Let d be 1/(-2*(-3)/12). Find n, given that h*n**4 - 2/3 - 4/3*n**3 + 0*n**d + 4/3*n = 0.
-1, 1
Let y(n) = 2*n**5 + n**3 - 3*n**2. Let r(f) = f**5 - f**2. Let x be 84/(-108) - (-2)/(-9). Let d(m) = x*y(m) + 3*r(m). Suppose d(u) = 0. Calculate u.
-1, 0, 1
Suppose 0 = -2*g + 2*g + 4*g. Factor g - 2/3*u**2 + 2*u.
-2*u*(u - 3)/3
What is v in 6*v - 9*v**2 + 3*v**4 + 0*v**4 + 0*v**4 = 0?
-2, 0, 1
Let u = 8 + -6. Find d such that -u*d**3 - 2*d**2 + 0 + 0 = 0.
-1, 0
Factor -3/4*g**2 + 0 + 1/4*g + 3/4*g**3 - 1/4*g**4.
-g*(g - 1)**3/4
Let u(j) = 3*j**4 - 3*j**2. Let x(g) = g**3 - g**2. Let q(d) = -u(d) + 9*x(d). Solve q(t) = 0.
0, 1, 2
Factor -767*u**3 + 4*u + u - 5*u**2 + 707*u**3.
-5*u*(3*u + 1)*(4*u - 1)
Let f(z) be the second derivative of z**9/15120 - z**8/8400 + 2*z**3/3 + z. Let m(l) be the second derivative of f(l). Factor m(w).
w**4*(w - 1)/5
Let 0 - 2/5*g**3 - 1/5*g**4 - 4/5*g + 7/5*g**2 = 0. What is g?
-4, 0, 1
Suppose l - o - 5 = -4, -3*o + 3 = 0. Suppose 4/11 + 2/11*g - 2/11*g**l = 0. What is g?
-1, 2
Suppose 6*y = -2*y. Let g(j) be the third derivative of -1/150*j**5 + y*j**3 - 3*j**2 + 0 + 0*j**4 + 0*j - 1/525*j**7 + 1/150*j**6. Factor g(t).
-2*t**2*(t - 1)**2/5
Let b(r) = -r**3 - 2*r**2 + 8*r + 4. Let a be b(-4). Let l(u) be the second derivative of 0 - 1/6*u**a + 1/10*u**5 - 1/3*u**3 - 2*u + u**2. Factor l(y).
2*(y - 1)**2*(y + 1)
Factor -2/11*q**2 + 0 - 2/11*q.
-2*q*(q + 1)/11
Suppose 0 = -0*s + 4*s - 12. Let z(d) be the second derivative of 1/12*d**s + 0 + 0*d**4 - d + 0*d**2 - 1/40*d**5. Find b such that z(b) = 0.
-1, 0, 1
Let f(y) be the third derivative of 4*y**2 + 0*y + 0*y**3 + 1/12*y**5 + 0 - 7/120*y**6 + 1/12*y**4. Factor f(o).
-o*(o - 1)*(7*o + 2)
Let l be 166/52 + (-5 - -2). Let u = l + 4/13. Factor 0 + u*f**2 - 1/2*f.
f*(f - 1)/2
Let -20*y**2 + 4*y**4 - 5*y**4 + 3*y**4 + 3*y**4 - 10*y**3 + 10*y + 15 = 0. Calculate y.
-1, 1, 3
Let y(s) be the third derivative of s**8/504 - 4*s**7/315 + s**6/60 + 28*s**2. Find v such that y(v) = 0.
0, 1, 3
Let h(n) be the first derivative of -n**2 + 0*n**5 + 0*n + 3 - 1/3*n**6 + n**4 + 0*n**3. Factor h(x).
-2*x*(x - 1)**2*(x + 1)**2
Find c, given that -4*c**4 + 20*c**3 + 24*c**2 - 47*c + 0*c**4 + 47*c = 0.
-1, 0, 6
Let u(i) be the second derivative of -i**6/2 - 5*i**5/2 - 15*i**4/4 - 5*i**3/3 + 5*i + 2. Factor u(r).
-5*r*(r + 1)*(r + 2)*(3*r + 1)
Let a(g) be the third derivative of -g**5/40 + g**4/8 + 3*g**2. Determine c, given that a(c) = 0.
0, 2
Let f = 4 + -2. Suppose 5 = 4*l - 5*n, 2*l + 3*n + 1 + f = 0. Factor 0 - 4 - 2*y + 0 + 2*y**2 + l.
2*(y - 2)*(y + 1)
Solve 9*c**3 - 8*c**4 + 3*c**4 + 9*c**3 - 27*c**2 + 2*c**4 = 0 for c.
0, 3
Solve -24/5*o + 36/5*o**2 + 3/5*o**5 + 0 - 9/5*o**4 - 6/5*o**3 = 0.
