**3 + 10/21 = 0.
-5, -1
Let b = 9875 + -9875. Factor 1/2*h**3 + b - 1/2*h**5 + 0*h**4 + 0*h + 0*h**2.
-h**3*(h - 1)*(h + 1)/2
Let s = 373/6860 + -3/686. Let k(l) be the second derivative of 1/6*l**3 + 12*l + 0*l**2 + s*l**5 + 0 - 1/6*l**4. Factor k(z).
z*(z - 1)**2
Let s(d) = -2*d**5 - 12*d**4 - 2*d**3 + 4*d - 4. Let f = 26 - 21. Let g(o) = o**5 + 13*o**4 + 2*o**3 - 5*o + 5. Let m(q) = f*s(q) + 4*g(q). Factor m(n).
-2*n**3*(n + 1)*(3*n + 1)
Let q(u) = -u**3 + 7*u**2 - 7*u - 3. Let m be q(6). Let w be 2/m - 112/(-99). Let 4/11 - 2/11*o**3 - w*o + 8/11*o**2 = 0. What is o?
1, 2
Let o be ((-35)/7)/(1/(-1)). Let z(m) be the first derivative of 1/3*m**3 + o + 0*m**2 + 0*m**4 - 1/2*m - 1/10*m**5. Factor z(p).
-(p - 1)**2*(p + 1)**2/2
Let s(m) be the first derivative of -35*m**2 - 245*m - 5/3*m**3 - 1. Factor s(v).
-5*(v + 7)**2
Let o(d) be the third derivative of d**8/40320 + d**7/5040 + d**6/1440 + 7*d**5/20 - 9*d**2. Let i(n) be the third derivative of o(n). Factor i(p).
(p + 1)**2/2
Let g(h) = -h**3 + 25*h**2 - 17*h - 16. Let f(p) = 8*p**2 + 5*p**2 - 8 - p**2 - 8*p. Let l(j) = 9*f(j) - 4*g(j). Factor l(a).
4*(a - 1)*(a + 1)*(a + 2)
Let p be 22/12 + 11/((-33)/1). Factor -p*c**5 + 3*c**3 - 3*c**2 + 3/2*c**4 - 3/2*c + 3/2.
-3*(c - 1)**3*(c + 1)**2/2
Let g(k) be the first derivative of 17 - 2/9*k**3 - 1/3*k**2 - 1/6*k. Factor g(j).
-(2*j + 1)**2/6
Determine z, given that -33*z - 2*z**3 - 137*z + 38*z - 2*z**3 - 72*z**2 - 64 = 0.
-16, -1
Solve -4*j**2 - 393 + 32*j - 386 + 835 + 20*j = 0 for j.
-1, 14
Let w = -9623/3 - -3213. Let -w*x**2 - 22/3*x - 2 = 0. Calculate x.
-1, -3/8
Factor 38/7*d**2 + 20/7*d + 16/7*d**3 - 2/7*d**4 + 0.
-2*d*(d - 10)*(d + 1)**2/7
Let p(h) be the first derivative of -1/4*h**3 - 3/2*h**2 - 8*h + 1/8*h**4 - 2. Let v(z) be the first derivative of p(z). Factor v(u).
3*(u - 2)*(u + 1)/2
Solve 7/2*c**3 - 5*c - 17/2*c**2 + c**4 + 0 = 0.
-5, -1/2, 0, 2
Let o(k) = -k**3 - 44*k**2 + 198*k + 288. Let x be o(-48). Factor 0 + x*l - 4/3*l**4 - 1/3*l**2 + 5/3*l**3.
-l**2*(l - 1)*(4*l - 1)/3
Let z(x) = -20*x**3 + 136*x**2 + 306*x - 2414. Let v(n) = -28*n**3 + 204*n**2 + 460*n - 3620. Let l(r) = 7*v(r) - 10*z(r). Factor l(j).
4*(j - 3)*(j + 10)**2
Suppose 37*g - 894 = -98*g - 219. What is y in -5/2*y**4 + 10*y**3 - 25/2*y**2 + g*y + 0 = 0?
0, 1, 2
Let a(p) be the first derivative of 107*p**5/10 + p**4/8 + 92. What is k in a(k) = 0?
-1/107, 0
Let o(c) be the second derivative of c**4/24 - 45*c**3/2 - 271*c**2/4 + 3*c + 106. Let o(f) = 0. What is f?
-1, 271
Let o = 43 + -64. Let y = o + 24. Factor -3/2*k**y - 3/2*k - 3*k**2 + 0.
-3*k*(k + 1)**2/2
Let s(w) be the second derivative of -w**8/53760 - 2*w**4/3 + 3*w. Let v(d) be the third derivative of s(d). Solve v(j) = 0.
0
Suppose -76*f**2 + 68*f + 4*f**4 - 40*f**3 + 327205 - 44*f**3 - 327133 + 16*f**3 = 0. Calculate f.
