p be ((-12)/24)/((-2)/(-444)). Let y = p - -114. Find r such that 32*r**3 - 33*r**y + r**2 + 2*r + 0 + 0 = 0.
-1, 0, 2
Factor -351*i + 76*i**2 + 90*i**2 - 358*i + 701*i.
2*i*(83*i - 4)
Let t be (-288)/(-1224) - (-1 - 5057/1989). Factor t*q - 2/9*q**2 - 32/9.
-2*(q - 16)*(q - 1)/9
Let v(d) be the first derivative of 0*d + 105 + 3/4*d**4 + 6*d**2 - 4*d**3. Factor v(a).
3*a*(a - 2)**2
Let t(o) = 8*o**2 + 14*o + 2 - 7*o**2 - 2*o**2. Let s be t(14). Factor 2*u + s*u - 5*u**3 + 2*u - u.
-5*u*(u - 1)*(u + 1)
Let t(p) be the second derivative of 5*p**7/189 + 4*p**6/5 + 128*p**5/45 + 85*p**4/27 - 7*p**3/9 - 38*p**2/9 - 8742*p. Let t(f) = 0. What is f?
-19, -1, 2/5
Let g(d) = d**3 - 12*d**2 + 10*d + 15. Let q be g(11). Let r be ((-1)/(-2))/((-1)/(-22)). Factor 4*z**2 - q*z - z**3 - 11 + r.
-z*(z - 2)**2
Let k(w) be the third derivative of w**6/30 + 39*w**5/5 - 123*w**4 + 71*w**2 - 15. Let k(r) = 0. What is r?
-123, 0, 6
Suppose -12*a + 8*a = 16. Let y = 1 - a. Determine v, given that -8*v**4 + 6*v**2 - 32*v**3 + 11*v + 68 - 66 - 6*v**5 + 27*v**y = 0.
-1, -1/3, -2/7, 1
What is q in -2/21*q**4 - 40/3*q + 272/21*q**2 - 62/21*q**3 + 0 = 0?
-35, 0, 2
Let y(a) be the third derivative of a**5/20 - 67*a**4/4 + 133*a**3/2 - 2*a**2 - 1171*a. Factor y(m).
3*(m - 133)*(m - 1)
Let g(z) = -5*z**2 + 5. Suppose 24*a + 5 = 23*a. Let n(p) = 5*p**2 - p - 4. Let v(w) = a*n(w) - 6*g(w). Determine y, given that v(y) = 0.
-2, 1
Let v(w) be the second derivative of -13/4*w**4 + 0 - 41*w + 9*w**2 + 23/2*w**3. Factor v(d).
-3*(d - 2)*(13*d + 3)
Let y = -2/27101 - -81311/108404. Let l(b) be the first derivative of -b**3 + y*b**4 - 28 + 0*b + 0*b**2. Solve l(f) = 0.
0, 1
Let b(g) be the third derivative of -g**8/1176 - 53*g**7/735 - 123*g**6/70 - 666*g**5/35 - 90*g**4 + 750*g**2 + 9. Factor b(w).
-2*w*(w + 6)**3*(w + 35)/7
Factor 2297*b**3 - 345*b**3 - 3136*b**2 + 220*b**4 + 4*b**5 + 960*b**3.
4*b**2*(b - 1)*(b + 28)**2
Determine w, given that -5*w**5 + 21*w**2 + 14*w**2 - 9*w**4 - 10*w**4 + 65*w**3 + 44*w**4 = 0.
-1, 0, 7
Determine y so that -3282/13*y**2 - 5920/13 - 8848/13*y + 2/13*y**4 - 352/13*y**3 = 0.
-4, -1, 185
Let s(y) be the first derivative of -2/3*y - 91 + 5/9*y**3 - 1/2*y**2. Find d such that s(d) = 0.
-2/5, 1
Let t(r) be the second derivative of -5*r**5/4 - 85*r**4/12 - 40*r**3/3 - 10*r**2 - 2206*r + 1. Factor t(s).
-5*(s + 1)*(s + 2)*(5*s + 2)
Let p(t) be the third derivative of t**9/16128 - 83*t**8/26880 - 17*t**7/3360 - 71*t**5/20 + 31*t**2 + 2. Let g(x) be the third derivative of p(x). Factor g(c).
3*c*(c - 17)*(5*c + 2)/4
Let o(m) = m**2 - m - 1. Let h(z) = -4*z**4 - 2*z**2 + 10*z + 6. Let n be (16/(-16))/((-1)/16). Suppose 229 = n*i + 69. Let a(r) = i*o(r) + h(r). Factor a(y).
