 - 1/3*a**3 + 1/3*a**2 + d.
-a*(a - 1)*(a + 1)**2/3
Let i = 1634739/5 - 326927. Factor 256/5*z - i + 2*z**2.
2*(z + 26)*(5*z - 2)/5
Determine i so that -4140/7*i - 8/7*i**4 - 1058/7 - 3866/7*i**2 + 360/7*i**3 = 0.
-1/2, 23
Let a(g) be the second derivative of -g**5/130 - 233*g**4/39 - 4074*g. Find n, given that a(n) = 0.
-466, 0
Let y(m) be the third derivative of m**7/280 + m**6/360 - m**5/10 - m**4/6 + 14*m**3/3 - 100*m**2. Let l(z) be the first derivative of y(z). Factor l(n).
(n - 2)*(n + 2)*(3*n + 1)
Suppose 17 = 1185*k - 1184*k. Solve 3*m**2 - 7*m + 3*m**2 + k*m - 12*m**4 + 12*m**2 + 10*m**4 + 6*m**3 = 0 for m.
-1, 0, 5
Factor -360/7 - 50/7*l**2 - 13/7*l**3 + 1/7*l**4 + 324/7*l.
(l - 15)*(l - 2)**2*(l + 6)/7
Let g(h) be the third derivative of -h**6/900 + 2*h**5/75 - 7*h**4/60 - 98*h**3/45 + 13*h**2 + 24*h. Factor g(x).
-2*(x - 7)**2*(x + 2)/15
Let u(s) be the third derivative of -7*s**6/40 - 2421*s**5/10 - 209157*s**4/2 + 119716*s**3 + 4*s**2 - 1. Factor u(y).
-3*(y + 346)**2*(7*y - 2)
Suppose -5*r + 5 = 0, r + 16 - 1 = 4*v. Let x(n) be the second derivative of 4*n + 0 - 1/24*n**v - n**2 - 5/12*n**3. Determine y so that x(y) = 0.
-4, -1
Let j be (-20 + -1)/(18/(-48)). Suppose 2 = -4*y - 2*h + j, -5*y + 3*h + 51 = 0. Solve -64 + 35*o**4 - y*o - 31*o**4 + 32*o**3 - 20*o + 60*o**2 = 0.
-4, -1, 1
Let o(f) be the third derivative of 49/75*f**5 + 0 - 1/30*f**6 - 10/3*f**3 - 23/6*f**4 - 65*f**2 + 0*f. Factor o(t).
-4*(t - 5)**2*(5*t + 1)/5
Let l(q) be the first derivative of -2*q**3/3 + 1254*q**2 + 634. Find k, given that l(k) = 0.
0, 1254
Factor 75/2*r**2 - 5/4*r**3 - 285/4*r + 35.
-5*(r - 28)*(r - 1)**2/4
Factor -490000 - 456*q**3 - 41498*q - 172826*q - 7254*q**2 - 4*q**4 + 54724*q - 8542*q**2.
-4*(q + 7)**2*(q + 50)**2
Let m(j) = 6*j**2 + j - 5. Let b(n) = -154*n**2 - 1096*n + 514. Let z(c) = -2*b(c) - 28*m(c). Factor z(i).
4*(5*i - 2)*(7*i + 111)
Suppose 175*l + 2018 = 177*l. Let t = -1007 + l. Factor 2/5*g - 2/5*g**3 + 0 + 2/5*g**4 - 2/5*g**t.
2*g*(g - 1)**2*(g + 1)/5
Let z(o) be the first derivative of 37/10*o**2 + 36/5*o - 22 + 1/15*o**3. Factor z(p).
(p + 1)*(p + 36)/5
Factor 100*g + 13/2*g**3 + 185/4*g**2 + 0 + 1/4*g**4.
g*(g + 5)**2*(g + 16)/4
Let d(s) be the second derivative of -3*s**5/20 - 51*s**4/4 - 279*s**3/2 + 31713*s**2/2 + 1591*s. Factor d(y).
-3*(y - 11)*(y + 31)**2
Let x(n) be the first derivative of -31 - 30*n - 14*n**2 + 2/3*n**3. Determine g so that x(g) = 0.
-1, 15
Let v(w) be the first derivative of w**4/20 + 36*w**3/5 + 1944*w**2/5 - 78*w - 42. Let g(d) be the first derivative of v(d). Factor g(x).
3*(x + 36)**2/5
Let t = 272276/105847 - 14/15121. Let -t*s + 3/7*s**2 + 24/7 = 0. Calculate s.
2, 4
Factor -2804/5*z - 1965604/5 - 1/5*z**2.
