 z be ((-32)/14)/((-2640)/8316). Find t, given that z + 24/5*t + 3/5*t**2 = 0.
-6, -2
Let r(a) be the second derivative of -a**5/45 - a**4/9 - 2*a**3/9 - 22*a**2 + 61*a + 2. Let h(b) be the first derivative of r(b). Solve h(q) = 0 for q.
-1
Suppose 32 = -5*b + 17, b = n - 19. Let z be ((-3876)/(-336) - 11)/(6/n). Let 10/7*c**2 + 0 + 2/7*c**5 + 6/7*c**3 - 8/7*c - z*c**4 = 0. What is c?
-1, 0, 1, 4
Let a be (-76)/(-190190)*70 - 4/(-26). Factor -20/11*m**2 - 34/11*m - 16/11 - a*m**3.
-2*(m + 1)**2*(m + 8)/11
Let z be (-4)/(-18) - 3/((-135)/2195). Suppose -z + 45 = -2*w. Find x, given that 4*x + 183*x**w - 2*x**3 - 93*x**2 - 88*x**2 = 0.
-1, 0, 2
Find k such that -75*k**3 + 120 - 128*k**3 + 159*k + 206*k**3 + 42*k**2 = 0.
-8, -5, -1
Let i(c) be the first derivative of 0*c + 0*c**2 + 1/2*c**6 + 9/5*c**5 + 0*c**3 + 3/2*c**4 - 257. Factor i(a).
3*a**3*(a + 1)*(a + 2)
Let t(q) = -3*q**3 - 296*q**2 - 296*q + 2. Let g(n) = n**3 - 2*n**2 - 2. Let l(h) = g(h) + t(h). Find k such that l(k) = 0.
-148, -1, 0
Let t be (-5)/5*1*(-11 + 6). Suppose 7*v - 23 = t. Determine a so that 4/3*a**3 - 4/3*a**2 - 2/3*a**5 - 2/3*a + 2/3*a**v + 2/3 = 0.
-1, 1
Suppose -1/3*r**2 + 52*r - 1043/3 = 0. What is r?
7, 149
Let u(f) be the first derivative of -f**4/2 + 45*f**3/2 - 273*f**2/2 - 145*f/2 - 1187. Factor u(v).
-(v - 29)*(v - 5)*(4*v + 1)/2
Factor 241/2*f + 1/4*f**2 + 0.
f*(f + 482)/4
Let y be 20 + (104/4)/(44/(-33)). Factor 3/2*t**3 + y + 1/2*t - 5/2*t**2.
(t - 1)**2*(3*t + 1)/2
Solve -68 + 1/9*n**3 + 139/3*n - 74/9*n**2 = 0 for n.
3, 68
Let b(n) = 27 - 4*n**2 - 20*n - 33 - 10. Let l(x) = -4*x**2 - 20*x - 16. Let j(d) = 5*b(d) - 4*l(d). Let j(w) = 0. Calculate w.
-4, -1
Let q(h) = -3*h**2 - 33*h - 32. Suppose 4*r = -86 + 90. Let j(u) = 2. Let x(a) = r*j(a) + q(a). Factor x(n).
-3*(n + 1)*(n + 10)
Let a(s) be the third derivative of -7*s**6/300 - 11978*s**5/75 - 20499491*s**4/60 - 5855042*s**3/15 + 8077*s**2. Suppose a(m) = 0. Calculate m.
-1711, -2/7
Let f(j) = j**3 + 10*j**2 + 18*j + 19. Let z be f(-8). Factor r**4 + 2*r**2 + 0*r**4 + 1089*r - 1091*r + 2*r**z - 3*r**4.
-2*r*(r - 1)**2*(r + 1)
Let l(j) = j**3 + j. Let p(a) be the first derivative of -9*a**4/4 - 4*a**3/3 + 15*a**2/2 - 12*a + 21. Let d(s) = 5*l(s) + p(s). Determine g so that d(g) = 0.
-3, 1
Let d(l) = -l**2 + 8*l + 2. Let s be d(8). Let k = 3800/7007 + 2/637. Determine p, given that -2/11*p**5 + 0*p**4 - k*p + 8/11*p**3 + 4/11 - 4/11*p**s = 0.
-2, -1, 1
Factor -576*n + 11264/3 - 1/3*n**3 + 25*n**2.
-(n - 32)**2*(n - 11)/3
Factor -1/8*m - 1/8*m**4 - 3/8*m**2 - 3/8*m**3 + 0.
-m*(m + 1)**3/8
Determine u, given that 324/5 + 333/5*u + 6/5*u**2 - 3/5*u**3 = 0.