-4*(y - 1)**2*(y + 1)**2
Let b be 26/8*11067/47957. Let 0 - b*m**3 + 18*m + 3/2*m**2 = 0. What is m?
-4, 0, 6
Suppose -9*p = k - 14*p + 226, -5*p + 437 = -2*k. Let x = 223 + k. Solve 6 + 3/2*m**3 + x*m + 15/2*m**2 = 0.
-2, -1
Suppose 3847*m + 1728*m**2 + 61 + 185*m - 513*m**3 + 36*m**5 + 1475 + 36*m**4 - 9*m**5 - 771*m**3 = 0. What is m?
-8, -2/3, 4
Let v(y) be the third derivative of -11/2*y**3 - 12 + 45/8*y**4 + 3/40*y**6 + 0*y - 4*y**2 - 37/20*y**5. Let v(o) = 0. What is o?
1/3, 1, 11
Let d = 300040 - 1500156/5. Determine k so that 2/5*k**2 + d*k + 16 = 0.
-20, -2
Let v be (20 - 8)/(-12) + (-29)/(-28). Let r(g) be the second derivative of 0 + 2/7*g**3 + 0*g**2 - v*g**4 - 10*g. Suppose r(z) = 0. What is z?
0, 4
Let b = -220951 + 220953. Determine i, given that 4/3*i**3 - 8/3 - 24*i**b + 8*i**4 - 20*i = 0.
-1, -1/6, 2
Let h = -15 - -17. Factor -9*d - 144 - 149 + 290 - 6*d**h.
-3*(d + 1)*(2*d + 1)
Suppose 4*y + 4*s = -8, -s + 22 = 3*y - 8*y. Let x(n) = 5*n**2 - 12*n - 5. Let m be x(y). Factor m*z - 28 - 8*z + 29*z - 47*z**2 + 16*z**3 - 85*z**2.
4*(z - 7)*(z - 1)*(4*z - 1)
Suppose -8 = -2*r + 13*n - 11*n, 2*r - 3*n - 9 = 0. Let q(t) be the first derivative of -3/16*t**2 - 1/8*t**r + 31 + 0*t. Find j, given that q(j) = 0.
-1, 0
Let p(f) be the second derivative of f**7/7 + 289*f**6/15 - 99*f**5/5 - 193*f**4/3 + 65*f**3 + 97*f**2 - 268*f. Find u such that p(u) = 0.
-97, -1, -1/3, 1
Let b(t) = -20*t**2 + 28*t + 20. Let d(n) = -7*n**2 + 10*n + 7. Suppose -459*f + 98 = -452*f. Let o(s) = f*d(s) - 5*b(s). Factor o(j).
2*(j - 1)*(j + 1)
Let l(a) = 11*a**2 + 2*a - 2. Let v be l(1). Suppose -k = v*k - 48. Solve -3*s**4 + 2*s**2 + 1 - k*s + 27*s**3 + 0*s + s**5 + s - 25*s**3 = 0 for s.
-1, 1
Let p be 16/144*-2*(-6)/8. Let b(a) be the first derivative of 0*a**2 + 0*a - 14 + p*a**3. Factor b(r).
r**2/2
Factor -96*x - 61/2*x**2 + 1/2*x**3 + 0.
x*(x - 64)*(x + 3)/2
Let c(q) be the second derivative of -5*q**7/42 - 4*q**6/3 - 6*q**5 - 40*q**4/3 - 40*q**3/3 - 8*q + 80. Factor c(z).
-5*z*(z + 2)**4
Suppose -12*n**4 - 2*n**5 - 22*n**3 - 1311 + 2654 - 12*n**2 - 1343 = 0. What is n?
-3, -2, -1, 0
Let y(w) be the first derivative of w**6/1800 - 41*w**5/300 + 1681*w**4/120 - 10*w**3/3 + w**2/2 + 163. Let k(r) be the third derivative of y(r). Factor k(a).
(a - 41)**2/5
Let v = -110687/48 + 2306. Let t(w) be the third derivative of -v*w**4 - 26*w**2 + 0*w**7 + 1/120*w**6 + 0*w**3 - 1/672*w**8 + 0*w**5 + 0*w + 0. Factor t(k).
-k*(k - 1)**2*(k + 1)**2/2
Let a(z) be the second derivative of -z**5 - 5*z**2 + 5/2*z**3 + 5/6*z**4 + 0*z**6 + 5/42*z**7 - 76 + 2*z. Suppose a(g) = 0. Calculate g.
-2, -1, 1
Let n(v) be the second derivative of v**7/105 - v**5/30 - 26*v**2 - 12*v. Let l(g) be the first derivative of n(g). Factor l(x).
