78615*o**4 - 342 + 67908*o**4 - 595254*o**3 + 3966*o = 0. What is o?
-1/221, 1, 3
Let s(l) be the first derivative of l**5/15 - 25*l**4/3 + 1250*l**3/3 - 11*l**2/2 - 3*l - 1. Let o(p) be the second derivative of s(p). Factor o(u).
4*(u - 25)**2
Suppose 9*o = 19*o - 30. Factor 2*f + f - 2*f**2 + 2*f + 6*f + o*f.
-2*f*(f - 7)
Suppose 2*w + 46 = -l + 41, -l = -3*w - 15. Let z(k) be the third derivative of -7/240*k**5 + 0 - 1/480*k**6 - 5/32*k**4 + 0*k - 3/8*k**3 - l*k**2. Factor z(m).
-(m + 1)*(m + 3)**2/4
Let g(i) = 8*i - 19. Let y be g(-4). Let o = -47 - y. Factor 3*w**2 + 25*w**3 + 5*w**2 + 2*w**o - 17*w**3.
2*w**2*(w + 2)**2
Let n(i) be the first derivative of 8/3*i**5 - 2/3*i**6 + 31 + 0*i**2 + 0*i - 11/3*i**4 + 16/9*i**3. Factor n(q).
-4*q**2*(q - 1)**2*(3*q - 4)/3
Let v(j) be the second derivative of -1 - 8/3*j**6 + 0*j**2 + 51/10*j**5 + 0*j**3 + 1/3*j**7 + 3*j**4 - 39*j. Factor v(d).
2*d**2*(d - 3)**2*(7*d + 2)
Let h(w) = 3*w**2 - 74*w - 1093. Let c(g) = 1 + 0*g + 3*g - g**2 - 3*g + 2*g. Let r(t) = -4*c(t) - h(t). Factor r(p).
(p + 33)**2
Let h = -22772 + 22800. Let a(g) be the second derivative of 0*g**2 + 0*g**3 - h*g + 0 - 1/8*g**4. Find p, given that a(p) = 0.
0
Let z(v) be the second derivative of v**4/60 + 11*v**3/15 + 4*v**2 - 3238*v. Suppose z(n) = 0. What is n?
-20, -2
Factor 1/5*q**4 + 0 + 456/5*q - 682/5*q**2 + 45*q**3.
q*(q - 2)*(q - 1)*(q + 228)/5
Let u(n) be the third derivative of n**5/12 - 40*n**4/3 - 680*n**3/3 - 11*n**2 + 2*n - 3. Determine v, given that u(v) = 0.
-4, 68
Suppose 78/5*k**3 + 8/3*k**4 + 544/15*k + 548/15*k**2 + 64/5 + 2/15*k**5 = 0. What is k?
-12, -4, -2, -1
Let z(f) be the first derivative of f**4/7 + 1532*f**3/21 - 2*f**2/7 - 1532*f/7 + 974. Determine m, given that z(m) = 0.
-383, -1, 1
Let r(w) be the third derivative of -w**5/240 + 121*w**4/96 - 5*w**3 + w**2 + 121*w. Factor r(o).
-(o - 120)*(o - 1)/4
Let y(v) be the first derivative of -3*v**4/28 + 84*v**3 - 3519*v**2/14 + 1758*v/7 - 1554. Factor y(a).
-3*(a - 586)*(a - 1)**2/7
Let n(d) = 9*d**2 + 21*d + 24. Let z(w) = 80*w**2 + 190*w + 215. Suppose 23 = c + 3*r, r = -27 + 23. Let a(o) = c*n(o) - 4*z(o). Factor a(h).
-5*(h + 1)*(h + 4)
Suppose 4*g - 9*g = 3*l - 2986, 0 = 5*l - 10. Let v = 596 - g. Factor -2/3*a**3 + v + 4/3*a + 2/3*a**2.
-2*a*(a - 2)*(a + 1)/3
Let d(q) be the third derivative of 25/132*q**4 + 1/110*q**6 - 43*q**2 - 2*q + 0*q**3 + 1/1848*q**8 + 4/33*q**5 - 8/1155*q**7 + 0. Factor d(y).
2*y*(y - 5)**2*(y + 1)**2/11
Let o(l) be the third derivative of 0*l - 11 - 25/2*l**3 + 13/4*l**4 - 1/20*l**5 - 15*l**2. Suppose o(y) = 0. Calculate y.
1, 25
Let i(y) be the second derivative of y - 1/96*y**4 + 39 - 1/4*y**2 - 1/12*y**3. Factor i(o).
-(o + 2)**2/8
Let s(y) be the second derivative of y**5/2 - 59*y**4/6 + 43*y**3/3 + 11*y**2 + 324*y + 2. Factor s(x).
