42*c**5 - 140*c**5 + 13000*c**2 + 2344*c**3 + 8788 + 50*c**5 + 19604*c + 164*c**4 + 52*c**5 = 0. Calculate c.
-13, -1
Suppose -3*n - 2 = 4, 0 = 2*d + 3*n + 2. Let v be -2 + (3/d)/((-6)/(-16)). Factor i - 5*i**2 + 4*i - 2*i**3 + 16 + i**v + 3*i.
-2*(i - 2)*(i + 2)**2
Let a(b) be the third derivative of -3*b**7/350 + 29*b**6/100 - 26*b**5/25 - 228*b**4/5 - 576*b**3/5 - 33*b**2 + 13*b. Let a(z) = 0. Calculate z.
-4, -2/3, 12
Let r(p) = -27*p**2 - 372*p - 768. Let m(l) = -2*l**2 - 8*l + 1. Let q(t) = 15*m(t) - r(t). Factor q(b).
-3*(b - 87)*(b + 3)
Let w = -156989 + 1098927/7. Suppose w*b**5 - 32/7*b + 4*b**3 - 16/7 - 4/7*b**2 + 20/7*b**4 = 0. What is b?
-2, -1, 1
Let s = 8026311/7 - 1146609. Factor 9/7 - 12/7*n**3 - s*n + 51/7*n**2.
-3*(n - 3)*(n - 1)*(4*n - 1)/7
Find j, given that -564/5*j + 104/5 + 4*j**4 + 164/5*j**2 + 276/5*j**3 = 0.
-13, -2, 1/5, 1
Let t(k) be the first derivative of 0*k**3 + 48*k**2 - 320*k - 3*k**4 + 2*k**4 - 65 + 17 + 4*k**3. Factor t(h).
-4*(h - 4)**2*(h + 5)
Suppose -13*r - 57 + 83 = 0. Factor -2*a + 22*a + 28*a**3 - 40*a**r - 6*a**4 - 4*a.
-2*a*(a - 2)**2*(3*a - 2)
Let x(i) be the first derivative of 3*i**5/20 + 7*i**4/4 + 5*i**3 + 16*i - 335. Let h(r) be the first derivative of x(r). Factor h(g).
3*g*(g + 2)*(g + 5)
Let a = -14198706/19 + 747302. Suppose -448/19*y**2 - a + 232/19*y + 98/19*y**3 = 0. Calculate y.
2/7, 4
Factor 5329 - 3*s**4 + 24165 + 5*s**4 + 5272*s**3 + 12600*s + 1754*s**2 - 5172*s**3 + 2258.
2*(s + 7)**2*(s + 18)**2
Let i = 12183 + -12183. Let a(c) be the third derivative of 1/336*c**8 + 0 + 0*c**3 + i*c - 21*c**2 + 1/18*c**6 + 0*c**4 + 2/45*c**5 + 1/45*c**7. Factor a(v).
v**2*(v + 2)**2*(3*v + 2)/3
Let p(d) = 14340 + 15*d**3 + 27*d**2 - 14340 + 4*d**4 + 25*d. Let g(t) = t**4 + 4*t**3 + 7*t**2 + 6*t. Let l(m) = 9*g(m) - 2*p(m). Suppose l(s) = 0. What is s?
-4, -1, 0
Let b(s) be the second derivative of s**4/3 + 12*s**3 - 38*s**2 + 928*s + 2. Let b(m) = 0. Calculate m.
-19, 1
Let m = -358 + 534. Let z(d) = d**2 - 6*d + 13. Let n be z(7). Factor -m + 176 - 2*x**2 + n*x.
-2*x*(x - 10)
Let g be (1539/1140 - (-3)/(-4))*5*1. Let r(w) be the first derivative of 6*w + 1/3*w**g + 3 - 7/2*w**2. Find c such that r(c) = 0.
1, 6
Let w(p) be the second derivative of -1/30*p**5 + 0*p**2 - 2 + p - 1/9*p**4 + 0*p**3. Suppose w(m) = 0. Calculate m.
-2, 0
Let w be 1/2 + 1 + 649/22. Factor 20*b**2 + 11 - w + 5*b**3 - b + 3*b - 7*b.
5*(b - 1)*(b + 1)*(b + 4)
Let p(m) be the first derivative of 179 - 10*m**2 - 40*m**3 + 129*m**5 - 90*m**6 + 0*m + 35/4*m**4. Solve p(f) = 0 for f.
-1/4, -2/9, 0, 2/3, 1
Let c be ((-140)/12)/5*(122/42 - 3). Solve 20/9 + c*v**2 - 14/9*v = 0 for v.
2, 5
Let o(t) be the first derivative of -t**6/21 - 12*t**5/35 - 13*t**4/14 - 8*t**3/7 - 4*t**2/7 - 11210. Let o(g) = 0. What is g?
