**2 - 2/9*j**3 - 2/9*j**4 = 0. Calculate j.
-1, 0, 1
Solve 3 - 3*s**2 + 3/2*s**3 - 3/2*s = 0 for s.
-1, 1, 2
Let u(m) = -m - 10. Let t be u(-10). Factor 0*v + 2/7*v**4 + 4/7*v**3 + t + 2/7*v**2.
2*v**2*(v + 1)**2/7
Solve -1/2*i + 0 + 1/2*i**2 = 0.
0, 1
Suppose 0 = -3*u + 2*u. Let d(r) be the third derivative of -1/60*r**5 - r**2 + 0*r**3 + 0*r + u*r**4 + 0. Determine n, given that d(n) = 0.
0
Suppose 0 = 6*k - 3*k. Factor 1 + k*g**2 + 3/2*g - 1/2*g**3.
-(g - 2)*(g + 1)**2/2
Determine a so that 5*a - 35*a**2 + 15*a**2 + 11*a**2 - 10 + 14*a**2 = 0.
-2, 1
Let h(k) = k**3 + 2*k**2 - 4*k. Let d be h(-3). Suppose -d*y + 2*y = -2*f + 10, 5*f - 35 = 5*y. Let -4/3*g**2 + 2/3*g + 0 + 2/3*g**f = 0. What is g?
0, 1
Let w(y) = y**3 + 4*y**2 - y + 8. Let r be w(-5). Let p = r + 40/3. Factor 2/9*b**3 - 16/9 + 8/3*b - p*b**2.
2*(b - 2)**3/9
Let p(i) be the first derivative of -i**4/12 - 7*i**3/9 - 11*i**2/6 - 5*i/3 - 41. Factor p(v).
-(v + 1)**2*(v + 5)/3
Let q(a) = -2*a**2 - 9*a - 25. Let r(t) = 3*t**2 + 18*t + 51. Let w(y) = -9*q(y) - 5*r(y). Let w(l) = 0. What is l?
-2, 5
Determine z so that -2*z**4 - 11*z**2 - 19*z**2 - 13*z**3 - 26*z - z**3 - 8 = 0.
-4, -1
Let f(k) be the first derivative of k**4/18 - 2*k**3/9 + 8*k/9 - 48. Factor f(s).
2*(s - 2)**2*(s + 1)/9
Suppose l = 2*l - 1. Find v such that -2*v**4 + 0*v**2 + 3*v**4 - 2*v**2 + 0*v**2 + l = 0.
-1, 1
Let d(g) be the third derivative of 0*g - 1/20*g**5 + 0 + 0*g**4 - g**2 + 1/2*g**3. Factor d(q).
-3*(q - 1)*(q + 1)
Let s be 15/(-2)*4/(-5). Suppose -4*n + 2 = -s. Factor v - v**n - v.
-v**2
Let n(i) be the first derivative of -i**7/280 + 2*i**3 + 4. Let c(z) be the third derivative of n(z). Factor c(g).
-3*g**3
Suppose -4*x + 3*r = 15, -2*r + 10 = -5*x - 0*r. Let k = -1411/9 + 157. What is i in 0 + x*i + k*i**2 = 0?
0
Let k(v) be the first derivative of v**5/30 - 5*v**4/24 + 7*v**3/18 - v**2/4 - 1. Find o such that k(o) = 0.
0, 1, 3
Let t(q) be the first derivative of 2/35*q**5 + 0*q - 1 - 1/14*q**4 + 0*q**2 + 1/21*q**6 - 2/21*q**3. Factor t(u).
2*u**2*(u - 1)*(u + 1)**2/7
Let i be 3/3*3 + (0 - 3). Find q such that -2/3*q**5 + 2/3*q**4 + 0*q + 0*q**2 + 0 + i*q**3 = 0.
0, 1
Determine t, given that -1/2*t**3 + 1/2*t - 1/4*t**2 + 1/4*t**4 + 0 = 0.
-1, 0, 1, 2
Let o = 12/223 - 10529/892. Let h = o - -12. Factor 0*m - 1/4*m**2 + h*m**3 + 0.
m**2*(m - 1)/4
Let d(u) = u**2 + 6*u + 7. Let q be d(-5). Determine r, given that 4*r**2 + q + 1 - 2 - 5*r**2 = 0.
-1, 1
Let a(k) be the second derivative of k**4/6 - k**3 + 2*k**2 + 32*k. Solve a(v) = 0.
1, 2
Let a = 973/1938 - 2/969. Factor -2 - a*w**2 - 2*w.
-(w + 2)**2/2
Let g(m) = 8*m**5 - 6*m**4 + 2*m**3 + 2*m - 6. Let t(y) = -7*y**5 + 5*y**4 - y**3 - 2*y + 5. Let k(o) = 5*g(o) + 6*t(o). Factor k(a).