-1, 1, 18
Let q(a) be the second derivative of a**7/2520 + a**6/60 + 3*a**5/10 - 2*a**4 + 25*a. Let p(w) be the third derivative of q(w). Factor p(b).
(b + 6)**2
Find g, given that -36/7*g + 16/7 - 4/7*g**3 + 24/7*g**2 = 0.
1, 4
Let p be 0/(-2) + 5*(-1)/(-30). Let w(y) be the third derivative of 0 - 4*y**2 + 1/60*y**5 - p*y**3 + 0*y + 0*y**4. Factor w(i).
(i - 1)*(i + 1)
Let x be (-16)/(-40) + 546/(-15). Let n be 9/12 + (-45)/x. Find g, given that -g**4 + 0 + g**n + 1/2*g**5 - 1/2*g + 0*g**3 = 0.
-1, 0, 1
Determine b, given that 4*b - 36/7*b**5 + 8*b**2 - 60/7*b**4 + 4/7 + 8/7*b**3 = 0.
-1, -1/3, 1
Find k such that 0*k**4 + 1/5*k**5 + 0*k**2 - k**3 + 0 + 4/5*k = 0.
-2, -1, 0, 1, 2
Let w be (-52)/(-6) - (3 + (-49)/21). Suppose 4 = 3*h + 5*u, -w*u + 10 = 3*h - 9*u. Factor -2/21*i**2 - 2/7 - 2/21*i**h + 10/21*i.
-2*(i - 1)**2*(i + 3)/21
Suppose -5*w = -3*u + 11, -w + u + 211 - 216 = 0. Factor 1/5 - 4/5*j**3 + 1/5*j**4 + 6/5*j**w - 4/5*j.
(j - 1)**4/5
Factor 328*b**2 + 210*b**2 + 4 + 84*b + 20*b + 138*b**2.
4*(13*b + 1)**2
Let g be (-10)/(-8) + (-284)/240. Let m(i) be the second derivative of 1/42*i**7 + g*i**6 + 0*i**3 + 1/20*i**5 + 0*i**4 + 4*i + 0 + 0*i**2. Factor m(c).
c**3*(c + 1)**2
Solve 128*y - 337*y**5 - 26*y**4 + 50*y**3 + 339*y**5 + 70*y**3 - 224*y**2 = 0.
0, 1, 4
Let c(w) = -2*w**4 + 10*w**3 + 12*w**2 - 43*w + 20. Let a(d) = 3*d**4 - 20*d**3 - 23*d**2 + 87*d - 40. Let x(j) = 3*a(j) + 7*c(j). Solve x(i) = 0.
-2, 1, 2
Let x(j) = -4*j**3 + 4*j**2 + 3*j. Let t(r) = -3*r**3 + 3*r**2 + 2*r. Let a(g) = -3*t(g) + 2*x(g). Factor a(i).
i**2*(i - 1)
Let r be (-9 - 44/(-4))*3/2. Suppose -h = -4*u + 6, r*h - 4 = -4*u + 10. Suppose 1 + 1/4*w**u + w = 0. Calculate w.
-2
Let q = 987 + -982. Let n(z) be the first derivative of z**4 - 2*z**2 + 8*z - 20/3*z**3 + 12/5*z**5 + q. Solve n(o) = 0.
-1, 2/3, 1
Let s(r) = 2*r**2 - 6*r - 475. Let g be s(17). Factor 1/3*v**3 - 1/3*v + v**2 - g.
(v - 1)*(v + 1)*(v + 3)/3
Let o = -14 + 15. Let f be (-6)/(-6)*(-1)/(-7)*o. Solve 5/7*t**2 + f*t + 0 = 0.
-1/5, 0
Suppose -10 = -5*p + 5*w, 66*p - 4 = 64*p - w. Factor 5/2*f**p - 5/2*f**3 - 5/2*f**4 + 0 + 5/2*f.
-5*f*(f - 1)*(f + 1)**2/2
Suppose 4*q = -5*q + 9387. Factor 5*n**3 - 150*n**2 + 1500*n - 4360 + 403 - q.
5*(n - 10)**3
Let g be (-200)/120*(36/(-15) + 2). Factor g*n**2 + 0 + 4/3*n.
2*n*(n + 2)/3
Suppose -4*c = -10 + 34. Let z = c - -22/3. Suppose z*v**2 - 10/9*v - 2/9 = 0. What is v?
-1/6, 1
Let c be (-16)/(-5) - (-2)/(-10). Suppose -2*o - 5*r = -8, -2*r + 12 = 3*o + 3*r. Determine a, given that -3*a**2 + a**c + a**o - a + a**4 + a**4 = 0.
-1, -1/3, 0, 1
Factor 32/3 + 2/3*i**3 + 0*i**2 - 8*i.