-(z + 1402)**2/5
Suppose -s + r + 4 = 0, 7680*s + 2*r = 7683*s - 11. Let -6*v**2 + 0 + 1/4*v**s + 36*v = 0. Calculate v.
0, 12
Let x(g) be the first derivative of g**6/3 - g**5/5 - 9*g**4/2 + 16*g**3/3 + 8*g**2 - 15*g - 1195. Find z such that x(z) = 0.
-3, -1, 1, 5/2
Let v(x) be the first derivative of x**3/12 + 95*x**2 + 36100*x + 709. Solve v(g) = 0 for g.
-380
Suppose 40/9 + 1/9*j**4 - 41/9*j**2 - 2/3*j**3 + 2/3*j = 0. Calculate j.
-4, -1, 1, 10
Let j(d) be the first derivative of d**5 + 2*d**4/3 - 88*d**2 + 102. Let r(n) be the second derivative of j(n). Factor r(i).
4*i*(15*i + 4)
Let p(s) be the third derivative of s**8/5040 + s**7/2520 + 73*s**3/6 - 65*s**2. Let v(h) be the first derivative of p(h). Suppose v(j) = 0. What is j?
-1, 0
Factor 0 + 1/5*o**3 - 2*o**2 - 144/5*o.
o*(o - 18)*(o + 8)/5
Suppose -111*g + 615 - 1023780*g**2 + 1023785*g**2 + 731*g = 0. Calculate g.
-123, -1
Let x be (-109750)/375*(-34)/4. Let u = x + -2487. Determine i so that 82/3*i**3 - 32/3*i - 50/3*i**5 + u*i**2 + 8/3 - 10/3*i**4 = 0.
-1, 2/5, 1
Let g = 4277/25734 + 2/4289. Let z(x) be the third derivative of 0*x**3 + 12*x**2 + 0*x**5 + 0*x + 2/21*x**7 + 0 - 5/336*x**8 - g*x**6 + 0*x**4. Factor z(t).
-5*t**3*(t - 2)**2
Let i(d) = -20*d**2 - 274*d - 1272. Let c(g) = 235*g**2 + 3290*g + 15265. Let p(w) = 3*c(w) + 35*i(w). Factor p(z).
5*(z + 5)*(z + 51)
Let v(a) be the first derivative of -a**6/1440 + a**5/480 - 2*a**3/3 - 3*a**2 + 49. Let x(l) be the third derivative of v(l). Solve x(y) = 0.
0, 1
Let l = 239521/30 - 7984. Let s(z) be the third derivative of 1/240*z**6 + l*z**5 + 0*z + 0 - 32*z**2 + 5/48*z**4 + 1/6*z**3. Determine p so that s(p) = 0.
-2, -1
Let y(t) be the third derivative of 2*t**2 + 1/50*t**5 - 7/60*t**4 + 4/15*t**3 - 37 + 0*t. Factor y(r).
2*(r - 1)*(3*r - 4)/5
Let h be ((-2)/(-10) - 0)/((-433)/(-6495)). Find y, given that 0*y + 1/5*y**4 + 1/5*y**h + 0 + 0*y**2 = 0.
-1, 0
Let l(h) be the second derivative of h**6/30 + 3*h**5/80 - h**4/48 - 1225*h. Factor l(c).
c**2*(c + 1)*(4*c - 1)/4
Find l, given that -44/3*l**2 - 16/3*l**4 + 0 + 14*l**3 + 16/3*l + 2/3*l**5 = 0.
0, 1, 2, 4
Factor 17/4*w**3 - 5/2*w**2 + 0*w + 0 - 2*w**4 + 1/4*w**5.
w**2*(w - 5)*(w - 2)*(w - 1)/4
Solve 2758*t**3 - 13718*t + 2*t**5 - 231*t**4 - 706*t**3 + 343*t**4 + 11552*t**2 = 0 for t.
-19, 0, 1
Determine z, given that 2*z**3 + 6*z**2 + 7*z**2 - 1093*z + 3*z**2 - 4*z**3 + 1223*z = 0.
-5, 0, 13
Let l(r) be the second derivative of -r**5/4 - 7895*r**4/4 - 12466205*r**3/2 - 19684137695*r**2/2 + 27*r + 77. Factor l(v).
-5*(v + 1579)**3
Let k be ((-12)/32)/(12/(-784)) + -24. Factor 0 + k*t**2 - 7*t.
t*(t - 14)/2
Suppose 5*m**4 - 82*m**2 - 415*m + 15*m**3 - 60*m**2 - 178 - 181 + 149 - 53*m**2 = 0. Calculate m.
