et v = 276 - 4138/15. Let w(u) be the third derivative of 2/3*u**3 - u**2 + v*u**5 + 0 + 0*u - 3/4*u**4. Factor w(l).
2*(l - 2)*(4*l - 1)
Let d(r) be the second derivative of -r**5/5 + 4*r**4 - 40*r**3/3 + 149*r. Factor d(w).
-4*w*(w - 10)*(w - 2)
Let n = 317/1548 + 3/172. Factor 1/9*o**2 + 1/9 + n*o.
(o + 1)**2/9
Let w(t) be the second derivative of 1/96*t**4 + 5/2*t**2 + 5*t + 1/480*t**6 + 0 + 0*t**3 - 1/120*t**5. Let c(h) be the first derivative of w(h). Factor c(i).
i*(i - 1)**2/4
Let m(s) be the second derivative of 9*s**5/20 - 19*s**4/2 - 13*s**3/2 + 12*s - 1. Factor m(g).
3*g*(g - 13)*(3*g + 1)
Let n(o) be the third derivative of 1/100*o**6 + 1/12*o**4 + 0*o - 4*o**2 + 8/75*o**5 + 0 + 0*o**3. Factor n(m).
2*m*(m + 5)*(3*m + 1)/5
Let d(f) = f**2 - 4*f - 13. Let y(u) = u**2 - 5*u - 14. Let w(q) = -3*d(q) + 4*y(q). Let l be w(10). Solve 8/7*h**4 + 0*h + 18/7*h**l + 0 + 4/7*h**2 = 0 for h.
-2, -1/4, 0
Suppose -3*v - 31 = -40. Factor 6*y**2 - 6*y**v - y**2 + 2 + 4*y**2 - 5.
-3*(y - 1)**2*(2*y + 1)
Let j = 2140/57 + -80/19. Factor j - 220/3*u + 47*u**2 + 1/3*u**4 - 22/3*u**3.
(u - 10)**2*(u - 1)**2/3
What is t in -107 - 112 - 2888*t + 219 + 0*t**3 - 2*t**3 - 152*t**2 = 0?
-38, 0
Let w be 11 + (-6 + 1 - (-12 + 15)). Let r(g) be the second derivative of 3/160*g**5 + 3/2*g**2 + 3/4*g**w + 9*g + 3/16*g**4 + 0. Factor r(f).
3*(f + 2)**3/8
Let o(q) be the second derivative of -q**4/84 + 23*q**3/42 + 221*q. Factor o(m).
-m*(m - 23)/7
Let a(k) be the second derivative of -k**6/30 + 17*k**5/30 + 23*k**4/12 - 8*k**3/3 - 26*k**2/3 + 322*k. Determine r, given that a(r) = 0.
-2, -2/3, 1, 13
Let w = -5 + 20. Let k be (36/(-10))/(w/(-10)). Factor -k*g + 0 + 48/5*g**2 - 21/5*g**3.
-3*g*(g - 2)*(7*g - 2)/5
Let m = 16 - 47/3. Suppose 70 = 2*l + 64. Suppose m*v**2 - 1/6*v**l - 1/6*v + 0 = 0. What is v?
0, 1
Let d = -241 - -245. Let u be (2 - d)/((-2 - -7)*-2). Factor -1/5*g**5 + 1/5 + 1/5*g**4 + 2/5*g**3 - u*g - 2/5*g**2.
-(g - 1)**3*(g + 1)**2/5
Let a(g) be the third derivative of -g**6/60 + 9*g**5/10 - 81*g**4/4 + 243*g**3 - 3*g**2 + 29. Factor a(b).
-2*(b - 9)**3
Let o(y) = 7*y**4 - 9*y**3 + 5*y**2 + 3*y + 3. Let s(c) = -34*c**4 + 46*c**3 - 26*c**2 - 14*c - 14. Let x(v) = 14*o(v) + 3*s(v). Factor x(l).
-4*l**2*(l - 2)*(l - 1)
Factor -1/2*q**4 - 3*q**3 + 27*q + 81/2 + 0*q**2.
-(q - 3)*(q + 3)**3/2
Suppose 2*v + 3*v = -2*y, -28 = -4*y + 4*v. Factor 2*n**5 + y*n + 0*n - 5*n - 2*n**3.
2*n**3*(n - 1)*(n + 1)
Let k be ((-1)/4 - (-4890)/18920)/(-2). Let y = 8/43 + k. Factor 0*j + 2/11*j**3 + y*j**4 + 0 - 2/11*j**2 - 2/11*j**5.
-2*j**2*(j - 1)**2*(j + 1)/11
Solve 74*r**4 - 14*r**5 - 59*r**4 + 28*r + 191*r**3 + 11*r**3 + 51*r**4 + 150*r**2 = 0 for r.
