e the second derivative of -7/4*a**4 - 1/6*a**6 - 6*a - a**2 + 11/6*a**3 + 17/20*a**5 + 0. Let q(b) = 0. Calculate b.
2/5, 1
Solve -4/3*d**4 - 144 + 8/3*d**3 + 0*d + 36*d**2 = 0.
-3, 2, 6
Let k(r) be the second derivative of 2/3*r**6 + 0*r**3 + 22*r + 0 + 2/3*r**4 - 7/5*r**5 + 0*r**2. Factor k(d).
4*d**2*(d - 1)*(5*d - 2)
Suppose -4*b = 20, b = 2*f - 0*b - 57. Let l be (-4)/f + 178*(-8)/(-1144). Solve 8/11*x**2 - 2/11*x**5 - 2/11*x + 0 + 8/11*x**4 - l*x**3 = 0.
0, 1
Let m(o) = 5*o**3 + 40*o**2 + 25*o + 15. Let l(w) = -8*w**3 - 59*w**2 - 38*w - 22. Let p(v) = -5*l(v) - 7*m(v). Factor p(i).
5*(i + 1)**3
Suppose -542*p = -504*p. Factor p + 0*h + 1/6*h**3 + 1/3*h**2.
h**2*(h + 2)/6
Let n = 2069 - 41377/20. Let s(v) be the first derivative of n*v**4 - 2/5*v**2 + 3 + 0*v - 4/15*v**3. Let s(d) = 0. What is d?
-2/3, 0, 2
Let b(u) be the second derivative of -u**4/72 - 16*u**3/9 - 256*u**2/3 + 71*u + 1. Factor b(v).
-(v + 32)**2/6
Factor 52/7*x - 2/7*x**2 + 0.
-2*x*(x - 26)/7
Let p(d) be the first derivative of d**7/1680 - d**6/360 + d**5/240 + 4*d**3 + 17. Let r(a) be the third derivative of p(a). Suppose r(m) = 0. What is m?
0, 1
Suppose -173*y - 197*y + 882 = 71*y. Factor 2/11*n**y - 16/11 - 4/11*n.
2*(n - 4)*(n + 2)/11
Solve 8/3*q**2 + 4/3 - 2/3*q**3 - 10/3*q = 0 for q.
1, 2
Find y, given that 2/7 + 0*y - 4/7*y**2 + 0*y**3 + 2/7*y**4 = 0.
-1, 1
Suppose 4*o + 41 - 49 = 0. Let j(v) be the second derivative of 0 + 2/3*v**3 + 1/5*v**5 - 2/3*v**4 - 3*v + 0*v**o. Factor j(b).
4*b*(b - 1)**2
Let r(g) be the second derivative of -12*g**6/5 + 9*g**5/5 + 5*g**4/2 + 17*g**3/18 + g**2/6 - 3*g + 41. Determine y, given that r(y) = 0.
-1/6, 1
Suppose -5*j + 204 = 5*r - 11, 2*j - 3*r - 61 = 0. Suppose -j + 73 + 22*b + 6*b**2 - 43 = 0. What is b?
-4, 1/3
Let f = -98171/4 + 24543. Factor -75*u + 15/2*u**2 - f*u**3 + 250.
-(u - 10)**3/4
Let w(b) be the first derivative of 18 + 0*b + 4/3*b**3 - 1/6*b**4 - 3*b**2. Factor w(z).
-2*z*(z - 3)**2/3
Factor -8*d**4 + 4*d**4 + 128*d + 18*d**2 - 6*d**4 - 32 - 162*d**2 + 64*d**3.
-2*(d - 2)**3*(5*d - 2)
Let a(j) be the third derivative of 0*j**6 + 2*j**2 + 1/15*j**5 + 0*j**4 + 0*j - 2/105*j**7 + 0 + 0*j**3. Solve a(i) = 0 for i.
-1, 0, 1
Let b(o) be the first derivative of -o**7/490 + 3*o**5/70 - o**4/7 + 3*o**3/14 - 19*o**2/2 - 7. Let q(l) be the second derivative of b(l). Factor q(h).
-3*(h - 1)**3*(h + 3)/7
Let n be (5 - 1788/378) + 10/(-45). Let z(l) be the first derivative of n*l**6 + 1/7*l**2 + 3/7*l**4 + 8/21*l**3 + 0*l + 8/35*l**5 - 2. Factor z(j).
2*j*(j + 1)**4/7
Let i(h) be the third derivative of h**5/60 - 3*h**4/2 - 37*h**3/6 - 19*h**2. Solve i(j) = 0.
-1, 37
Let j(f) be the second derivative of -f**5/60 - 2*f**4/3 - 40*f**3/9 + 24*f. Factor j(n).
-n*(n + 4)*(n + 20)/3
Let c = 1192/7 + -1180/7. Suppose 2/7 - 2/7*s**3 + 2/7*s - 2*s**2 + c*s**4 = 0. What is s?