-2, 0, 1, 2
Let w(g) be the third derivative of -g**8/151200 + g**6/5400 + g**5/12 - 4*g**2. Let p(j) be the third derivative of w(j). Factor p(u).
-2*(u - 1)*(u + 1)/15
Suppose -2*b + 6 - 2 = -4*z, 5*b + 20 = -5*z. Let i = b - -5. Solve 0*d**2 - 7*d**i - d - 2 - 2*d + 12*d**2 = 0 for d.
-2/7, 1
Let i = -75 - -75. Let c(x) be the second derivative of 0*x**2 + 1/3*x**3 - 1/6*x**4 - x + i. Factor c(y).
-2*y*(y - 1)
Let i(d) be the first derivative of 3*d**6/4 + 3*d**5/10 - 17*d**4/8 - 7*d**3/6 + 2*d**2 + 2*d - 22. Suppose i(t) = 0. What is t?
-1, -2/3, 1
Suppose 4*p - 7 = -5*z, -2*z - 32 = 2*p - 36. Factor 0*o**2 + 4/5 + 2/5*o**p - 6/5*o.
2*(o - 1)**2*(o + 2)/5
Let w = 568/7 + -2546/35. Factor 18/5 + 32/5*k**2 - w*k - 8/5*k**3.
-2*(k - 1)*(2*k - 3)**2/5
Let g(u) be the first derivative of 5*u**4/16 + 10*u**3/3 + 105*u**2/8 + 45*u/2 + 19. What is i in g(i) = 0?
-3, -2
Let z(x) be the first derivative of x**3/21 - 4*x/7 + 41. Find q such that z(q) = 0.
-2, 2
Let h = 80/11 + -609/55. Let j = h + 62/15. Factor -2/3 + 1/3*x**2 + j*x.
(x - 1)*(x + 2)/3
Suppose 0 = -2*f - f - 6. Let v be (6/(-4))/(6/(-4)). Let u(l) = l. Let g(w) = -6*w**2 + 4. Let k(c) = f*u(c) + v*g(c). Determine d, given that k(d) = 0.
-1, 2/3
Let i(w) = 2*w**2 - 5*w - 3. Let k be i(4). Let y(t) = -t**2 + 10*t. Let a be y(k). Factor -a*n + 1 + 9*n - n**2.
-(n - 1)*(n + 1)
Let h(b) be the third derivative of b**6/100 - 2*b**5/75 - 13*b**4/60 - 2*b**3/5 - 22*b**2. Factor h(t).
2*(t - 3)*(t + 1)*(3*t + 2)/5
Let p be (-4)/(-10) + (-88)/(-130). Let u = p - 44/65. Factor 2/5*x**3 + 0 - 2/5*x - 2/5*x**4 + u*x**2.
-2*x*(x - 1)**2*(x + 1)/5
Let z(d) be the first derivative of -1/16*d**4 + 1/8*d**2 + 0*d - 9 + 0*d**3. Solve z(y) = 0.
-1, 0, 1
Let w(n) = 4*n**3 + 44*n**2 + 16*n - 8. Let a(u) = -3*u**3 - 29*u**2 - 11*u + 5. Let z(f) = -8*a(f) - 5*w(f). Factor z(v).
4*v*(v + 1)*(v + 2)
Suppose 5*k = 3 + 22. Let 3*w + 3*w - k*w - w**3 = 0. Calculate w.
-1, 0, 1
Factor -13*n + 6*n**5 + 14*n**4 + 2*n + 0*n**5 - 6*n**2 + 7*n + 6*n**3.
2*n*(n + 1)**3*(3*n - 2)
Suppose -5*b = -b - 5*r - 23, -2*b = -5*r - 19. Factor 2*h**3 + 0*h**3 + b*h**3 + 2*h**2 - 3*h**3.
h**2*(h + 2)
Let f(m) be the third derivative of 0*m**6 + 0*m + 1/35*m**7 + 0 + 0*m**3 + 1/112*m**8 + 3*m**2 - 1/10*m**5 - 1/8*m**4. Suppose f(h) = 0. What is h?
-1, 0, 1
Let c(i) be the third derivative of -25*i**8/96 + 51*i**7/56 - 589*i**6/480 + 41*i**5/48 - 11*i**4/32 + i**3/12 - 7*i**2. What is g in c(g) = 0?
1/5, 2/7, 1/2, 1
Let u(c) be the third derivative of -c**6/300 + c**5/50 - c**4/30 + 15*c**2. Suppose u(z) = 0. Calculate z.
0, 1, 2
Let z = 1037 + -1034. Let 4*a**2 - 4/3*a - 3*a**z + 0 = 0. What is a?
0, 2/3
Let a(u) be the second derivative of -1/90*u**5 + 0 - 1/27*u**3 - 5*u - 1/27*u**4 + 0*u**2. Determine b so that a(b) = 0.
