 - 2)/2
Suppose -11 + 6 = -p. Let v be (0 + p + -2)*1. Factor -102*h**5 - 41*h**3 + 99*h**5 - 7*h**v + 24*h**4.
-3*h**3*(h - 4)**2
Let f(n) be the third derivative of -n**5/330 - 5*n**4/12 - 18*n**3/11 + 1189*n**2. Factor f(w).
-2*(w + 1)*(w + 54)/11
Let x = 214 + 83. Find o such that -301*o**2 + x*o**2 - 17*o - 31*o = 0.
-12, 0
Let g(c) be the second derivative of -c**4/3 - 868*c**3/3 - 94178*c**2 + 1785*c. Suppose g(y) = 0. Calculate y.
-217
Let c(h) = 5*h**2 - 93*h - 3. Let b(p) = 16*p**2 - 286*p - 10. Let x(v) = -6*b(v) + 20*c(v). Suppose x(j) = 0. What is j?
0, 36
Find p such that 4 + 2*p**3 + 10*p**2 - 2/3*p**4 + 34/3*p = 0.
-1, 6
Let y(s) be the first derivative of -s**5/35 - s**4/7 + 29*s**3/21 - 12*s**2/7 - 6224. Factor y(z).
-z*(z - 3)*(z - 1)*(z + 8)/7
Let o(w) be the first derivative of 5/2*w**2 - 5/4*w**4 + 0*w + 0*w**3 + 11. Factor o(g).
-5*g*(g - 1)*(g + 1)
Let z(d) be the second derivative of 1/12*d**4 - 81 - 1/30*d**6 + 1/4*d**3 - 1/10*d**5 + 1/84*d**7 + 2*d + 0*d**2. Factor z(m).
m*(m - 3)*(m - 1)*(m + 1)**2/2
Find o, given that 120/17*o**4 - 60/17 - 60/17*o**2 - 194/17*o + 208/17*o**3 - 14/17*o**5 = 0.
-1, -3/7, 1, 10
Let x(t) be the third derivative of -t**8/168 - 943*t**7/105 - 110447*t**6/30 + 66835*t**5/3 - 670241*t**4/12 + 223729*t**3/3 + 80*t**2 + 1. Factor x(p).
-2*(p - 1)**3*(p + 473)**2
Let m be (38/15295)/((-3)/5). Let r = m + 1612/483. Suppose -2/3*n**2 - 2*n**5 + 2/3*n**4 + 0 - 4/3*n + r*n**3 = 0. Calculate n.
-1, -2/3, 0, 1
Let k(h) be the second derivative of -h**6/12 + 23*h**5/60 - 2*h**4/3 + h**3/2 - 87*h**2/2 + 8*h + 3. Let u(o) be the first derivative of k(o). Factor u(p).
-(p - 1)**2*(10*p - 3)
Let n(o) be the first derivative of 5*o**4/4 + 1120*o**3/3 + 1115*o**2/2 + 4914. Factor n(a).
5*a*(a + 1)*(a + 223)
Let v(t) = 9 - 9 - t. Let k(c) = 0*c**2 + 14*c**2 - 19*c**2 - 4*c + 4*c**2. Let h(u) = -5*k(u) + 35*v(u). Factor h(m).
5*m*(m - 3)
Factor 0 - 201/2*s**2 + 0*s + 3/4*s**3.
3*s**2*(s - 134)/4
Let q(g) be the third derivative of g**9/1890 - g**8/1260 - 13*g**7/840 - g**6/20 + 73*g**5/60 - 15*g**2. Let h(z) be the third derivative of q(z). Factor h(s).
2*(s - 2)*(4*s + 3)**2
Suppose 0 = 19*m + 483 - 616. Let x(l) be the second derivative of 5/3*l**6 - 3*l**5 + 0*l**2 - 5/14*l**m + 0 + 5/2*l**4 - 5/6*l**3 - 15*l. Factor x(v).
-5*v*(v - 1)**3*(3*v - 1)
Determine m, given that 1/5*m**4 - 9*m + 9/5*m**3 + 28/5 + 7/5*m**2 = 0.
-7, -4, 1
Let m = -64/39 + 218/117. Let y(c) be the first derivative of 0*c - 1/3*c**4 + 2/3*c**2 - 2/15*c**5 - 16 + m*c**3. Let y(q) = 0. Calculate q.
-2, -1, 0, 1
Let n be -3 - (-24)/9 - ((-333)/27 - (-16 + 4)). Factor -2/3*h**4 + n - 7/6*h + 31/6*h**3 - 10/3*h**2.
-h*(h - 7)*(h - 1)*(4*h + 1)/6
Let x(p) = -12*p**4 - 176*p**3 - 1832*p**2 - 5724*p - 5824. Let b(l) = -8*l**4 - 177*l**3 - 1833*l**2 - 5724*l - 5826. Let d(v) = -4*b(v) + 3*x(v). Factor d(g).
