 i + -16. Determine x so that 8*x + 6 + 5*x + 3*x**3 + c*x**2 + 2*x = 0.
-2, -1
Let t(d) be the first derivative of d**4/46 + 2*d**3/23 - 13*d**2/23 - 30*d/23 - 189. Let t(g) = 0. Calculate g.
-5, -1, 3
Let f(p) = p**5 - 3*p**3 + 2*p**2 + 2. Let d(x) = -1. Let j(a) = 2*d(a) + f(a). Factor j(w).
w**2*(w - 1)**2*(w + 2)
Let p(c) be the second derivative of -3*c**5/100 + 13*c**4/10 + 27*c**3/10 - 75*c - 2. What is v in p(v) = 0?
-1, 0, 27
Let j = 174561/5 - 34912. Let o = 52 - 257/5. Find x, given that 2/5*x + j*x**2 - o = 0.
-3, 1
Let x(w) = -3*w**3 + 18*w**2 - 12*w - 7. Let a(s) = -s**2. Let b(i) = 6*a(i) + x(i). Let m(v) be the first derivative of b(v). Let m(q) = 0. Calculate q.
2/3, 2
Suppose 4*g + 6*g = 100. Let q(f) = 5*f**2 + 20*f - 5. Let l(p) = -2*p. Let w(d) = g*l(d) + q(d). Factor w(r).
5*(r - 1)*(r + 1)
Let f = -40 + 47. Suppose 20 = 2*k + 2*p, -5*k - f = -p - 27. Find a, given that -49*a**3 - k*a - a - 17*a**3 + 44*a**4 + 38*a**2 - 26*a**4 = 0.
0, 1/3, 3
Solve -52/17 - 2/17*i**3 + 6*i - 48/17*i**2 = 0.
-26, 1
Solve -1/3*k**5 + 64/3 - 4/3*k**3 + 7/3*k**4 - 44/3*k**2 + 32/3*k = 0.
-2, -1, 2, 4
Let q(a) = 20*a**3 - a**2 + 3*a - 2. Let d be q(1). Suppose -o - i + 5 = 6, -4*o + d = -4*i. Find u, given that 1/3*u**o + 1/6*u**3 - 1/6*u - 1/3 = 0.
-2, -1, 1
Let f = 433/12 - 36. Let u(z) be the third derivative of 5*z**2 - 1/60*z**5 + 0*z**4 + 0*z + f*z**3 + 0 + 0*z**6 + 1/420*z**7. Solve u(m) = 0.
-1, 1
Suppose 3*c - 37 + 70 = 0. Let n = c + 13. Factor -1/7*w**n + 2/7*w + 0.
-w*(w - 2)/7
Let n(o) be the first derivative of -5*o**3/3 - 35*o**2 - 65*o + 100. Determine j so that n(j) = 0.
-13, -1
Suppose 3*b - 1 = 5*t, 6*b - 3*t = 2*b + 5. Factor b*a**5 + 4*a - 4*a**5 - 6*a + 4*a**3.
-2*a*(a - 1)**2*(a + 1)**2
Let v be 3/(-5) + (6976/(-240))/(-4). Factor -50/3*j**2 + v*j - 2/3.
-2*(5*j - 1)**2/3
Suppose -4 = 4*k + 3*p - 4*p, 0 = 5*k + 2*p + 18. Let z be 3 - (-124)/(-44) - k. Find r, given that 8/11 - 6/11*r**3 - z*r + 2*r**2 = 0.
2/3, 1, 2
Let z(y) be the second derivative of 0 + 1/105*y**6 + 0*y**2 - 1/70*y**5 + 0*y**4 + 0*y**3 - 18*y. Factor z(o).
2*o**3*(o - 1)/7
Let x be (-788)/11426 - 1*(-1317)/174. Factor x*z**2 - 3/2*z**3 - 12 - 3*z.
-3*(z - 4)*(z - 2)*(z + 1)/2
Let j(h) be the first derivative of -h**6/240 + h**5/40 - h**4/16 + h**3/12 - 9*h**2/2 + 13. Let i(g) be the second derivative of j(g). Factor i(u).
-(u - 1)**3/2
Determine k so that 4/3*k**4 - 2*k**3 - 2/9*k**5 + 0*k + 8/9*k**2 + 0 = 0.
0, 1, 4
Let r be (-5)/(-4 - 1) - -2. Factor 6*j**r - 13 + 13 - j**2 - 7*j**3.
-j**2*(j + 1)
Factor -10*s**2 + 6*s**2 - 5*s**3 + 7*s + s**2 + 4*s**3 + 2*s + 27.
-(s - 3)*(s + 3)**2
Let q(c) be the first derivative of -3*c**4/4 + 6*c**2 - 48. Solve q(z) = 0 for z.
