 Let r be t(z). Find a such that -2/3*a**r + 1/3 + a - a**3 + 1/3*a**2 = 0.
-1, -1/2, 1
Let c(g) = -g**3 - 11*g**2 + 2. Let w be c(-11). Let b = w + 1. Factor t - b*t - 2*t**3 + t**5 + 3*t.
t*(t - 1)**2*(t + 1)**2
Suppose t - 2*g - 1 = 3, t = -3*g - 1. Let -7*v**5 + 2*v**3 - 3*v**4 - t*v + 4*v**5 + 3*v**3 + 4*v**4 - v**2 = 0. Calculate v.
-1, -2/3, 0, 1
Let j(d) be the first derivative of -d**6/6 - 2*d**5/5 + 2*d**3/3 + d**2/2 + 8. Factor j(y).
-y*(y - 1)*(y + 1)**3
Let m(v) be the third derivative of 0*v - 1/210*v**5 + 0 + 0*v**4 + 0*v**3 - 1/420*v**6 + 3*v**2. Factor m(x).
-2*x**2*(x + 1)/7
Let b(n) be the second derivative of -n**6/45 + n**4/18 + 3*n. Factor b(h).
-2*h**2*(h - 1)*(h + 1)/3
Suppose 0*h + 4 = h. Determine i so that 3*i**5 - 3*i**2 + 9*i**2 + h*i**4 - 10*i**4 - 3*i = 0.
-1, 0, 1
Let s(a) be the second derivative of -5*a - 1/5*a**6 - 1/14*a**7 + 0*a**2 + 1/2*a**3 + 0*a**5 + 1/2*a**4 + 0. Factor s(o).
-3*o*(o - 1)*(o + 1)**3
Let f be 7/2 - (-2)/(-4). Factor -9 - 2*a**2 + 9 + 3*a**f.
a**2*(3*a - 2)
Let j = -1 - -3. Solve -s + 4*s**2 - s**2 - s**j - s**3 = 0.
0, 1
Let y = -18061 + 921167/51. Let q = y + 4/17. Let 2*x + 10/3*x**2 - q = 0. What is x?
-1, 2/5
Let h = -13 - -8. Let a be h + 6 + 3 + -2. Factor 10/13*r**a + 2/13*r**5 + 0 - 4/13*r - 6/13*r**3 - 2/13*r**4.
2*r*(r - 1)**3*(r + 2)/13
Let c(s) be the second derivative of s**5/10 - 3*s**4/2 + 8*s**3 - 16*s**2 + 24*s. Solve c(x) = 0.
1, 4
Let b(d) = d**3 - 4*d**2 + 2*d + 4. Let l be b(3). Let p = l + 2. Factor -3 - p*n**2 - 3 - 9*n - 4*n**2 + 4*n**2.
-3*(n + 1)*(n + 2)
Let a be (12 - (1 - -3)) + -5. Factor -2/9*q + 2/9*q**a - 2/9 + 2/9*q**2.
2*(q - 1)*(q + 1)**2/9
Suppose 3*u = 5*u - 2*f, f = 4. Suppose -5*c = n - 8 - 14, u = 3*c - 4*n. Factor t**3 - 1/2*t**5 + 1/2*t**c - t**2 + 1/2 - 1/2*t.
-(t - 1)**3*(t + 1)**2/2
Suppose 1 + 8 = 3*o. Let t = 1 + o. Find l such that 0 - 1/3*l**t - l**3 - 1/3*l - l**2 = 0.
-1, 0
Let w = 49/2 + -97/4. Let -1/2 + 1/4*h + 1/2*h**2 - w*h**3 = 0. What is h?
-1, 1, 2
Let x(d) be the second derivative of 3*d**5/10 - d**4/4 - d**3/2 + d. Suppose x(v) = 0. Calculate v.
-1/2, 0, 1
Let u(x) be the first derivative of 2*x**5/5 + 2*x**4 - 2*x**3/3 - 4*x**2 + 21. Determine f, given that u(f) = 0.
-4, -1, 0, 1
Let c(t) = t - 7. Let g be c(10). Suppose g = -3*y, 2*q + q + 2*y = 10. Factor 7 + 3*l**2 - 10*l + 16*l - q.
3*(l + 1)**2
Let h(a) be the third derivative of 0*a**4 + 0*a**3 + 5*a**2 - 1/330*a**6 + 1/616*a**8 - 1/1155*a**7 + 0 + 0*a + 0*a**5. Suppose h(r) = 0. What is r?
-2/3, 0, 1
Let n(p) be the first derivative of 2*p**3/39 + 12*p**2/13 + 22*p/13 + 9. Find i, given that n(i) = 0.
-11, -1
Let s be 159/(-810) + -1 + 2. Let m = -1/270 + s. Factor -18/5*h**2 - m*h + 0.