-1, -1/3, 1/2, 1
Let s = -69 - 22. Let l = 459/5 + s. Determine g so that -2/5*g**4 + l + 6/5*g**2 + 2/5*g**3 - 2*g = 0.
-2, 1
Let g(u) = -33*u**4 - 86*u**3 - 55*u**2 - 11*u. Let v(f) = -67*f**4 - 170*f**3 - 109*f**2 - 21*f. Let n(d) = -5*g(d) + 3*v(d). Factor n(s).
-4*s*(s + 1)**2*(9*s + 2)
Suppose 3*b + 5*t + 3 = -b, 5*b = 4*t - 55. Let a be (-7)/(14/6) - b. Let 9/2*f**a - 19/2*f**2 + 6*f + 2 + 2*f**5 - 5*f**3 = 0. What is f?
-2, -1/4, 1
Suppose -4*m - 5*u = -1001, 242 = -2*m + 3*m + 4*u. Factor s**2 + 33*s + 229 - m - 6*s**2 - 3*s.
-5*(s - 5)*(s - 1)
Let o(c) be the second derivative of -c**5/120 - 17*c**4/12 - 289*c**3/3 - 9826*c**2/3 + 22*c. Factor o(w).
-(w + 34)**3/6
Suppose -2*l - 5 = -a, 0 = -4*a + 3*l + 4 + 6. Let c be (-22)/40 + a + (-3)/12. Factor -c*i**2 + 1/5*i + 2/5.
-(i - 2)*(i + 1)/5
Let i(y) = 5*y**3 - 9*y**2 + 3*y + 23. Let m(b) = -10*b**3 + 20*b**2 - 5*b - 45. Let v(r) = -5*i(r) - 3*m(r). Factor v(a).
5*(a - 2)**2*(a + 1)
Let b(v) = -v**4 + 9*v**3 + 19*v**2 - 3*v - 34. Let d(l) = -2*l**4 + 9*l**3 + 18*l**2 - 4*l - 36. Let y(h) = -6*b(h) + 4*d(h). Determine i, given that y(i) = 0.
-5, -3, -2, 1
Suppose -s + 4*k - 15 = 0, -4*s + k + 3 - 18 = 0. Let i be (-42)/9 - (s + -2). Find w such that i*w**5 + 0*w + 0*w**2 - 1/3*w**4 + 0*w**3 + 0 = 0.
0, 1
Let y(u) = 3*u**3 + 14*u**2 - 30*u + 3. Let k(z) = 4*z**3 + 21*z**2 - 45*z + 6. Let m(j) = 5*k(j) - 7*y(j). Factor m(q).
-(q - 3)**2*(q - 1)
Let w = 1956 - 1952. Let -4/7*b**2 + 4/7*b**w + 2/7*b - 2/7*b**5 + 0 + 0*b**3 = 0. What is b?
-1, 0, 1
Let j = -27240 + 81728/3. Factor j*x - 8/3*x**2 + 2/3*x**3 + 0.
2*x*(x - 2)**2/3
Let r = 549 - 537. Find k such that 104/5*k**2 + r*k**3 + 52/5*k + 8/5 = 0.
-1, -2/5, -1/3
Suppose -166*h**3 + 8*h - 17*h**4 + 79*h**3 + 20*h**2 + 81*h**3 - 5*h**5 = 0. Calculate h.
-2, -2/5, 0, 1
Suppose -3/4*c**3 + 0*c - 3/4*c**5 - 9/2*c**2 + 0 + 3*c**4 = 0. What is c?
-1, 0, 2, 3
Factor -50231*d - 5*d**3 + 5*d**4 + 50231*d.
5*d**3*(d - 1)
Find s such that 2 - 5*s + 5/4*s**3 - 3/4*s**4 + 5/2*s**2 = 0.
-2, 2/3, 1, 2
Suppose 108 = 103*c - 99*c. Factor -c*f**2 + 12*f - 4/3.
-(9*f - 2)**2/3
Let k(m) be the second derivative of 1/9*m**6 + 0 + 18*m + 4/9*m**3 - 1/3*m**4 + 1/3*m**2 - 2/15*m**5. Let k(w) = 0. What is w?
-1, -1/5, 1
Let f(q) be the second derivative of q**4/84 + 22*q**3/7 + 2178*q**2/7 + q + 287. Determine t so that f(t) = 0.
-66
Let i be (0 - 1 - 1)/(84/(-126)). Let n = 1/2 + i. Determine w, given that 5/2*w**2 - n*w**5 - 5/2*w**4 - w + 0 + 9/2*w**3 = 0.