-2, 0, 2
Suppose 328*x**2 - x**3 - 15*x**3 + 8*x**3 + 6*x**3 - 747*x - 12367*x - 27556 = 0. What is x?
-2, 83
Let n(j) be the first derivative of j**6/60 - j**5/20 - j**4/6 + 2*j**3/3 - j - 42. Let w(y) be the first derivative of n(y). Factor w(m).
m*(m - 2)**2*(m + 2)/2
Let m(h) be the first derivative of -h**6/360 - h**5/60 - h**4/24 - 5*h**3/3 - 6. Let q(d) be the third derivative of m(d). What is u in q(u) = 0?
-1
Let y(x) be the third derivative of 0*x**3 + 0 + 0*x + 1/270*x**5 - 1/540*x**6 - 1/945*x**7 + 1/108*x**4 - 7*x**2. Factor y(g).
-2*g*(g - 1)*(g + 1)**2/9
Find s, given that -5*s - 7*s**4 + 11*s**4 - 2*s - 4 - s**4 + 7*s**3 + s**2 = 0.
-4/3, -1, 1
Let p(z) = -62*z - 744. Let a be p(-12). Factor -5*o**3 + a*o**4 + 0*o + 10/3*o**2 + 0 + 5/3*o**5.
5*o**2*(o - 1)**2*(o + 2)/3
Factor 10*g - 83*g**2 - 5*g**3 - 86*g**2 + 246*g**2 - 82*g**2.
-5*g*(g - 1)*(g + 2)
Find q, given that 1/5*q**3 - 2 + 6/5*q**2 + 3/5*q = 0.
-5, -2, 1
Let x be (-2)/((-3 - -4)*-1). Let 0*g**2 + 10 - 7*g**2 - 2*g**2 + 4*g**x - 5*g = 0. Calculate g.
-2, 1
Suppose -84*g = -82*g. Let n be ((-1)/(-5) - 0) + g. Factor 0*q + n*q**2 - 3/5*q**3 + 3/5*q**4 + 0 - 1/5*q**5.
-q**2*(q - 1)**3/5
Let j(d) be the first derivative of -3*d**4/4 + 61*d**3 - 357*d**2/2 + 177*d - 214. Suppose j(r) = 0. Calculate r.
1, 59
Let i(u) be the second derivative of u**4/24 - 5*u**3/12 - 6*u**2 - 101*u. Factor i(g).
(g - 8)*(g + 3)/2
Let k = 5982/7 - 854. Solve 0 - 2/7*x - 2/7*x**3 + k*x**2 = 0.
0, 1
Let x(o) be the first derivative of 2*o**3/21 + 76*o**2/7 + 2888*o/7 - 131. Find h, given that x(h) = 0.
-38
Let 12/5*n**3 - 63/5*n**2 + 18/5 - 57/5*n = 0. What is n?
-1, 1/4, 6
Let w = -880 - -880. Let u(q) be the first derivative of 1/5*q**5 + w*q - 5/3*q**3 - q**2 - 8 + 1/6*q**6 - 3/4*q**4. Factor u(m).
m*(m - 2)*(m + 1)**3
Suppose 2*l + 20 = 2*j - 184, 4*l = -j + 87. Let g be 3/(j/105) + 40/(-220). Let 0 + 9*z - 51/2*z**2 + 15/2*z**g = 0. What is z?
0, 2/5, 3
Let r = -615 + 615. Solve r*q - 10/11*q**5 - 56/11*q**3 - 16/11*q**2 + 0 - 4*q**4 = 0 for q.
-2, -2/5, 0
Suppose -3*k = 12, -5 = 4*q + 3*k - 1. Factor w**3 + 2*w**3 - w**2 + q - 6*w**3 - w**4 + 3*w.
-(w - 1)*(w + 1)**2*(w + 2)
Let v(h) be the second derivative of -h**6/105 + 8*h**5/35 - 13*h**4/7 + 16*h**3/3 - 7*h**2 - 592*h. Factor v(t).
-2*(t - 7)**2*(t - 1)**2/7
Let f(t) = 6*t + 59. Let g be f(-10). Let r be 3/(36/16) + g. Factor r*v**2 + v + 2/3.
(v + 1)*(v + 2)/3
Let k be 1 + ((-18)/(-15))/(10/25). Suppose -5*h + 4*n - 6*n + 18 = 0, 4*h = 5*n + 21. Let 5*v**h + 2*v + k + 3*v - 5*v**3 + 6 - 15*v**2 = 0. What is v?
-1, 1, 2
Let y(t) = -2*t - 4. Let v be y(-3). Suppose 5*o - 8 = o. Find u such that -2 - 5*u - o*u**v - 4 + u - 4*u = 0.
-3, -1
Factor -5*k + 17*k**2 + 6*k**3 - 3 - 9*k**2 - 3*k**2 - 3*k**2 + k**4 - k**5.
