
Let r = 244057 - 244054. Factor 3/7*n**2 + 0 + 0*n - 1/7*n**r.
-n**2*(n - 3)/7
Let s(k) = 6*k**4 - 26*k**3 + 44*k**2 + 124*k - 176. Let i(l) = 11*l**4 - 51*l**3 + 88*l**2 + 247*l - 344. Let w(m) = -4*i(m) + 7*s(m). Factor w(t).
-2*(t - 6)**2*(t - 1)*(t + 2)
Let c(n) be the third derivative of -n**5/60 - 41*n**4/48 - 5*n**3/3 - 1285*n**2. Factor c(s).
-(s + 20)*(2*s + 1)/2
Let d be (8/3)/(9/27)*140/560. What is q in 38/13*q + 4/13 - 20/13*q**d = 0?
-1/10, 2
Suppose t + 14 = 4*h, -t - 2*t - 4*h + 22 = 0. Suppose 0 = -2*a + 3*j + 2 - 5, -4*j + 44 = 4*a. What is k in -a*k**t + 5964 - 5968 - 16*k - k**2 = 0?
-2, -2/7
Suppose -5*l - 4*u = -2106 + 79, 2*u = 4*l - 1606. What is x in 18 - 804*x**2 + 402*x**2 + 11*x + l*x**2 = 0?
-9, -2
Let y = -8486 + 594021/70. Let c(t) be the second derivative of 3/10*t**2 - 1/10*t**4 - 2*t + 0 + 1/50*t**6 + 1/10*t**3 + y*t**7 - 3/50*t**5. Factor c(p).
3*(p - 1)**2*(p + 1)**3/5
Let n(g) be the first derivative of g**5/70 + 3*g**4/14 + 8*g**3/21 + 106*g + 111. Let x(f) be the first derivative of n(f). Factor x(t).
2*t*(t + 1)*(t + 8)/7
Suppose -15*p = -20 - 70. Suppose p = -16*m + 6. Let m*t**2 + 0 - 1/2*t**3 - 1/2*t**4 + 0*t = 0. Calculate t.
-1, 0
Let t = -1716 - -1718. Let f(v) be the second derivative of -1/18*v**3 + 0 + 35*v - 1/36*v**4 + 1/60*v**5 + 1/6*v**t. Factor f(d).
(d - 1)**2*(d + 1)/3
Let r(x) be the second derivative of x**9/7560 - x**8/336 - 67*x**4/12 - 5*x. Let p(b) be the third derivative of r(b). What is v in p(v) = 0?
0, 10
Let u = 15529729/39052072 - 35/109084. Let s = u - 4/179. Suppose 27/2*q + s*q**3 - 9/2*q**2 + 0 = 0. What is q?
0, 6
Factor 248566 + 4265*z**2 + 251*z**3 + 85*z**3 + 84254 + 34*z**3 + 5*z**4 - 95460*z.
5*(z - 6)**2*(z + 43)**2
Let h(q) be the third derivative of q**10/176400 - q**9/105840 - q**8/70560 - 29*q**5/12 + q**2 - 17. Let i(o) be the third derivative of h(o). Factor i(y).
2*y**2*(y - 1)*(3*y + 1)/7
Factor -1854738 - 2/9*n**2 + 1284*n.
-2*(n - 2889)**2/9
Suppose -g - 3*g = 20. Let i be (-2 - g)*(-267)/(-9). Let 262*a**2 + 111*a - 228*a**3 + 266*a**2 + 48 - 135*a**4 - 14*a**5 + i*a**5 - 399*a = 0. What is a?
-2, 2/5, 1, 2
Suppose 0 = -2*u - 4, 0*c + c + 3*u - 3 = 0. Let 5*y - c*y + 2*y**5 - 30*y**3 + 40*y**2 - 11*y + 3*y**5 = 0. What is y?
-3, 0, 1
Let x(l) be the second derivative of 3*l**5/10 - 13*l**4/6 + 154*l - 4. Let p(c) = c**3 + c**2. Let d = 6 + -4. Let v(n) = d*p(n) - x(n). Solve v(s) = 0 for s.
0, 7
Let b(m) = -m**2 - 16*m - 46. Let p be (-33)/8 - (-3 + 1)/16. Let a be b(p). What is x in 5/6*x + 1/6*x**a - 1 = 0?
-6, 1
Let w = -278 - -215. Let b = w - -443/7. Factor 0*q + 0*q**2 + 0 - b*q**3 - 1/7*q**4.
-q**3*(q + 2)/7
Let q(p) be the second derivative of -p**4/18 - 514*p**3/9 - 66049*p**2/3 + 1192*p. Factor q(j).