-4*(g - 54)*(g + 3)**3
Find c such that -74*c**4 - 94/5 + 284/5*c - 292/5*c**3 + 464/5*c**2 + 8/5*c**5 = 0.
-1, 1/4, 1, 47
Let a = -181950 - -545852/3. Let l(j) = j + 1. Let m be l(1). Factor 0 + 10/3*z + a*z**m.
2*z*(z + 5)/3
Let a(k) = 7*k**4 + 710*k**3 + 2772*k**2 + 3451*k + 1376. Let z(r) = -r**4 - 2*r**3 - r. Let l(b) = a(b) + 3*z(b). Factor l(y).
4*(y + 1)**2*(y + 2)*(y + 172)
Suppose 444*h - 16744 = -200*h. Find p, given that -27*p + 3/2*p**4 - 3/2*p**2 + 23/4*p**3 - h = 0.
-2, 13/6
Factor 6/5*r**2 - 4/5*r - 2/5*r**3 + 0.
-2*r*(r - 2)*(r - 1)/5
Find f, given that -840/11 - 2/11*f**3 - 218/11*f**2 - 848/11*f = 0.
-105, -2
Let m(o) = -o**3 - 32*o**2 - 34*o - 76. Let v be m(-31). Let k be (-2)/7*(10 - v). Solve 1/2*f - 1/8*f**5 + 1/2*f**4 - 1/8*f**3 + 1 - 5/4*f**k = 0.
-1, 2
Let t(c) = 93*c**2 + 162*c + 174. Let g(y) = -19*y**2 - 2. Let d(j) = 5*g(j) + t(j). What is a in d(a) = 0?
-1, 82
Factor 28/3*m**2 + 2*m**3 + 0 - 10/3*m.
2*m*(m + 5)*(3*m - 1)/3
Let 14/5*y**3 - 1/5*y**4 - 28/5*y**2 - 24*y + 0 = 0. Calculate y.
-2, 0, 6, 10
Let p(c) be the third derivative of -c**6/450 - 7*c**5/300 + c**4/15 - 43*c**3 - c**2 - 3. Let g(v) be the first derivative of p(v). Find r such that g(r) = 0.
-4, 1/2
Suppose -r + 3*r = 4*r. Suppose r = 7*o - 26 + 12. Factor -2*x**o + 13*x - 21*x + 4*x**2.
2*x*(x - 4)
Let j be (-145 - -143)/((6 - 3) + -4). Factor -1/11*f**4 + 8/11*f**3 - 5/11 + 16/11*f - 18/11*f**j.
-(f - 5)*(f - 1)**3/11
Solve -808*s + 385*s**2 + 530*s**2 - 3*s**3 - 2*s**3 + 2658*s = 0 for s.
-2, 0, 185
Let k = -11849/216 + 10200439/185112. Let a = k - -2/857. Solve 1/2*s - 1/4*s**2 - a = 0.
1
Factor 0*m**3 - 32*m**2 - 3*m - 28*m + 77*m - 18*m + 4*m**3.
4*m*(m - 7)*(m - 1)
Let r be (20/(-21))/((-17870)/58971). Factor -2/7*j**2 - 60/7 + r*j.
-2*(j - 6)*(j - 5)/7
Let q be ((-252)/(-400) - 270/(-2250))*(5 + -1). Determine a so that -2 + 12769/4*a**q + 227*a - 12995/2*a**2 = 0.
2/113, 2
Suppose a + a - 6 = 0. Let x(n) = -2*n**3 + 8*n**2 + 68*n - 32. Let i be x(8). Factor 1/6*l**2 + 2/3*l**a + 0*l + i.
l**2*(4*l + 1)/6
Let u(v) = 3*v**3 + 2*v**2 + v + 1. Let i(x) = 68*x**3 - 76*x**2 - 260*x - 36. Let p(f) = i(f) - 28*u(f). Let p(d) = 0. Calculate d.
-4, -1/4
Let r(s) be the second derivative of -7 + 1/30*s**5 + 0*s**6 + 0*s**3 - 8*s - 1/189*s**7 + 1/27*s**4 + 0*s**2. Find v, given that r(v) = 0.
-1, 0, 2
Let k(l) = 24*l**3 - 435*l**2 - 15*l + 480. Let f(h) = 11*h**3 - 220*h**2 - 7*h + 240. Let d(q) = 9*f(q) - 4*k(q). Determine y so that d(y) = 0.
-1, 1, 80
Solve -166/11*z**4 + 26*z**2 + 232/11*z - 10/11*z**5 - 222/11*z**3 - 120/11 = 0 for z.
