the second derivative of -c**6/120 + 27*c**5/80 - 81*c**4/16 + 243*c**3/8 - 250*c. What is x in h(x) = 0?
0, 9
Let j be 3 + -1 + (-21)/(-3). Suppose 6*u + 12 = j*u. Determine n so that n**4 - n**2 - 6*n**3 - 2*n**2 + 3*n**5 + 3*n**3 + 2*n**u = 0.
-1, 0, 1
Let y(o) be the first derivative of o**6/6 - 27*o**5/20 - 55*o**4/16 + 25*o**3/3 + 39*o**2/2 + 8*o - 697. Determine k so that y(k) = 0.
-2, -1, -1/4, 2, 8
Factor -3200/9*u + 2/9*u**4 + 3040/9*u**2 + 0 + 158/9*u**3.
2*u*(u - 1)*(u + 40)**2/9
Let r(b) be the first derivative of -b**6/40 + b**5/20 - 6*b**2 + 11. Let c(w) be the second derivative of r(w). Factor c(p).
-3*p**2*(p - 1)
Find k, given that 24/5*k + 0 + 26/5*k**2 - 8/5*k**3 = 0.
-3/4, 0, 4
Let k be (15/10 + 0)/(594/176). Determine y, given that -16/9 + 16/9*y - k*y**2 = 0.
2
Let f(r) be the third derivative of 0 + 0*r + 7/9*r**5 + 25/189*r**7 - 17/27*r**4 - 55/108*r**6 - 12*r**2 + 8/27*r**3. Factor f(a).
2*(a - 1)*(5*a - 2)**3/9
Let f(w) be the first derivative of w**4/28 + w**3/21 - w**2/14 - 9*w - 4. Let b(z) be the first derivative of f(z). Factor b(y).
(y + 1)*(3*y - 1)/7
Let x be (1 - 7/(-35))*(-10)/(-3). Suppose 0 = 4*c + w - x, 5*c - 3*w = -4 + 26. Let 4/3*g**5 + 20/3*g**4 + 0*g + 28/3*g**3 + 0 + 4*g**c = 0. Calculate g.
-3, -1, 0
Factor 0*q + 0 + 19/4*q**2 + 1/4*q**3.
q**2*(q + 19)/4
Let g be (-10)/15*(-114)/4. Let z = g - 16. Let d(s) = s**2 + 7. Let i(p) = 6. Let k(q) = z*d(q) - 4*i(q). Let k(r) = 0. What is r?
-1, 1
Solve -2*r**4 + 5*r + 32*r**2 + 19*r - 274*r**3 + 280*r**3 = 0.
-2, -1, 0, 6
Factor -7*u**4 + 0*u**4 + 8*u + 60*u**5 + 7*u**2 + 47*u**5 - 9*u**3 - 106*u**5.
u*(u - 8)*(u - 1)*(u + 1)**2
Let q(t) = -2*t**2 - 4*t + 7. Let c(h) = 3*h**2 + 4*h - 8. Let x(k) = -3*c(k) - 4*q(k). Determine p, given that x(p) = 0.
2
Suppose 37*x = -29*x. Let d(w) be the third derivative of x*w + 0 + 1/80*w**5 + 0*w**3 + 1/32*w**4 + 8*w**2. Factor d(u).
3*u*(u + 1)/4
Let o(x) be the second derivative of -20*x + 0 - 33/10*x**3 + 1/10*x**4 + 24/5*x**2. Find s, given that o(s) = 0.
1/2, 16
Let q be 1*2 + (-2448)/1232. Let u = q - -1075/231. Factor -u*o**3 + 52/3*o**2 - 40/3*o - 16/3.
-2*(o - 2)**2*(7*o + 2)/3
Let h(g) be the second derivative of g**5/4 + 35*g**4/6 - 5*g**3/6 - 35*g**2 + 3*g + 1. Suppose h(n) = 0. What is n?
-14, -1, 1
Let k = -26165/4 - -6542. Suppose -3/4*l**3 - k*l**2 + 0*l + 0 = 0. Calculate l.
-1, 0
Suppose 3*t - 164 = -4*q, 5*q - 4*t - 104 - 132 = 0. Let w be 2/4*(-3 + q/12). Solve -1/3*b - w*b**4 + 1/3*b**3 + 1/3*b**2 + 0 = 0 for b.
-1, 0, 1
Solve 6/5 + 14/5*f - 2/5*f**5 + 4/5*f**2 - 12/5*f**3 - 2*f**4 = 0 for f.
-3, -1, 1
Determine v so that -1/8*v**5 - 9/2*v**4 - 17/2*v**3 + 1/4*v**2 + 17/4 + 69/8*v = 0.
-34, -1, 1
Let i(t) be the third derivative of -t**7/1260 + 4*t**4/3 + 9*t**2. Let j(g) be the second derivative of i(g). Factor j(v).