2*(i - 2)**2*(i + 4)/3
Suppose 0 = m - 0*m + 5, -4*m - 14 = 3*z. Factor -8 + 8 + 9*j**3 + 9*j**z - 2*j + 5*j + 3*j**4.
3*j*(j + 1)**3
Suppose -28*f + 3*s + 29 = -23*f, -5*f = s - 17. Let n(t) be the second derivative of 8*t**3 + t + 18*t**2 + 0 + 4/3*t**f. Factor n(g).
4*(2*g + 3)**2
Let q(y) be the third derivative of y**8/336 + 2*y**7/105 - y**6/8 - 23*y**5/30 + 11*y**4/6 + 20*y**3 + 12*y**2 - 2. What is l in q(l) = 0?
-5, -2, 2, 3
Solve 7/6*h**5 - 19/6*h**4 + 4/3*h**3 + 2/3*h**2 + 0*h + 0 = 0 for h.
-2/7, 0, 1, 2
Let n be ((-381)/117 - -3)*(-81)/135. Factor n + 6/13*v**2 + 2/13*v**3 + 6/13*v.
2*(v + 1)**3/13
Suppose 3*q - 2*q + 2*r = -10, 5*r = 5*q + 20. Let a be q/(-2) + 10/5. Let 6*k**2 + 43*k**4 - 44*k**4 - a*k**2 = 0. Calculate k.
-1, 0, 1
Factor -38/5*n - 2/5*n**2 + 0.
-2*n*(n + 19)/5
Suppose 0 = -14*l + 13*l - 5. Let x(b) = -b**2 - 8*b - 15. Let z be x(l). Determine y so that -1/2*y**3 + 2*y + 0 + z*y**2 = 0.
-2, 0, 2
Let s(n) be the third derivative of n**6/60 - n**5/6 + n**4/6 + 8*n**3/3 - 420*n**2. Factor s(b).
2*(b - 4)*(b - 2)*(b + 1)
Suppose 1 = m - 3*g - 7, 0 = -3*m + 3*g + 18. Determine z, given that 0*z + 0*z**2 + 0 - 16/11*z**4 - 32/11*z**3 - 2/11*z**m = 0.
-4, 0
Suppose -3*m + 2420 = 4*c - 363, 0 = 4*m - 4*c - 3664. Factor 7*d**2 + 2*d**2 + m*d - 3*d**4 - 927*d.
-3*d*(d - 1)**2*(d + 2)
Suppose -11*c - 35*c = -138. Let v(f) be the second derivative of -3/4*f**4 + 4*f**c + 0 + 9/2*f**2 - 3*f. Determine q so that v(q) = 0.
-1/3, 3
Let l(i) be the first derivative of i**3/2 - 9*i**2 + 81*i/2 + 33. Let l(b) = 0. Calculate b.
3, 9
Let a(u) = -u**2 - u - 1. Let r(n) be the third derivative of n**5/12 + 2*n**3/3 + 7*n**2. Let s(k) = -4*a(k) - r(k). What is w in s(w) = 0?
0, 4
Let b(l) = -2*l**4 + 6*l**3 + 12*l**2 - 16*l - 2. Let n(z) = 2*z**4 - z**3 + z**2 - 6*z - 1. Let f(s) = 2*b(s) - 4*n(s). Factor f(q).
-4*q*(q - 2)*(q + 1)*(3*q - 1)
Let c(l) be the first derivative of l**5/30 + 11*l**4/24 + 2*l**3 + 4*l**2/3 - 32*l/3 + 246. Find w such that c(w) = 0.
-4, 1
Let m(x) be the first derivative of 2*x**5/5 + 15*x**4/4 + 19*x**3/3 + 3*x**2 - 347. What is a in m(a) = 0?
-6, -1, -1/2, 0
Let u(s) be the third derivative of -s**7/630 + s**6/45 - 11*s**4/12 + 18*s**2. Let w(y) be the second derivative of u(y). Factor w(f).
-4*f*(f - 4)
Suppose 26*m - 27*m + 133 = 0. Suppose 0 = m*v - 128*v. Solve 0 - 2/9*r**4 + v*r + 2/9*r**2 + 0*r**3 = 0.
-1, 0, 1
Find q, given that 78/7*q**2 + 6/7*q**3 - 51/7*q**4 - 27/7 - 15/7*q**5 + 9/7*q = 0.
-3, -1, 3/5, 1
Suppose -4*r**2 + 2 + 16/3*r**3 - 22/3*r = 0. What is r?
-1, 1/4, 3/2
Let t(w) = 12*w**5 + 14*w**4 - 20*w**3 + 6*w**2 + 18*w + 10. Let s(y) = y**5 + 2*y**4 - y**3 + y + 1. Let l(m) = -10*s(m) + t(m). Solve l(p) = 0.
-1, 0, 1, 4
Let u(f) be the third derivative of 