-2*a*(a - 1)**2*(a + 1)**2
Factor 2/7*l**3 + 0 + 18/7*l**2 + 0*l.
2*l**2*(l + 9)/7
Let p(b) be the third derivative of b**7/10 + 3*b**6/10 + 3*b**5/20 - b**4/4 - 16*b**2. Solve p(v) = 0 for v.
-1, 0, 2/7
Factor -3*g**2 + 2*g**2 - 6*g**2 + 2*g**2 + 20*g.
-5*g*(g - 4)
Suppose 6*z - 3*z - 12 = 0. Suppose 0 = -4*m + z + 8. Factor 0*j**3 - m*j**3 + j**3.
-2*j**3
Let j(m) be the second derivative of -m**5/100 + 7*m**4/60 - m**3/3 + m - 7. Factor j(v).
-v*(v - 5)*(v - 2)/5
Let j(p) = -p**5 - 6*p**4 + 8*p**3 + p**2 - 7*p. Let v(z) = -z**5 - 7*z**4 + 9*z**3 + z**2 - 8*z. Let k(i) = -6*j(i) + 5*v(i). Factor k(u).
u*(u - 1)**2*(u + 1)*(u + 2)
Let l(v) be the third derivative of v**7/490 - v**6/280 + v**2 + 16. Factor l(r).
3*r**3*(r - 1)/7
Let h(r) = -2*r**3 - 7*r**2 + 15*r - 9. Let i(s) = 5*s**3 + 14*s**2 - 30*s + 18. Let p(z) = 14*h(z) + 6*i(z). Factor p(d).
2*(d - 3)**2*(d - 1)
Let r be 30/8 - (-6)/(-8). Let q(d) be the first derivative of 2 - 1/3*d**r - 1/2*d**2 + 0*d. Suppose q(f) = 0. Calculate f.
-1, 0
Let u(a) be the third derivative of -2*a**2 + 0 - 1/12*a**4 + 1/30*a**5 + 0*a + 1/60*a**6 - 1/3*a**3. Factor u(p).
2*(p - 1)*(p + 1)**2
Let a = -8 + 13. Let z(f) = 33*f**3 + 45*f**2 - 9*f + 21. Let b(c) = 8*c**3 + 11*c**2 - 2*c + 5. Let u(p) = a*z(p) - 21*b(p). Let u(l) = 0. What is l?
-1, 0
Factor 9/7*o**5 + 0 + 3/7*o**3 + 0*o**2 + 0*o - 12/7*o**4.
3*o**3*(o - 1)*(3*o - 1)/7
Let o = -4 + 7. Find x such that -18*x**2 - 48 + 24 + 3*x**o - 19*x + 55*x = 0.
2
Let a(m) be the second derivative of -m**5/30 + m**4/6 + 3*m**2/2 - 3*m. Let q(b) be the first derivative of a(b). Factor q(r).
-2*r*(r - 2)
Suppose 0 = -h - 5, -2*w + 21 = w - 3*h. Let z(g) be the first derivative of -1/6*g**3 - 1/4*g**w + 1/10*g**5 + 0*g - 1 + 1/8*g**4. Factor z(a).
a*(a - 1)*(a + 1)**2/2
Factor 0*y - 2/3 + 4/3*y**2 - 2/3*y**4 + 0*y**3.
-2*(y - 1)**2*(y + 1)**2/3
Factor -v**5 - 4*v**2 - 2*v**4 + 18*v**4 + 11*v**5 - v**3 + 3*v**3.
2*v**2*(v + 1)**2*(5*v - 2)
Suppose 4*l + 0 = 56. Solve 11 + 1 + 0 - l*y + 2*y + 3*y**2 = 0 for y.
2
Let v = -2 + 6. Let x(t) be the second derivative of -2*t + 1/3*t**3 + 0 - 1/2*t**2 - 1/12*t**v. Solve x(p) = 0 for p.
1
Let c be (0 + -1)*3/3. Let n be (4/(-6))/(c - 0). Factor -n*z + 2/3*z**2 + 0.
2*z*(z - 1)/3
Let w = -18 + 18. Let a(c) be the second derivative of -1/3*c**4 + w + 1/3*c**3 + 2*c + c**2. Suppose a(y) = 0. Calculate y.
-1/2, 1
Let b(k) be the first derivative of -k**5/5 - k**4/2 + k**3/3 + k**2 - 13. Suppose b(s) = 0. Calculate s.
-2, -1, 0, 1
Suppose 0 = -k + 5*w - 5 - 18, -k + w = 3. Let 0 + 1/2*r**4 - 1/2*r**k + 1/2*r**5 - 1/2*r**3 + 0*r = 0. Calculate r.
-1, 0, 1
Let t = 19/60 - -1/60. Let m(r) be the first derivative of 1/2*r**4 + 0*r**3 + 0*r**2 - 4/5*r**5 + 0*r + t*r**6 + 3. Suppose m(k) = 0. Calculate k.
