Let w be i(3). Let l be 1 - ((-13)/52 + 6/w). Factor -4/13 + 0*z**l - 2/13*z**3 + 6/13*z.
-2*(z - 1)**2*(z + 2)/13
Suppose -5*y - 5*f = 80, -4*y - f - 40 - 18 = 0. Let d(s) = -s**2 - 16*s - 25. Let o be d(y). Solve -2*j - o - 1/3*j**2 = 0.
-3
Let n(u) be the first derivative of 2*u - 9/14*u**2 + 11 - 1/84*u**4 - 1/7*u**3. Let k(q) be the first derivative of n(q). Solve k(x) = 0.
-3
Let t(h) be the first derivative of 3*h**6/5 + 6*h**5/5 - 11*h**4/6 + 2*h**3/3 - 22*h + 20. Let d(o) be the first derivative of t(o). Factor d(y).
2*y*(y + 2)*(3*y - 1)**2
Let u(o) = -5*o**2 - 114*o + 28. Let k be u(-23). Solve -2/3*a**2 + 10/3*a**3 + 0 - 6*a**k + 0*a - 2*a**4 = 0.
-1, 0, 1/3
Suppose -24*z**2 + 12*z**3 + 18/5*z**4 + 192/5 - 144/5*z - 6/5*z**5 = 0. What is z?
-2, 1, 2, 4
Let z be 106/(-5) - 2/(40/(-4)). Let j be 1/4 - (z/(-36) - 5). Factor 0 + 8/3*n**5 - 2/3*n**2 + j*n**4 + 4/3*n**3 + 0*n.
2*n**2*(n + 1)**2*(4*n - 1)/3
Factor -1/2*x + 0 + 5*x**3 - 11/4*x**4 - 7/4*x**2.
-x*(x - 1)**2*(11*x + 2)/4
Factor 5/2 - 145/4*z + 135/4*z**2.
5*(z - 1)*(27*z - 2)/4
Let o(n) be the second derivative of 2*n**7/147 - 4*n**6/105 - n**5/7 + 2*n**4/7 - 10*n + 2. Let o(y) = 0. What is y?
-2, 0, 1, 3
Let w(h) be the third derivative of -5*h**8/336 - 5*h**7/42 - 5*h**6/12 - 5*h**5/6 - 25*h**4/24 - 5*h**3/6 + 9*h**2 - 1. Find l, given that w(l) = 0.
-1
Let w(v) be the first derivative of 4/5*v**2 + 1/10*v**4 + 13 + 0*v + 8/15*v**3. Factor w(i).
2*i*(i + 2)**2/5
Factor 17*l**3 - 9*l**2 + 36*l**3 - 578*l**4 + 83*l**3 + l**2.
-2*l**2*(17*l - 2)**2
Let l = -38 + 38. Let y(n) be the third derivative of 0*n + l - 13/120*n**5 - 1/3*n**3 - 1/4*n**4 - 1/40*n**6 - 1/420*n**7 - n**2. Factor y(r).
-(r + 1)**2*(r + 2)**2/2
Suppose a - 5 = -4*a, -4*a = -5*i + 36. Let u be i/(-72) + (-2)/(-6). Factor -2/3*h + u*h**2 + 0.
2*h*(h - 3)/9
Let z(y) be the first derivative of 15 + 1/25*y**5 - 1/15*y**3 + 0*y - 1/10*y**2 + 1/20*y**4. Determine u so that z(u) = 0.
-1, 0, 1
Suppose 2*f - 2*n = 12, -6 = -2*f + n + 2. Factor -18 - 11*y + 10 - 8 - 2*y**f - 7*y.
-2*(y + 1)*(y + 8)
Let a(q) = 87*q**2 + 2*q - 49*q + 7 + 9*q. Let n(s) = -436*s**2 + 190*s - 34. Let k(i) = -28*a(i) - 6*n(i). Factor k(j).
4*(5*j - 1)*(9*j - 2)
Let n(l) be the third derivative of 0*l**4 - l**2 + 0*l**6 + 5/672*l**8 - 1/84*l**7 + 0 + 0*l**3 + 0*l**5 + 0*l. What is b in n(b) = 0?
0, 1
Let j(c) be the third derivative of c**9/5040 + c**8/1120 + c**7/840 + c**4/6 - 9*c**2. Let f(h) be the second derivative of j(h). Let f(w) = 0. What is w?
-1, 0
Let t be 2 - (2 + -12 + -4). Factor -49*c**4 + 75*c**4 + 4*c**3 - 38*c**4 - t*c**5.
-4*c**3*(c + 1)*(4*c - 1)
Let o(u) be the first derivative of -u**6/36 + u**5/15 + u**4/4 - 10*u**3/9 + 19*u**2/12 - u + 77. Factor o(x).