-2, -1, 0
Let d = 18752 - 18808258/1003. Let v = 1009/3009 + d. Factor 2/3 + 0*n**2 - v*n**3 + n.
-(n - 2)*(n + 1)**2/3
Let s(l) be the third derivative of 2/15*l**4 - 3*l**2 - 10*l + 1/300*l**5 + 32/15*l**3 + 0. Let s(p) = 0. Calculate p.
-8
Let s = 276745 + -276743. Let h = -963/7 + 138. Factor -2/7*j**s + 4/7*j**3 - 1/7*j**5 + 0*j**4 + 2/7 - h*j.
-(j - 1)**3*(j + 1)*(j + 2)/7
Let p(s) = -41*s**3 + 64*s**2 + 18*s - 19. Let h(n) = -8*n**3 + 13*n**2 + 3*n - 4. Let a(i) = -11*h(i) + 2*p(i). Solve a(q) = 0.
-1/2, 1, 2
Let h(o) be the third derivative of 0 + 13/60*o**5 - 19/240*o**6 + 0*o - 11/280*o**7 - 1/12*o**4 + 0*o**3 - 4*o**2. Let h(m) = 0. Calculate m.
-2, 0, 2/11, 2/3
Let f(b) be the third derivative of 12*b**2 + 0 + 1/70*b**7 + 0*b**5 + 1/2*b**4 - 3/40*b**6 + 0*b + 0*b**3. Factor f(u).
3*u*(u - 2)**2*(u + 1)
Let i = 775 + -725. Suppose 60*f - i*f = 0. Solve -14/9*p**3 + 4/9*p**2 + 0*p + f = 0.
0, 2/7
Let x(q) be the first derivative of q**5/20 - q**4/4 - 3*q**2 - 4*q - 13. Let o(k) be the second derivative of x(k). Let o(z) = 0. What is z?
0, 2
Let n be 3148/2361*3/7. Let -n*c**3 - 112 + 4*c + 40/7*c**2 = 0. What is c?
-4, 7
Let x(n) = n**3 - 6*n**2 - 54*n - 9. Let g be x(11). Let j(r) be the first derivative of 5/4*r**g + 5/6*r**3 - 5*r - 4. Factor j(i).
5*(i - 1)*(i + 2)/2
Suppose 3*y + 26 = g, -3*y = 7*g - 0*g + 10. Factor -1/5*n**g + 9/5 - 8/5*n.
-(n - 1)*(n + 9)/5
Determine g so that -44402/15 - 8524/3*g**3 - 26284/3*g**2 - 2/15*g**5 + 118/3*g**4 - 26522/3*g = 0.
-1, 149
Let p be (4/(-42))/((-80)/(-31 - 529))*(-18)/4. Factor 108/5*a + 0*a**2 - 9/5*a**p - 1/5*a**4 + 0.
-a*(a - 3)*(a + 6)**2/5
Let w = -107 + 108. Suppose -2*n + 19 - w = 0. Factor 7 - 2*k**2 + n - 2 + 6 + 6*k.
-2*(k - 5)*(k + 2)
Let t(r) be the first derivative of -r**7/168 + r**6/36 - 34*r**3/3 + 3*r**2/2 - 172. Let d(w) be the third derivative of t(w). Factor d(n).
-5*n**2*(n - 2)
Let b(u) = u**2 - 102*u + 485. Let h be b(5). Let j(a) be the first derivative of -8/9*a**3 + h*a**2 + 0*a**4 - 4 + 16/3*a + 1/15*a**5. Factor j(f).
(f - 2)**2*(f + 2)**2/3
Let x(v) be the second derivative of v**5/160 + v**4/16 + 11*v**3/48 + 3*v**2/8 + 449*v. Factor x(y).
(y + 1)*(y + 2)*(y + 3)/8
Let v = -3680 - -3680. Let y(q) be the first derivative of -1/15*q**3 + 0*q - 7 + v*q**2. Find j such that y(j) = 0.
0
Let v(c) be the third derivative of c**8/80640 + c**7/1344 - c**6/180 + 11*c**5/5 - 130*c**2. Let z(b) be the third derivative of v(b). Let z(g) = 0. What is g?
-16, 1
Let w be 12 + (-1 - 11) + 2/2. Let q(p) = -28*p**2 + 34*p - 1. Let n be q(w). Find y, given that 2/7*y**n - 2/7*y**2 + 2*y**3 - 16/7*y + 10/7*y**4 - 8/7 = 0.
-2, -1, 1
Let m(s) be the second derivative of s**9/75600 + s**8/11200 + 3*s**4/2 + s**2 + 169*s. Let j(l) be the third derivative of m(l). Factor j(g).
g**3*(g + 3)/5
Factor -72/5 - 32/5*m**2 - 2/5*m**3 - 102/5*m.