-2*v**2
Find s, given that 9 + 6*s + 38 + s**2 + 0*s**2 - 38 = 0.
-3
Let s = 6 + -2. Suppose 3 = -5*h + 18. Solve -3*o**4 - 7*o**h + o**2 + 3*o**3 + 5*o**s + 4*o**5 - 3*o**4 = 0 for o.
-1, 0, 1/4, 1
Let a(l) be the third derivative of -l**6/30 + 7*l**5/15 - 4*l**4/3 - 32*l**3/3 - 263*l**2. Suppose a(i) = 0. Calculate i.
-1, 4
Let i = -9937 + 168979/17. Factor -i - 8/17*w**2 + 40/17*w.
-2*(2*w - 5)**2/17
Suppose 4*s = j + 11, -s + 10 = -j + 2*s. Let o be (235/(-40) - j)/(9/84). What is t in -o*t**3 - 12*t**4 - 3*t**2 + 0*t + 0 - 9/2*t**5 = 0?
-1, -2/3, 0
Suppose b - 78 = -12*b. Let t(h) = h + 7. Let w be t(-5). Let 7*z**2 + 12*z**w + 8*z**2 - 12*z**3 - b*z = 0. Calculate z.
0, 1/4, 2
Let a(t) be the second derivative of t**4/48 - t**3/4 - 24*t - 2. Factor a(h).
h*(h - 6)/4
Let j = -7 - -11. Let a be (-8)/(-150)*(-205)/246*-18. Factor 2/5 + 2/5*n**j + 0*n**3 + 0*n - a*n**2.
2*(n - 1)**2*(n + 1)**2/5
Let r be (-2)/(224/(-34)) + 13/104. Let 0*f**3 - 6/7*f**4 + r*f + 6/7*f**2 + 0 - 3/7*f**5 = 0. Calculate f.
-1, 0, 1
Let s(d) = 2*d**2 - 10*d + 54. Let v(y) = y**2 - 11*y + 53. Let k(p) = 5*s(p) - 6*v(p). Factor k(i).
4*(i - 2)*(i + 6)
Let t(y) be the third derivative of -y**5/40 + 91*y**4/16 + 23*y**3 - 290*y**2. Factor t(p).
-3*(p - 92)*(p + 1)/2
Let x(w) be the third derivative of -7/12*w**4 + 34*w**2 + 2/3*w**3 + 0 + 0*w - 1/30*w**6 + 1/168*w**8 - 2/105*w**7 + 4/15*w**5. Factor x(g).
2*(g - 1)**4*(g + 2)
Suppose 0 - 4/17*v**3 + 6/17*v**2 - 2/17*v**4 + 0*v = 0. Calculate v.
-3, 0, 1
Solve 304*m**2 - 218*m**4 - 8*m**5 - 43*m**5 + 14*m**3 + 2*m**3 - 32*m + 121*m**5 - 32 = 0 for m.
-1, -2/7, 2/5, 2
Suppose 10*y + 54 = 54. Let d(l) be the third derivative of 0*l**3 + 4*l**2 - 1/60*l**6 + 0*l**5 + 1/36*l**4 + 0 + y*l + 2/315*l**7. Factor d(g).
2*g*(g - 1)**2*(2*g + 1)/3
Factor -121*r**3 - 800*r + 42*r**3 + 87*r**3 + 220*r**2 - 4*r**4.
-4*r*(r - 5)**2*(r + 8)
Suppose 5*s - 3*s + 3*a - 16 = 0, s = 2*a + 15. Factor 6*i - 8*i**2 - 8 - s*i - 15*i + 4*i**5 + 16*i**3 + 16*i**4.
4*(i - 1)*(i + 1)**3*(i + 2)
Let t(a) = 7*a**2 - 35*a + 64. Let c(n) = n**2 - 4*n + 3. Let b(h) = -2*h**2 + 7*h - 5. Let i(k) = -3*b(k) - 5*c(k). Let s(o) = 3*i(o) - t(o). Factor s(w).
-4*(w - 4)**2
Let n(w) be the second derivative of -w**4/6 + 61*w**3/6 + 31*w**2/2 - 91*w. Suppose n(c) = 0. What is c?
-1/2, 31
Factor 42/11*y - 2/11*y**2 - 40/11.
-2*(y - 20)*(y - 1)/11
Solve -3/4*m**2 + 0*m + 3 = 0.
-2, 2
Let n(a) be the first derivative of a**7/56 + a**6/36 - a**5/24 - 4*a**3/3 + 12. Let s(y) be the third derivative of n(y). Factor s(p).
5*p*(p + 1)*(3*p - 1)
Suppose 0*m - 10 = -2*m. Let b(y) = 3 + 2*y + 6*y**2 - 4 + y - m*y**2. Let a(k) = -6*k**2 - 16*k + 6. Let x(q) = -3*a(q) - 16*b(q). What is o in x(o) = 0?
