v + 2*v**w - 4/3 = 0. What is v?
-1, -2/5, 1
Let r be 5 - (-3)/(-8)*14 - (-5)/20. What is n in -1/7*n**5 + 0*n - 5/7*n**4 + r - 4/7*n**2 - 8/7*n**3 = 0?
-2, -1, 0
Let z be (-3)/(840/(-124)) - 330/(-5775). What is w in -108 - 9*w**2 - 54*w - z*w**3 = 0?
-6
Let x(w) = -8*w**2 + 155*w + 163. Let d(r) = -2*r**2 + 39*r + 41. Let o(i) = 22*d(i) - 6*x(i). What is j in o(j) = 0?
-1, 19
Suppose -2*t - t + 5*h = -2, t - 2*h - 1 = 0. Let k(a) = -5*a**3 - a - 1. Let n be k(t). Factor j**4 - 6*j**5 + 5*j**5 + 2*j**n.
j**4*(j + 1)
Let y be ((-3)/(855/(-76)))/((-2)/(-5)). What is v in -4/3*v**2 + 2*v - y = 0?
1/2, 1
Let a(k) be the second derivative of 2*k**7/21 + 2*k**6/3 + k**5/5 - 7*k**4 - 12*k**3 - 348*k. Factor a(z).
4*z*(z - 2)*(z + 1)*(z + 3)**2
Let o = -141 - -148. Suppose 4 = 5*r - 11. Factor -r*p**3 - p**3 - 2*p**5 + p**4 - 2*p**3 - o*p**4 - 2*p**2.
-2*p**2*(p + 1)**3
Find a, given that 4 - 13*a**2 + 20/3*a**4 + 20/3*a - 9*a**3 = 0.
-1, -2/5, 3/4, 2
Let i(z) = z + 1. Let s be i(1). Suppose 3*l = 4*f + 18, -3*f + s + 4 = l. Suppose -15*t + 12*t**2 + 6 - t**3 - l*t**3 + 4*t**3 = 0. What is t?
1, 2
Let a(q) = -4*q**4 - 244*q**3 - 479*q**2 - 296*q - 65. Let x(c) = 3*c**4 + 163*c**3 + 319*c**2 + 197*c + 43. Let d(u) = 5*a(u) + 8*x(u). Solve d(g) = 0.
-19, -1, -1/2
Let g = 1 - 11. Let t be 2/(9 - g/(-5)). Determine s, given that -8/7*s - t - 4/7*s**2 + 8/7*s**3 + 6/7*s**4 = 0.
-1, -1/3, 1
Factor -4*l**2 + 43702 - 43702 - 452*l.
-4*l*(l + 113)
Let g = -13 + 15. Solve -8*k + 1 - 11*k**3 + 15 - 4*k**g + 13*k**3 = 0.
-2, 2
Suppose -4*d + 3*q + 3 = -d, -d + 7 = q. Suppose d*l - 4 = 2*l. Factor -99*t + 99*t - l*t**4.
-2*t**4
Let g(q) be the second derivative of q**6/105 + q**5/70 - q**4/21 + 142*q. Factor g(f).
2*f**2*(f - 1)*(f + 2)/7
Suppose 3*h - 6 = 4*c, -341*h + 338*h + 6 = 3*c. Factor -24/5*g**3 + 21/5*g**4 - 3*g**h + 18/5*g + 0.
3*g*(g - 1)**2*(7*g + 6)/5
Suppose 0 = 36*g - 1848 + 1704. Solve 0 + 0*f**2 + 0*f**3 + 0*f + 4/3*f**g = 0 for f.
0
Let u(w) be the third derivative of -w**6/300 - w**5/75 + w**4/60 + 2*w**3/15 - 98*w**2. Factor u(x).
-2*(x - 1)*(x + 1)*(x + 2)/5
Let i(b) be the first derivative of 2*b**6/21 - 24*b**5/35 + 9*b**4/7 - 16*b**3/21 + 152. Determine w, given that i(w) = 0.
0, 1, 4
Let n = 6327 - 6327. Let y be 2/(-40) + 3/12. Find r, given that -2/5*r + n - y*r**2 = 0.
-2, 0
Factor 10 - 5/4*l**2 - 5/2*l.
-5*(l - 2)*(l + 4)/4
Let j(c) be the third derivative of -c**8/84 + c**6/5 - 8*c**5/15 + c**4/2 - 5*c**2 - 17. Factor j(x).
-4*x*(x - 1)**3*(x + 3)
Let r(h) = -6*h**3 - 81*h**2 - 141*h - 69. Let t(q) = -11*q**3 - 160*q**2 - 282*q - 138. Let a(u) = 5*r(u) - 3*t(u). Determine m, given that a(m) = 0.