-1, 0
Suppose -29*h = -36*h + 14. Factor 4/7*u**3 + 0 - 4/7*u - 2/7*u**h + 2/7*u**4.
2*u*(u - 1)*(u + 1)*(u + 2)/7
Let i(z) be the first derivative of -z**6/900 + z**5/300 + z**4/30 + 2*z**3 + 3. Let f(n) be the third derivative of i(n). Factor f(r).
-2*(r - 2)*(r + 1)/5
Suppose 3*x - 2*r - 2 = 2*r, -5*r + 26 = x. Suppose -3*o - 2*a = -x*o + 6, -o - 2*a = -2. Find v, given that 2*v**o + v**2 + 2*v**3 + v**2 + 2*v = 0.
-1, 0
Factor 2/13*v**4 + 0*v + 4/13*v**3 - 6/13*v**2 + 0.
2*v**2*(v - 1)*(v + 3)/13
Let n(c) be the second derivative of c**7/252 - c**6/60 - c**5/120 + 7*c**4/72 - c**2/3 - 13*c. Suppose n(s) = 0. Calculate s.
-1, 1, 2
Let t(x) be the first derivative of x**3/12 + x**2/2 + x - 2. Factor t(s).
(s + 2)**2/4
Let o(k) be the first derivative of -k**4/4 - k**3/3 + 20. Determine f, given that o(f) = 0.
-1, 0
Let j(n) = -7*n**5 + 2*n**4 + 8*n**3 - 4*n**2 - 7*n + 2. Let f(v) = v**5 - v**3 + v. Let b(s) = 30*f(s) + 5*j(s). Solve b(q) = 0 for q.
-1, 1, 2
Let v be 6/4 - 1/(-2). Factor -53*g**3 - 2*g**5 + 17*g**3 - 8*g**4 - 16*g + 22*g**4 + 40*g**v.
-2*g*(g - 2)**3*(g - 1)
Suppose -b + 4*h = -21, -3 = 3*b + 3*h - 6. Factor 0*v + 0 + 2*v**3 + 2*v**4 + 2/3*v**2 + 2/3*v**b.
2*v**2*(v + 1)**3/3
Let n be 4/(2/1 + 0). Let -1/3*p**n + p**3 + 0 - p**5 + 0*p + 1/3*p**4 = 0. Calculate p.
-1, 0, 1/3, 1
Let r(c) be the third derivative of 7*c**6/20 + c**5/30 - 4*c**4/3 + 4*c**3/3 - 6*c**2. Factor r(q).
2*(q + 1)*(3*q - 2)*(7*q - 2)
Let n(t) = -t - 3. Let h be n(-5). Let -4 + 0*j + h*j + 0*j**2 + 2*j**2 = 0. Calculate j.
-2, 1
Suppose -216 = -39*r + 36*r. Factor r*k + 8*k**3 + 54 + 36*k**2 + 2/3*k**4.
2*(k + 3)**4/3
Suppose 6/5*j**3 + 0*j + 0 - 24/5*j**2 = 0. Calculate j.
0, 4
Suppose -4*p - 5*b = -8*p + 48, 0 = -3*p + 3*b + 33. Let m(t) = 9*t**2 - 11*t + 2. Let d(q) = -5*q**2 + 6*q - 1. Let w(u) = p*d(u) + 4*m(u). Solve w(f) = 0.
1
Let j(l) = l. Let t(w) = 4*w**3 - 20*w. Let h(i) = -4*j(i) - t(i). Let h(o) = 0. What is o?
-2, 0, 2
Let f = 11 + -10. Let b be 3 - (2 + (f - 3)). Let -2*p**b + p + 3*p + 4*p**3 + p**2 - 5*p = 0. What is p?
-1, 0, 1/2
Let d(m) be the third derivative of 5*m**8/504 + 13*m**7/315 + m**6/45 - 2*m**5/45 + 2*m**2 - 32. Determine t, given that d(t) = 0.
-2, -1, 0, 2/5
Suppose 3*c - 4*h = 8*c + 1, -5*h = 2*c + 14. Let 8*o**4 - 10*o**4 + 7*o**c + 0*o**2 - 2*o**2 - 3*o**3 = 0. Calculate o.
0, 1
Factor 4*w**2 - w**2 + 5 - 7*w**2 + 5*w**4 - 6*w**2.
5*(w - 1)**2*(w + 1)**2
Let a(u) be the third derivative of 1/336*u**8 + 0*u**5 + 0*u**4 + 0*u**6 + 0*u**7 + 3*u**2 + 0*u + 0 + 0*u**3. Factor a(p).
p**5
Let q(m) = m**5 - 5*m**4 - 5*m**3 + m**2 + 4*m. Let h(g) = -6*g**5 + 24*g**4 + 24*g**3 - 6*g**2 - 21*g. Let t(d) = -4*h(d) - 21*q(d). Find o such that t(o)