-2*(j + 257)**2/3
Let f be ((-33)/(-6) + -5)*6. Determine a, given that 28*a**f - 34*a**2 + 110*a + 27*a**2 - 58*a**2 + 30*a**3 - 53*a**3 = 0.
0, 2, 11
Let y be 36/10 - (-8)/20. Find z, given that -3*z + y*z - z**5 - 5*z**2 + z**4 + 3*z**3 + z = 0.
-2, 0, 1
Let w(z) be the first derivative of 2*z**5/85 + 29*z**4/34 + 52*z**3/51 - 56*z**2/17 - 1115. Find d, given that w(d) = 0.
-28, -2, 0, 1
Factor -18/11 + 1/11*m**2 + 17/11*m.
(m - 1)*(m + 18)/11
Let t(d) = d**5 + 6*d**4 + 15*d**3 + 6*d**2. Let p(r) = -r**4 + r**3. Let x = -57 + 59. Let c(a) = x*t(a) - 4*p(a). Factor c(n).
2*n**2*(n + 1)**2*(n + 6)
Let u(i) be the first derivative of -14 - 8*i**4 - 64*i**3 - 2/5*i**5 - 512*i - 256*i**2. Solve u(o) = 0 for o.
-4
Let h(j) be the first derivative of 26/9*j**3 + 15 - 35/3*j**2 - 1/6*j**4 - 98/3*j. Suppose h(r) = 0. Calculate r.
-1, 7
Let w(c) be the second derivative of c**2 + 1/80*c**5 - 1/6*c**3 + 67 - 1/8*c**4 + 1/120*c**6 + 2*c. Solve w(r) = 0.
-2, 1, 2
Let w = 77 - 143. Let x = 68 + w. Let i + 8 - 4 + 2*i**x - 4 + i**3 = 0. Calculate i.
-1, 0
Suppose -241 + 5*k**2 + 3364*k - k**2 - 6737*k + 3365*k - 79 = 0. What is k?
-8, 10
Let s be 67 - (-57 - (-33990)/275). Factor -4/5*m**3 - 2/5*m**2 + 4/5*m + 0 + s*m**4.
2*m*(m - 2)*(m - 1)*(m + 1)/5
Let t(l) be the first derivative of 4*l**5/25 + 32*l**4/5 - 4*l**3/15 - 64*l**2/5 - 801. Factor t(u).
4*u*(u - 1)*(u + 1)*(u + 32)/5
Let t(z) = -z**2 + 3*z. Let r be t(2). Let v(q) = -q**2 - 3*q + 4*q + 0*q**r + 0*q. Let j(m) = -20*m**2 + 3*m. Let o(b) = j(b) - 5*v(b). Solve o(h) = 0 for h.
-2/15, 0
Let g(v) be the third derivative of -2*v**2 - 5/12*v**4 - 20/3*v**3 + 1/12*v**5 - 36 + 0*v. Suppose g(r) = 0. What is r?
-2, 4
Solve 282*z**2 + 2/5*z**3 + 0*z + 0 = 0.
-705, 0
Let y = 876373/4 + -219093. Factor 0*z + 0*z**3 + y*z**4 + 0 - z**2.
z**2*(z - 2)*(z + 2)/4
Let w be ((-9)/(-6))/(-395*3/(-6)). Let p = 407/1580 - w. Factor -1/4*h - 1/4*h**2 + p*h**3 + 1/4.
(h - 1)**2*(h + 1)/4
Let g(a) be the third derivative of a + 2/5*a**6 + 7/12*a**4 + 1/168*a**8 + 0*a**3 - 2/21*a**7 - 11/15*a**5 + 0 + 3*a**2. Factor g(u).
2*u*(u - 7)*(u - 1)**3
Factor 5/3*l**2 - 4700*l + 3313500.
5*(l - 1410)**2/3
Suppose -154*f + 311*f - 138*f = 0. Let p(d) be the second derivative of -1/16*d**4 - 19*d + f - 75/8*d**2 - 5/4*d**3. Determine y, given that p(y) = 0.
-5
Let i(v) = v**3 + 38*v**2 + 277*v - 42. Let k be i(-28). Let p(t) be the first derivative of k - t**2 - 4/3*t**3 + 4*t + 1/2*t**4. Factor p(b).
2*(b - 2)*(b - 1)*(b + 1)
Let c = 1 - -3. Suppose 4158*y = 4159*y - 3. Factor -3*z**y - 8 + 2*z**c - z**4 + 12*z - 5*z**2 + 3*z**2 + 0*z**2.
(z - 2)**2*(z - 1)*(z + 2)
Let q(n) = 28*n**3 + 173*n**2 + 294*n + 64. Let t(x) = -9*x**3 - 57*x**2 - 99*x - 21. Let w(l) = 6*q(l) + 17*t(l). Find a such that w(a) = 0.