-7, -1, 6
Let f = -358103/8 - -44763. What is m in -1/2*m**3 + 0*m - f*m**4 + 0 + 1/8*m**5 + 1/2*m**2 = 0?
-2, 0, 1, 2
Let h be (-66)/(-280) + (-994)/27832. Factor 1/5*p + 4/5*p**2 - h*p**3 - 4/5.
-(p - 4)*(p - 1)*(p + 1)/5
Suppose -7 = 8*v - 31. Suppose v*i + 2*i - 250 = 0. Factor 115*o**3 - i*o**2 + 177 + 25*o**4 - 177.
5*o**2*(o + 5)*(5*o - 2)
Let m(c) be the first derivative of -c**9/756 + c**7/105 - c**5/30 - 68*c**3/3 + 36. Let f(o) be the third derivative of m(o). Factor f(z).
-4*z*(z - 1)**2*(z + 1)**2
Let 40/3*s**2 - 1/6*s**3 + 0 - 26*s = 0. Calculate s.
0, 2, 78
Find g, given that -4622*g**4 + 24*g**2 - 10*g**3 - 5*g**5 + 3*g**5 + 4610*g**4 = 0.
-4, -3, 0, 1
Let n(x) be the first derivative of -x**2 + 24*x - 2/3*x**3 - 270. Factor n(z).
-2*(z - 3)*(z + 4)
Let j(g) = -2*g**2 - 26*g + 4. Let w be j(-13). Factor -12*b**3 - 172*b - 40*b**3 - 204*b**2 + 2*b**w - 48 + 8 - 11*b**4 + 29*b**4.
4*(b - 5)*(b + 1)**2*(5*b + 2)
Let q(v) = -v**2 - v + 122. Let m be q(0). Let j = 245/2 - m. Suppose 7/6*y**5 + 1/3 + 2*y**4 - 2/3*y**3 - j*y - 7/3*y**2 = 0. Calculate y.
-1, 2/7, 1
Let i(m) be the first derivative of m**6/120 - 7*m**5/40 - m**4 - 27*m**3 + 105. Let w(p) be the third derivative of i(p). Factor w(v).
3*(v - 8)*(v + 1)
Let o be (0 - -5)/((-6)/12). Let p be (4/o)/((-261)/(-45) + -7). Factor -p*a**2 - 1/6*a**3 + 0 - 1/6*a.
-a*(a + 1)**2/6
Let g = -290790 + 290799. Let g + 3/4*a**3 - 9/4*a**2 - 3*a = 0. Calculate a.
-2, 2, 3
Let d(t) be the third derivative of 2*t**7/105 - 12*t**6/5 - 153*t**5/5 - 117*t**4 + 4*t**2 - 10*t - 102. Determine v so that d(v) = 0.
-3, 0, 78
Suppose -20 = -22*t + 12*t. Let g be ((-6)/4)/((-1)/178). Find v, given that -t*v**2 - g + 267 = 0.
0
Let s(a) be the first derivative of -a**6/600 + a**5/150 + a**4/15 + 33*a**2/2 + 78. Let d(x) be the second derivative of s(x). Determine m so that d(m) = 0.
-2, 0, 4
Let k(p) be the second derivative of -p**5/110 + 444*p**4/11 - 788544*p**3/11 + 700227072*p**2/11 + 369*p - 3. Factor k(g).
-2*(g - 888)**3/11
Let z(d) = 43*d**3 + 52*d**2 + 235*d + 298. Let s(f) = -10*f**3 - f**2 - f - 1. Let g(y) = -4*s(y) - z(y). Factor g(h).
-3*(h + 2)*(h + 7)**2
Let h(u) be the first derivative of -50 - 44/3*u**3 + 0*u**2 + 1/2*u**4 + 0*u. Factor h(d).
2*d**2*(d - 22)
Let d(n) be the first derivative of 0*n**2 - 3/2*n**4 - 3/5*n**5 + 0*n - n**3 + 34. Suppose d(q) = 0. Calculate q.
-1, 0
Let r = 10318036 - 26362581489/2555. Let n = r + 4/511. Let -n*b**2 + 1/5*b**3 + 0 + 0*b = 0. What is b?
0, 1
Factor -2*d**3 - 1/2*d**4 - 8 + 1/4*d**5 + 4*d**2 + 4*d.
(d - 2)**3*(d + 2)**2/4
Let k = -1285641/5 + 257133. Factor k*f + 37/5*f**2 + 21/5*f**3 + 4/5*f**4 + 4/5.
(f + 1)*(f + 2)**2*(4*f + 1)/5
Suppose 0 = 3*s + 4*w + 50, s - 5*w = -2*s - 86. Let i(o) = 3*o**2 + 69*o + 70