-9, -1, 12
Let b(x) = x**2 + 2*x - 21. Let f be b(4). Factor 133*v**f - 4594 - 90*v**2 + 1594 - 136*v**3 - 900*v.
-3*(v + 10)**3
Suppose 4*g - 167*w + 168*w - 10 = 0, 5*g + w = 12. Let m = 2/5 - 8/45. Suppose -2/9*c + 2/9*c**g + m*c**3 - 2/9 = 0. What is c?
-1, 1
Suppose -10*f = -12*f - 6, -a - 466 = -4*f. Let r = a + 1915/4. Let 1/4*o**2 + 0 + r*o = 0. Calculate o.
-3, 0
Let v(u) be the third derivative of 5/48*u**4 - 1/48*u**6 + 0*u + 25/36*u**3 - 5/72*u**5 + 76*u**2 + 0. Let v(h) = 0. What is h?
-5/3, -1, 1
Suppose 5*z - 12 = 8. Factor l**2 - 4*l**2 - l - l + z*l**2.
l*(l - 2)
Let a be 2/4*(-116 + 108). Let s be (-36)/(-270)*(-10)/a. Factor 1/3 - s*t - 1/3*t**2 + 1/3*t**3.
(t - 1)**2*(t + 1)/3
Let f(m) be the third derivative of -m**5/30 - 389*m**4/12 + 1970*m**3/3 - 425*m**2 - 3*m + 1. Factor f(p).
-2*(p - 5)*(p + 394)
Let t(o) = o**2 + 2101*o + 400470. Let l be t(-212). Factor l*z - 1/6*z**2 - 9/2.
-(z - 9)*(z - 3)/6
Let g(h) be the first derivative of h**7/105 - h**6/12 + 4*h**5/15 - h**4/3 + 33*h**2/2 + 294. Let u(i) be the second derivative of g(i). What is x in u(x) = 0?
0, 1, 2
Let q be 378/756*(0 - 0). Find l such that 2/13*l - 2/13*l**2 + q = 0.
0, 1
Suppose -12*o = 8*o. Let g(d) be the third derivative of 0 + 0*d**3 + 1/132*d**6 + o*d - 2*d**2 - 1/66*d**4 - 1/110*d**5. Factor g(c).
2*c*(c - 1)*(5*c + 2)/11
Let d = -15 + 16. Let b be (d/(-3))/(4/(-24)). Determine o, given that -2*o**b + o**2 + 4*o**2 - o - 8*o = 0.
0, 3
Let c(u) = -13*u**3 - 2005*u**2 + 4044*u - 2011. Let m(z) = 16*z**3 + 2002*z**2 - 4046*z + 2010. Let p(f) = -6*c(f) - 5*m(f). Find i, given that p(i) = 0.
1, 1008
Let n(m) = -7*m + 26. Let l(r) = -20*r + 77. Let h(t) = 4*l(t) - 11*n(t). Let a be h(7). Factor -5*z**3 - 68*z - a - 20*z**2 + 1 + 88*z + 5*z**4.
5*z*(z - 2)*(z - 1)*(z + 2)
Suppose 24*g + 204 = 7*g. Let a be 14/6 + (4 - (-60)/g). Let -a*u**2 + 2/3*u**3 + 0 + 2/3*u = 0. What is u?
0, 1
Let p(j) be the first derivative of j**5 - 185*j**4/4 - 3681. Factor p(u).
5*u**3*(u - 37)
Let j(b) be the first derivative of 2*b**3/9 - 2222*b**2/3 + 2468642*b/3 + 761. Find f such that j(f) = 0.
1111
Suppose t - 43*l = -46*l + 27, 5*l - 87 = -4*t. Suppose -t*h = -45*h. Suppose 0*z**3 + 2/7*z**2 - 2/7*z**4 + h + 0*z = 0. Calculate z.
-1, 0, 1
Let s(j) be the first derivative of j**5/4 - 25*j**4/12 + 5*j**3 - 33*j + 7. Let w(g) be the first derivative of s(g). Factor w(m).
5*m*(m - 3)*(m - 2)
Let o = 19480 + -19478. What is i in 0 - 6/13*i - 8/13*i**o - 2/13*i**3 = 0?
-3, -1, 0
Let z(s) be the first derivative of -s**8/336 + s**7/56 - s**5/6 + 20*s**3/3 + 68. Let q(w) be the third derivative of z(w). Let q(d) = 0. Calculate d.
-1, 0, 2
Suppose 9*k**2 - 80*k + 31 - 89*k**2 + 40*k**3 + 129 - 5*k**5 + 0*k**4 + 10*k**4 = 0. Calculate k.
-2, 2
Let g = -5707 + 5709. Let h(p) be the first derivative of -9*p - 5*p**3 - 17 + 3/4*p**4 + 21/2*p**g. Factor h(m).