-23, -1
Let o be 492/60 + (1 - -13)/(-2). Determine u, given that -6/5*u**3 - 9/5*u**2 + 9/5*u + o = 0.
-2, -1/2, 1
Let h = 19 - 10. Let d be 29/h + (11/(-9) - -1). Factor 0*i**2 - 4/5*i + 2/5 - 2/5*i**4 + 4/5*i**d.
-2*(i - 1)**3*(i + 1)/5
Let c(v) be the first derivative of v**4 - 8*v**3/3 - 6*v**2 + 67. Find n such that c(n) = 0.
-1, 0, 3
Let i(q) be the second derivative of -9*q**5/20 - 11*q**4/12 + 8*q**3/3 + 2*q**2 + 21*q. Let i(o) = 0. What is o?
-2, -2/9, 1
Let p(g) be the second derivative of g**4/3 + 18*g**3 + 52*g**2 + g + 75. Factor p(q).
4*(q + 1)*(q + 26)
Suppose 4*t = 2*f + 4, -23 = -2*f - t - 4*t. Find g such that 23*g**4 - 8*g**f - 14*g**4 - 8*g**5 + 16*g**3 - 13*g**4 - 8*g + 12*g**2 = 0.
-2, -1, 0, 1/2, 1
Let v(x) = 2*x**2 + 5*x - 2. Let z be v(4). Let p be 4/(-10) + 120/z. Suppose 5*a**2 - 15*a**p + 0*a - 2*a + 8*a**2 = 0. Calculate a.
-1, 0
Suppose -71*d + 117 + 3 = -22. Find b such that 3/2*b**d + 1/2 + 3/2*b + 1/2*b**3 = 0.
-1
Let y(g) be the third derivative of 0 + 3/4*g**4 - 3*g**3 - 12*g**2 + 1/180*g**6 - 1/10*g**5 + 0*g. Factor y(d).
2*(d - 3)**3/3
Let y(h) be the first derivative of 4/5*h + 4/5*h**2 + 34 + 4/15*h**3. Determine d, given that y(d) = 0.
-1
Let s be (12/(-34))/((-93)/1054). Let u(c) be the second derivative of -7/30*c**3 + 8*c + 2/5*c**2 + 0 - 1/30*c**s. Factor u(z).
-(z + 4)*(2*z - 1)/5
Let j(a) be the second derivative of -a**5/5 - 2*a**4 - 2*a**3 + 20*a**2 + 92*a. Determine q so that j(q) = 0.
-5, -2, 1
Let v(l) be the first derivative of -l**4/3 + 4*l**3/9 + 4*l**2/3 + 19. What is b in v(b) = 0?
-1, 0, 2
Let b be (0/(-21))/((-2)/(4/(-6))). Let d(w) be the second derivative of 1/36*w**4 - 3*w - 1/6*w**2 + b + 1/60*w**5 - 1/18*w**3. Factor d(i).
(i - 1)*(i + 1)**2/3
Let i = -27 - -29. Factor 11*v**i - 8*v - 28*v**2 + 13*v**2.
-4*v*(v + 2)
Let q(x) be the second derivative of x**7/252 - x**6/20 + x**5/24 + 29*x**4/72 - 7*x**3/6 + 4*x**2/3 - 25*x - 7. Determine i, given that q(i) = 0.
-2, 1, 8
Let n(f) be the second derivative of -4*f**2 + 1/2*f**4 - 5*f + 4/3*f**3 + 0. Factor n(g).
2*(g + 2)*(3*g - 2)
Suppose 0*g - g - 13 = -5*c, -g - c + 5 = 0. Find a such that -3*a**4 + 7*a**4 - 6*a**2 + 4 - g*a**3 + 2*a + 3*a**4 - 5*a**4 = 0.
-1, 1, 2
Let w(a) be the third derivative of -a**6/120 - 7*a**5/60 + a**4/24 + 7*a**3/6 - 403*a**2. Factor w(v).
-(v - 1)*(v + 1)*(v + 7)
Let q(d) be the first derivative of d**6/48 - d**5/5 + 9*d**4/16 - 2*d**3/3 + 5*d**2/16 + 114. Factor q(r).
r*(r - 5)*(r - 1)**3/8
Let t(h) be the second derivative of -32*h**2 + 0 + 20*h + 31/5*h**5 + 24*h**4 + 88/3*h**3 + 8/15*h**6. Factor t(p).
4*(p + 2)**2*(p + 4)*(4*p - 1)
Let v(c) = -c**2 - 72*c + 307. Let m be v(4). Factor 0*h + 3*h**2 + 3/2*h**5 + 0 + 15/2*h**m + 6*h**4.
3*h**2*(h + 1)**2*(h + 2)/2
Let l = 26/9 - 121/45. Let u(h) be the second derivative of 0 + 5*h - 2/3*h**3 + 0*h**2 + l*h**5 - 1/3*h**4 + 2/15*h**6. Let u(n) = 0. What is n?