-1, 1
Let k(u) be the first derivative of u**6/27 + 2*u**5/45 - u**4/18 - 2*u**3/27 - 63. What is x in k(x) = 0?
-1, 0, 1
Let c(d) be the first derivative of d**4/2 - 16*d**3/3 - 37*d**2 + 88*d + 289. Let c(w) = 0. What is w?
-4, 1, 11
Let j(x) = x**3 - 9*x**2 + 11*x - 16. Let n be j(8). Let l be (-26)/(-22) + 2 + n/(-44). Let 0 - 2/3*m**l - 2/3*m**4 + 8/3*m**2 + 8/3*m = 0. What is m?
-2, -1, 0, 2
Let x(d) be the second derivative of -d**5/30 + 47*d**4/3 - 8836*d**3/3 + 830584*d**2/3 + 58*d + 5. Let x(o) = 0. Calculate o.
94
Suppose 0 = -4*b - 5*o - 81, 2*b + 0*o + 42 = -2*o. Let l = b + 24. Find c, given that 6/13*c**2 - 2/13*c + 2/13*c**4 - 6/13*c**3 + l = 0.
0, 1
Let d = 4470/11 + -406. Let d*t**2 - 4/11 - 2/11*t + 2/11*t**3 = 0. Calculate t.
-2, -1, 1
Let k(t) be the third derivative of t**8/784 + 2*t**7/245 + 3*t**6/280 - 17*t**2 + 4*t. Find b, given that k(b) = 0.
-3, -1, 0
Let 81/5*u**4 + 159/5*u**2 + 33*u**3 + 72/5*u + 3*u**5 + 12/5 = 0. Calculate u.
-2, -1, -2/5
Let z = -1927 - -7709/4. Factor -1/4*y**2 + 1/2*y**3 + 0 - z*y.
y*(y - 1)*(2*y + 1)/4
Find v such that -26/7*v**2 - 2/7*v**4 - 12/7*v + 0 - 16/7*v**3 = 0.
-6, -1, 0
Let i(r) be the third derivative of -r**6/180 + 11*r**5/90 - 35*r**4/36 + 25*r**3/9 - 83*r**2. Factor i(p).
-2*(p - 5)**2*(p - 1)/3
Let x(t) = -6*t**2 - 12*t - 9. Let o(m) = 11*m**2 + 24*m + 18. Let z(d) = 3*o(d) + 5*x(d). Suppose z(c) = 0. What is c?
-3, -1
Let t be (141/(-188))/((-30)/32). What is u in -t*u + 6/5*u**2 + 0 - 2/5*u**3 = 0?
0, 1, 2
Let c(w) = -w**3 - 17*w**2 - 31*w - 13. Let j be c(-15). Solve -10/9 - 8/9*n - 2/9*n**4 + 8/9*n**3 + 4/3*n**j = 0.
-1, 1, 5
Let v = -22653 - -22657. Suppose -16/9 + 4/9*p**v + 8/9*p**3 - 4/3*p**2 - 32/9*p = 0. What is p?
-2, -1, 2
Let q(g) = g**2 - 101*g - 91. Let n(m) = -m**2 + 51*m + 46. Suppose -4*r - w = -0*r - 42, -3*r + w = -35. Let b(h) = r*n(h) + 6*q(h). Factor b(j).
-5*(j + 1)*(j + 8)
Find t, given that 118/5*t - 4/5*t**3 + 2*t**2 + 56/5 = 0.
-4, -1/2, 7
Factor 3/4*u**5 - 63/4*u**3 + 15/4*u**4 + 69/4*u**2 + 0 - 6*u.
3*u*(u - 1)**3*(u + 8)/4
Let b = 204 - 201. Suppose 0 = -3*y + 5*m - 0*m - 19, -3*y - b*m = -21. Factor -2/15 + 8/15*n - 4/5*n**y + 8/15*n**3 - 2/15*n**4.
-2*(n - 1)**4/15
Suppose 5*g - f - 34 = 0, -g + 3*f - 10 = -2*g. Suppose 4*h - g = 17. Find r such that r + 2 - 7*r**3 + 4*r**4 + 2*r**4 - 8*r**4 - h*r**2 + 0*r**4 = 0.
-2, -1, 1/2
Let d(k) = k**2 - 10*k + 19. Let y be d(8). Let a(q) = q**2 + 4*q + 1. Let c be a(y). Factor 10 + c*b**2 + 11*b + 4*b - 17*b**2.
5*(b + 1)*(b + 2)
Let y(r) be the second derivative of r**7/84 - r**6/30 - r**5/40 + r**4/12 - 6*r. Suppose y(n) = 0. Calculate n.
-1, 0, 1, 2
Determine a so that