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Let g(r) be the second derivative of -r**5/150 + 4*r**4/45 + r**3/5 + 68*r - 1. Factor g(m).
-2*m*(m - 9)*(m + 1)/15
Factor -50 + 1/4*p**3 - 11/2*p**2 + 35*p.
(p - 10)**2*(p - 2)/4
Let k(y) = -12*y**2 - 529*y - 44. Let s be k(-44). Determine j, given that 2/5*j**3 + s*j + 6/5*j**2 - 8/5 = 0.
-2, 1
Let f(p) be the third derivative of p**9/37800 - p**7/1050 + p**6/225 - p**5/100 - 3*p**4/4 + 20*p**2. Let v(l) be the second derivative of f(l). Factor v(k).
2*(k - 1)**3*(k + 3)/5
Let y(s) be the first derivative of -6/7*s + s**2 + 1/14*s**4 - 10/21*s**3 - 3. Solve y(k) = 0.
1, 3
Suppose -4*s = 5*u - 6, 2*s = 207*u - 208*u. Determine l, given that -4/3*l**u + 8/3*l + 0 + 4/3*l**4 - 8/3*l**3 = 0.
-1, 0, 1, 2
Let -125*x + 5/2*x**4 - 28 - 64*x**3 - 327/2*x**2 = 0. Calculate x.
-1, -2/5, 28
Let t be ((-78)/(-312))/(-2*1/(-24)). Let s(g) be the third derivative of 0*g - 1/390*g**5 + 0 + 2/39*g**t + 1/156*g**4 + 11*g**2. Factor s(a).
-2*(a - 2)*(a + 1)/13
Let f(a) be the second derivative of 0 - 1/18*a**3 - 1/72*a**4 + 23*a - 1/12*a**2. Factor f(i).
-(i + 1)**2/6
Let w(m) = 2*m + 14. Let p be w(-6). Determine u so that -2*u + 2*u - 3*u**2 + u**3 + p*u**2 = 0.
0, 1
Let u(g) be the third derivative of 1/12*g**4 + 0*g + 1/20*g**5 + 0*g**6 - 1/210*g**7 + 0*g**3 + 8*g**2 + 0. Find a such that u(a) = 0.
-1, 0, 2
Let s(z) be the third derivative of z**7/210 - 9*z**6/40 - 7*z**5/15 + 202*z**2. Find q, given that s(q) = 0.
-1, 0, 28
Let b(p) = 6*p**2 - 2 - 8*p**2 - 3 - 4. Let z(w) = 6 - 1 - 1 + w**2. Let h(y) = 4*b(y) + 9*z(y). Find r, given that h(r) = 0.
0
Let p(v) be the first derivative of -15*v**4 - 16/3*v**3 - 7 - 14/5*v**5 + 0*v**2 + 0*v. Factor p(k).
-2*k**2*(k + 4)*(7*k + 2)
Let c(v) be the second derivative of v**9/45360 + v**8/10080 - v**7/7560 - v**6/1080 - 2*v**4/3 + 9*v. Let q(s) be the third derivative of c(s). Factor q(i).
i*(i - 1)*(i + 1)*(i + 2)/3
Let b(m) be the third derivative of -m**5/15 + 5*m**4 - 150*m**3 + 40*m**2. Suppose b(h) = 0. Calculate h.
15
Let l = 64 + -38. Let n = l + -26. Factor 4/9*k + 2/9*k**2 + n.
2*k*(k + 2)/9
Let -92*p**2 + 178 + 97 - 183*p + 357*p**2 - 191*p - 171*p + 5*p**3 = 0. What is p?
-55, 1
Let g be (0/(-9))/(10/(12/(5 - -1))). Find p, given that 16/13*p + 8/13*p**2 - 2/13*p**4 - 4/13*p**3 + g = 0.
-2, 0, 2
Let n(r) = 45*r**3 + 215*r**2 + 4355*r + 24565. Let o(x) = -2*x**3 + 2*x**2 - x. Let v(i) = n(i) + 20*o(i). Factor v(d).
5*(d + 17)**3
Let i = 28 - 22. Let b(w) = 4*w - 24. Let p be b(i). Find h, given that -h**3 - 1/2*h**2 + 1/2*h + p = 0.
-1, 0, 1/2
Suppose l = -9*u + 13*u - 15, 2*u - 4 = 4*l. Let c be (3 - l)/1 + 48/(-30). Determine w so that 7/5*w**4 + c*w + 0 + 11/5*w**2 + 16/5*w**3 = 0.
-1, -2/7, 0
Let r(w) be the third derivative of -5*w**8/1176 - 8*w**7/735 + 3*w**6/140 + 4*w**5/105 - w**4/21 - 51*w**2. Suppose r(i) = 0. Calculate i.