2*(x - 11)*(x - 1)*(5*x + 1)
Determine s, given that 18/5*s**2 - 84/5*s - 24 + 3/5*s**4 + 21/5*s**3 = 0.
-5, -2, 2
Let v(i) be the first derivative of i**6/360 + i**5/90 - 5*i**4/72 - i**3/3 - 43*i**2/2 + i + 248. Let x(z) be the second derivative of v(z). Solve x(d) = 0.
-3, -1, 2
Let x(v) be the second derivative of 8/3*v**3 - 32/3*v**4 - 1/4*v**2 + 178*v + 0. Suppose x(s) = 0. What is s?
1/16
Let a(r) be the second derivative of 10/7*r**3 - 1/42*r**4 + 2*r - 29/7*r**2 + 2. Factor a(i).
-2*(i - 29)*(i - 1)/7
Let y(v) = 22449*v - 67345. Let r be y(3). Find o such that 0 - 2/9*o**4 + 0*o + 8/9*o**3 + 10/9*o**r = 0.
-1, 0, 5
Let q(h) be the first derivative of 1/20*h**4 - 8/5*h**2 + 12/5*h + 1/5*h**3 - 283. Factor q(m).
(m - 2)*(m - 1)*(m + 6)/5
Let q(f) = 3*f**2 - 105*f - 252. Let p(y) = -2*y**2 + 53*y + 127. Let u(n) = 9*p(n) + 5*q(n). Factor u(v).
-3*(v + 3)*(v + 13)
Let 2/3 + 2092/3*l + 2090/3*l**2 = 0. Calculate l.
-1, -1/1045
Let v = -11819 - -11822. Factor -2/3*y**v + 10/3*y - 4/3*y**2 + 4.
-2*(y - 2)*(y + 1)*(y + 3)/3
Solve 0 + 14336/11*f + 142/11*f**3 + 2/11*f**4 + 2944/11*f**2 = 0 for f.
-32, -7, 0
Let p(u) = -1 - 7*u**3 + 22*u**3 + 30*u**2 - 8*u + 9. Let k be (0 + 5 - 7)*4. Let v(z) = 5*z**3 + 10*z**2 - 3*z + 3. Let o(i) = k*v(i) + 3*p(i). Factor o(n).
5*n**2*(n + 2)
Let q(w) be the second derivative of 49*w**5/5 + 273*w**4 + 2880*w**3 + 13824*w**2 + 9018*w. Factor q(z).
4*(z + 3)*(7*z + 48)**2
Determine g so that -894*g**2 - 132*g - 14*g**4 - 4147 + 4355 - 320*g + 64*g**3 - 312*g**3 = 0.
-13, -4, -1, 2/7
Determine t so that 750*t**2 - 164*t**3 + 64*t**3 + 48*t**3 + 306*t**2 + 48*t**3 = 0.
0, 264
Suppose 0 = -9*f + 4*f + 14*f. Let j(x) be the third derivative of 0 + 22*x**2 + 1/60*x**6 + 0*x**5 + 16/3*x**3 + f*x - x**4. Solve j(n) = 0 for n.
-4, 2
Let u be (-4 - 52/(-16))*(5 - 470/78). Find k, given that 56/13*k + 24/13 - u*k**2 = 0.
-2/5, 6
Let y = 277120 - 831332/3. Let w**2 + 1/3*w**3 - 8*w + y = 0. Calculate w.
-7, 2
Let n(f) be the second derivative of -f**5/150 + f**4/60 + 2*f**3/5 + 9*f**2/2 - f + 8. Let z(y) be the first derivative of n(y). Let z(v) = 0. Calculate v.
-2, 3
Let t be (129/216 + 2/(-9))*(-812)/(-29). Let -6 + 3/2*g**5 + t*g + 3*g**4 - 12*g**3 + 3*g**2 = 0. Calculate g.
-4, -1, 1
Suppose 9 + 4 - 3 - 7 - 5*j + j**2 - 9 = 0. Calculate j.
-1, 6
Let r = -808 - -902. Find o, given that -20664*o**2 - 4*o**4 - 295856*o + r*o**3 - 275684 - 134*o**3 - 223*o**3 - 233*o**3 = 0.
-41, -1
Let q = -12744 - -12746. Let w(b) be the third derivative of 0*b + 0 + 1/10*b**5 + 4/3*b**3 + 20*b**q - 1/120*b**6 - 1/2*b**4. Factor w(p).
