(s) = 0 for s.
-23, 0
Factor 49152 + 144*i**2 + 4608*i + 3/2*i**3.
3*(i + 32)**3/2
Let q(z) = z**2 + 10*z - 22. Let w be q(-12). Factor -130*v**2 + 4*v - 3*v**3 + 126*v**w + 0*v**3.
-v*(v + 2)*(3*v - 2)
Let c(a) = 2*a - 5. Let v = 6 - 2. Let s be c(v). What is b in 0*b**3 - 4*b**s - 6 + 20 + 2 - 12*b**2 = 0?
-2, 1
Let d = 1202 - 108179/90. Let h(m) be the third derivative of 0*m**3 + 0 - 6*m**2 + 1/450*m**5 - d*m**4 + 0*m. What is y in h(y) = 0?
0, 2
Suppose 47*w = 1 + 3 + 90. Factor 0 - 1/6*r**3 + 1/2*r + 1/3*r**w.
-r*(r - 3)*(r + 1)/6
Let y = -10 + 2. Let c = y + 13. Factor -9 + c*f**2 + 3*f**2 + 3 - 22*f.
2*(f - 3)*(4*f + 1)
Let p(b) be the third derivative of b**7/315 - 2*b**6/45 + 7*b**5/30 - 11*b**4/18 + 8*b**3/9 + 85*b**2. Factor p(t).
2*(t - 4)*(t - 2)*(t - 1)**2/3
Let h(g) be the first derivative of 675*g**4/28 + 30*g**3/7 + 3*g**2/14 - 58. Factor h(d).
3*d*(15*d + 1)**2/7
Let j(y) be the first derivative of -y**5/10 - y**4/6 + y**3/3 + y**2 + 10*y - 20. Let f(n) be the first derivative of j(n). Determine o, given that f(o) = 0.
-1, 1
Let q(i) be the second derivative of -i**7/5460 + i**6/4680 + i**5/390 - 5*i**4/3 + 11*i. Let h(t) be the third derivative of q(t). Factor h(n).
-2*(n - 1)*(3*n + 2)/13
Let a be ((-9)/4)/(11 + -11 - 27/18). Factor 0 - 3/2*w**2 + a*w.
-3*w*(w - 1)/2
Let s(j) = 4*j**3 + 4*j**2 - 8*j. Let d(l) = 5*l**3 + 3*l**2 - 8*l. Let u(q) = -2*d(q) + 3*s(q). Factor u(z).
2*z*(z - 1)*(z + 4)
Let w(i) be the first derivative of i**9/3780 - i**7/350 + i**6/225 - 10*i**3/3 - 1. Let r(l) be the third derivative of w(l). Factor r(z).
4*z**2*(z - 1)**2*(z + 2)/5
Let g(d) be the third derivative of d**8/6720 + d**7/420 + d**6/80 + d**5/10 + 13*d**2. Let q(s) be the third derivative of g(s). Factor q(a).
3*(a + 1)*(a + 3)
Let n(h) be the first derivative of -27*h**5/20 + h**4/2 - 9*h - 9. Let b(l) be the first derivative of n(l). Factor b(s).
-3*s**2*(9*s - 2)
Let b(j) = j - 15. Suppose 4*z + 38 = -2*u + 4*u, 5*u + 2*z = 83. Let d be b(u). What is x in 0 - 1/3*x - x**3 + 1/3*x**4 + x**d = 0?
0, 1
Factor -6*d + 3*d**3 - 30*d + 2*d**2 - 60*d + 4*d**2 - 288.
3*(d - 6)*(d + 4)**2
Let s be (-8)/(-3)*((-36)/8)/(-1). Let y(w) = 2*w**2 - 25*w + 16. Let o be y(s). Factor 0*u - 3/8*u**3 + 0 - 1/8*u**2 - 3/8*u**o - 1/8*u**5.
-u**2*(u + 1)**3/8
Let j be (-3)/(-24) + (-209)/(-88) + -1. Suppose -3*z**3 + 3*z + 0*z**2 + j - 3/2*z**4 = 0. What is z?
-1, 1
Let w(p) = p**2 + 2*p - 9. Let t be w(-4). Let c(m) = -2*m**4 - 12*m**3 + 8*m**2 + 4*m - 6. Let b(k) = k**3 - k**2 + 1. Let n(z) = t*c(z) - 8*b(z). Factor n(g).
2*(g - 1)*(g + 1)**3
Suppose 16*w - 3/2*w**2 - 13/4*w**3 - 1/2*w**4 + 8 = 0. Calculate w.
-4, -1/2, 2
Suppose 4*m = -1 + 13. Suppose -31 = -m*s - 25. Find o, given that -2/7*o + 2/7 + 2/7*o**3 - 2/7*o**s = 0.