2*x**2*(x - 1)*(x + 1)
Let d(j) be the second derivative of 19*j**4/6 + 31*j**3/3 + 12*j**2 - 2600*j. Factor d(a).
2*(a + 1)*(19*a + 12)
Let t be (-9 - 2325/124) + 28. What is k in 1/4*k**3 - 5*k**2 + 5 - t*k = 0?
-1, 1, 20
Let t(x) be the first derivative of 21 + 1/2*x**2 + 0*x + 1/15*x**5 - 1/18*x**6 + 2/3*x**4 + 8/9*x**3. Let o(r) be the second derivative of t(r). Factor o(m).
-4*(m - 2)*(m + 1)*(5*m + 2)/3
Let n(w) be the first derivative of -w**3/3 - 39*w**2 - 152*w - 2157. Determine k, given that n(k) = 0.
-76, -2
Let l(y) be the first derivative of 1/6*y**4 + 1/75*y**6 + 0*y**2 + 2/15*y**3 + 11 + 3*y + 2/25*y**5. Let g(h) be the first derivative of l(h). Solve g(k) = 0.
-2, -1, 0
Let z(d) = 2*d**3 - 308*d**2 - 5443*d + 19194. Let r(f) = 4*f**3 - 924*f**2 - 16328*f + 57584. Let v(k) = 3*r(k) - 8*z(k). Factor v(j).
-4*(j - 3)*(j + 40)**2
Let n = 4139/145 - 822/29. Let b(l) be the second derivative of 0 - n*l**5 - 24*l - 1/6*l**4 - 1/15*l**6 + 0*l**3 + 0*l**2. Let b(w) = 0. What is w?
-1, 0
Factor -2/5*t**3 - 20 + 48/5*t**2 + 54/5*t.
-2*(t - 25)*(t - 1)*(t + 2)/5
Let s(x) be the first derivative of 2*x**3/57 + 508*x**2/19 + 3030*x/19 - 177. Suppose s(z) = 0. What is z?
-505, -3
Let x(j) be the third derivative of -j**6/120 - 7*j**5/30 - 41*j**4/24 + 28*j**3/3 - 2*j**2 - 1456. Factor x(p).
-(p - 1)*(p + 7)*(p + 8)
Let d(h) be the first derivative of 9*h**5/20 - 25*h**4/16 - 11*h**3/6 + 25*h**2/2 - 14*h - 520. Factor d(z).
(z - 2)**2*(z + 2)*(9*z - 7)/4
Let w(f) be the third derivative of 2/105*f**7 - 3*f**4 + 0 - 16/3*f**3 - f**2 - 21*f + 0*f**6 - 11/15*f**5. Factor w(h).
4*(h - 4)*(h + 1)**2*(h + 2)
Suppose 144*d - 12*d = 74*d. Let d - 2/7*a**4 - 12/7*a**2 + 2*a**3 + 0*a = 0. What is a?
0, 1, 6
Let x be (-6 - -9) + -11 + 12. Let o(z) be the first derivative of -8 + 3/20*z**x + 3/2*z**2 - 4/5*z**3 - 6/5*z. Factor o(q).
3*(q - 2)*(q - 1)**2/5
Let j = -874139 - -874141. Determine a, given that -2*a**3 - 1/3 + j*a + 1/3*a**2 = 0.
-1, 1/6, 1
Let j(t) = -t**3 + 2*t**2. Let w be j(0). Let s be (9/(-135))/((-4)/30). Factor 1/4*o**3 + s*o + 3/4*o**2 + w.
o*(o + 1)*(o + 2)/4
Let r(o) be the first derivative of -4*o**5/15 + 1096*o**4/3 + 1464*o**3 + 6592*o**2/3 + 4396*o/3 + 3643. Factor r(m).
-4*(m - 1099)*(m + 1)**3/3
Suppose 3*l + 2*z - 19 = 0, -2*l = -0*l + 2*z - 10. Solve -4*h + l*h - 2*h + 3*h - 3*h**2 = 0 for h.
0, 2
Suppose 0 = 6*v - 41 + 29. Let -4*u**3 + 3*u**v + 6*u**2 + 1 + 3*u**2 + 20*u + 7 - 4*u**4 = 0. Calculate u.
-1, 2
Suppose -11*v - 142 = -5*r, -32*r + 34*r + v + 8 = 0. Factor -210/11 + 204/11*x + 6/11*x**r.
6*(x - 1)*(x + 35)/11
What is u in 25917/5*u - 50562/5 + 1/5*u**3 - 64*u**2 = 0?
2, 159
Determine o, given that 720/17 - 520/17*o**3 - 1582/17*o**2 - 1284/17*o - 54/17*o**4