-(k - 3)*(k - 1)*(k + 1)**3
Suppose -2*w**4 + 69*w**2 - 108 + 23*w**2 + 19*w**2 - 15*w**3 + 78*w + w**3 - 65*w**2 = 0. Calculate w.
-9, -2, 1, 3
Let g(w) = -7*w**3 + 62*w**2 - 52*w + 3. Let d(r) = 76*r**3 - 680*r**2 + 572*r - 32. Let p(y) = -3*d(y) - 32*g(y). Factor p(s).
-4*s*(s - 13)*(s - 1)
Factor 256/9*j**2 - 2/9 - 56/9*j.
2*(4*j - 1)*(32*j + 1)/9
Let x(v) = -23*v**3 - 46*v**2 - 28*v + 19. Let d(w) = w**4 - 46*w**3 - 90*w**2 - 56*w + 39. Let p(q) = -3*d(q) + 7*x(q). Factor p(s).
-(s + 2)**2*(s + 4)*(3*s - 1)
Let t(v) be the third derivative of v**7/1155 - v**6/220 + v**5/165 - 8*v**2 + 3*v. Factor t(a).
2*a**2*(a - 2)*(a - 1)/11
Let s(w) = -w**2 - 3*w + 1. Let p be s(-4). Let a be (4/p - -1)*-12. Let 48*f**2 + 0*f + 18*f**4 - 40*f**3 - 2 - 24*f + 6 - 6*f**a = 0. What is f?
1/3, 1
Let 7/3*o**2 - 1/3*o**3 + 1/3*o - 1 - 4/3*o**4 = 0. What is o?
-1, 3/4, 1
Let z(j) be the third derivative of j**6/240 - 41*j**5/240 + 29*j**4/48 - 19*j**3/24 - 4*j**2 - 11*j. What is g in z(g) = 0?
1/2, 1, 19
Let n(a) be the third derivative of 0 + 0*a - 1/40*a**6 - 1/20*a**5 + 0*a**3 + 0*a**4 + 11*a**2. Suppose n(o) = 0. Calculate o.
-1, 0
Let w(b) = b - 10. Let m be w(12). Suppose -2*j = -2*t + 10, 3*t = -t - 2*j + m. Factor 5*o**3 + 3*o**3 + 2*o**t + 8*o**4 + o**5 - 3*o**4 + 2*o**2.
o**2*(o + 1)*(o + 2)**2
Let o be 10/(-25)*-5 - (-688)/6. Let k = o - 116. Solve -k*v**3 + 0 - 2/3*v**5 - 4/3*v**4 + 0*v + 0*v**2 = 0.
-1, 0
Suppose -30*x**2 - 96 - 3/2*x**5 + 27/2*x**4 - 30*x**3 + 144*x = 0. Calculate x.
-2, 1, 2, 4
Let v(n) be the second derivative of -4/3*n**3 + 0*n**2 - n - 13 - n**4 - 1/5*n**5. Suppose v(f) = 0. Calculate f.
-2, -1, 0
Let v(q) = -4*q - 6. Let r be v(-2). Let y(h) be the third derivative of 0*h + 0 - r*h**2 - 1/2*h**3 + 3/4*h**4 - 1/4*h**5. What is a in y(a) = 0?
1/5, 1
Let s = -35 - -38. Let p(l) be the second derivative of 1/24*l**4 + 0 + 1/12*l**s - 1/2*l**2 + 5*l. Solve p(f) = 0 for f.
-2, 1
Factor 201/5 + 207/5*r**2 + 81*r + 3/5*r**3.
3*(r + 1)**2*(r + 67)/5
Let i be (248/32 - 8) + 1/4. Factor i + 2/9*v**2 + 2/9*v.
2*v*(v + 1)/9
Let x(p) be the first derivative of -2*p**3/3 + 49*p**2 + 100*p + 96. Factor x(g).
-2*(g - 50)*(g + 1)
Let a(i) be the third derivative of 1/1512*i**8 + 0*i + 0*i**4 + 2/315*i**7 + 0*i**3 + 0*i**6 + 0 - 16/135*i**5 - 38*i**2. Factor a(c).
2*c**2*(c - 2)*(c + 4)**2/9
Let p(w) be the third derivative of 18*w**2 + 0*w - 5/14*w**4 + 16/21*w**3 + 0 - 2/105*w**5. Let p(j) = 0. What is j?
-8, 1/2
Let v be 84/117 - (-36)/(-702). Factor v*d + 0 + 2*d**2 + 4/3*d**3.
2*d*(d + 1)*(2*d + 1)/3
Let v(u) = -u**2 + u + 10. Let z(w) = 3*w**2 - 4*w - 31. Let i(y) = -11*v(y) - 4*z(y). Determine x so that i(x) = 0.
-2, 7
Let z = 64 + -61. Suppose 14*v = z*v