0, 1
Let n(c) = c**3 - 27*c**2 + 28*c - 49. Let k be n(26). Let f(q) be the first derivative of 3 - 3/2*q**2 - q**k + 6*q. Solve f(u) = 0 for u.
-2, 1
Let y be 28/8 + 1/2. Suppose 0 = -3*k + y*k. Factor k*b + 1/2 - 1/2*b**2.
-(b - 1)*(b + 1)/2
Let y(k) be the first derivative of -k**2 - 3 - 1/3*k**3 - k. Factor y(h).
-(h + 1)**2
Let s(d) be the second derivative of -d**7/17640 - d**6/5040 + d**4/3 + 6*d. Let m(g) be the third derivative of s(g). Factor m(t).
-t*(t + 1)/7
Factor -300/7*f + 60/7*f**2 + 500/7 - 4/7*f**3.
-4*(f - 5)**3/7
Let a = -7 + 9. Let l = 5 + -5. Factor a*y**3 - 2/3*y**4 + 2/3*y + l - 2*y**2.
-2*y*(y - 1)**3/3
Let t(a) be the third derivative of 11*a**8/168 + 31*a**7/105 + 9*a**6/20 + a**5/6 - a**4/6 - 24*a**2. Factor t(z).
2*z*(z + 1)**3*(11*z - 2)
Find k such that 3*k**4 - 9*k**5 + 20*k**3 - 3*k**5 - 7*k**4 - 8*k + 4*k**2 = 0.
-1, 0, 2/3, 1
Let o = -481/7 + 69. Factor 2/7*v**2 + o*v - 2/7*v**3 + 0 - 2/7*v**4.
-2*v*(v - 1)*(v + 1)**2/7
Let z(r) = r + 1. Let g(t) = -4*t**3 - 12*t**2 + 24*t + 24. Let m(u) = -g(u) + 24*z(u). Suppose m(q) = 0. Calculate q.
-3, 0
Let l(o) = 3*o - 7. Let b be l(4). Suppose p = 3*g - p - 12, -b*g - 5*p = 5. What is z in -1/3*z - 2/3*z**g + 0 - 1/3*z**3 = 0?
-1, 0
Find f, given that 2504*f**4 + 90*f**2 + 2430*f**5 + 14*f**3 - 30*f + 331*f**4 + 1066*f**3 - 5 = 0.
-1/3, 1/6
Let a be 4/6*27/540. Let g(c) be the second derivative of -c + 0 - a*c**4 + 2/15*c**3 - 1/5*c**2. Factor g(z).
-2*(z - 1)**2/5
Suppose t - 2*o = -2*t - 4, -4*t = 4*o - 8. Factor -3*b**3 - 7*b + 3*b - 6*b**2 + t*b**2 + b**3.
-2*b*(b + 1)*(b + 2)
Determine w so that 1/2*w - 1 - 1/2*w**3 + w**2 = 0.
-1, 1, 2
Let f be (-1)/7*4*(2 - 9). Let x(p) be the first derivative of 0*p + 0*p**2 - 1/14*p**f - 1 - 2/21*p**3. Factor x(c).
-2*c**2*(c + 1)/7
Let u(m) be the third derivative of 1/180*m**5 + 8*m**2 + 1/144*m**4 + 0*m + 0 + 1/720*m**6 + 0*m**3. Suppose u(a) = 0. Calculate a.
-1, 0
Let r(y) be the first derivative of -y**6/15 - 8*y**5/25 - 3*y**4/5 - 8*y**3/15 - y**2/5 + 3. Determine a so that r(a) = 0.
-1, 0
Let t(i) = -i + 2. Let m be t(-4). Factor z**5 + 3*z**2 + 5*z**4 - m + 5*z + 7*z**2 + 7 + 10*z**3.
(z + 1)**5
Let c(q) = -20*q - 24*q + 45*q - 2. Let v be c(4). Solve 1/2*k - 1/2*k**v + 0 = 0.
0, 1
Let p(k) be the third derivative of 2*k**7/35 + 2*k**6/15 + k**5/15 + 8*k**2. Determine w so that p(w) = 0.
-1, -1/3, 0
Suppose -2*j - 2*j = -8. Factor 5*r + 1 + r**j - 6*r - 3.
(r - 2)*(r + 1)
Let k(a) = -a**3 + 34*a**2 + 36*a - 33. Let l be k(35). Suppose -2/5 - 4/5*o**l + 1/5*o**3 + o = 0. What is o?
1, 2
Let p = -138 + 141. Factor b**p + 0*b - 1/2*b**5 - 1/2*b**4 + 0*b**2 + 0.
-b**3*(b - 1)*(b + 2)/2
Let l(p) be the second derivative of -1/36