5/45 - 73*a**4/27 - 22*a**3/9 - 4*a**2/9 - 283*a. Solve z(h) = 0.
-1, -1/14, 2
Let z(i) be the second derivative of i**6/30 - i**5/20 - i**3/6 + i**2/2 + i + 82. Let x(r) = -12*r**2 + 8*r + 4. Let b(n) = x(n) + 4*z(n). Factor b(y).
4*(y - 2)*(y - 1)*(y + 1)**2
Let v(q) be the first derivative of -1/360*q**6 + 0*q**4 + 33/2*q**2 - 1/180*q**5 + 0*q + 0*q**3 - 44. Let d(f) be the second derivative of v(f). Factor d(x).
-x**2*(x + 1)/3
Let n(h) be the third derivative of 55*h**8/84 + 157*h**7/42 + 73*h**6/12 + h**5/12 - 35*h**4/6 + 10*h**3/3 - 1648*h**2. Suppose n(f) = 0. Calculate f.
-2, -1, 2/11, 1/4
Let u(m) be the second derivative of 78*m - 9/20*m**5 - 29/4*m**4 - 9/2*m**2 + 0 - 55/6*m**3. Factor u(r).
-(r + 9)*(3*r + 1)**2
Suppose 1076*r - 1081*r - 8 = q, 3*r - 2*q - 16 = 0. Find i such that -2/5*i**3 - 2/5*i**2 + 0*i - 6/5*i**5 + r + 2*i**4 = 0.
-1/3, 0, 1
Factor -30 + 0*k**3 - 3*k**2 - 3*k - k + 7*k**2 - 7*k + k**3.
(k - 3)*(k + 2)*(k + 5)
Let n(r) be the third derivative of -1/60*r**5 - 58*r**2 + 3/8*r**4 + 0 - 7/3*r**3 + 0*r. Solve n(v) = 0 for v.
2, 7
Let r = 3653/71860 + -3/3593. Let i(t) be the third derivative of 2/105*t**7 + 0 + 1/15*t**6 - r*t**5 + 0*t + 1/3*t**3 - 5/24*t**4 + 18*t**2. Factor i(l).
(l + 1)*(l + 2)*(2*l - 1)**2
Suppose -45*h = 671 - 761. Let z(k) be the first derivative of 4*k - k**h + 1/2*k**4 - 4/3*k**3 + 2. Factor z(w).
2*(w - 2)*(w - 1)*(w + 1)
Let v(r) be the third derivative of -r**7/105 + 29*r**6/10 - 7393*r**5/30 - 1276*r**4 - 7744*r**3/3 + r**2 + 259*r. Let v(z) = 0. What is z?
-1, 88
Let u = -167/1378 + 10381601/20670. Let n = u + -502. Factor 24/5 + 8/5*p + n*p**2.
2*(p + 6)**2/15
Suppose 9*z - 18 - 9 = 0. Find a such that -a**3 - a**4 + 9 + 0*a**2 + 11*a + z*a**2 - 3 + 0 - 2*a**3 = 0.
-3, -1, 2
Let y(v) be the third derivative of -v**7/11340 - v**6/3240 + v**4/12 + 2*v**3/3 + 13*v**2 - v. Let n(t) be the second derivative of y(t). Factor n(w).
-2*w*(w + 1)/9
Let o be 3*(-5)/(-3)*(-8)/(-10). Find i such that -9 + 5 + o*i**2 + 0 = 0.
-1, 1
Let f(k) be the third derivative of -5*k**7/28 + 23*k**6/80 + 13*k**5/10 + k**4/4 + 3*k**2 + 769. Suppose f(m) = 0. What is m?
-1, -2/25, 0, 2
Let t(s) be the second derivative of -s**6/150 - 443*s**5/25 - 196249*s**4/10 - 173876614*s**3/15 - 38513670001*s**2/10 - 844*s. Factor t(p).
-(p + 443)**4/5
Suppose 3*s + 22*v - 118 = 17*v, s - 54 = 2*v. Suppose -4*r = 3 - 11. Factor r*o + 2*o**2 + s*o + 245 + 22*o + 3*o**2.
5*(o + 7)**2
Suppose o**3 + 107*o - 141/5*o**2 + 1/5*o**4 - 80 = 0. Calculate o.
-16, 1, 5
Let n = -266361 - -266363. Factor 0 - 2/3*h + 4/9*h**n + 2/9*h**3.
2*h*(h - 1)*(h + 3)/9
Let m = -1669889 + 1669891. Let -6/11*n - 80/11 + 2/11*n**m = 0. Calculate n.
-5, 8
Let m be 16 - -78 - (3 - 6). Let i = 101 - m. Find d such that 3*d**i + 0 - 2/7*d - 34/7*d**3 + 15/7*d**2 = 0.
