2 - 1/240*n**6 + 0. Factor c(t).
(t - 2)*(t - 1)**2*(t + 1)/6
Let j(g) be the first derivative of -3*g**5/5 + 21*g**4/2 - 72*g**3 + 240*g**2 - 384*g - 79. Factor j(y).
-3*(y - 4)**3*(y - 2)
Factor 2/9*t**4 + 0 + 0*t**3 - 8/3*t**2 - 32/9*t.
2*t*(t - 4)*(t + 2)**2/9
Let u = 729 + -728. Solve -1/2*g**2 + 3/2*g - 1/2*g**4 + u - 3/2*g**3 = 0 for g.
-2, -1, 1
Let x(h) = -17*h**4 + 2*h**3 - 10*h**2 - 23*h + 13. Let f(n) = 5*n**4 - n**3 + 3*n**2 + 7*n - 4. Let p(z) = 21*f(z) + 6*x(z). Suppose p(s) = 0. What is s?
-1, 1, 2
Let u be (-4016)/(-364) - 60/130. Solve 120/7*n + u*n**2 + 72/7 + 20/7*n**3 + 2/7*n**4 = 0 for n.
-3, -2
Let p(v) be the second derivative of 0*v**2 + 4/3*v**3 + 7/3*v**4 - 1/6*v**7 + 0 - 22*v - 3/10*v**5 - 23/30*v**6. Let p(j) = 0. What is j?
-2, -2/7, 0, 1
Solve -3/5*v**3 + 93/5*v + 18 + 0*v**2 = 0 for v.
-5, -1, 6
Suppose 2*a + l + 4 = 5*l, -3*l = -9. Let y be (-1)/4 - (-36)/80. Factor -1/5*p**5 - 1/5*p**a + 0 + y*p**2 + 1/5*p**3 + 0*p.
-p**2*(p - 1)*(p + 1)**2/5
Factor -32*m - 9*m**3 - 3*m**3 + 158*m**2 - 90*m**2 + 4*m**4 - 4*m**3 - 24*m**3.
4*m*(m - 8)*(m - 1)**2
Let f(j) be the second derivative of 0*j**4 + 0*j**3 + 0*j**2 + 22*j - 1/15*j**6 - 3/20*j**5 + 1/42*j**7 + 0. Solve f(q) = 0 for q.
-1, 0, 3
Let m(g) be the second derivative of g**6/720 + g**5/240 - g**4/24 - 19*g**3/6 - 9*g. Let s(v) be the second derivative of m(v). What is y in s(y) = 0?
-2, 1
Let w(b) be the third derivative of 0*b**5 - 1/660*b**6 - 11*b**2 + 0 + 0*b**3 + 0*b + 0*b**4. Find v, given that w(v) = 0.
0
Suppose 50*h - 12 = 38*h. Let w(l) be the first derivative of 0*l + 1/13*l**4 - 2/65*l**5 - 2/39*l**3 - h + 0*l**2. Find b, given that w(b) = 0.
0, 1
Suppose 23*h = 48*h + 48*h. Factor h + 10/3*i**2 + 4/3*i.
2*i*(5*i + 2)/3
Let r(c) be the third derivative of c**8/30240 + c**5/15 + 11*c**2. Let q(d) be the third derivative of r(d). Suppose q(m) = 0. What is m?
0
Let k(a) = -a**3 - 4*a**2 - 4*a. Let o(b) = -b**3 - 4*b**2 - 3*b. Let d(w) = 3*k(w) - 4*o(w). Factor d(g).
g**2*(g + 4)
Let u = 21109/42210 - 2/21105. Let 0 + u*b**5 + 0*b**2 + 1/2*b**3 + 0*b + b**4 = 0. Calculate b.
-1, 0
Let z(g) = -g + 4. Let s be z(9). Let w = -2 - s. Determine f so that 2*f**4 - 2*f**4 + 4*f**w - 2*f**5 - 2*f**4 = 0.
-2, 0, 1
Let i be -2 - (-28315)/(-25)*-1. Let x = i - 1127. Factor 2/5*d**3 + x + 14/5*d**2 + 6*d.
2*(d + 1)*(d + 3)**2/5
Let y = -79 - -81. Let i(f) be the first derivative of -1/8*f**y + 4 + 0*f + 1/12*f**3. Factor i(z).
z*(z - 1)/4
Let f(v) be the second derivative of 5/4*v**4 + 27/2*v**3 - 22*v + 15*v**2 + 0. Factor f(t).
3*(t + 5)*(5*t + 2)
Let c be 3/(-18) + 625/390. Let w = c + -4/39. Determine d, given that -2/3*d**2 + w*d - 2/3 = 0.
