second derivative of -2/27*a**3 + 0*a**2 + 0 + g*a + 1/54*a**4. What is l in m(l) = 0?
0, 2
Let z = -1257 - -1257. Solve -1/3*y**3 + z + 1/3*y - 1/3*y**4 + 1/3*y**2 = 0.
-1, 0, 1
Factor 0 - 4/5*s - 8/5*s**4 - 24/5*s**3 - 18/5*s**2.
-2*s*(s + 2)*(2*s + 1)**2/5
Let b be (-10)/(-2 - (-5 - -2 - -3)). Suppose f + 12 = b*t - f, f + 9 = 4*t. Factor 0 - 3/5*y**4 + 0*y - 1/5*y**5 - 2/5*y**3 + 0*y**t.
-y**3*(y + 1)*(y + 2)/5
Let q(t) = -t**3 + 9*t**2 + 10*t - 24. Let s be q(10). Let u be ((-12)/(-80))/(1 + 23/s). Factor -8/5*g + u*g**4 + 8/5 + 12/5*g**3 - 22/5*g**2.
2*(g + 1)**2*(3*g - 2)**2/5
Let -1/4*r**3 + 63/4 - 51/4*r + 13/4*r**2 = 0. Calculate r.
3, 7
Let k(v) be the second derivative of -v**7/10080 + v**6/720 - v**5/120 + 5*v**4/6 + 3*v. Let o(l) be the third derivative of k(l). Find n, given that o(n) = 0.
2
Let z be 25/78 - 6*(-7)/(-252). Determine g, given that 0*g**2 + 0*g - 4/13*g**4 + z*g**3 + 0 + 2/13*g**5 = 0.
0, 1
Let a(j) = 2*j**4 + 13*j**3 - 2*j**2 - 13*j. Let c(g) = g**4 + 6*g**3 - g**2 - 6*g. Let k(l) = -4*a(l) + 9*c(l). Factor k(h).
h*(h - 1)*(h + 1)*(h + 2)
Let d(w) be the first derivative of 2*w**6/3 - 16*w**5/5 + 4*w**4 + 8*w**3/3 - 10*w**2 + 8*w + 109. Factor d(k).
4*(k - 2)*(k - 1)**3*(k + 1)
Let i(h) be the third derivative of -h**6/900 + h**4/60 + 7*h**3/3 - 15*h**2. Let s(w) be the first derivative of i(w). Factor s(x).
-2*(x - 1)*(x + 1)/5
Let r(g) be the third derivative of 1/560*g**8 + 2/25*g**6 - 6*g**2 - 4/25*g**5 + 0*g + 2/15*g**4 + 0 + 0*g**3 - 2/105*g**7. Find m, given that r(m) = 0.
0, 2/3, 2
Factor -9/2*i - 1/2*i**3 - 3*i**2 + 0.
-i*(i + 3)**2/2
Let w(b) be the first derivative of b**3/18 + 31*b**2/12 - 16*b/3 - 272. Factor w(r).
(r - 1)*(r + 32)/6
Let f(x) be the first derivative of 5*x**3/3 - 255*x**2/2 + 250*x - 18. Factor f(u).
5*(u - 50)*(u - 1)
Let y(f) = -4*f**2 + 16*f + 36. Let h = 56 - 48. Let k(m) = -m**2 + 5*m + 12. Let r(p) = h*k(p) - 3*y(p). Factor r(w).
4*(w - 3)*(w + 1)
Let u(z) be the second derivative of z**7/560 + z**6/120 + z**5/60 - 13*z**4/12 - 11*z. Let b(a) be the third derivative of u(a). Factor b(g).
(3*g + 2)**2/2
Let d(m) be the second derivative of -m**4/12 - 3*m**3/2 - 2*m - 12. Factor d(k).
-k*(k + 9)
Let q(t) = -t**4 - t**3 + t**2 + 2*t + 2. Let x(b) = 5*b**4 + 28*b**3 + 158*b**2 + 424*b + 397. Let h(o) = -12*q(o) - 3*x(o). Factor h(l).
-3*(l + 3)**3*(l + 15)
Let b(t) be the second derivative of 1/13*t**3 + 1/273*t**7 + 0*t**6 - 33*t - 2/65*t**5 - 1/39*t**4 + 0 + 2/13*t**2. Solve b(d) = 0.
-1, 1, 2
Let x = 57 + -55. Factor 7*r**2 + x*r - 3*r**2 + 2*r**3 - 8*r**2.
2*r*(r - 1)**2
Let f(n) = -2*n**3 - 19*n**2 - 23*n + 14. Let c be f(-8). Factor 1/2*q**2 - c*q + 18.
(q - 6)**2/2
Suppose -2*u - 9*u + 165 = 0. Suppose u = v + 13. Solve 2/9*b + 2/9*b**3 + 4/9*b**v + 0 = 0 for b.