-1, 0, 2/7, 1
Suppose -36 = -2*s - 2*s. Suppose -6*p = s - 123. Factor -22*q**5 + 2*q - q**2 + 43*q**5 - 6*q**3 - q**4 - p*q**5.
q*(q - 2)*(q + 1)**2*(2*q - 1)
Factor -38*n + 110*n - 79*n**2 - 173*n**2 - 12*n**4 + 112*n**3.
-4*n*(n - 6)*(n - 3)*(3*n - 1)
Let w(j) be the first derivative of j**6/1080 + j**5/540 - j**4/108 + 6*j**2 - 4. Let u(m) be the second derivative of w(m). Solve u(a) = 0 for a.
-2, 0, 1
Let s(u) be the second derivative of -u**5/300 - u**4/15 - 8*u**3/15 + 2*u**2 + 5*u. Let l(c) be the first derivative of s(c). Factor l(y).
-(y + 4)**2/5
Let p(c) = -c**2 + 6*c + 10. Let g be p(7). Let q = g + -1. Suppose 6*a**q + 10*a**3 + 13*a**3 - 25*a**3 - 6*a + 2 = 0. What is a?
1
Suppose 4*k + 8 + 27 = 5*j, 0 = 4*k. Find l, given that 5*l + 12 + 5*l + 3*l**2 - j + 2*l**2 = 0.
-1
Let o(h) = -4*h**3 - 2*h**2 - h. Let v be o(-1). Suppose 6*y = u + v*y + 2, 0 = 5*y - 10. Factor q**5 - 2*q**5 + u*q**3 + 0*q**5 + 2*q**2 - 3*q - 2.
-(q - 2)*(q - 1)*(q + 1)**3
Let x be 35/140*(-2 + 2). Let j = -41/3 - -14. What is t in x - j*t**4 + 2/3*t**3 - 1/3*t**2 + 0*t = 0?
0, 1
Let c(z) = -12*z**3 + 32*z**2 + 140*z + 64. Let r(u) = 8*u**3 - 22*u**2 - 93*u - 43. Let l(y) = -5*c(y) - 8*r(y). Find a, given that l(a) = 0.
-1, 6
Suppose 0 = 5*q + 8*q - 78. Let d be -4 + 6 + -2 + q/4. Solve 9/4*m**2 + 0 + 3/4*m**5 - d*m - 9/4*m**4 + 3/4*m**3 = 0 for m.
-1, 0, 1, 2
Let s(w) = w**2 - w - 1. Suppose 3*c - q - 1 = -c, 0 = -2*c + 5*q - 13. Let i(o) = -12*o**2 + 6*o + 9. Let m(h) = c*i(h) + 9*s(h). Find a, given that m(a) = 0.
-1, 0
Let m = 7 - 5. Factor -2*k**5 - 3*k**4 + 2 + 4*k**3 - 30*k + 28*k + 0*k**4 + 5*k**4 - 4*k**m.
-2*(k - 1)**3*(k + 1)**2
Let s(i) be the first derivative of i**6/720 - i**4/144 - 11*i**2/2 - 7. Let l(v) be the second derivative of s(v). Factor l(f).
f*(f - 1)*(f + 1)/6
Let 5*a**4 - 3*a**4 + 8*a - 3*a**4 + a**5 - 4*a**2 + 0*a**4 + 2*a**4 - 6*a**3 = 0. What is a?
-2, 0, 1, 2
Let p be (33/44)/((-45)/(-2)). Let k(o) be the second derivative of o + 4/15*o**3 + p*o**4 + 0 + 4/5*o**2. Factor k(u).
2*(u + 2)**2/5
Factor 4/5*n + 14/5*n**3 + 0 - 18/5*n**2.
2*n*(n - 1)*(7*n - 2)/5
Let u(g) be the second derivative of g**7/42 - g**6/10 + g**5/20 + g**4/4 - g**3/3 + 195*g. Let u(r) = 0. Calculate r.
-1, 0, 1, 2
Let s(w) = w**3 - w**2 + 22 + 10*w + 0*w**2 + 11*w**2 - 10. Let f be s(-9). Factor 11*l**2 + 18 - l**f + 3*l**3 - 30*l - 4*l**3 + 3*l**2.
-2*(l - 3)**2*(l - 1)
Let i be 3/3*11*24/132. Let 0 + 3/2*t - 15/2*t**i = 0. What is t?
0, 1/5
Let l(k) be the first derivative of k**7/14 + 3*k**6/10 - k**4 + 19*k - 47. Let x(s) be the first derivative of l(s). What is y in x(y) = 0?
-2, 0, 1
Let v(i) = 2*i**3 + 18*i**2 - 19*i - 6. Let k(x) = x**3 + 10*x**2 - 10*x - 4. Let m(y) = 11*k(y) - 6*v(y). Solve m(r) = 0.
-2, 2
Let f(r) = -r**3 + r**2 - 1. Let l be f(-2). Suppose -l = c - 5*q - 0*q, 11 = 2*c + q. Factor -4*d**4 + 4*d**3 + 19