-2*(m + 1)*(m + 3)*(m + 12)/5
Let i = -539 + 535. Let a be (-4 - -5) + ((-5)/i)/5. Suppose 11/4*d**3 - 17/4*d**4 + 1 + 13/4*d**2 - 4*d + a*d**5 = 0. Calculate d.
-1, 2/5, 1, 2
Let s = -47/39 - -20/13. Let f be (-51)/9*((-27602)/(-629) + -44). Factor s*p - 1/3*p**4 - 1/3*p**3 + p**2 - f.
-(p - 1)**2*(p + 1)*(p + 2)/3
Suppose 6*u = -18*u + 336. Solve u*l**4 - 4*l**5 + 18*l**3 - 391*l**2 + 10*l**3 + 401*l**2 = 0 for l.
-1, -1/2, 0, 5
Let k be (22/(-1))/(-2) - (-66 - -444)/42. Determine l so that -2/3*l + 7/9 - 1/9*l**k = 0.
-7, 1
Let j(r) = -38*r**2 - 373*r + 678. Let y(n) = -7*n**2 - 74*n + 136. Let t(w) = 6*j(w) - 33*y(w). Factor t(z).
3*(z - 2)*(z + 70)
Let h(u) be the third derivative of -u**5/30 - u**4/24 + 6*u**3 + 22*u**2. Let l be h(4). Suppose 1/6*f**4 - 1/2*f**3 + l + 0*f**2 + 2/3*f = 0. Calculate f.
-1, 0, 2
Factor 12*h**2 - 41*h - 728 - 29*h - 14*h**2 - 12*h.
-2*(h + 13)*(h + 28)
Let h(l) = 2*l**3 - l + 3. Let v(t) = -22*t**3 + 198*t**2 - 3620*t - 66580. Let g(x) = 20*h(x) + 2*v(x). Find y, given that g(y) = 0.
-11, 55
Solve -40*h + 72*h**4 - 281*h + 333*h**2 + 379*h**2 - 287*h + 416*h**3 + 188*h - 784 + 4*h**5 = 0.
-7, -4, -1, 1
Let w(d) be the third derivative of d**6/900 + d**5/30 + 13*d**4/90 + 533*d**2. Let w(v) = 0. Calculate v.
-13, -2, 0
Let r = -9 - -14. Suppose -q - 2*q + r = -5*g, -3*g + 6 = 0. Let -4*v**5 - v + 40*v**4 - 2*v + 20*v**q - 3*v**2 - 19*v**2 - 31*v**3 = 0. What is v?
-3, -1/4, 0, 1
What is b in 51/10*b**3 + 7/10*b**5 - 127/5*b**4 - 362/5*b + 72/5 + 388/5*b**2 = 0?
-2, 2/7, 1, 36
Let b(t) = -31*t**3 + 36*t**2 - 19*t - 49. Let c(d) = d**2 + d + 7. Let y(u) = 5*b(u) + 35*c(u). Suppose y(x) = 0. What is x?
0, 12/31, 1
Suppose -z + 3*r + 5 = 0, -2*z + 14 - 34 = 4*r. Let q be (z/18)/(4/(-36)) + 2. Factor 0 + 3/7*m**5 + 3/7*m**q - 3/7*m**2 + 0*m - 3/7*m**3.
3*m**2*(m - 1)*(m + 1)**2/7
Let q = 430262 + -430260. Factor -1/2*z**3 + 2*z - 2*z**q + 8.
-(z - 2)*(z + 2)*(z + 4)/2
Solve -38*w + 1/8*w**2 + 2888 = 0 for w.
152
Let x = -1218316/3 - -406106. Factor x*m**3 + 8/3*m**2 + 10/3*m + 4/3.
2*(m + 1)**2*(m + 2)/3
Let l = -766790 - -766792. Factor -2/13*j**3 + 0 + 30/13*j**l + 0*j.
-2*j**2*(j - 15)/13
Let l be 24/(-20) - 48/(-40). Suppose 0 - 4/5*k**2 + l*k + 6/5*k**3 - 2/5*k**4 = 0. What is k?
0, 1, 2
Let t = -142299 + 426937/3. Factor -80 + t*g + 25/3*g**2 - 5/3*g**3.
-5*(g - 4)**2*(g + 3)/3
Suppose -5*p + 10 = -0*p. Factor 7 - 8*r**2 - r**p + 5 + r**2 - 2*r**3 - 2*r.
-2*(r - 1)*(r + 2)*(r + 3)
Let c(j) be the third derivative of j**5/180 + 175*j**4/6 - 615*j**2. Determine s, given that c(s) = 0.
-