-1, 1
Let h(q) = q**3 + q**2. Let r(y) = 6*y**3 + 7*y**2 + y. Let j(t) = -34*h(t) + 6*r(t). Solve j(a) = 0 for a.
-3, -1, 0
Let r(p) = p**4 + 10*p**3 - 11*p**2 - 18*p - 4. Let h(y) = -3*y**4 - 31*y**3 + 33*y**2 + 54*y + 14. Let f(b) = 6*h(b) + 21*r(b). Let f(g) = 0. Calculate g.
-9, -1, 0, 2
Let n(r) = r**3 - 3*r - 10. Let g be n(3). Suppose g*l = 7*l. Factor -d**2 + 3/4*d**4 + 0*d**3 + l*d - 1/4*d**5 + 0.
-d**2*(d - 2)**2*(d + 1)/4
Let j(k) be the first derivative of -9 + 1/6*k**3 - k + 1/4*k**2. Factor j(u).
(u - 1)*(u + 2)/2
Let u(l) = -l + 7. Let s be u(-5). Suppose s*j = 11*j + 2. Suppose 0 - 2/13*d**4 + 0*d**3 - 4/13*d**5 + 0*d**j + 0*d = 0. What is d?
-1/2, 0
Let k(n) = -3*n**5 + 6*n**4 - 6*n**2 + 3*n - 6. Let v(z) = 3*z**5 - 6*z**4 + 6*z**2 - 3*z + 7. Let d(g) = 7*k(g) + 6*v(g). Let d(a) = 0. Calculate a.
-1, 0, 1
Let k(z) be the third derivative of -z**7/105 - 5*z**6/12 - 18*z**5/5 - 41*z**4/3 - 80*z**3/3 + z**2 - 107*z. Factor k(f).
-2*(f + 1)*(f + 2)**2*(f + 20)
Let f(q) be the second derivative of -q**5/150 - q**4/6 + 11*q**3/15 - 17*q**2/15 + 4*q - 2. Factor f(u).
-2*(u - 1)**2*(u + 17)/15
Suppose -1090 - 137 = -409*s. What is n in -12/11*n - 34/11*n**2 + 16/11*n**4 - 14/11*n**s + 8/11*n**5 + 0 = 0?
-2, -1, -1/2, 0, 3/2
Let l(q) = -q**2 + 9*q + 1. Suppose 4*u - 68 = -80. Let y(d) = d**2 - 17*d - 3. Let x(j) = u*y(j) - 5*l(j). Factor x(r).
2*(r + 1)*(r + 2)
Let c(b) = 133*b**4 + 1221*b**3 + 1411*b**2 - 944*b + 123. Let y(o) = 66*o**4 + 610*o**3 + 706*o**2 - 472*o + 62. Let x(p) = -2*c(p) + 5*y(p). Factor x(j).
4*(j + 2)*(j + 8)*(4*j - 1)**2
Let j(r) be the first derivative of -1/2*r**6 - 5 + 0*r**3 + 0*r**5 + 0*r + 3/2*r**4 - 3/2*r**2. Suppose j(f) = 0. Calculate f.
-1, 0, 1
Let w(q) be the first derivative of -q**7/560 - q**6/40 + 3*q**5/16 - q**4/2 + 25*q**3/3 + 46. Let g(f) be the third derivative of w(f). Solve g(a) = 0 for a.
-8, 1
Factor -2/7*u**4 + 0*u + 2/7*u**2 + 0*u**3 + 0.
-2*u**2*(u - 1)*(u + 1)/7
Let g(a) be the third derivative of a**7/945 + 16*a**6/135 + 256*a**5/45 + 4096*a**4/27 + 65536*a**3/27 + 28*a**2 - 2*a. Suppose g(o) = 0. What is o?
-16
Let m(b) = -25*b**2 - 755*b + 5345. Let n(v) = v**2 + 28*v - 198. Let a(l) = 2*m(l) + 55*n(l). Factor a(c).
5*(c - 4)*(c + 10)
Let q(h) be the second derivative of -49*h**5/60 - 14*h**4/9 - 8*h**3/9 + 157*h. Solve q(j) = 0.
-4/7, 0
Factor -70*c - 45*c**2 + 12*c + 3*c**3 - 9*c - c - 34*c.
3*c*(c - 17)*(c + 2)
Let g(j) be the second derivative of j**4/120 - 11*j**3/15 + 121*j**2/5 + 358*j. Factor g(a).
(a - 22)**2/10
Factor 10*v**2 + 4*v + 15*v**2 + 0*v**2 - 40*v - v**2 - 3*v**3.
-3*v*(v - 6)*(v - 2)
Find g, given that 0 + 9*g + 3/2*g**2 = 0.