-(x - 2)*(x - 1)**3*(x + 3)/6
Let z be (-150)/(-1425) + 0 + (-87)/(-76). Find c such that 1/2 - z*c**4 + 7/4*c + 3/4*c**2 - 7/4*c**3 = 0.
-1, -2/5, 1
Suppose 0 = -457*o + 418*o + 78. Let 6/5*d**3 + 0*d + 4/5*d**4 + 0*d**o - 2/5*d**5 + 0 = 0. What is d?
-1, 0, 3
Factor -4/5*c**2 + 4/5*c**4 - 28/5*c + 0 + 28/5*c**3.
4*c*(c - 1)*(c + 1)*(c + 7)/5
Suppose 2 = -i - 2. Let h be (2/i)/(2/(-300)). Let -9*w - 85*w**3 + 2*w + 32*w**2 + 3*w + h*w**4 = 0. What is w?
0, 1/3, 2/5
Suppose 20 = -3*l + 8*l. Factor -29*d**3 + 4*d - l + 28*d**3 - d**2 + 2*d**2.
-(d - 2)*(d - 1)*(d + 2)
Let t = -987 + 989. Factor -7/4*x**t + 0 - 15/4*x**3 - 9/4*x**4 - 1/4*x.
-x*(x + 1)*(3*x + 1)**2/4
Let r be 0 + -2 - (-8)/(11 + -7). Let a(o) be the third derivative of -2/195*o**5 + 0*o**4 - 1/195*o**7 + 0 + 4/195*o**6 + 5*o**2 + 0*o + r*o**3. Factor a(c).
-2*c**2*(c - 2)*(7*c - 2)/13
Let m(t) be the third derivative of -1/255*t**5 + 0 + 0*t**4 - 26*t**2 + 1/340*t**6 + 0*t + 0*t**3 - 1/1785*t**7. Determine n so that m(n) = 0.
0, 1, 2
Let r(y) = 120*y**2 - y - 1. Let l be r(-1). Let t be 6/(-10) - (-732)/l. Factor 0 + 0*u - t*u**3 + 3/2*u**4 + 3*u**2.
u**2*(u - 3)*(3*u - 2)/2
Let c = -722/1061 + 1005383/44562. Let m = c + -121/6. Suppose 9/7*q**3 + 15/7*q**4 - m*q**5 + 3/7*q + 0 - 15/7*q**2 = 0. What is q?
-1, 0, 1/4, 1
Let v be (-40)/(-12)*6/4. Solve -15*k**3 + 10*k**2 + v*k**4 - 43 + 43 = 0.
0, 1, 2
Suppose -4*s - 20 = -64. Factor -26*v**2 - 11*v - s*v - 2*v - 18*v**3 - 8 + 6*v**3 - 2*v**4.
-2*(v + 1)**2*(v + 2)**2
Let z be (-33)/(-561) - 37/918. Let q(c) be the second derivative of 0*c**2 + 0 - 8*c + z*c**4 + 0*c**3. Solve q(x) = 0.
0
Factor -722/13 - 76/13*j - 2/13*j**2.
-2*(j + 19)**2/13
Let x(n) be the third derivative of 4/9*n**3 - 4/45*n**6 + 29/90*n**5 - 5/9*n**4 + 16*n**2 + 0 + 1/105*n**7 + 0*n. Let x(w) = 0. Calculate w.
1/3, 1, 2
Let t(u) be the first derivative of -8/15*u**5 - 3/2*u**2 - 2/3*u**4 + 0*u - 3 - 1/10*u**6 + 0*u**3. Let y(s) be the second derivative of t(s). Factor y(z).
-4*z*(z + 2)*(3*z + 2)
Let p = -607 + 4255/7. Let g = 372/7 + -52. Factor -2/7*l**2 - p + g*l.
-2*(l - 3)*(l - 1)/7
Suppose 10*c - 33 = 17. Let q(u) be the first derivative of 0*u - 3*u**3 + 3 + 9*u**4 - 21/5*u**c - 3*u**2. Factor q(o).
-3*o*(o - 1)**2*(7*o + 2)
Let k be (-6)/(7 + (-280)/25 + 0). What is y in 1/7*y**4 - 6/7*y**3 + 12/7*y**2 + 3/7 - k*y = 0?
1, 3
Let x(g) = -5*g**2 + 24*g - 75. Let b(p) = 29*p**2 - 144*p + 449. Let c(j) = j**2 - 17*j + 54. Let u be c(12). Let y(q) = u*b(q) - 34*x(q). Factor y(l).
-4*(l - 6)**2
Factor 5 - 44/3*x + 2/3*x**3 + 9*x**2.
(x - 1)*(x + 15)*(2*x - 1)/3
Let i be ((7 - 3)/(-32))/(6/(-8)). Factor 0 + 0*c**2 - 1/6*c**3 + i*c.
