. Let s(m) be the third derivative of 16*m**2 + 0 + 1/540*m**5 + b*m + 0*m**3 - 5/216*m**4. Factor s(z).
z*(z - 5)/9
Let t(b) = 3*b**3 - b - 2. Let u(k) = -120*k**3 - 530*k**2 - 20*k + 10. Let y(f) = -5*t(f) - u(f). Solve y(l) = 0 for l.
-5, -1/21, 0
Suppose 8 - 12 = -4*p, -2*u + 61 = -5*p. Let r(q) be the first derivative of -q**2 - u - 5/3*q**3 + 0*q. Factor r(j).
-j*(5*j + 2)
Determine k, given that 0 - 4*k**3 + 48/5*k + 2/5*k**5 + 8*k**2 - 2*k**4 = 0.
-2, -1, 0, 2, 6
Let i = -1333288/105 + 12698. Let x(q) be the third derivative of 0*q**3 + 0*q**5 - i*q**7 - 2/15*q**6 + 0*q - 7*q**2 + 0*q**4 + 0. Let x(y) = 0. Calculate y.
-4, 0
Let y be 14*(1 - (16 - (-1188)/(-84))) + 16. Factor 0 + 5/2*v**3 + 1/2*v**y + 3/2*v + 7/2*v**2.
v*(v + 1)**2*(v + 3)/2
Let t(g) be the first derivative of -g**3/3 - 2*g**2 - 6*g + 2. Let m(a) = 1. Let r(u) = -9*u + 3. Let s be r(1). Let p(o) = s*m(o) - t(o). Factor p(f).
f*(f + 4)
Factor -4/3*y**4 + 808 + 7268/3*y + 2420*y**2 + 804*y**3.
-4*(y - 606)*(y + 1)**3/3
Suppose 0 = -4*w + f + 12, w - 3*w + 11*f = -48. Factor 3/5*j**w + 0 - 1/10*j**3 + 0*j.
-j**2*(j - 6)/10
Determine c so that -35/2*c + 115/4*c**2 + 5/4*c**5 - 15/4*c**3 + 0 - 35/4*c**4 = 0.
-2, 0, 1, 7
Let f(w) be the third derivative of 0 + 38*w**2 - 3*w**3 + 1/20*w**5 + 0*w + 5/8*w**4. Suppose f(j) = 0. Calculate j.
-6, 1
Factor 64/7*i**2 - 4332/7 + 2/7*i**3 + 38*i.
2*(i - 6)*(i + 19)**2/7
Let d(w) be the first derivative of 2*w**6/3 - 52*w**5/5 + 51*w**4 - 36*w**3 - 432*w**2 + 1296*w - 1340. Factor d(f).
4*(f - 6)*(f - 3)**3*(f + 2)
Let s(a) = -a**3 + 3*a + 2. Let m be s(-1). Let c = -412 + 415. Factor m*b - 2/7*b**2 + 2/7*b**c + 0.
2*b**2*(b - 1)/7
Let l(o) = 83*o + 338. Let c be l(-4). Let b(n) be the first derivative of 0*n + 15 - 4/3*n**3 - 36/5*n**5 + 0*n**2 - c*n**4. Factor b(i).
-4*i**2*(3*i + 1)**2
Let z(f) = f**3 + 9*f**2 + 3*f - 2. Let p be z(-8). Let j = p - 34. Factor k**2 - 3*k**4 + 3*k**j + 17*k - k**4 - k**3 - 16*k.
-k*(k - 1)*(k + 1)**2
Let z(h) be the third derivative of -1/420*h**7 + 1/40*h**6 - 2/3*h**4 + 0*h**5 - 2*h**2 + 0 - 89*h + 0*h**3. Factor z(f).
-f*(f - 4)**2*(f + 2)/2
Factor 730*d**3 + 380 + 503*d**3 + 272*d**2 + 1231*d - 1236*d**3.
-(d - 95)*(d + 4)*(3*d + 1)
Let n(k) be the third derivative of k**6/720 + k**5/120 - k**4/144 - k**3/12 + 12*k**2 + 44. Find d, given that n(d) = 0.
-3, -1, 1
Let v be (1*5/(-30))/((-170)/24 + 7). Factor -32*j - 1/2*j**v - 512.
-(j + 32)**2/2
Let a(z) be the third derivative of z**7/210 + 101*z**6/60 + 231*z**5 + 14157*z**4 + 191664*z**3 - 558*z**2. Factor a(l).
(l + 4)*(l + 66)**3
Suppose -109*p + 131*p - 110 = 0. Determine j, given that p + j**4 - 108*j**2 + 52*j**3 - 16*j + 11 - 156*j**3 + 0 - 29*j**4 = 0.