-2, -1, 0, 2/5, 1
Factor -1/4*n**2 + 0 - 23/4*n.
-n*(n + 23)/4
Let r = -280 - -296. Let o(a) = a**3 - 14*a**2 - 33*a + 16. Let w be o(r). Factor w + 6/7*g + 3/7*g**2.
3*g*(g + 2)/7
Let h be (-3)/30*58 + -3. Let u = h - -9. Solve 0 + u*r**3 - 1/5*r + 0*r**2 = 0 for r.
-1, 0, 1
Suppose -1807*z + 8 = -1805*z. Factor -4/7*q**5 + 0*q**2 + 0*q + 0*q**3 + 0 + 0*q**z.
-4*q**5/7
Let 4*x**2 - 3*x**3 + 0*x**3 + 6*x**3 + 7 - 13*x - 1 = 0. Calculate x.
-3, 2/3, 1
Let t(y) = -2*y**3 + 7*y**2 + 5*y + 3. Let w be t(4). Suppose w = 6*l - 5. Determine x, given that -120/7*x**3 - 24/7*x - 2/7 - 92/7*x**l - 50/7*x**4 = 0.
-1, -1/5
Let s(u) be the second derivative of 1/10*u**5 + 0*u**2 + 2*u + 0 - 1/15*u**6 + 1/6*u**4 - 1/3*u**3. Factor s(c).
-2*c*(c - 1)**2*(c + 1)
Let g(b) be the first derivative of -b**6/72 - b**5/12 - 5*b**4/24 + 13*b**3 + 19. Let a(i) be the third derivative of g(i). Factor a(z).
-5*(z + 1)**2
Let k = 144 + -113. Suppose -2*m - 25 = -k. Suppose 2/3*t**2 + 2/9 + 2/3*t + 2/9*t**m = 0. Calculate t.
-1
Let p(k) be the third derivative of k**8/1176 - k**7/147 + k**6/60 + k**5/210 - 2*k**4/21 + 4*k**3/21 + 2*k**2 - 87*k. Suppose p(d) = 0. What is d?
-1, 1, 2
Let w(z) be the first derivative of z**7/210 - z**6/120 - z**5/20 + 5*z**4/24 - z**3/3 - 11*z**2/2 + 22. Let u(x) be the second derivative of w(x). Factor u(k).
(k - 1)**3*(k + 2)
Let h(l) = -l**3 + 2*l**2 - 3. Let t be h(5). Let d be (t/27 - -3)/(5/15). Determine x so that 1/3 + d*x**2 + 2/3*x = 0.
-1
Let d(b) = b**3 + 3*b**2 + 8*b + 12. Let l be d(-2). Suppose 5 - 25 = -4*k. What is s in 1/5*s**k + 4/5*s**4 + l + 1/5*s + 4/5*s**2 + 6/5*s**3 = 0?
-1, 0
Let y be (-10)/((-66)/12 + 3). Factor 1/2*v - 1/4*v**y + 3/4*v**3 + 5/4*v**2 - 1/4*v**5 + 0.
-v*(v - 2)*(v + 1)**3/4
Let u(a) = -2. Let x be 517/77 - (-2)/7. Suppose 3*z + 8 = -x. Let q(l) = -l**2 + l + 5. Let n(c) = z*u(c) - 2*q(c). Factor n(v).
2*v*(v - 1)
Factor 191 + 268 - 3*f**2 - 545 + 2*f**2 - 45*f.
-(f + 2)*(f + 43)
Let g(r) be the first derivative of -r**8/840 + 2*r**7/525 - r**6/300 - 23*r**2/2 + 1. Let z(i) be the second derivative of g(i). Let z(x) = 0. Calculate x.
0, 1
Let c(p) be the first derivative of 16*p**6/27 - 176*p**5/45 - 47*p**4/18 - 4*p**3/9 - 166. Factor c(s).
2*s**2*(s - 6)*(4*s + 1)**2/9
Let b = -2/23631 + 63026/118155. Let b*z**4 + 0*z - 2/15*z**5 + 0*z**2 - 8/15*z**3 + 0 = 0. Calculate z.
0, 2
Let f(y) be the third derivative of -y**7/70 - 7*y**6/40 - 17*y**5/20 - 17*y**4/8 - 3*y**3 - 109*y**2. Let f(i) = 0. What is i?
-3, -2, -1
Let c be (-74)/(-312) - -7*(-6)/273. Let v(u) be the third derivative of 0*u + 0 - 1/120*u**5 + c*u**3 + 2*u**2 + 0*u**4. Solve v(o) = 0.
