0. Calculate m.
1, 4
Factor 4/3*u**4 + 0 + 0*u**3 - 2/3*u**5 - 4/3*u**2 + 2/3*u.
-2*u*(u - 1)**3*(u + 1)/3
Suppose 4/5*s**2 + 64/5 + 32/5*s = 0. What is s?
-4
Let a be (-198)/972 - 2/(-9). Let v(k) be the second derivative of -3*k - a*k**4 + 0*k**2 + 0 - 1/27*k**3. Factor v(y).
-2*y*(y + 1)/9
Let g(b) be the second derivative of 0 - 1/3*b**3 - 1/150*b**5 + 1/60*b**4 + 0*b**2 + 1/900*b**6 + 2*b. Let u(n) be the second derivative of g(n). Factor u(v).
2*(v - 1)**2/5
Let c be 2337/27 - (-2)/9. Let f = 87 - c. Factor -8/9*g**3 + f*g**4 + 2/9 + 4/3*g**2 - 8/9*g.
2*(g - 1)**4/9
Let j = 37/56 - 3/8. Factor 0*t + 2/7*t**3 + 0*t**2 - j*t**5 + 0*t**4 + 0.
-2*t**3*(t - 1)*(t + 1)/7
Let i be 8 - ((-4 - -16) + -4). Suppose -4/3*f**4 + 2/3*f**5 - 2/3*f + 4/3*f**2 + i + 0*f**3 = 0. Calculate f.
-1, 0, 1
Let s(n) be the second derivative of n**7/10080 - n**6/960 + n**5/240 - 7*n**4/12 - 3*n. Let t(w) be the third derivative of s(w). Factor t(b).
(b - 2)*(b - 1)/4
Let v(m) be the second derivative of m**6/30 - 3*m**5/10 - 7*m**4/12 - 9*m + 2. Factor v(z).
z**2*(z - 7)*(z + 1)
Let r(g) = g**3 - 2*g**2 - g + 3. Let d(k) = k - 6. Let s be d(6). Let w be r(s). Suppose 0*i + 0*i**2 - 1/6*i**w + 0 = 0. Calculate i.
0
Suppose 2*d + 4*o - 13 = 11, -4*o + 10 = -5*d. Let x(h) be the second derivative of 1/27*h**3 - 1/9*h**4 + 0*h**d + 0 - 3*h + 1/10*h**5. Factor x(t).
2*t*(3*t - 1)**2/9
Let u(b) be the second derivative of b**8/840 - 2*b**7/525 + b**2/2 - 3*b. Let q(i) be the first derivative of u(i). Factor q(l).
2*l**4*(l - 2)/5
Factor 28*z**3 + 2*z**5 - 4*z**2 - 5*z + 13*z**4 - 5*z - 5*z**4 - 4 - 20*z**3.
2*(z - 1)*(z + 1)**3*(z + 2)
Let -10/13*d**2 - 8/13*d**3 - 4/13*d - 2/13*d**4 + 0 = 0. What is d?
-2, -1, 0
Let z(f) = f**4 - f**3 - f**2 + f - 1. Let g(d) = 7*d**4 - 6*d**3 - 6*d**2 + 5*d - 5. Let x(b) = -g(b) + 5*z(b). Factor x(r).
-r**2*(r - 1)*(2*r + 1)
Let k(d) = 2*d**4 - 2*d**3 + 3*d**2 + 2*d. Let i(a) = -9*a**3 + 1 + 9*a**4 + 12*a**2 - 1 + 13*a - 4*a. Let v(y) = -5*i(y) + 21*k(y). Factor v(f).
-3*f*(f - 1)**2*(f + 1)
Let t(g) be the second derivative of -g**6/60 + g**5/10 - g**4/6 + 11*g. Factor t(l).
-l**2*(l - 2)**2/2
Suppose -2 = c - 11. Let i(r) = 5*r**2 - 15*r - 45. Let u(x) = 2*x**2 - 8*x - 22. Let v(y) = c*u(y) - 4*i(y). Factor v(q).
-2*(q + 3)**2
Let r(v) be the first derivative of -v**5 + 25*v**4/4 - 15*v**3 + 35*v**2/2 - 10*v + 40. Solve r(c) = 0 for c.
1, 2
Let x(r) be the second derivative of r**6/180 - r**5/120 - r**4/72 + r**3/36 + 18*r. Let x(h) = 0. What is h?
-1, 0, 1
Let r(g) = -7*g**3 + 7*g**2 + 6*g. Let o(i) = -i**3 + i**2 + i. Let b(a) = -6*o(a) + r(a). Factor b(n).
-n**2*(n - 1)
Let a(c) = 4*c**2 - 8*c - 23. Let b(h) = h**2 - 2*h - 6. Let n(v) = -2*a(v) + 9*b(v). Determine o so that n(o) = 0.