3*(m - 3)*(m - 1)**2
Let b be ((360/(-81))/(-10))/(2/(-9)) + -6 + 8. Factor 3/2*h**4 - 3/2*h**2 + 3*h**3 - 3*h + b.
3*h*(h - 1)*(h + 1)*(h + 2)/2
Let y(i) = 4*i**2 - 29*i - 18. Let n(c) = 5*c**2 - 31*c - 18. Suppose 245*d - 30 = 251*d. Let h(z) = d*n(z) + 6*y(z). Determine b, given that h(b) = 0.
-18, -1
Suppose 0 = 3*l - 0*l - 3*r - 15, -13 = -2*l + r. Let k be 1/l + ((-39)/(-8) - 2). Factor 5*j + 10 - k*j + 5*j + 5*j**2 + 8*j.
5*(j + 1)*(j + 2)
Let c(r) be the first derivative of -2*r**5/15 + 29*r**4/6 - 478*r**3/9 + 619*r**2/3 - 272*r - 8585. What is p in c(p) = 0?
1, 3, 8, 17
Let h(l) be the second derivative of -l**7/189 + 4*l**6/135 + 2*l + 105. Factor h(p).
-2*p**4*(p - 4)/9
Let y be (-12)/(-104)*(20 + 1175/(-75)). What is x in y*x**2 + 0*x - 1/8*x**5 + 7/8*x**3 + 0 + 1/4*x**4 = 0?
-1, 0, 4
Let n = -4419428/3661 - -1356/523. Let g = n - -1206. Solve -g*b**2 - 22/7*b - 4/7 = 0 for b.
-2, -1/5
Solve -16/3*h**2 - 64 + 232/3*h - 2/3*h**4 - 22/3*h**3 = 0.
-8, -6, 1, 2
Let z(l) be the first derivative of 0*l**2 + 10/3*l**3 - l**5 + 0*l + 5/4*l**4 + 42. Factor z(x).
-5*x**2*(x - 2)*(x + 1)
Let f(x) be the third derivative of -x**6/8 + 17*x**5/3 - 55*x**4/6 - 272*x**2 + x. Factor f(z).
-5*z*(z - 22)*(3*z - 2)
Let g(w) be the first derivative of -8*w**2 - 3*w**4 - 32/3*w**3 + 0*w + 176. Let g(f) = 0. What is f?
-2, -2/3, 0
Let o(s) be the first derivative of 0*s + 2/3*s**3 - 8*s**2 - 234. Let o(u) = 0. Calculate u.
0, 8
Let m(f) = -f**2 - 21*f - 16. Let w be m(-20). Suppose -c + w = -5*h - 5*c, -h = -4*c - 4. What is y in 2/9*y**4 - 2/9*y**3 + 0*y**2 + h*y + 0 = 0?
0, 1
Suppose -12*p + 11*p = 5*k, 4*p + 2*k - 90 = 0. Let f = 33 - 17. Find l, given that 11*l**4 + 27*l**3 + 16*l**2 - f*l + p*l**3 + 9*l**4 = 0.
-2, -1, 0, 2/5
Suppose 32 = -130*c + 146*c. Let n(q) be the first derivative of -6/11*q**c - 1/33*q**3 - 36/11*q - 23. Factor n(k).
-(k + 6)**2/11
Let v(o) = -2*o**2 - 1521*o - 290283. Let r(w) = -w - 13. Let i(p) = 6*r(p) + 2*v(p). Factor i(b).
-4*(b + 381)**2
Let j(n) be the third derivative of -n**8/80640 - n**7/6720 + 3*n**5/10 + n**4/24 - 2*n**2 + 7. Let o(x) be the third derivative of j(x). Factor o(w).
-w*(w + 3)/4
Factor 0 - 19*z - 1/2*z**2.
-z*(z + 38)/2
Factor 63*p - 17 + 196 - 341 + 100*p**2 - 414 + 9*p + 4*p**3.
4*(p - 2)*(p + 3)*(p + 24)
Let w be 4/(-72)*5*3*11/(-5). Let r(o) be the second derivative of w*o**4 + 25*o**2 + 1/10*o**5 + 35/3*o**3 - 30*o + 0. Factor r(p).
2*(p + 1)*(p + 5)**2
Find l such that 11*l**3 - 7*l**5 + 168*l + 491761*l**4 - 340*l**2 + 3*l**5 - 491757*l**4 + 161*l**3 = 0.
-7, 0, 1, 6
Suppose 32*m + 3942 = 86*m. Factor -u - 60 - m*u - 6*u**2 - 6*u - 5*u**3 - 29*u**2.
-5*(u + 2)**2*(u + 3)
Let i(t) be 