-3, -1, -3/5
Let b = 1619/15 - 538/5. Let u be (1 + 18/(-10))*(20 + -25). Let 0 - 1/3*l**2 + 1/3*l**u + b*l**3 - 1/3*l = 0. What is l?
-1, 0, 1
Let i(n) be the third derivative of 3*n**6/100 - 8*n**5/25 + 5*n**4/4 - 12*n**3/5 - 1290*n**2. Factor i(k).
6*(k - 3)*(k - 1)*(3*k - 4)/5
Let c(q) = 11*q**2 - 25*q + 8. Let s(u) = 177 + 4*u**2 - 17*u + 3*u**2 - 172. Let t(m) = -5*c(m) + 8*s(m). Let t(g) = 0. What is g?
0, 11
Let p be (891/27 + -54)/(-7). Factor 2*k - 1/3*k**2 - p.
-(k - 3)**2/3
Let y(v) be the first derivative of -12*v - 2/3*v**3 + 74 - 7*v**2. Factor y(l).
-2*(l + 1)*(l + 6)
Let t(v) be the first derivative of -9*v**4/4 - 19*v**3 + 156*v**2 - 180*v - 281. Factor t(c).
-3*(c - 3)*(c + 10)*(3*c - 2)
Let h(q) = -q**3 + 13*q**2 - 5*q - 6. Let x be h(10). Let 447*i + i**3 + 281*i + x*i - 73*i**2 - 35*i**2 + 2*i**3 = 0. Calculate i.
0, 18
Let l = 75 - 26. Find t such that -16 - 112*t + 8*t**2 - 135*t**2 - 248*t**3 - 182*t**2 - 84*t**4 + l*t**2 = 0.
-1, -2/3, -2/7
Suppose 0 = 46*i - 5*i - 82. Suppose -12*u**3 + 21*u + 4*u**4 + 2*u**5 + 23*u - 6*u**2 - 36*u + 2*u**2 + i*u**5 = 0. Calculate u.
-2, -1, 0, 1
Let n = -22479517771/1995 - -11267929. Let x = n + -2/285. Factor 0 + 2/7*o**3 - 2/7*o**2 + 2/7*o**4 + 0*o - x*o**5.
-2*o**2*(o - 1)**2*(o + 1)/7
Let i = -444 - -1342/3. Let s(x) be the first derivative of -i*x**2 + 21 + 0*x - 5/9*x**3. Find a, given that s(a) = 0.
-4, 0
Let p(x) be the first derivative of -3*x**4/10 + 41*x**3/15 + 121*x**2/5 + 39*x + 2529. Factor p(n).
-(n + 1)*(n + 3)*(6*n - 65)/5
Let v be 32/180 + 4/18 - 371/(-1855). Suppose 0 + 2/5*b**3 + 1/5*b**5 - v*b + 4/5*b**2 - 4/5*b**4 = 0. Calculate b.
-1, 0, 1, 3
Factor 3*q**4 + 7/3*q**2 + 1/3*q**5 + 0*q + 0 + 5*q**3.
q**2*(q + 1)**2*(q + 7)/3
Let u(b) = -b**2 + 6*b + 9. Let x be u(7). Let n be (-1)/(-5)*405/513*19. Determine m, given that 0*m - 8/3*m**x + 2/3*m**4 + 7/3*m**5 - 28/3*m**n + 0 = 0.
-2, -2/7, 0, 2
Suppose 42*q - 12 = 40*q. Let p be 2/(-5)*(19 + q)/(-5). Factor p + 8/3*d + 2/3*d**2.
2*(d + 1)*(d + 3)/3
Suppose -12*l + 1071 = 5*l. Let q be (-18)/(3 + (-259)/l). What is r in -18/5*r + q*r**2 + 1/5 = 0?
1/9
Let u(l) be the first derivative of -6*l**5/5 - 19*l**4/2 - 56*l**3/3 + 4*l**2 + 32*l - 101. Solve u(s) = 0 for s.
-4, -2, -1, 2/3
Suppose 11/2*k + 11/4*k**2 - 23/4*k**3 + 1/4*k**5 - 4 + 5/4*k**4 = 0. Calculate k.
-8, -1, 1, 2
Let d(z) be the first derivative of -z**4/4 - 3*z**3 - 27*z**2/2 - 62*z + 43. Let w(u) be the first derivative of d(u). Factor w(i).
-3*(i + 3)**2
Let b(k) = -k**2 + 1. Let a(c) be the second derivative of c**4/6 - 35*c**3/6 + 63*c**2/2 + 66*c. Let f(z) = -a(z) + 3*b(z). Factor f(m).
-5*(m - 4)*(m - 3)
Let b(g) = 15*g**3 + 71*g