-2, 4
Let 1/2*h**3 + h**2 + 0*h - 1/2*h**5 + 0 - h**4 = 0. What is h?
-2, -1, 0, 1
Let p = 7 - 5. Solve -12*v + 2*v**p + 10 + 10 + 11 - 13 = 0.
3
Let a be ((-126)/28 + 2)*(-12)/10. Let -3/2*v - 3/2*v**2 + a = 0. What is v?
-2, 1
Suppose 19*z = 24*z - 15. Let u(i) be the first derivative of 0*i - 2/3*i**z - 2 + 0*i**2. Let u(h) = 0. Calculate h.
0
Let b(t) = t**3 + 4*t**2 + 3*t + 3. Let f be b(-3). Suppose 0 = 2*c - f*z - 5, 5*c + 0*z - 16 = 4*z. Factor 4*r + 2*r**4 - 2*r**3 - c*r**4 + 2*r**2 - 2*r.
-2*r*(r - 1)*(r + 1)**2
Let -17*r - 36*r**3 + 7*r**2 + 14*r**3 + 23*r**3 + 9 = 0. What is r?
-9, 1
Suppose -20 = 3*z - 13*z. Let s(v) be the first derivative of 1 + 2/25*v**5 + 0*v - 1/5*v**4 + 0*v**z + 2/15*v**3. Suppose s(o) = 0. Calculate o.
0, 1
Let k(h) be the third derivative of -8*h**2 + 1/30*h**4 + 0 + 0*h**3 + 0*h + 1/150*h**5. Factor k(q).
2*q*(q + 2)/5
Let k = -61/19 + 449/57. Determine h, given that 6*h**5 - k*h**4 + 0*h**2 - 4/3*h**3 + 0 + 0*h = 0.
-2/9, 0, 1
Let p be (-365)/75 + 5 + (-4)/(-20). Find g, given that p*g**2 + 2/3*g + 0 = 0.
-2, 0
Let z(d) = 4*d**4 + 6*d**2 - d. Let i(u) = -3*u**4 + u**3 - 3*u**2 - 2*u**2 + 3*u + 0*u**4 - 2*u. Let f(a) = -6*i(a) - 4*z(a). Factor f(k).
2*k*(k - 1)**3
Let s = -135/22 + 4673/66. Factor 32/3*v**4 + 48*v**3 + 24*v + s*v**2 + 8/3.
2*(v + 2)**2*(4*v + 1)**2/3
Let z(o) be the first derivative of o**6/1620 - o**5/270 + o**4/108 - 2*o**3/3 + 1. Let q(k) be the third derivative of z(k). Determine j so that q(j) = 0.
1
Solve 4/3*l**4 + 0 - 2/3*l**3 + 0*l - 2/3*l**5 + 0*l**2 = 0.
0, 1
Let k(z) be the second derivative of 9/5*z**2 - 2*z - 14/5*z**3 + 49/30*z**4 + 0. Suppose k(j) = 0. What is j?
3/7
Let q(s) be the second derivative of -s**3/2 + 10*s**2 + 7*s. Let w be q(6). Determine r so that -2/3*r**3 - 2/3*r**4 - 4/3 + w*r**2 + 2/3*r = 0.
-2, -1, 1
Let k(c) = c**3 - c**2 - c. Let w be k(0). Factor -2/3*p**3 + 4/3*p**4 + 0*p + w - 2/3*p**2.
2*p**2*(p - 1)*(2*p + 1)/3
Let p(y) be the third derivative of -y**7/630 - y**6/120 - y**5/60 - y**4/72 + 9*y**2. Let p(d) = 0. What is d?
-1, 0
Let u(g) be the third derivative of -g**5/300 - g**4/15 - 8*g**3/15 - 9*g**2. Factor u(k).
-(k + 4)**2/5
Let w = -41 + 124/3. Suppose 3*q + 12 = -4*f, -3*f = -q + 4*q + 9. Factor -1/3*k**2 + q*k + w.
-(k - 1)*(k + 1)/3
Factor 6 - 4*n + 2/3*n**2.
2*(n - 3)**2/3
Let u(d) be the first derivative of -7*d**5/120 + 23*d**4/72 - 5*d**3/9 + d**2/3 - 2*d - 3. Let n(t) be the first derivative of u(t). Factor n(a).
-(a - 2)*(a - 1)*(7*a - 2)/6
Factor 3 - 9 + 24*x**2 - 3*x**3 - 18*x**2 + 3*x.
-3*(x - 2)*(x - 1)*(x + 1)
Let g(b) = -14*b**5 - 52*b**4 - 28*b**3 + 70*b**2 + 38*b - 18. Let q(z) = -z**3 + z**2 - z - 1. Let r(w) = -2*g(w) + 4*q(w). Determine s so that r(s) = 0.