-1, 0, 1
Suppose 0 = 4*u - 6*u + t + 14, -u - 5*t = 4. Factor 2*h**3 + 18*h + 20 + u*h + 12*h**2 - 2 - 2.
2*(h + 2)**3
Suppose g = -3*w - 5, 1 = -3*g - 14. Suppose 0*s + 4*s - 12 = w. Determine l, given that -8*l**2 - 4*l**s + 8*l**2 + 4*l = 0.
-1, 0, 1
Factor 1/6*z**2 + 7/3*z + 13/6.
(z + 1)*(z + 13)/6
Factor -12*d**2 - 1/4*d**3 - 484 - 165*d.
-(d + 4)*(d + 22)**2/4
Let k be 72/27*(-6)/(-8). Suppose -k*n + 14 = 2. Factor 3*p**3 - 5*p**3 - 6*p + 0*p + n*p**2 + 2.
-2*(p - 1)**3
Let d(t) be the first derivative of 9/14*t**2 - 6/35*t**5 + 1/14*t**6 - 3/7*t**4 + 2/7*t**3 + 4 + 0*t. Find j such that d(j) = 0.
-1, 0, 1, 3
Let t(v) = v**2 + v + 1. Let n(m) = 25*m**2 + 1400*m + 95240. Let l(c) = n(c) - 20*t(c). Suppose l(y) = 0. What is y?
-138
Let g(b) be the first derivative of -3*b**4/8 + 7*b**3 - 18*b**2 + 132. Factor g(y).
-3*y*(y - 12)*(y - 2)/2
Let g(j) be the first derivative of -1/30*j**6 + 0*j**4 + 0*j**3 - 1/30*j**5 + 1/2*j**2 - 5 + 0*j. Let c(l) be the second derivative of g(l). Factor c(u).
-2*u**2*(2*u + 1)
Let d = 51 - 51. Let g be (d/3)/(1/(3/6)). Find q such that 0 + g*q**2 + 2/5*q**4 + 0*q - 2/5*q**3 = 0.
0, 1
Suppose -24 = 57*k - 69*k. Suppose s + 1 = -w - 0, 0 = -4*w - 2*s. Factor 7/2*z**k + w + 9/2*z.
(z + 1)*(7*z + 2)/2
Let v(l) be the third derivative of l**6/720 + 7*l**5/360 + l**4/36 - l**3/3 + 3*l**2 + 15. Solve v(y) = 0.
-6, -2, 1
Let c(y) be the second derivative of y**7/21 - 11*y**6/30 - 9*y**5/5 - 31*y**4/12 - 4*y**3/3 - y + 17. Determine s, given that c(s) = 0.
-1, -1/2, 0, 8
Solve 3*j**4 + 27 + 12*j**4 - 18*j + 2*j**4 - 22*j**4 + 18*j**3 - 24*j**2 + 2*j**4 = 0 for j.
-1, 1, 3
Let c = 39 + -37. Factor 37*s - 74*s + 2*s**c + 35*s.
2*s*(s - 1)
Let f(t) = -15*t**3 - 30*t**2 - 3*t + 36. Let j(c) = -c**3 - c**2 + c. Let i(k) = f(k) - 12*j(k). Suppose i(v) = 0. What is v?
-4, -3, 1
Let z(m) = 10*m**2 + 5*m. Let v(w) = 3*w - 4*w - 6*w**2 + 0*w + 5*w**2. Let h(d) = -36*v(d) - 4*z(d). Factor h(f).
-4*f*(f - 4)
Find h, given that 680*h - 2*h**2 - 12133 + 3412 - 2*h**2 - 20179 = 0.
85
Let u = -31552 + 347936/11. Factor 72/11*q**2 + 3456/11 - u*q - 2/11*q**3.
-2*(q - 12)**3/11
Suppose 5 = 5*m + 4*q + 1, -4*q = 3*m + 4. Solve 6*i**3 + m - 4*i - 4 + 10*i**2 = 0.
-2, 0, 1/3
Suppose 8/7*y**5 + 48/7*y**3 + 0*y + 0 + 36/7*y**2 - 44/7*y**4 = 0. What is y?
-1/2, 0, 3
Let x(s) be the third derivative of -s**10/982800 - s**9/78624 + s**5/10 + 4*s**2. Let z(b) be the third derivative of x(b). Factor z(a).
-2*a**3*(a + 5)/13
Find u such that 2*u**4 - 76*u**2 + 1917*u - 1893*u - 52*u**3 + 74*u**4 + 28*u**5 = 0.
-3, -1, 0, 2/7, 1
Let x(t) be the second derivative of t**5/60 - t**4/9 + 2*t**3/9 -