-c*(c - 1)*(c + 1)/6
Let f(i) be the second derivative of i**7/420 - i**5/60 + 9*i**3/2 + 33*i. Let m(x) be the second derivative of f(x). Factor m(o).
2*o*(o - 1)*(o + 1)
Let g(k) = k**5 + 4*k**4 - 7*k**2 + 2*k. Let i(u) = -u**3 - u**2 + 2*u. Let s(b) = 5*g(b) - 15*i(b). Find n, given that s(n) = 0.
-2, -1, 0, 1
Let v(j) be the first derivative of 0*j**4 - 7*j**2 + 11 + 0*j**3 + 0*j + 0*j**5 + 1/60*j**6. Let c(m) be the second derivative of v(m). Factor c(g).
2*g**3
Let q = 7/24 + 3/8. Suppose 55 = 16*g + 7. Factor -2/3 - 16/3*i**4 + q*i**g + 8/3*i**5 + 10/3*i**2 - 2/3*i.
2*(i - 1)**3*(2*i + 1)**2/3
Let o(m) be the first derivative of -m**7/4620 + m**6/990 - 7*m**3/3 + 2. Let q(x) be the third derivative of o(x). Factor q(c).
-2*c**2*(c - 2)/11
Suppose -2*o + h + 1 = 0, 0*o + 4*h - 16 = -2*o. Let g(s) be the second derivative of 0*s**o + 1/42*s**3 + 0 + 5*s + 1/84*s**4. Let g(m) = 0. Calculate m.
-1, 0
Suppose 9*o**2 + 6*o**2 - o - 15 + 3*o**3 - 2*o + 0 = 0. What is o?
-5, -1, 1
Let i(d) be the first derivative of -3/2*d**2 + 0*d + 7 + 2*d**6 + 33/5*d**5 + 27/4*d**4 + d**3. Solve i(y) = 0 for y.
-1, 0, 1/4
Let z = -105 - -110. Find q, given that -z*q**2 + 13*q - 21*q - 17*q = 0.
-5, 0
Let p(q) = 2*q**4 + q**3 + 2*q**2 + q + 2. Let d(n) = 75*n**3 + 78*n**2 - 99*n - 102. Let c(a) = d(a) + 6*p(a). Determine f, given that c(f) = 0.
-5, -2, -3/4, 1
Suppose -5*a = -5*f + 30, -4*f + 5*a - 9*a = 0. Let g(j) be the second derivative of -f*j + 0 + 27*j**2 + 9*j**3 + 3/2*j**4 + 1/10*j**5. Factor g(m).
2*(m + 3)**3
Let c(h) be the first derivative of 285/8*h**4 - 261/20*h**5 + 75/4*h + 63/2*h**3 + 9/8*h**6 - 405/8*h**2 - 41. Suppose c(t) = 0. Calculate t.
-1, 1/3, 5
Factor -52*c - c**3 + c**4 + 101*c - 44*c - 2 - 3*c**2.
(c - 1)**3*(c + 2)
Factor -2/5*m**3 - 6*m**2 - 76/5*m - 48/5.
-2*(m + 1)*(m + 2)*(m + 12)/5
Let o(k) = 9*k**4 + 15*k**3 - 3*k**2 - 21*k + 6. Let j(p) = p**4 - p + 1. Let z(r) = 6*j(r) - o(r). Factor z(v).
-3*v*(v - 1)*(v + 1)*(v + 5)
Let m(c) be the second derivative of -1/15*c**6 - 4*c**2 - 3/10*c**5 + 5/6*c**4 + c**3 + 12*c + 0. Determine x so that m(x) = 0.
-4, -1, 1
Let r = 84 + -52. Let f be r/6 - (-2)/(-6). Factor 40*s + 49 + 0*s**2 + 12 + 19 + f*s**2.
5*(s + 4)**2
Let f(t) = -4*t + 18. Let h be f(4). Suppose -40*b + 5*b**h - 233 + 0*b**2 - 3*b**2 + 433 = 0. Calculate b.
10
Let o be 19*(-1)/3*-3. Suppose 0 = -n - 3*d + o, -4*n + 3*n - d + 11 = 0. Factor -n + 12*l - 4*l**2 + 1 - 2.
-4*(l - 2)*(l - 1)
Suppose 58*j = 55*j. Let w(m) be the second derivative of 0*m**3 + 1/150*m**6 + j*m**5 + 4*m - 1/15*m**4 + 0 + 0*m**2. Determine t so that w(t) = 0.
-2, 0, 2
Let t(u) be the first derivative of u**3/12 - 13*u**2/8 + 11*u/2 - 59. Find a such that t(a) = 0.
2, 11
Factor 3164*a**3 + 19*a - 3209*a**3 + 46 + 44 - 5*a**4 + 15*a**2 + 126*a.
-5*(a - 2)*