-(p - 2)**3
Let l(w) be the second derivative of w**5/40 + w**4/24 - 6*w**3 + 5649*w. Factor l(c).
c*(c - 8)*(c + 9)/2
Let v = -320 + 340. What is w in -9*w + 9 - 5*w**2 + v*w**3 + 2*w**3 - w**5 + w**4 - 5*w**2 - 12*w**3 = 0?
-3, -1, 1, 3
Suppose 0 = -5*u - 49 + 64. Suppose 0 = -4*z - 1 + 17. Factor 5*m + 8*m**2 - 12*m**3 + 19*m**u - 12*m**3 - 5*m**z - 10 + 7*m**2.
-5*(m - 1)**2*(m + 1)*(m + 2)
Let z be (-58)/(-140) - 38/266*-2. Factor 13/2*i - 9/5 - z*i**2.
-(i - 9)*(7*i - 2)/10
Suppose 5*l + 25 = 5*p, 17 = -2*p - 13*l + 6*l. Determine m so that 22/5*m**3 - 29/5*m + 7/5*m**5 + 24/5*m**p + 6/5 - 6*m**4 = 0.
-1, 2/7, 1, 3
Let w(i) be the third derivative of i**7/490 + 47*i**6/280 + 13*i**5/20 + 45*i**4/56 - 25*i**2 + 5. Suppose w(p) = 0. What is p?
-45, -1, 0
Let l be (6/40)/(13/(-4) + (-2983)/(-628)). Let f(k) be the first derivative of -l*k**5 - 1/4*k**2 + 0*k - 1/2*k**3 - 3/8*k**4 + 33. Factor f(y).
-y*(y + 1)**3/2
Let v(x) be the third derivative of 4/3*x**3 + x**2 - 1/4*x**4 - 1/30*x**5 - 24 + 0*x. Find s, given that v(s) = 0.
-4, 1
Let w(i) = i**3 + 249*i**2 - 489*i + 247. Let h(o) = 2*o**3 + 247*o**2 - 485*o + 246. Let t(n) = -4*h(n) + 5*w(n). Factor t(m).
-(m - 1)**2*(3*m - 251)
Factor -142/17*g**2 + 144/17*g + 0 - 4/17*g**3 + 2/17*g**4.
2*g*(g - 9)*(g - 1)*(g + 8)/17
Let o(s) be the first derivative of -s**8/5040 + s**7/280 - s**6/40 + 3*s**5/40 + 65*s**3/3 - 67. Let q(w) be the third derivative of o(w). Factor q(k).
-k*(k - 3)**3/3
Let l(x) be the first derivative of -3*x**5/20 - x**4/2 - 81*x + 28. Let w(h) be the first derivative of l(h). Solve w(g) = 0.
-2, 0
Let y(k) be the second derivative of -1/27*k**4 - 7*k + 1/90*k**5 + 0 + 8/135*k**6 + 0*k**3 + 5/189*k**7 + 0*k**2. Factor y(v).
2*v**2*(v + 1)**2*(5*v - 2)/9
Find n, given that 13/5*n**4 + 1/5*n**5 + 0*n + 0*n**2 - 14/5*n**3 + 0 = 0.
-14, 0, 1
Suppose 13*t = 17*t - 20, -3*t = -5*p - 5. What is m in -3*m**2 - 51 + 7*m + 111 - m**4 + p*m**4 - 54 - 3*m**3 = 0?
-1, 2, 3
Let a be ((-355)/(-142))/(36/16). Let t(n) be the first derivative of -a*n**3 + 5/3*n**2 + 14 + 0*n + 5/24*n**4. Find q, given that t(q) = 0.
0, 2
Let z = 24504/25 + -72962/75. Factor -2/3*v**2 + z - 20/3*v.
-2*(v - 1)*(v + 11)/3
Suppose -6*f = -23*f + 68. Suppose -2 = -d - f*t + 10, 0 = -d + 2*t - 6. Let d*a + 1/3*a**3 + 0 + 0*a**2 = 0. What is a?
0
Let n(d) be the first derivative of -d**4/34 + 104*d**3/51 + 53*d**2/17 - 1234. Factor n(t).
-2*t*(t - 53)*(t + 1)/17
Suppose -3*r - 5 = -2*p, -3*p + 31*r = 36*r - 36. Suppose 2*k - k = -4, 5*c = -3*k + 3. Factor -c*a**4 - 9*a - 9*a**3 - 6*a**2 + p*a + 2*a.
-3*a**2*(a + 1)*(a + 2)
Let a be (-8 + -3 - -10)*(1 + -3). Factor 596*p**2 - 600*p**a - 3 + 3 + 4*p**3.
4*p**2*(p - 1)
Let v be (-212)/(-290) + 78225/30450 + 15/(-6). Factor -1/5*o**2 + v - 3/5*o.
-(o - 1)*(o + 4)/5
Let 