0, 2/7, 1/3, 1
Suppose -2*s - 42 = -3*i + s, -s = i - 8. Factor 19*h**4 + i*h**3 + 5*h**4 + 114*h**2 + 17 - 62*h**3 - 3*h**5 - 84*h - 24*h**3 + 7.
-3*(h - 2)**3*(h - 1)**2
Let a = 55 + -51. Suppose -3*h = -5*h + a. Determine d so that -4*d**2 + d**2 + 3*d**h + d**2 = 0.
0
Suppose 2*u - 4*u - 55 = -13*z, 0 = 3*z + u - 1. Let n(v) be the first derivative of -1/14*v**4 + 0*v - v**2 + 16/21*v**z + 27. Let n(r) = 0. Calculate r.
0, 1, 7
Let m = -9479 - -9479. Let h(i) be the first derivative of 2/45*i**5 + m*i**2 - 1/18*i**4 - 30 + 1/27*i**6 - 2/27*i**3 + 0*i. Factor h(k).
2*k**2*(k - 1)*(k + 1)**2/9
Suppose 0*c**2 + 2/3*c**3 + 0 - 128/3*c = 0. Calculate c.
-8, 0, 8
Suppose -2*k + 450*f + 16 = 445*f, 3*k - 4*f = 17. Let -s - 1 + 111/4*s**2 - 27/2*s**k = 0. Calculate s.
-1/6, 2/9, 2
Let k(h) = 9*h**4 + 21*h**3 + 51*h**2 + 39*h + 6. Let d(o) = -7*o**4 - 21*o**3 - 50*o**2 - 38*o - 4. Let u(s) = 3*d(s) + 2*k(s). Solve u(c) = 0 for c.
-3, -2, 0
Let c(w) = -w + 1. Suppose r + p = 0, 0 = -r - 3*p - 2*p - 4. Let k(i) = 3*i**2 - 60*i + 57. Let v(z) = r*k(z) + 6*c(z). Factor v(n).
3*(n - 21)*(n - 1)
Let o(m) be the first derivative of -3/4*m**2 - 21/20*m**5 + 13/4*m**3 + 3/2*m**4 - 52 + 0*m. Find f such that o(f) = 0.
-1, 0, 1/7, 2
Let c = -13655/3 + 27445/6. Let j(w) be the second derivative of -23*w - 25/3*w**3 - c*w**2 - 5/12*w**4 + 0. Solve j(r) = 0 for r.
-9, -1
Let d(w) = 21*w - 3440. Let p be d(164). Let f(l) be the first derivative of 4*l**p + 8*l**2 - 4*l - 40 - 8*l**3 - 4/5*l**5. Factor f(c).
-4*(c - 1)**4
Let z(w) be the first derivative of w**3/3 - 201*w**2 + 40401*w + 1673. Let z(g) = 0. Calculate g.
201
Let y(b) = -4*b + 34. Let u be y(8). Let l(d) = -d**2 - 17*d + 44. Let a(h) = -3*h**2 - 69*h + 177. Let v(n) = u*a(n) - 9*l(n). Factor v(o).
3*(o - 2)*(o + 7)
Let p be (-354)/(-40) + (-27 - (-415)/15)*(-30)/16. Factor -2/5*l**3 + 68/5 + p*l - 32/5*l**2.
-2*(l - 2)*(l + 1)*(l + 17)/5
Let j(q) be the first derivative of -q**6/40 + q**4/8 + 7*q**2 + 3*q - 125. Let p(m) be the second derivative of j(m). Suppose p(u) = 0. What is u?
-1, 0, 1
Let q = 1625861/4 - 406465. Factor -j**3 + j + 1/4*j**2 + 0 - q*j**4.
-j*(j - 1)*(j + 1)*(j + 4)/4
Let d(v) be the first derivative of -v**3 - 9/5*v**5 + 0*v + 1/2*v**6 + 17 + 0*v**2 + 9/4*v**4. Factor d(i).
3*i**2*(i - 1)**3
Suppose 44 = 2*y - 5*x, 40 = -y + 4*y - x. Factor -5*l**2 + 6*l**2 - y - 39*l - 21 + 7*l.
(l - 33)*(l + 1)
Suppose a + 4*d = -4*a + 24, d = 6. Suppose 3/4*n**2 - 27/4*n + a = 0. What is n?
0, 9
Let g(z) be the first derivative of -19/7*z**2 - 231 - 1/7*z**4 - 16/7*z - 9/7*z**3 + 1/35*z**5. What is a in g(a) = 0?
