72/1557. Suppose 4/3*y**2 - 4/9*y**3 + 4/9 - d*y = 0. What is y?
1
Let b(d) be the second derivative of 3*d**5/20 + 15*d**4/4 - 750*d**2 + d - 48. Suppose b(l) = 0. Calculate l.
-10, 5
Let a(r) be the third derivative of r**5/390 + 133*r**4/156 + 44*r**3/13 - 2*r**2 - 61*r. Factor a(k).
2*(k + 1)*(k + 132)/13
Let g(v) be the second derivative of v**4/4 - 30*v**3 - 183*v**2/2 - 449*v. Factor g(y).
3*(y - 61)*(y + 1)
Suppose 1/2*p**2 + 0 - 9*p = 0. What is p?
0, 18
Let x be 2*1*16/32. Let y = 3 - x. What is n in 0 - 4/3*n - 2/3*n**4 + 0*n**3 + 2*n**y = 0?
-2, 0, 1
Let x(l) = -l**3 + 4*l**2 + 19*l - 38. Let g be x(6). Let p(k) be the first derivative of 0*k**2 + 0*k - 11 - 1/22*k**g + 0*k**3. Suppose p(q) = 0. What is q?
0
Let c = 32702 - 10390. Let h = -200558/9 + c. Let h*w**4 + 400/9*w**3 + 32/9*w + 20*w**2 + 2/9 = 0. Calculate w.
-1, -1/5
Let y(u) be the third derivative of u**7/840 - u**6/120 - 3*u**5/40 - 5*u**4/24 - 7*u**3/24 + u**2 + 35. Solve y(b) = 0 for b.
-1, 7
Let a be (-47)/(-12) - (260/(-24) + 11). Factor -3/4*p**2 - 3/2 - 3/2*p**3 + a*p.
-3*(p - 1)*(p + 2)*(2*p - 1)/4
Let z(k) be the second derivative of 0 - 2/35*k**5 + 1/42*k**4 + 1/35*k**6 + 0*k**2 - 4*k + 0*k**3. Factor z(m).
2*m**2*(m - 1)*(3*m - 1)/7
Let p(i) be the first derivative of 2*i**5/5 - 3*i**4/2 + 4*i**3/3 + 115. Solve p(r) = 0 for r.
0, 1, 2
Let h(a) be the second derivative of -a**4/3 - 14*a**3 - 220*a**2 - 2*a + 58. Determine w so that h(w) = 0.
-11, -10
Let f(p) be the second derivative of 1/30*p**5 - 4/9*p**3 - 1/9*p**4 + 8/3*p**2 + 0 + 30*p. Factor f(u).
2*(u - 2)**2*(u + 2)/3
Let y = -2344 + 2346. Let -1/4*c**y - 1/2*c - 1/4 = 0. What is c?
-1
Let r(z) be the second derivative of 19*z**4/30 + 6*z**3/5 - z**2/5 - 431*z. Factor r(b).
2*(b + 1)*(19*b - 1)/5
Let q(n) be the third derivative of -n**5/20 - 20*n**4 - 3200*n**3 - 217*n**2. Factor q(c).
-3*(c + 80)**2
Let s be 1 + 180/(-156) + 5/(130/4). Solve 2/7*z**4 + 0*z**2 + 6/7*z**3 + s*z + 0 = 0.
-3, 0
Find s such that -205*s**3 + 672 + 190*s - 283 + 15*s**5 - 95*s**4 + 15*s**2 - 309 = 0.
-1, -2/3, 1, 8
Let l be (-1)/((-100)/24 + 1). Let n = l - -8/95. Find t such that -14/5*t**2 - 6*t - 18/5 - n*t**3 = 0.
-3, -1
Let b = 145 - 145. Suppose 5*n = m - 0*m - 5, b = n - 3*m + 15. Factor n*l + 0 - 2/3*l**3 + 4/3*l**2 - 56/3*l**4.
-2*l**2*(4*l - 1)*(7*l + 2)/3
Let o(s) be the first derivative of -10 + 0*s**2 + 1/10*s**4 - 1/15*s**3 + 0*s - 1/25*s**5. Factor o(f).
-f**2*(f - 1)**2/5
Factor -339/4*u**3 - 3/4*u**4 - 993/4*u - 165/2 - 999/4*u**2.
-3*(u + 1)**3*(u + 110)/4
Determine g, given that 65*g**4 + 3184*g**2 - 3254*g**2 + 6 + 2 - 3 + 60*g**3 - 60*g = 0.
-1, 1/13, 1
Let n(l) be the second derivative of -2*l**6/15 + 7*l**5/5 - 2*l**4 - 64*l**3/3 + 64*l**2 + 251*l. Factor n(g).
