2*(l + 27)/6
Let a(h) be the third derivative of h**6/24 + 10*h**5/3 + 185*h**4/6 + 120*h**3 + 9*h**2 - 32. Factor a(g).
5*(g + 2)**2*(g + 36)
Let z = -6005 - -7440193/1239. Let t = z + 11159/4956. Factor 1/4*b**3 - 7/4*b**2 - t + 15/4*b.
(b - 3)**2*(b - 1)/4
Let x(p) = -p**2 - 4*p - 9. Let v(d) = -d**2 - 5*d - 9. Let c(r) = 6*v(r) - 5*x(r). Let g be c(-1). Factor 0*h + g - 2/3*h**2 + 1/3*h**4 + 1/3*h**3.
h**2*(h - 1)*(h + 2)/3
Let j(x) be the third derivative of -x**6/120 + 7*x**5/60 + 85*x**4/24 - 91*x**3/6 + 12*x**2 - 9*x. Factor j(k).
-(k - 13)*(k - 1)*(k + 7)
Let x be (11/(-110))/(2/(-16)). Let n(f) be the first derivative of -8/3*f**3 - 12 - x*f**5 - f**2 - 5/2*f**4 + 0*f. Factor n(b).
-2*b*(b + 1)**2*(2*b + 1)
Let d(z) = -3*z + 28. Let j be d(8). Let y(k) = 580*k**4 - 528*k**3 + 165*k**2 - 26*k + 1. Let h(r) = -r**4 + r**2 + r. Let q(w) = j*h(w) + y(w). Factor q(t).
(3*t - 1)**2*(8*t - 1)**2
Let j be -8 - (-1602)/36 - 35. Factor -1/2*d**3 + 1/2*d + j - 3/2*d**2.
-(d - 1)*(d + 1)*(d + 3)/2
Determine y, given that 50*y**3 - 15*y - 2344*y**4 + 5 + 11*y**2 + 2449*y**4 + 45*y**5 - 41*y**2 = 0.
-1, 1/3
Let j(u) be the first derivative of -6*u**3 - 39*u**2/4 - 3*u/2 + 2794. Find f, given that j(f) = 0.
-1, -1/12
Let n(y) be the third derivative of 4/3*y**3 + 67/60*y**6 - 17 + 0*y + 29/105*y**7 + 1/42*y**8 - y**2 + 67/30*y**5 + 29/12*y**4. Find u, given that n(u) = 0.
-4, -1, -1/4
Let i(t) be the first derivative of 5*t**6/8 + 17*t**5/20 - 133*t**4/16 - 51*t**3/4 - 9*t**2/4 + 1835. Determine a so that i(a) = 0.
-3, -1, -2/15, 0, 3
Let w be ((-8 + 90/12)*(-200)/(-700))/(1/(-22)). Factor w*r + 1/7*r**2 + 0.
r*(r + 22)/7
Let u(q) be the first derivative of q**6/6 - 23*q**5/5 + 559. Factor u(f).
f**4*(f - 23)
Suppose 54*x - 156*x + 90 = -57*x. Factor -5/6*r**4 - 1/2*r**x + 0 - 1/6*r**5 - 7/6*r**3 + 0*r.
-r**2*(r + 1)**2*(r + 3)/6
Let h be 23976/(-370) + 64 + (34/(-10))/(-3*1). Factor 1/3*a**3 + 0*a + 0 + 1/3*a**2 - 1/3*a**4 - h*a**5.
-a**2*(a - 1)*(a + 1)**2/3
Let a(u) be the first derivative of -2*u**3/21 - 9098*u**2/7 - 41386802*u/7 - 13396. Factor a(y).
-2*(y + 4549)**2/7
Let o(i) be the third derivative of 1/20*i**4 - 4/15*i**3 + 43*i**2 - 1/300*i**5 + 2 + 0*i. Find b such that o(b) = 0.
2, 4
Factor 1119/8*x + 3/8*x**2 - 1125/4.
3*(x - 2)*(x + 375)/8
Let a(f) be the second derivative of f**6/3060 + 4*f**5/255 + 5*f**4/68 + 22*f**3/3 + 27*f. Let k(m) be the second derivative of a(m). Factor k(b).
2*(b + 1)*(b + 15)/17
Suppose -g - 28*t + 30*t + 1 = 0, -4*t + 7 = g. Let v(h) be the first derivative of 1/2*h**4 - 14/3*h**g - 18 - h**2 + 14*h. Determine k so that v(k) = 0.
-1, 1, 7
Suppose 4*q - 20 + 44 = 0. Let g = q - -9. Solve -g*a + 4*a**2 - 2*a**5 + 4*a**3 - 2*a - 2*a**4 + 0*a + 3*a - 2 = 0.