-1, -2/7, 0, 7
Let r(f) be the second derivative of -f**8/588 - 2*f**7/735 + f**6/210 + f**5/105 - 12*f**2 + 14*f. Let c(t) be the first derivative of r(t). Factor c(y).
-4*y**2*(y - 1)*(y + 1)**2/7
Let r(h) be the third derivative of h**6/420 + h**5/105 - h**4/21 - 8*h**3/21 - 98*h**2. Factor r(p).
2*(p - 2)*(p + 2)**2/7
Let h(q) be the first derivative of -4*q**3/3 + 884*q**2 - 195364*q - 509. Factor h(i).
-4*(i - 221)**2
Let j(h) be the first derivative of h**6/2 - 3*h**4/2 + 3*h**2/2 - 76. Factor j(b).
3*b*(b - 1)**2*(b + 1)**2
Let p(w) = -w**2 + 48*w - 549. Let k be p(19). What is y in 3/5*y**k + 12/5 - 12/5*y = 0?
2
Let 0*c**4 + 68*c**3 + 7*c**4 - 2*c**4 - 10*c**2 - 63*c**3 = 0. Calculate c.
-2, 0, 1
Let h = 1175 - 1172. Factor -4/7 - 4/7*w**4 - 16/7*w**h - 24/7*w**2 - 16/7*w.
-4*(w + 1)**4/7
Let b be 11/(110/(-25))*128/(-10). Let f be (-4 - b/(-6))/((-4)/(-6)). Factor 4/13*h - 2/13*h**f + 6/13.
-2*(h - 3)*(h + 1)/13
Let a(g) be the third derivative of 0 - 1/48*g**4 + 0*g + 30*g**2 + 0*g**3 - 1/120*g**5. Factor a(x).
-x*(x + 1)/2
Let d(c) = -35*c - 18. Let m be d(-4). Find t such that -34*t**5 + 30*t + 52*t**2 - 38*t - 11*t**5 - m*t**3 + 123*t**4 = 0.
0, 2/5, 2/3, 1
Suppose -8*k + 6*k = 58. Let g = 31 + k. Solve 14 - p**2 - 4*p + 4*p**4 + 0*p**g - 11*p**2 + 4*p**3 - 6 = 0.
-2, -1, 1
Let c(l) be the first derivative of -1/42*l**4 - 2/7*l**2 - 1 + 1/7*l**3 + 2*l. Let j(o) be the first derivative of c(o). Suppose j(y) = 0. Calculate y.
1, 2
Let a(i) = i**2 + i + 2. Let q(d) = 10*d**2 - 18*d - 12. Let k(n) = 8*a(n) - q(n). Factor k(f).
-2*(f - 14)*(f + 1)
Let v(r) be the third derivative of 3*r**8/280 - 38*r**7/175 + 397*r**6/300 - 38*r**5/25 + 3*r**4/5 - r**2 + 9. Solve v(i) = 0 for i.
0, 1/3, 6
Let f be 6 - 0 - (12/32 + (-708)/(-160)). Suppose -6*o - f*o**2 - 24/5 = 0. Calculate o.
-4, -1
Let i(c) be the third derivative of 1/6*c**3 + 0 + 11/48*c**4 + 3/40*c**5 + 22*c**2 + 0*c. Factor i(m).
(m + 1)*(9*m + 2)/2
Let l(y) = -15*y**4 - 605*y**3 - 9605*y**2 - 8995*y + 10. Let z(s) = 22*s**4 + 908*s**3 + 14407*s**2 + 13493*s - 14. Let u(g) = -7*l(g) - 5*z(g). Factor u(k).
-5*k*(k + 1)*(k + 30)**2
Let i(r) be the third derivative of 0*r + 15/2*r**3 + 15/8*r**4 + 1/6*r**5 + 0 - 27*r**2. Factor i(m).
5*(m + 3)*(2*m + 3)
Let v(l) = 0*l - 6*l - 16 - l**3 + 24*l**2 - 15*l**2. Let g be v(8). Factor 0 + g*o**2 + 0*o + 1/2*o**3.
o**3/2
Let -2/7*q**4 + 2/7*q**3 + 2/7*q**2 - 2/7*q + 0 = 0. Calculate q.
-1, 0, 1
Suppose 10 + 45 = 28*z - 1. Solve 3/4*y**z + 3/4*y**3 - 3/4 - 3/4*y = 0.
-1, 1
Let h(s) be the third derivative of -s**6/200 - 19*s**5/100 - 119*s**4/40 - 49*s**3/2 + 4*s**2 - 17*s. Factor h(g).
-3*(g + 5)*(g + 7)**2/5
Let q be (-3)/15*-1*10. Factor -4*o - 5*o**3 - 130*o**2 - 11*o**3 + 150*o**q.