-2*h*(9*h + 2)/5
Let v(b) = -b**3 - b**2 - 1. Let t(k) = -16*k**3 - 41*k**2 - 35*k - 16. Let c(n) = -t(n) + 6*v(n). Factor c(f).
5*(f + 1)*(f + 2)*(2*f + 1)
Let v(u) be the second derivative of -u**4/30 + 2*u**3/15 - u**2/5 + 2*u. Factor v(q).
-2*(q - 1)**2/5
Let u(o) = -o**2 - 11*o + 4. Let p be u(-11). Let 6/5*m + 3*m**2 + 0 + 12/5*m**3 + 3/5*m**p = 0. What is m?
-2, -1, 0
Solve -2/13*h**2 + 0 - 6/13*h = 0 for h.
-3, 0
Let g(p) be the second derivative of -p**8/224 + p**7/140 + p**6/80 - p**5/40 + 7*p**2/2 - 6*p. Let f(k) be the first derivative of g(k). Factor f(h).
-3*h**2*(h - 1)**2*(h + 1)/2
Suppose -5*c + 6 = -m, 2*c = -4*m + 2*m + 48. Let m*y - 6*y**4 + 3*y**5 - y**2 + 7*y**2 - 22*y = 0. Calculate y.
-1, 0, 1
Let d(t) be the first derivative of t**4/30 + 35. Suppose d(w) = 0. What is w?
0
Let u(m) be the third derivative of -m**6/300 + m**5/300 - 15*m**2. Factor u(i).
-i**2*(2*i - 1)/5
Suppose -2*n - 4 = -2. Let q be (n - -5)/(1 - -1). Factor w - 1/3 - w**q + 1/3*w**3.
(w - 1)**3/3
Factor 114*v - 57*v - 57*v - 2*v**5 + 2*v**4.
-2*v**4*(v - 1)
Let v be (-96)/(-189) - (-2)/(-7). Factor -v*l**2 - 4/9 + 2/3*l.
-2*(l - 2)*(l - 1)/9
Let x(u) = 2*u + 18. Suppose 5*a - 20 + 60 = 0. Let h be x(a). Factor -1/2*p**3 - h*p**2 - 1 - 5/2*p.
-(p + 1)**2*(p + 2)/2
Let t(h) be the third derivative of h**7/420 - h**5/40 - h**4/24 + 7*h**2. Solve t(m) = 0 for m.
-1, 0, 2
Let v(j) = j**2 - j - 1. Let b(q) = q**3 - 5*q**2 + 6*q + 6. Let y(i) = -b(i) - 6*v(i). Factor y(r).
-r**2*(r + 1)
Let f(r) be the third derivative of r**5/30 - r**4/3 + 4*r**3/3 + 8*r**2. Suppose f(o) = 0. Calculate o.
2
Let t(y) be the third derivative of -y**8/112 + y**7/70 + y**6/40 - y**5/20 - 4*y**2. Factor t(b).
-3*b**2*(b - 1)**2*(b + 1)
Let u(f) = f**3 + 10*f**2 - f - 8. Let h be u(-10). Factor -5*o**3 + 27*o + 9*o**h + 4*o**3 + 27 - 3*o**3 + 5*o**3.
(o + 3)**3
Let s = -333/5 + 67. Let -4/5 + s*m + 6/5*m**2 = 0. Calculate m.
-1, 2/3
Let a(h) = -2*h**2 - 10*h + 31. Let y be a(-7). Let c(f) be the first derivative of -1 + 1/2*f - 1/6*f**y + 0*f**2. Factor c(g).
-(g - 1)*(g + 1)/2
Factor 3/2*j**2 + 0 + 3/2*j.
3*j*(j + 1)/2
Let m = -8 - -9. Suppose -3*x = 5*j - 4, -j - m = 4*x + 5. Determine k so that -2*k**5 + 2*k**4 + 2*k**3 - 4*k**2 + 2*k**j + 0 + 0 = 0.
-1, 0, 1
Let s(z) be the third derivative of 0*z**6 + 0*z**4 + 1/840*z**7 - 3*z**2 + 0 + 0*z - 1/240*z**5 + 0*z**3. Factor s(n).
n**2*(n - 1)*(n + 1)/4
Let i(y) = -y**2 + 51*y - 268. Let v be i(6). Find q such that -q**v - 4/5*q**3 - 1/5*q + 0 = 0.
-1, -1/4, 0
Let b be 2/5 - (-240)/25. Determine d, given that 5*d + b*d - 6 + d**2 + 3*d**3 - 13*d**2 = 0.
1, 2
Let l be 10*5*(-12)/(-150) - 2. Let 3/5*c**4 + 0 + 2/5*c**5 - 3/5*c**l - 1/5*c - 1/5*c**3 = 0. What is c?