-1, 0
Let i(z) = 30*z**2 - 1065*z + 53830. Let v(b) = b**2 - b - 10. Let p(o) = -i(o) + 25*v(o). Determine m, given that p(m) = 0.
104
Let k(d) be the third derivative of d**5/12 - 15*d**4/2 - 185*d**3/6 + 489*d**2 - 2*d. Suppose k(a) = 0. What is a?
-1, 37
What is u in -139*u + 168*u**2 - 214342*u**3 - 25*u + 214338*u**3 = 0?
0, 1, 41
Let f be 6 - (5 - (6 - 2)). Factor 10*i + f*i - 10*i + 5*i**2 + 0*i**2.
5*i*(i + 1)
Let y(a) be the third derivative of a**6/120 - 13*a**5/60 + 17*a**4/8 - 21*a**3/2 + 442*a**2. Determine t so that y(t) = 0.
3, 7
Suppose 0 = -7*c - 7*c - 742. Let q = c + 53. Factor 2/3*o**3 - 2/3*o**5 + 0*o**4 + 0*o**2 + 0*o + q.
-2*o**3*(o - 1)*(o + 1)/3
Factor -51 - 42*k**2 - 23*k**2 - 150*k + 11.
-5*(k + 2)*(13*k + 4)
Let a(p) be the second derivative of 4*p**6/15 + 13*p**5/5 - 56*p**4/3 - 206*p**3/3 - 72*p**2 + 4*p + 1. Let a(q) = 0. Calculate q.
-9, -1, -1/2, 4
Let w(h) = -3*h**3 + 60*h**2 - 6*h + 3. Let f(a) = -6*a**3 + 121*a**2 - 10*a + 5. Let r(l) = -3*f(l) + 5*w(l). Factor r(n).
3*n**2*(n - 21)
Factor 128/5*u + 124/5 + 4/5*u**2.
4*(u + 1)*(u + 31)/5
Let o(y) = 7*y**5 - 30*y**4 + 51*y**3 - 33*y**2 - 3*y + 3. Let q(w) = 20*w**5 - 89*w**4 + 154*w**3 - 97*w**2 - 8*w + 8. Let k(g) = 8*o(g) - 3*q(g). Factor k(l).
-l**2*(l - 3)**2*(4*l - 3)
Suppose 0 = 2*q + j - 11, 60*q = 61*q - j + 2. What is a in -18/11*a**4 - 4/11*a**2 + 0 + 0*a - 2*a**q = 0?
-1, -2/9, 0
Let g(f) = 3*f**2 + 61*f - 172. Let l(u) = -20*u**2 - 365*u + 1030. Let r(p) = -25*g(p) - 4*l(p). Factor r(k).
5*(k - 9)*(k - 4)
Let c(h) be the second derivative of h**5/90 + 11*h**4/108 - h**3/9 + 52*h - 3. Factor c(m).
m*(m + 6)*(2*m - 1)/9
Let s(r) be the first derivative of 5*r**3/3 - 45*r**2 + 325*r - 3. Factor s(l).
5*(l - 13)*(l - 5)
Let n(d) be the second derivative of -d**7/6300 - d**6/1200 - d**5/600 - 11*d**4/12 + 11*d. Let z(t) be the third derivative of n(t). Factor z(x).
-(x + 1)*(2*x + 1)/5
Suppose 498 - 370*y + 53*y**2 - 48*y**2 - 133 = 0. Calculate y.
1, 73
Let g(n) be the third derivative of 5/32*n**4 - 7/240*n**6 - 1/120*n**5 + 3/8*n**3 + 8*n**2 - 1/120*n**7 + 0 - 1/1344*n**8 + 0*n. Solve g(h) = 0.
-3, -1, 1
Suppose 254 = -a - 131. Let b be (-30)/a + 4/14. Let -2/11*v**5 - 2/11*v + 4/11*v**3 + 2/11*v**4 - b*v**2 + 2/11 = 0. Calculate v.
-1, 1
Let l(k) be the third derivative of -k**6/240 + 3*k**5/8 - 11*k**4 + 121*k**3/3 - 138*k**2. What is d in l(d) = 0?
1, 22
Let g(x) be the third derivative of -119*x**5/120 + 5*x**4/12 + x**3/3 + 22*x**2. Factor g(s).
-(7*s - 2)*(17*s + 2)/2
Suppose -4*k + 12 = -3*o - o, -o = 2*k - 6. Let q(a) = a - 5. Let u be q(8). Determine f, given that -2*f**2 - f**4 - f + o*f**3 - f**2 - 3*f**u = 0.