-6, 0
Suppose c = y + 3*c + 7, -3*c = -2*y + 21. Suppose 0 = 5*w - y*s - 25, -w + 3 = -5*s - 2. Factor -2*b**3 - b**3 + w*b**3 - b**3 - b.
b*(b - 1)*(b + 1)
Let b(x) be the third derivative of x**8/53760 - x**6/1920 - x**5/480 - 2*x**4 + 42*x**2. Let j(h) be the second derivative of b(h). Factor j(o).
(o - 2)*(o + 1)**2/8
Let q be 140/(-20)*(-4)/16. Factor 1/4*c**5 + 2*c**2 + q*c**4 + 4*c**3 - 4*c - 4.
(c - 1)*(c + 2)**4/4
Suppose -12*h = -40*h + 84. Let a(c) be the first derivative of 1/8*c**4 + 0*c + 0*c**h + 3/20*c**5 + 0*c**2 + 1/24*c**6 - 4. Let a(t) = 0. What is t?
-2, -1, 0
Let p(z) be the third derivative of 0*z**3 + 0*z + 1/32*z**4 + 6*z**2 + 0 + 1/160*z**5. Find l such that p(l) = 0.
-2, 0
Let q be (-2)/6*-1 - (-3150)/(-54). Let v = q + 60. Suppose 8/7 + 50/7*g**v + 40/7*g = 0. What is g?
-2/5
Let t(k) be the first derivative of -k**4 - 8*k**3 - 18*k**2 - 16*k + 109. Factor t(c).
-4*(c + 1)**2*(c + 4)
Let x(o) = 2*o**2 - 7*o + 4. Let l be x(3). Let w be ((4/(-2))/l)/(-6). Factor 4/3*a**4 + 0*a**2 + 0*a + 0 - w*a**3.
a**3*(4*a - 1)/3
Solve -231/4*a**2 - 1083 - 1140*a - 3/4*a**3 = 0.
-38, -1
Factor -1/5*f**3 - 44/5*f**2 + 9*f + 0.
-f*(f - 1)*(f + 45)/5
Suppose -2*u = 2*u + 8. Let o(i) = -3*i**2 + 3*i - 2. Let y(z) = z**2 - z + 1. Let j(a) = u*y(a) - o(a). Factor j(d).
d*(d - 1)
Suppose -8*c - 7*c = -45. Let g be (c/(-2))/(-3 + 27/12). Find m such that -13/5*m**g - 6/5*m**3 - 12/5*m - 1/5*m**4 - 4/5 = 0.
-2, -1
Let n(t) be the second derivative of -t**6/90 + t**5/12 - t**4/36 - 7*t**3/6 + 3*t**2 - 68*t. Factor n(q).
-(q - 3)**2*(q - 1)*(q + 2)/3
Let o = 4161/16 + -260. Let u(n) be the third derivative of 2*n**2 - 1/4*n**4 - 1/160*n**6 + 1/2*n**3 + 0*n + o*n**5 + 0. Find c, given that u(c) = 0.
1, 2
Let u be (-1)/(22/(-102) + (-20)/170). Suppose 0 = 2*z + x - 4, 2*z - x - 8 = -u*x. Factor 3/4*b**2 + 1/2*b + z + 1/4*b**3.
b*(b + 1)*(b + 2)/4
Let h(d) be the first derivative of d**7/140 + d**6/80 - d**5/40 - d**4/16 - 2*d**2 + 16. Let z(t) be the second derivative of h(t). Factor z(u).
3*u*(u - 1)*(u + 1)**2/2
Solve 16/11*l**2 - 12/11*l**3 - 4/11*l**4 + 10/11*l - 12/11 + 2/11*l**5 = 0.
-2, -1, 1, 3
Let q(a) be the second derivative of a**6/300 + a**5/50 + a**4/30 + 7*a**2/2 + 34*a. Let n(w) be the first derivative of q(w). Determine h, given that n(h) = 0.
-2, -1, 0
Let i(u) be the first derivative of -u**8/252 + u**7/105 - u**5/90 + 19*u**2/2 + 16. Let v(r) be the second derivative of i(r). Factor v(w).
-2*w**2*(w - 1)**2*(2*w + 1)/3
Factor -y**4 + 3*y**2 - 564*y**3 - 3*y + 565*y**3 + 2*y - 2.
-(y - 2)*(y - 1)*(y + 1)**2
Let o(a) be the third derivative of a**6/660 + 4*a**5/165 + 7*a**4/132 + 2*a**2 + 9. Factor o(y).
2*y*(y + 1)*(y + 7)/11
Let p be ((-12)/24)/((-1)/(92/649) + 7). Find s, given that -p*s**2 + 8*s + 1