1
Suppose 0 = 2*v - 2. Let q be ((-30)/(-8) + -3)*v. Solve -q*w**2 - 1/2*w - 1/4*w**3 + 0 = 0 for w.
-2, -1, 0
Let l(i) be the first derivative of 2*i**6/9 + 28*i**5/15 + 8*i**4/3 - 64*i**3/9 - 203. Find p, given that l(p) = 0.
-4, 0, 1
Let n(d) = d**2 - 4. Let r(o) = -3*o**2 - 7*o + 16. Let p(q) = -4*n(q) - r(q). Factor p(k).
-k*(k - 7)
Let q(f) be the first derivative of 13 - 1/4*f**4 - 1/10*f**5 + 0*f**2 + 0*f - 1/6*f**3. Factor q(u).
-u**2*(u + 1)**2/2
Let z = 39865/50559 - -32/887. Let c = 22/19 - z. Find b such that 8/3*b + 4/3 - 8/3*b**3 - c*b**2 - b**4 = 0.
-2, -1, -2/3, 1
Suppose 30*x = 26*x + 16. Solve -6 - 38*q**2 - 8*q**x + 32*q**5 - 33*q**5 - 25*q**3 - 28*q - 2 = 0.
-2, -1
Suppose 4*p - 14 = 3*i, 9*i - 8*i + 5*p - 27 = 0. Factor -5*a**3 + 551*a**2 - 571*a**i - 10 - 9*a - 16*a.
-5*(a + 1)**2*(a + 2)
Let n(a) = -a**3 + 2*a**2 + 24*a + 4. Let c be n(6). Factor 12*d**3 - 1390*d + 3*d**c + 9*d**2 + 1390*d.
3*d**2*(d + 1)*(d + 3)
Let r = -34 - -27. Let s(t) = t**3 + 8*t**2 + 8*t + 9. Let c be s(r). What is w in -16*w**3 + 1 + 2 + 13*w**3 + 9*w**c - 9*w = 0?
1
Let l be 3/7 + (208/(-28) - -7). Let x(y) be the second derivative of 0*y**5 + 0*y**3 - 4*y + l - 1/210*y**6 + 0*y**4 + 0*y**2. Factor x(v).
-v**4/7
Let o be ((-231)/28 + 5)/(2/(-8)). Suppose -12*x + o*x = 2. Suppose 10/3*i**x + 4/3*i**3 + 8/3*i + 2/3 = 0. What is i?
-1, -1/2
Let i(v) be the third derivative of -3*v**2 - 2/9*v**4 + 0 + 16/9*v**3 + 1/90*v**5 + 0*v. Solve i(o) = 0 for o.
4
Let a(x) = -4*x**2 + 0 + 0 - 11*x**2 + 6 - 21*x. Let l(n) = -n**2 - n + 1. Let r(s) = -a(s) + 12*l(s). Let r(g) = 0. What is g?
-2, -1
Let k(u) = -30 - 24*u + 25*u**3 + 55*u**2 + 5*u - 21*u. Let s(j) = -13*j**3 - 28*j**2 + 20*j + 15. Let x(n) = -3*k(n) - 5*s(n). Factor x(z).
-5*(z - 1)*(z + 3)*(2*z + 1)
Let i(a) be the third derivative of -a**8/252 + 8*a**7/315 - a**6/30 - 106*a**2. Factor i(p).
-4*p**3*(p - 3)*(p - 1)/3
Suppose 4*a = y + 1283, -3*y + 110 = 2*a - 521. What is c in 52*c**3 + 486*c - 66 - a*c**2 - 33 + 27 + 30*c = 0?
2/13, 3
Let m(q) be the third derivative of 2*q**7/105 + q**6/10 - q**5/5 - 11*q**4/6 - 4*q**3 - 144*q**2. Solve m(b) = 0 for b.
-3, -1, 2
Let o(w) be the third derivative of w**8/2016 + 29*w**7/1260 + 13*w**6/90 + 5*w**5/18 - 80*w**2 + 1. Factor o(v).
v**2*(v + 2)**2*(v + 25)/6
Find b such that 4*b**3 - 2*b**3 + 202*b + 128 - 32*b**2 - 101*b - 109*b = 0.
-2, 2, 16
Let j(t) be the first derivative of t**7/280 + t**6/120 + 16*t**3/3 - 3. Let u(q) be the third derivative of j(q). Suppose u(y) = 0. What is y?
-1, 0
Let 2/11*a**2 + 6/11*a - 8/11 = 0. What is a?
-4, 1
Suppose -328*t + 16 = -320*t. Suppose 3/7*m**t - 30/7*m + 75/7 = 0. What is m?
5
Suppose 4*b + 4*y - 24 = 0, y = 2*b - 5*b + 12. Find g such that g + 6*g**2 - 78*g**3 + g + 76*g**b - 6 = 0.