-1, -1/2, 0, 1
Let w(q) be the second derivative of 0 - q + 1/6*q**3 - 1/12*q**4 + 1/2*q**2 - 1/20*q**5. Determine s so that w(s) = 0.
-1, 1
Let x be 3 + (-3 - -3) - -6. Factor -21/5*u**5 - x*u**3 - 3/5*u**2 - 57/5*u**4 + 6/5*u + 0.
-3*u*(u + 1)**3*(7*u - 2)/5
Let a(d) be the first derivative of d**6/2 + 9*d**5/5 + 3*d**4/4 - 3*d**3 - 3*d**2 + 47. Factor a(q).
3*q*(q - 1)*(q + 1)**2*(q + 2)
Suppose 36*i + 6/5*i**2 + 270 = 0. What is i?
-15
Let k(h) be the first derivative of 1/3*h**3 - 2*h + 1/2*h**2 - 3. What is n in k(n) = 0?
-2, 1
Let q be (10/(-15))/((-1)/3). Suppose w**q + 4*w - 1 - 2*w + 2 = 0. Calculate w.
-1
Let v = 553275/7 + -79187. Let t = v + 148. Find f such that -8/7*f - t*f**2 - 8/7 = 0.
-2
Factor -3/5*o**3 - 2/5*o**2 + 0 - 1/5*o**4 + 0*o.
-o**2*(o + 1)*(o + 2)/5
Let u(l) be the second derivative of -l**6/30 - 3*l**5/10 - 5*l**4/12 + 16*l. Let u(f) = 0. Calculate f.
-5, -1, 0
Let u = 6 + -2. Factor -2*j**3 - j**3 - 2*j**5 + u*j**4 + j**3.
-2*j**3*(j - 1)**2
Let d(f) be the third derivative of -f**5/300 + f**4/120 + f**3/15 - 10*f**2. Solve d(z) = 0.
-1, 2
Let t = 2 - 0. Suppose 0 = t*o - 0 - 6. Factor 1/4 - 1/4*z**2 - 1/4*z + 1/4*z**o.
(z - 1)**2*(z + 1)/4
Let n = 2749 + -41257/15. Let l = 9/5 + n. Factor -1/3 + 1/3*u + 1/3*u**2 - l*u**3.
-(u - 1)**2*(u + 1)/3
Let q = 568 - 566. Factor 10/3*k + q*k**2 - 2/3*k**3 + 4/3 - 2/3*k**4.
-2*(k - 2)*(k + 1)**3/3
Solve -6 - 4*c - 1/2*c**2 = 0.
-6, -2
Let n = 112/159 - 2/53. Factor -1/3 + 1/3*t - 1/3*t**4 + 2/3*t**2 - n*t**3 + 1/3*t**5.
(t - 1)**3*(t + 1)**2/3
Determine s so that s**3 + 5/4*s - 1/4 - 2*s**2 = 0.
1/2, 1
Let z(o) be the first derivative of -1/2*o + 1/6*o**3 + 0*o**2 - 2. Suppose z(d) = 0. Calculate d.
-1, 1
Let 0 - 2/3*m**3 + 4/3*m**2 - 2/3*m = 0. What is m?
0, 1
Let m(q) = -q + 3. Let n(j) = -j - 5. Let y be n(-5). Let i be m(y). Let -h**3 - h**2 - 2*h**3 + 2*h**i = 0. Calculate h.
-1, 0
Let v(h) be the second derivative of -h**4/18 + h**2/3 + 4*h. Find d such that v(d) = 0.
-1, 1
Let j(s) = -s**3 + 8*s**2 - 7*s - 3. Let d be j(7). Let i be ((-2)/(-4))/(d/(-2)). Find c, given that 0*c - 1/3*c**2 + i*c**3 - 1/3*c**5 + 0 + 1/3*c**4 = 0.
-1, 0, 1
Let l(w) be the third derivative of -22*w**7/105 + 7*w**6/6 - 13*w**5/5 + 17*w**4/6 - 4*w**3/3 - 14*w**2. Factor l(o).
-4*(o - 1)**3*(11*o - 2)
Let h(l) be the third derivative of -l**6/30 - l**5/5 - l**4/3 - 3*l**2. Factor h(v).
-4*v*(v + 1)*(v + 2)
Let b(o) be the first derivative of o**4/6 - 8*o**3/9 + 5*o**2/3 - 4*o/3 - 9. Factor b(q).
2*(q - 2)*(q - 1)**2/3
Suppose 5*h - 6 = 9. Let c be (h - 2)*(-6)/(-2). Find n, given that 2/3*n + 8*n**c + 0 - 14/3*n**2 = 0.
0, 1/4, 1/3
Let n = 960 + -958. Suppose 4/7*c - 4/7*c**3 + 4/7*c**n - 4/7 = 0. What is c?
-1, 1
Suppose -3*d + 12 = 2*m, -4*d + 11 = 3*m - 5