-1, 1
Suppose 2*p + 2*h = -8, -h + 3 = -p - 7. Let s = p - -16. Factor -3*l**3 + 4 - 2 - 4 + 8 + s*l.
-3*(l - 2)*(l + 1)**2
Let l be -50 - -62 - 143/12. Let c(v) be the third derivative of 0 - 1/12*v**4 + 0*v**3 + 0*v - 9*v**2 + l*v**5. Suppose c(w) = 0. Calculate w.
0, 2/5
Solve -5/4*s**4 + 215/4*s**2 - 95/4*s + 95/4*s**3 - 105/2 = 0 for s.
-2, -1, 1, 21
Suppose -k + 23 = -47. Let q = k - 70. Factor 0*u**2 + q*u**4 + 1/3*u**5 + 0 + 0*u - 1/3*u**3.
u**3*(u - 1)*(u + 1)/3
Let o(p) be the third derivative of 1/102*p**5 - 7/204*p**4 + 0*p - 7*p**2 + 0 + 1/17*p**3 - 1/1020*p**6. Find k, given that o(k) = 0.
1, 3
Let m(y) be the third derivative of y**6/12 - 79*y**5/15 - 229*y**4/12 - 22*y**3 - 3*y**2 - 17*y. Find b such that m(b) = 0.
-1, -2/5, 33
Let q(p) = p**3 + 6*p**2 - 13*p + 16. Let a be q(-8). Let w(x) = 3*x + 28. Let y be w(a). Suppose -8/3 + 4*t**y + 20/3*t - 4/3*t**2 - 20/3*t**3 = 0. What is t?
-1, 2/3, 1
Let h(y) be the second derivative of y**4/16 + 61*y**3/8 + 45*y**2/2 - 36*y. Solve h(c) = 0 for c.
-60, -1
Let w = -90533/26 - -3481. Let r = w + 20/13. Let 0*i - 6*i**4 + 2*i**3 + 9/2*i**2 - r = 0. Calculate i.
-1/2, 1/3, 1
Let a(q) be the first derivative of 4*q**6/3 - 10*q**5 + 11*q**4 + 40*q**3/3 - 26*q**2 + 10*q + 38. Solve a(j) = 0 for j.
-1, 1/4, 1, 5
Suppose 40*p - 73 + 27 = 154. Let -16/3 - 8/3*c**3 + 16/3*c + 8/3*c**2 + 1/3*c**p - 1/3*c**4 = 0. Calculate c.
-2, 1, 2
Let r(w) be the first derivative of 0*w - 1/24*w**4 + 0*w**2 - 13 - 1/6*w**3. Find m, given that r(m) = 0.
-3, 0
Let o = -8786 + 8790. Find y, given that -1/2*y**3 + 0 - 1/2*y**o + 1/2*y + 1/2*y**2 = 0.
-1, 0, 1
Let s(m) be the second derivative of -m**5/6 - 67*m**4/9 - 524*m**3/45 - 104*m**2/15 - 12*m + 2. Let s(y) = 0. What is y?
-26, -2/5
Let l = -1/771 + -1111/332301. Let v = l + 868/1293. Determine y, given that -v*y**3 - 2*y + 0 - 8/3*y**2 = 0.
-3, -1, 0
Suppose t + 2 = -2*t - 5*s, -3*t - s = -14. Suppose -36 = -t*x - 0*x. Factor -13*v**3 + 8*v**4 - x*v + 2 - 8*v**2 + 38*v**2 - 8*v - 13*v**3.
2*(v - 1)**3*(4*v - 1)
Find r, given that 20 + 216*r**2 + 9 + 7 + 48*r**3 + 243*r + 45 = 0.
-3, -3/4
Let 108 + 30*q**3 - 93*q**2 - 23*q**4 + 8*q**4 - 139*q**3 + 10*q**3 - 90*q**3 + 189*q = 0. What is q?
-12, -1, -3/5, 1
Suppose d - 2 + 6 = 0. Let v be (2/d)/(1/(-10)). Factor -75*w**3 + 3 - 21*w + 48*w**4 + 57*w**2 - 9*w**5 - 6*w**v + 3*w**5.
-3*(w - 1)**3*(2*w - 1)**2
Let v be ((-88)/(-220))/((-5)/((-75)/18)). Determine o so that -2/3*o**3 + 1/3*o**2 + v*o**4 + 0*o + 0 = 0.
0, 1
Factor 2809/5 + 1/5*h**2 - 106/5*h.
(h - 53)**2/5
Let g(s) be the third derivative of s**5/40 + 13*s**4/16 + 3*s**3 + 62*s**2. Factor g(a).
3*(a + 1)*(a + 12)/2
Solve -2/5 - 17/5*l**2 - 19/5*l = 0 for l.
-1, -2/17
Let x = 839/1043