-1, 1
Factor 0 + 0*d**2 - 3/5*d**5 + 72*d**3 - 357/5*d**4 + 0*d.
-3*d**3*(d - 1)*(d + 120)/5
Let u = -13286 + 13295. Let k(r) be the second derivative of -3/5*r**5 - 7/4*r**4 + 0 - u*r - r**3 + 3/2*r**2. Factor k(h).
-3*(h + 1)**2*(4*h - 1)
Let p be 7*(-8)/(-252) + (-356)/1521. Let x = 173/338 + p. Solve 1/2*q**3 + 0 + 0*q + x*q**2 = 0 for q.
-1, 0
Let d be 8/10*(-32 + 2). Let n be 8/6*(-54)/d. Solve -5*v**4 - 2*v - 4*v + 3*v**5 + 13*v**2 - 4*v**4 + n*v**3 - 4*v**2 = 0.
-1, 0, 1, 2
Suppose -2*c = 410 - 416. Find w, given that -532*w**2 - 1056*w - 735 + 113 + 19*w**4 - w**5 + 46 - 32*w**c = 0.
-2, -1, 12
Let m(g) be the third derivative of g**8/1680 - g**6/360 - 4*g**3/3 - 106*g**2. Let l(y) be the first derivative of m(y). Factor l(d).
d**2*(d - 1)*(d + 1)
Let f = 37867/115 - 149/23. Let t = f - 322. Factor t*c - 4/5 + 4*c**2 + 12/5*c**3.
4*(c + 1)**2*(3*c - 1)/5
Let w(c) = c**3 - c**2 - 2. Let o(a) = 18*a**2 - 8*a - 60. Let m(s) = o(s) + 2*w(s). Factor m(n).
2*(n - 2)*(n + 2)*(n + 8)
Let f(i) be the third derivative of i**7/42 + 11*i**6/24 - 365*i**5/12 - 8125*i**4/8 - 3750*i**3 - 59*i**2 - 20*i. Solve f(u) = 0 for u.
-15, -1, 20
Suppose 0 = -100*p + 106*p - 7128. Let i = -5938/5 + p. Factor -4/5*d**2 + 0*d**4 + 6/5*d**3 + 0 - i*d**5 + 0*d.
-2*d**2*(d - 1)**2*(d + 2)/5
Let s(j) = -21*j**2 - 1103*j + 2284. Let l(u) = -462*u**2 - 24267*u + 50247. Let r(p) = 2*l(p) - 45*s(p). Find g such that r(g) = 0.
-381/7, 2
Let k(p) = -p**3 - 9*p**2 + 6*p - 4. Let i = 315 + -312. Let l(h) = 9*h**2 - 6*h + 3. Let y(t) = i*k(t) + 4*l(t). Find c, given that y(c) = 0.
0, 1, 2
Let m be (0 + 1)*((-109)/(-14) - (-1235)/(-190)). Find r such that -3/7*r**2 - m*r - 6/7 = 0.
-2, -1
Determine a so that 0 - 3/4*a**4 + 45*a + 69/4*a**2 - 3/2*a**3 = 0.
-4, -3, 0, 5
Let o(f) = 2*f**2 - 32*f + 56. Let m be o(2). Let h = 73/30 + -21/10. Factor c**4 + 5/3*c**3 - h*c + m + 1/3*c**2.
c*(c + 1)**2*(3*c - 1)/3
Let f(w) be the third derivative of 2*w**7/35 + 11*w**6/30 - 88*w**5/15 + 62*w**4/3 - 64*w**3/3 - w**2 + 2*w + 72. Solve f(n) = 0.
-8, 1/3, 2
Let f(t) be the second derivative of 8*t**6/15 - 31*t**5/5 + 24*t**4 - 88*t**3/3 - 32*t**2 + 7562*t. Factor f(l).
4*(l - 4)*(l - 2)**2*(4*l + 1)
Let j(b) be the first derivative of -3*b**5/20 - 9*b**4/8 + 31*b**3/4 + 9*b**2 - 81*b - 105. Find s, given that j(s) = 0.
-9, -2, 2, 3
Let w = 705935/7 + -100835. Factor 96/7 - 6/7*d**2 + w*d.
-6*(d - 16)*(d + 1)/7
Let c(w) be the first derivative of 338*w**5/35 - 102609*w**4/7 + 124662026*w**3/21 - 19164204*w**2/7 + 2947592*w/7 + 12715. Factor c(b).
2*(b - 607)**2*(13*b - 2)**2/7
Let t = 177 - 135. Factor -437 + t*h**2 - 10*h + 429 + h - 7*h.
2*(3*h - 2)*(7*h + 2)
Let d(p) be the first derivative of -3*p**5/25 - 3*p**4/5 + 3*p**3/5 + 27*p**2/5 - 481. Factor d(s).