-1, 1, 3
Let s be ((168/(-18))/4)/((-70)/60). Solve 0 - 1/3*r - 1/3*r**s = 0 for r.
-1, 0
Suppose 12*c - 9*c + 24 - 24 - c**2 = 0. What is c?
0, 3
Let p be 172/8 + (-22 - -2). Factor -2*h + 1/2*h**2 + p.
(h - 3)*(h - 1)/2
Let x = 7/5897 + 17663/23588. Factor 0 + 1/2*v**3 + 5/4*v**4 - x*v**2 + 0*v.
v**2*(v + 1)*(5*v - 3)/4
Let h(g) be the first derivative of 3*g**5/5 + 39*g**4/4 + 12*g**3 + 381. Factor h(x).
3*x**2*(x + 1)*(x + 12)
Let r(o) be the third derivative of 1/20*o**5 + 0*o**3 - 37*o**2 + 0*o**4 + 0 + 0*o. Factor r(d).
3*d**2
Let h be (3/(-2))/(1/(-2)). Let t = 51712/5 + -10341. Factor 2/5*g + 9/5*g**h + 0 + t*g**2 + g**4 + 1/5*g**5.
g*(g + 1)**3*(g + 2)/5
Suppose 3*q + 2*u - 4 = 0, -2*u + 8 = -5*q + 36. Suppose 2*i = 5*f - 8, -2*f - 4*i + q = -4. Solve 2/5*t**f + 4/5 + 6/5*t = 0.
-2, -1
Let u(h) be the second derivative of -3/2*h**2 - 1/12*h**4 + 6*h + 2/3*h**3 + 0. Determine g so that u(g) = 0.
1, 3
Let g(r) = r**2 + 492*r + 2439. Let s be g(-5). Find y such that 8/3*y**2 + 4/9*y**s + 16/9*y - 20/9*y**3 - 32/9 = 0.
-1, 2
Let d(k) = 15*k**2 + 29*k - 29. Let x(n) = -7*n**2 - 15*n + 14. Let o(r) = 2*d(r) + 5*x(r). What is s in o(s) = 0?
-4, 3/5
Let w(u) be the second derivative of -1/20*u**5 + 0 + 6*u - 3/200*u**6 - u**2 - 1/20*u**4 + 0*u**3. Let l(j) be the first derivative of w(j). Factor l(m).
-3*m*(m + 1)*(3*m + 2)/5
Let j(u) be the second derivative of -1/12*u**3 - u**2 - 1/24*u**4 - 1/120*u**5 + 0 + 5*u. Let l(x) be the first derivative of j(x). Factor l(c).
-(c + 1)**2/2
Let n = 10065/4 + -2511. Suppose 6*k + n*k**2 - 12 + 3/4*k**3 = 0. What is k?
-4, 1
Let h(i) be the second derivative of -4*i**7/21 - 43*i**6/105 + 39*i**5/70 + 2*i**4/3 + 4*i**3/21 + 7*i - 10. Solve h(y) = 0 for y.
-2, -2/7, -1/4, 0, 1
Solve -7 - 8 - 3 - 66*o**2 + 78*o**2 - 3*o - 3*o**3 = 0 for o.
-1, 2, 3
Factor 497 + 6*r**2 - 499 - r**2 + 847 - 130*r.
5*(r - 13)**2
Let y(j) be the first derivative of -j**6/150 + j**4/40 + j**3/30 - 2*j**2 + 7. Let w(g) be the second derivative of y(g). Determine x so that w(x) = 0.
-1/2, 1
Let h(d) = 7*d**5 - 10*d**4 - 30*d**3 + 100*d**2 - 97*d + 29. Let s(o) = 2*o**5 - 2*o - 1. Let p(b) = -h(b) + s(b). Let p(u) = 0. Calculate u.
-3, 1, 2
Let b(h) be the first derivative of 1/72*h**4 + 0*h**3 + 4 + 0*h + 3*h**2 - 1/360*h**6 + 0*h**5. Let m(l) be the second derivative of b(l). Factor m(i).
-i*(i - 1)*(i + 1)/3
Find u such that 4375*u**2 - 124 - 20*u**4 + 130*u**3 + 374*u - 4753*u**2 + 18*u**4 = 0.
1, 62
Factor 0*i - 4/3*i**4 + 8/3*i**2 + 4/3*i**3 + 0.
-4*i**2*(i - 2)*(i + 1)/3
Let y = 3979 - 51667/13. Let l = y + -394/91. Factor 2/7*z**3 + 2/7 - l*z**2 - 2/7*z.
2*(z - 1)**2*(z + 1)/7
Let b(y) = y**3 - 7*y**2 + y + 30. Let q be b(6). Suppose -8*v + 7 = -4*v + 5*a, -a - 1 = q. Suppose -2