-4*o*(o - 1)*(4*o - 1)
Let p be ((-110)/30)/(-11) + (1 - 0). Factor 4/3*c**2 + 2/3*c**3 - 2/3*c - p.
2*(c - 1)*(c + 1)*(c + 2)/3
Factor 0*o - 4/9*o**3 - 8/3*o**2 + 4/9*o**4 + 0.
4*o**2*(o - 3)*(o + 2)/9
Let k(b) = -8*b**4 + 56*b**3 + 59*b**2 - 5*b - 10. Let v(z) = 7*z**4 - 55*z**3 - 58*z**2 + 4*z + 8. Let s(q) = 4*k(q) + 5*v(q). Factor s(y).
3*y**2*(y - 18)*(y + 1)
Suppose -5*v = t + 4 + 19, 5*v - 2*t = -14. Let s be (-18)/(-8) + (-3)/v. Find m, given that -m**4 - s*m**2 + 25*m**3 + 20*m**3 - 42*m**3 + m = 0.
0, 1
Suppose -39 + 3 = -6*i. Let w be (-4 + i)/4*1. Factor t - 1/2 - w*t**2.
-(t - 1)**2/2
Suppose -5*r + 8 = -0*r + 2*m, 5*m + 1 = -2*r. Suppose 3*c**3 - 4*c**2 - 6*c**2 + 10*c**4 - 5*c**5 + r*c**3 = 0. What is c?
-1, 0, 1, 2
Let j(x) be the second derivative of -x**7/210 - 7*x**6/120 + 19*x**2/2 + 12*x. Let f(y) be the first derivative of j(y). Suppose f(i) = 0. Calculate i.
-7, 0
Let q(i) be the second derivative of -5*i**5/2 - 5*i**4 + 117*i**3 + 676*i**2 + 12*i + 32. Solve q(p) = 0.
-13/5, 4
Let f = -15 - -21. Find g such that f*g - 6*g**5 - 3*g**4 + 64*g**3 - 32*g**3 + 30*g**2 - 2*g**2 + 7*g**4 = 0.
-1, -1/3, 0, 3
Suppose 0 = -4*k + j + j + 374, -j = -3. Let l be (38/k)/((-12)/(-10)). Solve -4/3*n + l*n**2 + 1 = 0 for n.
1, 3
Let i(t) be the third derivative of t**4/24 + 5*t**3/6 - 6*t**2. Let g be i(-4). Factor r**4 - g - 2*r**3 - 4*r + 19*r - 13*r.
(r - 1)**3*(r + 1)
Let w(i) be the second derivative of -i**8/20160 + i**7/7560 + i**6/2160 - i**5/360 - 5*i**4/3 + 4*i. Let c(g) be the third derivative of w(g). Factor c(q).
-(q - 1)**2*(q + 1)/3
Let a(i) be the second derivative of i**8/504 - i**7/315 - i**6/180 + i**5/90 + 7*i**2 - 16*i. Let b(q) be the first derivative of a(q). Factor b(o).
2*o**2*(o - 1)**2*(o + 1)/3
Let s be (-7)/(504/852) - -12. Let -s*r**4 + 0*r**3 + 0*r + 0 + 0*r**2 = 0. Calculate r.
0
Let v be 7/(28*-3)*24/(-15). Let k(u) be the second derivative of -2/5*u**5 + 4/3*u**3 - 2*u**2 + 0 + 0*u**4 + v*u**6 + 4*u. Suppose k(b) = 0. Calculate b.
-1, 1
Factor -692*l - 548*l**3 + 86 + 97*l + 513*l**3 + 44 + 500*l**2.
-5*(l - 13)*(l - 1)*(7*l - 2)
Let q be (-3 + (930/(-35))/(-6))*1. Factor 25/7*b + 1/7*b**3 + 0 - q*b**2.
b*(b - 5)**2/7
Let g(w) be the first derivative of 0*w**2 + 1/16*w**4 - 1/20*w**5 + 0*w + 6 - 1/24*w**6 + 1/12*w**3. Factor g(v).
-v**2*(v - 1)*(v + 1)**2/4
Let j(n) be the first derivative of 3*n**4/20 + n**3 - 12*n**2/5 - 36*n/5 - 706. Determine i, given that j(i) = 0.
-6, -1, 2
Solve -2/3*n**3 - 160/3*n + 46/3*n**2 + 152/3 = 0 for n.
2, 19
Let x(h) = -2*h**2 - 56*h - 102. Let a(u) = u**2 + 7*u. Let y(c) = -4*a(c) - x(c). Let y(i) = 0. What is i?
-3, 17
Let q = 41/310 + -1/31. Let x(j) be the first derivative of 0*j + 0*j**2 + 5 + q*j**4 - 2/25*j**5 + 0*j**3. Suppose x(a) = 0. Calculate a