-4*(g - 4)**2*(g - 1)*(g + 2)
Suppose 5*t - 31 = -g, t - 5*g = -t + 34. Factor 21*z**5 - 17*z**5 - 2*z + 1 + 0*z**4 - 8*z**2 + t*z**4 - 2*z**3.
(z - 1)*(z + 1)**3*(4*z - 1)
Let y be 5 - 19 - (-2816)/198. Suppose -128/3*j - 1024/9 - y*j**3 - 16/3*j**2 = 0. What is j?
-8
Let l(i) be the third derivative of 1/10*i**4 + 4/75*i**5 + 7/600*i**6 + 0 + 0*i**3 + 1/1050*i**7 + 0*i + 29*i**2. Factor l(u).
u*(u + 2)**2*(u + 3)/5
Let i(u) be the second derivative of u**6/105 - 8*u**5/35 + 13*u**4/42 + 10*u**3/7 + 99*u + 2. Factor i(g).
2*g*(g - 15)*(g - 2)*(g + 1)/7
Let -3*b + b - 39*b**3 + 20*b**2 - 2*b**5 - 10*b**4 + 43*b**3 - 10 = 0. Calculate b.
-5, -1, 1
Let i(k) = -k**3 - 4*k**2 - 7*k - 24. Let r be i(-4). Suppose -14*z - 2 = -15*z. Factor 0*m + z*m**3 + 8/5*m**r + 0 + 2/5*m**2.
2*m**2*(m + 1)*(4*m + 1)/5
Let q(b) be the second derivative of b**6/135 + 7*b**5/90 + 4*b**4/27 - 16*b**3/27 + 326*b. Factor q(c).
2*c*(c - 1)*(c + 4)**2/9
Find r such that -26*r**3 + 28 + 102*r + 84*r**2 + 25*r**3 + 11*r**3 = 0.
-7, -1, -2/5
Suppose 143*w - 13 = -3*b + 142*w, 0 = 2*w + 10. Let m(z) be the first derivative of -2/5*z**5 + z**2 + 3/2*z**4 - 2*z**3 + 0*z - b. Factor m(k).
-2*k*(k - 1)**3
Let k(b) be the second derivative of -b**4/4 + 3*b**2/2 - 2*b + 35. Suppose k(f) = 0. What is f?
-1, 1
Let f(k) = -5*k + 0*k**3 + 16*k**3 + 4*k**3 - 17 + 2 + 15*k**2. Let z(c) = -c**3 - c**2 + 1. Let o(u) = f(u) + 15*z(u). Factor o(i).
5*i*(i - 1)*(i + 1)
Let p = -42 + 30. Let k be (-1)/4 + (-75)/p. Find m, given that k - 6 + 0 - 2*m**4 = 0.
0
Let a(l) be the first derivative of 0*l - 14 + 3/5*l**2 + 2/15*l**3. Factor a(b).
2*b*(b + 3)/5
Solve -54*a - 242/9 - 2/9*a**3 - 82/3*a**2 = 0 for a.
-121, -1
Let q(v) be the second derivative of -v**5/40 - 13*v**4/16 - 3*v**3 + 14*v**2 + 32*v. Let g(r) be the first derivative of q(r). Factor g(o).
-3*(o + 1)*(o + 12)/2
Let u(h) be the first derivative of h**7/840 + h**6/150 + 3*h**5/200 + h**4/60 + h**3 + 7. Let j(q) be the third derivative of u(q). What is o in j(o) = 0?
-1, -2/5
Suppose 4*m = -c + 5, 4*c - 5*m + 2 - 1 = 0. Let x = 1 + c. Determine h so that 5*h + h**x + 5*h**2 - 4*h**2 + 2 - h = 0.
-1
Let a(z) be the third derivative of z**7/21 - 4*z**6/5 + 23*z**5/6 - 3*z**4 - 12*z**3 - 3*z**2 + 48. Determine k, given that a(k) = 0.
-2/5, 1, 3, 6
Factor 33*i**2 - 13*i**2 + 46*i - 18*i**2.
2*i*(i + 23)
Factor 22*h**2 - 14*h + 30*h**2 - 50*h**2 - 36.
2*(h - 9)*(h + 2)
Let j(x) be the second derivative of 0*x**2 - 1/8*x**4 + 1/4*x**3 - 11*x + 0. Factor j(v).
-3*v*(v - 1)/2
Let o(y) be the second derivative of y**6/1080 + y**5/120 + y**4/36 + 5*y**3/3 - 17*y. Let z(h) be the second derivative of o(h). Factor z(g).
(g + 1)*(g + 2)/3
Factor -14*q**3 + 30*q**2 + 32/7 - 144/7*q.