-2, -1, 2/7
Factor 15*k - 641*k**3 + 1277*k**3 - 12*k**2 - 639*k**3.
-3*k*(k - 1)*(k + 5)
Suppose 5*i - 25 = -z - 2, 3*z - 49 = 5*i. Solve 1413*w**3 + z - 39*w + 15*w**2 + 3 - 1410*w**3 = 0 for w.
-7, 1
Determine h so that -120*h**2 - 400*h - 12*h**3 + 0 - 2/5*h**4 = 0.
-10, 0
Suppose 37 = 5*f + 2*q, -15*f + 17*f = -q + 14. Let p be f + (-80)/50 - 7. Factor p*l**2 - 8/5*l + 8/5.
2*(l - 2)**2/5
Let k = 7236/11825 + 316/473. Determine o so that 66/25*o**4 - 304/25*o**2 + k*o**3 - 288/25*o + 2/5*o**5 + 32/5 = 0.
-5, -2, 2/5, 2
Let x = 113716 - 1137039/10. Factor 0*u + 0 - 2/5*u**2 - x*u**4 + 22/5*u**3.
-u**2*(11*u - 2)**2/10
Let d(n) be the first derivative of -n**3/12 + 297*n**2/8 - 74*n + 1191. Solve d(i) = 0 for i.
1, 296
Let f be ((-4)/(-134) + (-17661)/136010)*(-1 + -35). Determine u so that f - 6/5*u + 1/10*u**2 = 0.
6
Let n(m) be the third derivative of m**7/15120 - m**6/4320 - m**5/360 + 11*m**4/12 + m**3/6 - 17*m**2. Let i(d) be the second derivative of n(d). Factor i(o).
(o - 2)*(o + 1)/6
Let v(s) = 6*s**4 - 8*s**2 - 2*s - 5. Let z(g) = 4 - 2 + 4 + 2*g + 7*g - 7*g + 9*g**2 - 7*g**4. Let n(w) = -6*v(w) - 5*z(w). Factor n(m).
-m*(m - 2)*(m + 1)**2
Let g = -256/1547 + 10562/7735. Factor -g*b**2 - 6/5*b - 2/5*b**3 - 2/5.
-2*(b + 1)**3/5
Suppose 0 = -4*h - 4, -h + 5226 = 5*b + 1562. Suppose 744*r - b*r - 44 = 0. Solve -141/7*y**r + 81/7*y**3 + 0 + 9*y**5 - 12/7*y + 9/7*y**2 = 0 for y.
-1/3, 0, 4/7, 1
Suppose 0 = -2*u - 53 + 59. Let n(p) be the third derivative of -1/40*p**6 - 1/20*p**5 + 0 + 1/8*p**4 + 0*p + 1/2*p**u + 16*p**2. Find g, given that n(g) = 0.
-1, 1
Let x(b) be the third derivative of -b**7/63 + 29*b**6/72 - 31*b**5/18 + 5*b**4/3 + 1834*b**2. Solve x(d) = 0 for d.
0, 1/2, 2, 12
Suppose -243 - 511 = 26*m. Let j(p) = p**3 + 28*p**2 - 30*p - 27. Let c be j(m). Factor 0 - 3/5*g + 3/5*g**4 - 9/5*g**3 + 9/5*g**c.
3*g*(g - 1)**3/5
Let b(o) be the first derivative of -o**4/3 + 44*o**3/9 + 112*o**2/3 + 80*o - 1594. Factor b(i).
-4*(i - 15)*(i + 2)**2/3
Let l(q) = 2*q - 1. Let f be l(1). Suppose 2*m + 0 = -4*w - 8, 0 = 2*m + w - f. Factor 2*y - y**m - 4*y + y.
-y*(y + 1)
Let r(i) = -i**2 + 5*i. Let v be (8/8)/(2/8). Let h be r(v). Let -h*s + 10*s**2 - 8*s**2 + 0*s = 0. Calculate s.
0, 2
Let g(h) be the second derivative of -5*h**4/12 + 115*h**3/6 - 190*h**2 + 106*h. Determine f so that g(f) = 0.
4, 19
Let y(h) = -40*h**2 + 17405*h + 2575470. Let r(s) = 7*s**2 - 2900*s - 429245. Let n(u) = -35*r(u) - 6*y(u). Factor n(a).
-5*(a + 293)**2
Let -246*q**2 + 294 - 3831*q**5 - 228*q**3 - 41*q - 48*q**4 + 1919*q**5 + 272*q + 1909*q**5 = 0. What is q?
-7, -2, -1, 1
Let v(h) be the second derivative of 67*h**5/5 + 44*h**4 - 8*h**3/3 + 1344*h. Suppose v(i) = 0. What is i?