-2, -1, 8
Let k(c) be the first derivative of -1/12*c**4 + 47 - 11/9*c**3 + 1/6*c**2 + 11/3*c. Factor k(q).
-(q - 1)*(q + 1)*(q + 11)/3
Let v(k) be the third derivative of -7*k**5/100 - 1107*k**4/20 - 316*k**3/5 - k**2 - 1322. Solve v(p) = 0.
-316, -2/7
Let c(j) be the third derivative of j**5/300 + 17*j**4/24 - 43*j**3/15 + 922*j**2. Determine a so that c(a) = 0.
-86, 1
Solve 2/9*m**3 + 12*m**2 + 616/3*m + 10192/9 = 0 for m.
-26, -14
Factor 28/15*s**2 - 4/15 - 18/5*s.
2*(s - 2)*(14*s + 1)/15
Let p(l) = -45*l**2 + 8570*l - 8525. Let z(k) = -5*k**2 + 952*k - 947. Let s(x) = 4*p(x) - 35*z(x). Let s(h) = 0. What is h?
1, 191
Solve 29/5 + 1/5*y**2 + 6*y = 0 for y.
-29, -1
Let h(m) be the second derivative of -12*m**2 + 0 + 10*m**3 + 21*m + 3/20*m**5 - 17/8*m**4. Determine y so that h(y) = 0.
1/2, 4
Let 32/3*y - 67/3*y**2 + 25/3*y**3 + 12 - 2/3*y**4 = 0. Calculate y.
-1/2, 2, 9
Let u(h) be the first derivative of h**6/12 + 2*h**5/5 - 11*h**4/8 + h**3 - 1609. Factor u(o).
o**2*(o - 1)**2*(o + 6)/2
Let y(a) be the second derivative of a**5/15 - 80*a**4/9 - 166*a**3/3 + 5*a + 173. Factor y(d).
4*d*(d - 83)*(d + 3)/3
Let m = 30227/18444 - -171/6148. Factor 5/3*x**3 + 1/3*x**4 - m*x - 1/3*x**2 + 0.
x*(x - 1)*(x + 1)*(x + 5)/3
Let x be (-2504)/56 + (-16)/56. Let f be ((-576)/x)/((-36)/(-30)). Factor -16/3 + f*g - 1/3*g**4 + 8/3*g**3 - 8*g**2.
-(g - 2)**4/3
Let i(q) = q**2 + q + 2. Let t(w) = -2*w**3 - 10*w**2 - 8*w - 8. Let v = 323 - 319. Let n(b) = v*i(b) + t(b). Factor n(g).
-2*g*(g + 1)*(g + 2)
Let h(i) be the third derivative of -i**6/360 - 17*i**5/30 + 23*i**4/8 - 52*i**3/9 + 23*i**2 + 55. What is k in h(k) = 0?
-104, 1
Suppose 357*h = -617*h - 809*h + 8915. Solve 0 + 14/3*l**3 + 0*l + 0*l**4 - 2/3*l**h + 4*l**2 = 0 for l.
-2, -1, 0, 3
Factor -4/7*l**2 - 1108/7*l + 1112/7.
-4*(l - 1)*(l + 278)/7
Let x be 21*(-24)/(-9) + 2. Let u be -11 + 4 - x/(-8). Factor -u*m**2 - 25 - 5*m.
-(m + 10)**2/4
Let a(l) = -8*l**2 + l + 7. Let d(q) = -26*q**2 + 4*q + 22. Let u(o) = -10*a(o) + 3*d(o). Let h be u(-2). Find m, given that -2/9*m - 2/3*m**2 + h = 0.
-1/3, 0
Let j(n) be the first derivative of n**7/168 + 17*n**6/36 + 289*n**5/24 + 86*n**3/3 - 99. Let a(h) be the third derivative of j(h). Solve a(o) = 0.
-17, 0
Let t(w) be the third derivative of 6*w - 2*w**2 - 37/18*w**4 - 1/90*w**6 + 4*w**3 + 4/9*w**5 + 0. Factor t(z).
-4*(z - 18)*(z - 1)**2/3
Let g(v) be the first derivative of 14*v**3/3 - 4*v**2 - 4*v - 67. Let s(z) = -12*z**2 + 7*z + 4. Let c(f) = 5*g(f) + 6*s(f). Determine t, given that c(t) = 0.
-1, 2
Let j(o) be the third derivative of -107*o**2 + 1/16*o**4 + 0*o - 1/60*o**5 + 0 - 1/240*o**6 + 0*o**3. Factor j(b).
-b*(b - 1)*(b + 3)/2
Let k(x) be the first derivative of -x**7/210 - 19*x**6/90 - 7*x**5/6 - 17*x**4/6 + 58*x**3/3 - 108. Le