-2*(q - 1)*(7*q - 4)**2/7
Let m = -4868 + 4871. Suppose 0 = 5*f - f - 8. Solve 2/9*g + 4/9*g**f + 2/9*g**m + 0 = 0.
-1, 0
Let b = -10 + 43. Suppose 3 - b = -10*l. Find o, given that -4/5*o**l + 0 + 4/5*o**4 + 0*o + 0*o**2 - 1/5*o**5 = 0.
0, 2
Suppose 0 = -3*o - 0*o + 9. Let t(d) = 6*d**3 + 38*d**2 + 108*d + 110. Let x(w) = 7*w**3 + 39*w**2 + 108*w + 111. Let f(h) = o*t(h) - 2*x(h). Factor f(q).
4*(q + 3)**3
Let t(y) be the first derivative of -2*y**5/25 + 4*y**4/5 - 14*y**3/15 + 8. Let t(f) = 0. Calculate f.
0, 1, 7
Factor 36/7*r**2 + 13/7 + 10/7*r**3 - 1/7*r**4 + 38/7*r.
-(r - 13)*(r + 1)**3/7
Let v(w) be the second derivative of 2/15*w**6 - 2/5*w**5 + 4/3*w**3 + 0*w**4 - 2*w**2 + 0 + 5*w. Factor v(r).
4*(r - 1)**3*(r + 1)
Let d be (5/((-15)/4))/(52/(-78)). Let a(l) be the first derivative of -3/4*l**4 - 3*l - 9/2*l**d + 2 - 3*l**3. Determine z, given that a(z) = 0.
-1
Let r be -3 + (8/4)/(-6). Let l = 4 + r. Solve 2/3*b**2 - l*b**4 - 1/3*b**5 + 1/3*b + 0*b**3 + 0 = 0 for b.
-1, 0, 1
Let n(h) = 5*h**3 - 11*h**2 + 10*h - 4. Let s(w) = -6*w**3 + 10*w**2 - 9*w + 5. Let l(m) = 5*n(m) + 4*s(m). Factor l(a).
a*(a - 14)*(a - 1)
Let y(r) be the first derivative of r**7/315 - r**6/90 - r**5/90 + r**4/18 - 11*r**2/2 - 3. Let k(z) be the second derivative of y(z). Factor k(v).
2*v*(v - 2)*(v - 1)*(v + 1)/3
Suppose 24 = -4*p, 2*p = 7*d - 8*d - 8. Find o such that -3/7*o**3 + 0*o + 0 + 3/7*o**d + 0*o**2 = 0.
0, 1
Let q(s) be the third derivative of -s**7/70 - 7*s**6/20 - 9*s**5/4 + 771*s**2. Factor q(n).
-3*n**2*(n + 5)*(n + 9)
Suppose -4*u + 32 = -3*a, -5*u - 3*a + 13 = -0*u. Let x(m) be the first derivative of 0*m**3 - 3/7*m**2 + 4/7*m + 1/14*m**4 + u. Factor x(r).
2*(r - 1)**2*(r + 2)/7
Let z(w) be the first derivative of 21/10*w**5 - 69/8*w**4 + 69/4*w**2 + 16 - 1/2*w**3 - 9*w. Suppose z(b) = 0. Calculate b.
-1, 2/7, 1, 3
Let z(l) be the second derivative of -l**6/165 + l**5/110 + l**4/33 + 285*l. Suppose z(w) = 0. Calculate w.
-1, 0, 2
Let n(x) be the second derivative of x**6/15 + x**5/10 - x**4/2 - x**3/3 + 2*x**2 - 35*x. Factor n(c).
2*(c - 1)**2*(c + 1)*(c + 2)
Let h(w) be the second derivative of w**7/28 - w**6/5 - 9*w**5/40 + 9*w**4/4 - 3*w - 30. Determine t, given that h(t) = 0.
-2, 0, 3
Let n(w) be the second derivative of w**5/20 + w**4/6 - 43*w**3/6 + 20*w**2 - 2*w - 376. Factor n(a).
(a - 5)*(a - 1)*(a + 8)
Let z(y) be the second derivative of -y**4/60 - 3*y**3/5 - 81*y**2/10 - 93*y. Let z(a) = 0. Calculate a.
-9
Let g be 1/(-1) - 138/(-46). Factor 21/4*c**g - 3/4*c**5 - 27/4*c**3 + 0 - 3/2*c + 15/4*c**4.
-3*c*(c - 2)*(c - 1)**3/4
Determine f, given that -86*f**3 - 4*f**3 - 30*f**4 - 34*f**4 + 69*f**4 = 0.
0, 18
Suppose 4*g + 73 = 5*f + 5, 3*f + 5*g = 26. Fin