-1, 0
Let h(q) be the third derivative of 0 - 5/84*q**8 + 0*q + 0*q**3 - 5*q**2 + 1/15*q**5 - 26/105*q**7 + 1/3*q**4 - 3/10*q**6. Factor h(l).
-4*l*(l + 1)**3*(5*l - 2)
Let i(z) be the second derivative of z**4/66 - 2*z**3/33 - 3*z**2/11 + 2*z + 8. Suppose i(q) = 0. What is q?
-1, 3
Let l(g) be the third derivative of 2/15*g**5 - 23*g**2 + 0*g**3 + 0*g - 1/60*g**6 + 0 - 1/3*g**4. Factor l(q).
-2*q*(q - 2)**2
Let v = 8/77 - -369/154. Let r(w) be the first derivative of 1/4*w**4 - 2*w + v*w**2 - 4/3*w**3 + 13. Let r(o) = 0. Calculate o.
1, 2
Let p(c) = 15*c**2 - 10*c - 15. Suppose -d - 4*l = 17, -d = 2*d + l + 18. Let m(o) = -8*o**2 + 5*o + 7. Let u(s) = d*m(s) - 2*p(s). Factor u(y).
5*(y - 1)*(2*y + 1)
Factor -3*d**2 - 3/4*d**5 + 0*d - 15/4*d**4 - 6*d**3 + 0.
-3*d**2*(d + 1)*(d + 2)**2/4
Factor 14610 + 38080 - 5126 + 4*g**2 + 32993*g + 79172 - 31569*g.
4*(g + 178)**2
Let n(l) be the third derivative of l**6/180 - l**4/12 + 2*l**3/9 + 205*l**2 + l. Factor n(r).
2*(r - 1)**2*(r + 2)/3
Let v = -1145/7 + 164. Let n be (1 + -3 - (-58 + 60))*(-3)/4. Determine u so that 0 - 6/7*u**n - v*u**2 + 15/7*u**4 + 0*u + 18/7*u**5 = 0.
-1, -1/3, 0, 1/2
Find q such that -3*q**3 - 7/2*q**2 - 1/2*q + 0 = 0.
-1, -1/6, 0
Suppose -v + 3 = v + f, 0 = 5*f + 25. Let i = -11 + 15. Suppose -v*k - 2*k**2 + k + 0*k - i*k**2 - 3*k**3 = 0. What is k?
-1, 0
Let 35/4*m**2 - 25/2*m + 6 + 1/4*m**4 - 5/2*m**3 = 0. What is m?
1, 2, 3, 4
Suppose m = -5*m + 18. Factor 2*a + 6*a + m*a**3 + a - 27 + 15*a**2.
3*(a - 1)*(a + 3)**2
Let v be (-2)/(-7) - (4 + 160/(-28)). Factor 11*k + 3 + 4*k - k**v - 17*k.
-(k - 1)*(k + 3)
Let j(y) = 3*y - 4. Let h be j(3). Let n be (-29)/(-87) + (-5)/(-3). Factor -h*u - u**n + 9 + 0*u**2 - 2*u**2 - u.
-3*(u - 1)*(u + 3)
Let g(m) be the first derivative of -2/7*m**4 + 0*m**3 + 16 + 0*m - 1/21*m**6 - 8/35*m**5 + 0*m**2. Factor g(t).
-2*t**3*(t + 2)**2/7
Factor 100 - 10*g + 1/4*g**2.
(g - 20)**2/4
Let h = -218/7 + 443/14. Let o(k) be the first derivative of -2*k + 2/3*k**3 + 2 - h*k**2 + 1/4*k**4. Find c such that o(c) = 0.
-2, -1, 1
Let t(w) be the first derivative of w**6/2 - 6*w**5/5 + 2*w**3 - 3*w**2/2 + 381. Factor t(n).
3*n*(n - 1)**3*(n + 1)
Let u(o) be the first derivative of -o**4/8 - o**3/2 + o**2/4 + 3*o/2 + 42. Solve u(v) = 0 for v.
-3, -1, 1
Let v be -16 - 294/56*-4. Determine n, given that 0 - n**2 + n**v - 5/2*n**3 - 1/2*n**4 + 0*n = 0.
-1, -1/2, 0, 2
Let j be (-5)/(((-2)/4)/((-2)/(-2))). Factor 3 + 16*m + 35*m - 11 - j - 15*m**2.
-3*(m - 3)*(5*m - 2)
Let o(w) = 91*w**3 - 289*w**2 + 321*w - 49. Let k(i) = 18*i**3 - 58*i**2 + 64*i - 10. Let n(q) = -11*k(q) + 2*o(q). Factor n(y).
-2*(y - 2)*(2*y - 3)*(4*y - 1)
Let w(o) be the third derivative of o**6/1800 + o**5/600 + o**3/3 - 39*o**2. Let s(a) be the f