-15, -2, -1, 2/5, 1
Suppose -22*g = -10*g + 48. Let y be g/18 + 172/(-36) + 5. Solve 1/2*r**2 + 1/4*r**3 - 1/2*r**4 + y*r + 0 - 1/4*r**5 = 0 for r.
-2, -1, 0, 1
Suppose 5*q + 4*j - 12 = 0, j + 5 = 3. Let k be 2 + (1 + 2 - 12/q). What is f in 16/3*f**3 + 8/3*f**k - 16/3*f + 4/3*f**4 - 4 = 0?
-3, -1, 1
Let f(v) be the second derivative of -v**5/110 - 8*v**4/33 + 37*v**3/11 + 126*v**2/11 + 312*v + 5. What is r in f(r) = 0?
-21, -1, 6
Let s(v) be the first derivative of -v**6/15 + 4*v**5/5 - 5*v**4/2 + 1977. Factor s(t).
-2*t**3*(t - 5)**2/5
Let w**4 + 5*w**3 + 5*w**3 + 0*w**4 + 83*w - 54*w + 28*w**2 - 5*w = 0. What is w?
-6, -2, 0
Let v(t) be the third derivative of -1/84*t**8 + 1/15*t**6 - 1/6*t**4 + 2/105*t**7 + 0*t - 2/15*t**5 + 21 + 2*t**2 + 2/3*t**3. Suppose v(s) = 0. What is s?
-1, 1
Let q(v) be the first derivative of -50/9*v + 24 - 4/9*v**4 - 2/45*v**5 - 4/9*v**3 + 40/9*v**2. Factor q(n).
-2*(n - 1)**2*(n + 5)**2/9
Factor -12/7*s**2 + 2/7*s**4 + 2/7*s**3 + 0*s + 0.
2*s**2*(s - 2)*(s + 3)/7
Let c(h) be the third derivative of h**7/525 - 3*h**5/25 - 8*h**4/15 - h**3 - 8*h**2 - h. Factor c(z).
2*(z - 5)*(z + 1)**2*(z + 3)/5
Determine m, given that -85/3*m - 2*m**2 + 1/3*m**3 - 26 = 0.
-6, -1, 13
Let l(j) be the third derivative of -4/15*j**6 - 2/105*j**7 - 129*j**2 + 0 + 4/3*j**4 - j**5 + 32/3*j**3 + 0*j. Solve l(r) = 0 for r.
-4, -1, 1
Let p(t) be the second derivative of -2*t**7/21 - 16*t**6/15 - 22*t**5/5 - 8*t**4 - 6*t**3 + 4*t - 186. Let p(x) = 0. Calculate x.
-3, -1, 0
Let -6*k + 6*k + 708*k**2 + 35*k**3 - 693*k**2 + 10*k**4 = 0. What is k?
-3, -1/2, 0
Let m be -2 - ((-171)/76 - 0). Let t be 0*(-2)/(8/(-4)). Suppose 0*g**3 + g**2 + 0 + t*g - m*g**4 = 0. What is g?
-2, 0, 2
Let z(b) be the first derivative of 2*b**5 - 175*b**4/4 + 935*b**3/3 - 1085*b**2/2 - 2205*b - 2248. Factor z(u).
5*(u - 7)**2*(u + 1)*(2*u - 9)
Let y be (7/((-21)/(-12)))/(-1 - 1). Let d(n) = -6*n - 8. Let k be d(y). Suppose -2*q - 2*q**5 - 2*q**4 - 3 - 30*q**2 + 34*q**2 + k*q**3 + 1 = 0. Calculate q.
-1, 1
Let i(w) = -w**3 - 6*w**2 + 11*w - 21. Let m be i(-8). Let p(t) be the first derivative of -2/15*t**3 - m + 1/30*t**4 + 0*t + 2/15*t**2. Factor p(b).
2*b*(b - 2)*(b - 1)/15
Suppose 19194 + 15401 = -55*g. Let i = g - -631. Suppose -12/5*u + 0 - 6/5*u**i + 6/5*u**3 = 0. Calculate u.
-1, 0, 2
Suppose -99*b - 1728 = -103*b. Factor -38*o**2 + 3158*o - 72 - 3398*o - 2*o**3 - b.
-2*(o + 6)**2*(o + 7)
Let 1472*d**3 + 0*d + 8464/3*d**2 + 31*d**4 + 0 + 1/6*d**5 = 0. Calculate d.
-92, -2, 0
Let u(f) be the third derivative of 0*f - 1/180*f**6 - 1/315*f**7 + 1/90*f**5 + 6*f**2 + 0 + 0*f**4 + 1/504*f**8 + 0*f**3. Factor u(s).
2*s**2*(s - 1)**2*(s + 1)/3
Let b be (-43 + (-137480)/(-3192))/(6/19). What is g in 130/3*g**3 - 338/9*g**2 - 6*g