1/2
Let l = 42 + -42. Suppose 0 = -9*c - l*c. Suppose 1/2*y**4 + y**3 + 0*y + 1/2*y**2 + c = 0. What is y?
-1, 0
Let q be 8/1 + -4 + 1. Factor 6*l**2 - 5*l**4 - 2*l + q*l**4 + 6*l**3 + 4*l + 2*l**4.
2*l*(l + 1)**3
Let j(t) be the first derivative of -1/22*t**4 - 4/11*t**2 + 0*t - 8/33*t**3 - 3. Let j(u) = 0. Calculate u.
-2, 0
Let f(l) be the second derivative of l**7/6300 - l**6/1800 + l**4/12 - 3*l. Let i(c) be the third derivative of f(c). Find r, given that i(r) = 0.
0, 1
Factor -54 + 1 + 6 - 1 - 3*o**2 + 24*o.
-3*(o - 4)**2
Let v = 19 - 10. Let a(w) = -3*w**2 - 2*w - 3. Let n(y) = -7*y**2 - 5*y - 7. Let z = -13 + 9. Let k(u) = v*a(u) + z*n(u). Factor k(s).
(s + 1)**2
Let d = -1206/7 + 4199/21. Let n = 28 - d. Solve 1/3*y**3 + n*y + 0 - 2/3*y**2 = 0 for y.
0, 1
Let j(h) be the third derivative of 3*h**6/70 - h**5/35 - 5*h**4/42 - 2*h**3/21 - 29*h**2. Factor j(m).
4*(m - 1)*(3*m + 1)**2/7
Let z(y) be the first derivative of 0*y**2 + 0*y - 1/12*y**3 - 1 + 1/24*y**6 - 1/16*y**4 + 1/20*y**5. Let z(i) = 0. What is i?
-1, 0, 1
Let b = 3 - -3. Find p such that -18 + 18 + 33*p**2 - 63*p**4 + 24*p**3 + b*p = 0.
-1/3, -2/7, 0, 1
Let f(a) be the third derivative of -a**7/525 - 5*a**2. Determine n so that f(n) = 0.
0
Let b = 134/11 + -235/22. Factor b*g + 3/4 + 3/4*g**2.
3*(g + 1)**2/4
Factor b**5 + 4*b**3 - 10/3*b**4 + 1/3*b - 2*b**2 + 0.
b*(b - 1)**3*(3*b - 1)/3
Suppose 7 = -2*f - 5*r, 4 + 5 = 3*f + r. Suppose -6*s = -f*s. Let 1/2*t**2 + s + 0*t + 2*t**3 = 0. Calculate t.
-1/4, 0
Let t(r) be the second derivative of -r**7/5040 - 5*r**4/12 - r. Let q(m) be the third derivative of t(m). Find g, given that q(g) = 0.
0
Suppose 3*w = 5*w - 3*q + 3, -3 = -5*w - 3*q. Solve -4/17*m**2 + 2/17*m + 4/17*m**4 + w - 2/17*m**5 + 0*m**3 = 0 for m.
-1, 0, 1
Solve -13 + 20*h + 11*h**2 + 21 - 3*h**2 = 0.
-2, -1/2
Let d(q) be the third derivative of q**8/15120 + q**7/15120 + q**5/15 + 7*q**2. Let t(v) be the third derivative of d(v). Factor t(b).
b*(4*b + 1)/3
Let z = -254/11 + 17791/770. Let s(r) be the second derivative of 0*r**4 + 1/50*r**6 + 3*r + 0*r**3 + 0*r**2 + 0 + 0*r**5 - z*r**7. Factor s(n).
-3*n**4*(n - 1)/5
Let c(s) be the first derivative of -3*s**4/2 + 10*s**3/3 + 4*s**2 - 8*s - 18. Factor c(q).
-2*(q - 2)*(q + 1)*(3*q - 2)
Let y(b) be the second derivative of -1/6*b**3 + 1/24*b**4 + 0*b**2 + 3/40*b**5 - 1/60*b**6 - 1/84*b**7 - 3*b + 0. Suppose y(d) = 0. What is d?
-2, -1, 0, 1
Let q(p) = 6*p**3 + 5*p**2 + 5*p - 5. Let l(d) = d**3 + d**2 + d - 1. Let i = 0 + 4. Let f(t) = i*q(t) - 22*l(t). Factor f(a).
2*(a - 1)**2*(a + 1)
Let g be -4 + (252/20)/3. Determine s, given that g*s**3 - 3/5*s**5 + 2/5*s**2 - 4/5*s**4 + 0 + 0*s = 0.
-1, 0, 2/3
Let m(y) be the second derivative of -2*y**6/3 + 12*y**5/5 - 3*y**4 + 4*y**3/3 + 6*y. Suppose m(p) = 0. What is p?
0, 2/5, 1
Let x(n) be the second derivative of -n**6/20 + 7*n**5/40 - 5*n**4/24 + n**3/12 + 42*n. Factor x(l).
-l*(l - 1)**2*(3*l - 1)/2
Factor 3/8*u**2 + 0 + 3/8*u**3 - 3/4*u.
3*u*(u - 1)*(u + 2)/8
Factor l**3 - 4/3*l - 1/3*l**4 + 0*l**2 + 0.
-l*(l - 2)**2*(l + 1)/3
Let p = -6 - -8. Factor -b**2 + b**2 + b**p - 2*b.
b*(b - 2)
Find j such that 0*j**2 + 0*j - 1/2*j**5 + 3/2*j**4 - j**3 + 0 = 0.
0, 1, 2
Let r(j) be the second derivative of -j**4/8 - 9*j**3/2 - 243*j**2/4 + 25*j. Determine b, given that r(b) = 0.
-9
Let t(v) be the third derivative of -v**9/30240 + v**8/5040 - v**7/2520 - v**5/30 - v**2. Let x(c) be the third derivative of t(c). Factor x(f).
-2*f*(f - 1)**2
Let s be 26/(-8) - (-3)/(-4). Let a be 3*(3 + 8/s). Factor 0 + 9/2*u**3 + 1/2*u + a*u**2.
u*(3*u + 1)**2/2
Let v(l) be the third derivative of -l**5/180 + l**4/72 + l**3/9 + 7*l**2. Determine t, given that v(t) = 0.
-1, 2
Let c be ((-30)/8)/(-5) - (-4)/(-6). Let q(r) be the third derivative of c*r**3 + 1/24*r**4 + 3*r**2 - 1/40*r**5 + 0 + 0*r. Solve q(x) = 0.
-1/3, 1
Suppose 37 = -4*i - 19. Let k be 3/1 - 6/i. Find o such that 2/7*o + 128/7*o**4 + 96/7*o**3 + k*o**2 + 0 = 0.
-1/4, 0
Let t(a) be the third derivative of a**6/120 + a**5/15 - 5*a**4/24 + 33*a**2. Factor t(m).
m*(m - 1)*(m + 5)
Suppose 3*t + 1 = 2*p, 4*p - 1 = t + 16. Let a = -14 - -24. Factor -8/9 - a*v**2 + 50/9*v**t + 16/3*v.
2*(v - 1)*(5*v - 2)**2/9
Let p(v) be the second derivative of -3*v**5/40 + 3*v**4/4 - 3*v**3 +