-2, -1, 2/7, 1
Let t(j) be the second derivative of 6/5*j**5 - 3/10*j**6 - 3*j + 0 - 7/4*j**4 + 0*j**2 + j**3. What is s in t(s) = 0?
0, 2/3, 1
Find n such that 1/4*n**4 + 0 - 1/4*n**2 + 1/4*n**3 - 1/4*n = 0.
-1, 0, 1
Let f(n) = -n**3 - 7*n**2 - 8*n - 7. Let m be f(-6). Let p be 1*(40/28)/m. Factor 4/7 + 2/7*k - p*k**2.
-2*(k - 2)*(k + 1)/7
Suppose 3*m - 2*l - 27 = l, 0 = -4*l - 12. Suppose 2*n - m = -n. Determine y, given that -n*y + 2*y + y**3 + 0*y**5 - 2*y**4 + y**5 = 0.
0, 1
Let c(q) be the second derivative of q**7/273 - q**5/130 + 16*q. Factor c(o).
2*o**3*(o - 1)*(o + 1)/13
Let l = 235/3 + -78. Determine f so that -l*f + 2/3 - 1/3*f**2 = 0.
-2, 1
Suppose -5*n + 64 + 11 = 0. Let f(x) = 3*x**4 - 3*x**2. Let d = -2 + 8. Let g(s) = -7*s**4 + 7*s**2. Let y(c) = d*g(c) + n*f(c). Factor y(z).
3*z**2*(z - 1)*(z + 1)
Let j = 84/17 + -554/119. Suppose -3*k + 4 = -2. Solve 0*s**k - 4/7 + 6/7*s - j*s**3 = 0 for s.
-2, 1
Factor 1/3*s**5 - s**3 + 4/3*s**2 - 2/3*s**4 + 4/3*s + 0.
s*(s - 2)**2*(s + 1)**2/3
Let u(x) be the third derivative of 1/120*x**6 + 0 + 1/630*x**7 + 0*x**3 + 1/60*x**5 - 2*x**2 + 1/72*x**4 + 0*x. Solve u(a) = 0 for a.
-1, 0
Let q = 1/24 + 5/24. Find n, given that q + 1/4*n**2 + 1/2*n = 0.
-1
Let b = 4/4949 - 203029/148470. Let p = -7/6 - b. Factor 1/5*o**3 + 0 + 2/5*o**2 + p*o.
o*(o + 1)**2/5
Let d(m) = 32*m + 68. Let x(n) = -n**2 + 1. Let t(g) = d(g) - 4*x(g). Factor t(f).
4*(f + 4)**2
Let s be -1 + 4 + (-579)/195. Let f = 59/195 + s. Factor f*r**2 + 1/3*r + 0.
r*(r + 1)/3
Suppose 0 = 2*t + 2*q + 10, -4*q - 4 = 3*t + 15. Let v be t/(-2) + 12/(-56). Find n, given that -8/7*n**3 - 4/7*n - v*n**4 - 10/7*n**2 + 0 = 0.
-2, -1, 0
Let q(t) be the third derivative of 4/105*t**5 + 1/735*t**7 - 1/84*t**6 + 0*t**3 + 3*t**2 + 0 + 0*t - 1/21*t**4. Factor q(m).
2*m*(m - 2)**2*(m - 1)/7
Let x(t) be the third derivative of t**5/30 + t**4/2 + 3*t**3 + 3*t**2. Factor x(l).
2*(l + 3)**2
Suppose -2*s = -5*f + 16, 3*f - 11 = -f + s. Determine b, given that -3/5*b**f + 0 + 3/5*b = 0.
0, 1
Suppose 0 = a + 2 - 4. Suppose 5*s = 5*q - q - 22, 0 = 4*q - s - 14. Determine g so that -q*g**a - 3*g**3 + 3*g + g**2 - g**2 + 3*g**4 = 0.
-1, 0, 1
Let x be (224/(-280))/((-4)/10). What is c in 27/5*c**x + 23/5*c**3 + 7/5*c**4 + 2/5 + 13/5*c = 0?
-1, -2/7
Let c be (2/7)/(3 - (-39)/(-14)). Solve 2*x**2 - c + 2/3*x = 0 for x.
-1, 2/3
Let c = 40 - 118/3. Determine k so that -2/3 + 4/3*k - c*k**2 = 0.
1
Let v(x) be the second derivative of x**4/78 - 2*x**3/39 + 10*x. Factor v(n).
2*n*(n - 2)/13
Let n = 238 + -234. Solve 2/13*i**2 + 0 + 0*i**3 + 0*i - 2/13*i**n = 0.
-1, 0, 1
Let i(n) = 7*n**2 + n + 4. Let t = 8 + -4. Let b(g) = -6*g**2 - 3. Let o be (-240)/(-84) - (-1)/7. Let w(s) = o*i(s) + t*b(s