-3*s*(s - 2)*(s + 3)**2/5
Suppose -183*m + 60*m + 58 + 65 = 0. Solve -1/2*l + 1/8*l**3 - m + 1/4*l**2 = 0 for l.
-2, 2
Let h be -2*((-6)/(-2))/(1 + -3). Factor -3*z**2 - 5*z**h - 29*z**2 - 85 + 165*z - 11*z**2 - 32*z**2.
-5*(z - 1)**2*(z + 17)
Let z(l) be the first derivative of -l**3/3 - 57*l**2 - 3249*l - 32. Factor z(j).
-(j + 57)**2
Factor 7/4*f - 3/2 - 1/4*f**2.
-(f - 6)*(f - 1)/4
Let s(t) = -56 - 89*t + 92*t - t**2 - 157 + 0*t**2 - 45*t. Let o be s(-36). Factor -1/3*l**2 - o*l - 8/3.
-(l + 1)*(l + 8)/3
Let o = -2 - -7. Suppose -o - 3 = -4*m. Let -80*l**3 + 49*l**5 - 51*l**2 + 32*l**4 - 18 + 112*l + m - 133*l**2 + 87*l**4 = 0. What is l?
-2, 2/7, 1
Let i(m) be the second derivative of 0 + 0*m**2 + 9/10*m**5 + 1/21*m**7 + 1/3*m**6 + 7/6*m**4 + 2/3*m**3 - 71*m. Factor i(t).
2*t*(t + 1)**3*(t + 2)
Suppose 3*s - 46 = -64, m + 4 = -s. Solve 2/3*y**5 + 0*y**2 + 0 - m*y**3 - 4/9*y**4 + 8/9*y = 0 for y.
-1, 0, 2/3, 2
Suppose -25*f - 5 = -11 - 69. Factor 0 - 9/2*h**4 + 6*h**2 + 0*h + 33/2*h**f.
-3*h**2*(h - 4)*(3*h + 1)/2
Suppose -7*d + 1735 = -1128. Let f = 1229/3 - d. Factor -f*z**3 + z**2 - 1/3*z**4 + 4/3 + 8/3*z.
-(z - 2)*(z + 1)**2*(z + 2)/3
Let v(d) = 24*d**3 + 1408*d**2 - 122464*d - 380204. Let q(a) = -89*a**3 - 5633*a**2 + 489856*a + 1520817. Let j(n) = -4*q(n) - 15*v(n). Factor j(p).
-4*(p - 178)**2*(p + 3)
Let j(r) be the first derivative of 8*r**4 + 0*r + 0*r**2 - 4/5*r**5 - 143 - 64/3*r**3. Factor j(t).
-4*t**2*(t - 4)**2
Let j(u) be the first derivative of -u**4 - 4568*u**3/3 - 4562*u**2 - 4560*u + 2886. Factor j(f).
-4*(f + 1)**2*(f + 1140)
Let d(k) be the third derivative of k**8/112 - 2*k**7/35 - k**6/5 + 16*k**5/5 - 14*k**4 + 32*k**3 + 4715*k**2. Factor d(c).
3*(c - 2)**4*(c + 4)
Let f = -10 + 31. Suppose -2*o + f = -o - 5*s, -5*o - 3*s + 77 = 0. Factor 18 + 15*a**2 + o - 28 + 9*a - 30*a.
3*(a - 1)*(5*a - 2)
Let q = 760 - 646. Let o be (-190)/q + 4 + 0. Find r such that 1/3*r**3 - o*r**2 + 5*r - 3 = 0.
1, 3
Let x(w) = -2*w**3 - 2*w**2 + 1. Let g be x(-2). Let v = g - -1. Let -1 - 16*s + 10*s - 4*s**2 - v*s - 15 = 0. What is s?
-2
Let g = 267165 + -2938777/11. Determine c so that 18/11 + 2*c**2 - g*c - 2/11*c**3 = 0.
1, 9
Let k = 1658462/5 - 331678. Factor 84/5*u**2 + 0 + 2/5*u**3 + k*u - 9/5*u**4 + 1/5*u**5.
u*(u - 6)**2*(u + 1)*(u + 2)/5
Factor 5*f**4 - 215*f**2 - 25*f**3 + 611*f**2 - 376*f**2.
5*f**2*(f - 4)*(f - 1)
Let t(m) be the second derivative of 7*m**7/15 + 252*m**6/25 - 2159*m**5/50 + 321*m**4/5 - 644*m**3/15 + 72*m**2/5 + 13*m. Determine q so that t(q) = 0.
-18, 2/7, 1
Let n(r) be the third derivative of r**6/660 - 59*r**5/165 + 227*r**4/44 - 336*r**3/11 - r**2 + 463. Suppose n(o) = 0. Calculate o.
3, 112
Suppose 243