-2, 0, 2/67
Suppose 3*z - l - 18 - 15 = 0, 0 = -z + 4*l + 22. Let v be 0/(-15 + z - -1*3). Suppose -2/3*h**4 + v + 2/3*h**3 + 0*h + 2/9*h**5 - 2/9*h**2 = 0. What is h?
0, 1
Let u(q) be the first derivative of -q**5/30 - q**2 + 9*q + 20. Let c(o) be the second derivative of u(o). What is b in c(b) = 0?
0
Let y(o) be the third derivative of -9*o**8/56 - 29*o**7/35 + 211*o**6/90 - 8*o**5/9 + 1096*o**2 - 3*o + 1. Find d, given that y(d) = 0.
-40/9, 0, 2/9, 1
Factor 32*x**4 + x**2 + 1016*x**5 - 8*x**3 - 35*x**2 - 22*x**2 - 1012*x**5 + 28*x**3.
4*x**2*(x - 1)*(x + 2)*(x + 7)
Factor 0*v**2 + 171*v - 198*v + v**2.
v*(v - 27)
Let m(u) be the first derivative of 0*u - 5/3*u**3 + 72 + 15*u**2 - 5/4*u**4. Factor m(p).
-5*p*(p - 2)*(p + 3)
Let p(h) be the first derivative of -5*h**3/3 - 470*h**2 - 44180*h - 442. Factor p(z).
-5*(z + 94)**2
Let q(d) be the third derivative of -d**7/1365 - 11*d**6/156 - 667*d**5/390 + 841*d**4/52 + d**2 + 1189*d. Solve q(a) = 0 for a.
-29, 0, 3
What is t in 14/5*t**2 - 21/5*t + 1/5*t**3 - 18 = 0?
-15, -2, 3
Suppose -29*z + 94 = -22. Let l(r) be the second derivative of -1/18*r**3 - 1/20*r**5 + 1/9*r**z + 0 + 0*r**2 + 3*r. Solve l(c) = 0.
0, 1/3, 1
Let n be (-34976)/6412 + (-12)/(-2). Let l = n + 6/229. Find q such that -2/7 + 0*q**2 + 2/7*q**4 - 4/7*q + l*q**3 = 0.
-1, 1
Let p = 1614685/310156 - -72/4081. Let k = -85/19 + p. Suppose -3/2 - k*i**2 + 9/4*i = 0. Calculate i.
1, 2
Suppose 5*l - 22 = 3. Suppose -2*n = l*z - 23, 3*z - 4*n + 1 = -2*z. Factor -16*v**4 - 10*v**2 - 5*v**3 + 9*v**2 + z*v**3 - 6*v**3.
-v**2*(4*v + 1)**2
Let s = 805 + -105453/131. Let u = 4206/917 - s. Factor 2/7*f - u*f**4 - 18/7*f**2 + 0 + 48/7*f**3.
-2*f*(f - 1)*(4*f - 1)**2/7
Let s(f) be the second derivative of f**4/36 + 869*f**3/9 + 755161*f**2/6 - f + 18. Determine v so that s(v) = 0.
-869
Let 2896/7*z**3 + 158/7*z - 1040/7*z**4 - 2308/7*z**2 - 2*z**5 + 44 = 0. What is z?
-77, -2/7, 1
Find o such that -8928/7*o**2 - 3664/7*o**3 - 3008/7 - 524/7*o**4 + 6/7*o**5 - 8992/7*o = 0.
-2, -2/3, 94
Let p be (-76)/(-96) + (-2)/(-6). Let w = -599/32 + 635/32. Factor -p*m - 3/8 - 3/8*m**3 - w*m**2.
-3*(m + 1)**3/8
Let w be 18/(-48)*-2 - 12/16. Suppose w = -4*o - 8 + 16. Find b such that -8/9*b**3 - 2/3 + 2/9*b**4 + 8/9*b + 4/9*b**o = 0.
-1, 1, 3
Suppose -6*d + 5*d + 34 = -4*c, 3*d - 102 = -4*c. Find r, given that 30*r - d*r - 3*r**3 + 21*r**2 + 15 - 29*r = 0.
1, 5
Suppose -4*n + 7 + 49 = -4*w, 5*w = -5*n + 30. Determine f so that f - n*f + 2*f + 2*f**2 + f = 0.
0, 3
Factor -123627/5 - 3/5*o**2 + 1218/5*o.
-3*(o - 203)**2/5
Let v(s) be the second derivative of -s**7/2520 + s**6/540 - s**5/360 - 41*s**3/3 - 34*s. Let q(m) be the second derivative of v(m). Factor q(l).
-l*(l - 1)**2/3
Suppose x + j = -4, -x = -0*j - 4*j - 16. Suppose l + 4*s = 