)*(-108)/(-24). Let f*z**4 + 8/7*z - 20/7*z**2 + 2/7*z**5 - 10/7*z**3 + 16/7 = 0. Calculate z.
-2, -1, 1, 2
Let q = 1/13282 + 79679/172666. Let d(v) be the second derivative of -81/130*v**5 + 0 + 22*v + 0*v**2 - 4/39*v**3 + q*v**4. What is t in d(t) = 0?
0, 2/9
Let t(q) be the first derivative of -5*q**4 - 1304*q**3/3 + 528*q**2 - 9579. Find u such that t(u) = 0.
-66, 0, 4/5
Suppose -56 = 4*i - 4*m, 2*m - 181 + 139 = -5*i. Factor 6/7*v**i + 6/7*v + 2/7*v**3 + 2/7.
2*(v + 1)**3/7
Let o(k) = -k**2 + 68*k - 2498. Let x(j) = j**2 - 33*j + 1248. Let z(t) = 6*o(t) + 11*x(t). Factor z(a).
5*(a - 12)*(a + 21)
Let n(w) = -69*w**2 + 2*w + 76. Let t(d) = -25*d**2 + d + 26. Let u(j) = -4*n(j) + 11*t(j). Solve u(m) = 0 for m.
-6, 3
Factor 14/15*s**2 + 962/15*s - 92/5.
2*(s + 69)*(7*s - 2)/15
Let y(g) = 5*g**3 - 3240*g**2 - 6420*g - 3220. Let x(o) = -4*o**3 + 1621*o**2 + 3209*o + 1611. Let v(b) = 5*x(b) + 3*y(b). Factor v(u).
-5*(u + 1)**2*(u + 321)
Let g be 1387/292 - 20/(-5). Find j such that -g + 9*j - 1/4*j**2 = 0.
1, 35
Let u = 62 - 54. Suppose 2*c = o - 20 - 4, 2*c = -o + u. Determine a, given that 4*a**2 + 10*a - a**3 - a**3 + 4 + 0*a**3 - o = 0.
-2, 1, 3
Let n be (156/(-10))/((-10)/375*3). Solve -50*l**4 + n*l**3 - 17*l**4 - 20*l**5 - 120*l**2 + 25*l + 7*l**4 - 20*l**3 = 0 for l.
-5, 0, 1/2, 1
Factor 14283/4*v - 328509/4 + 1/4*v**3 - 207/4*v**2.
(v - 69)**3/4
Suppose 47 = 3*v - 319. Let m = v + -87. Factor -720 + m*z**2 - 20*z**2 - 120*z - 20*z**2.
-5*(z + 12)**2
Suppose -4*o + 872 = -5*r, 2*r - 143 - 729 = -4*o. Factor 6*c + 114*c**4 - o*c**4 + 12*c**3 + 107*c**4 + 15*c**2.
3*c*(c + 1)**2*(c + 2)
Suppose -2*n - 2 = -2*x + 14, 0 = -5*n - 5*x + 60. Factor 2/17*d**n - 4/17 - 2/17*d.
2*(d - 2)*(d + 1)/17
What is y in 123 + 80962*y**2 + 2500*y - 80967*y**2 + 3151 + 1746 = 0?
-2, 502
Let p(t) be the first derivative of -4/15*t**5 + 1/3*t**4 + 0*t - 8 + 0*t**3 + 1/18*t**6 + 0*t**2. Factor p(a).
a**3*(a - 2)**2/3
Suppose -4*n = -4, -c - 44*n = -45*n - 53. Solve -261 + 47 - 210*q**2 + 320*q + 45*q**3 + c = 0 for q.
4/3, 2
Let g be (-99)/(-22) - (-3)/(-6). Solve -7 - 4 - 77*l**3 - 5 - 3*l**g + 16*l + 69*l**3 + 12*l**2 - l**4 = 0.
-2, 1
Suppose l = 2*f - 812 - 9316, 0 = -5*f - 4*l + 25398. Determine z so that -8/5 + 156*z - f*z**2 + 54925*z**3 = 0.
2/65
Let g be 12/(8 - 10) - (-1663)/133. Let z = g + -15/19. Factor 12/7 - 16/7*x**3 - z*x + 44/7*x**2.
-4*(x - 1)**2*(4*x - 3)/7
Let v(c) be the first derivative of -c**5/240 - 5*c**4/48 - 25*c**3/24 - 9*c**2/2 + 3*c + 110. Let y(k) be the second derivative of v(k). What is l in y(l) = 0?
-5
Let y(s) be the first derivative of 15*s**4/4 + 385*s**3/3 - 485*s**2 + 280*s - 1433. Find l, given that y(l) = 0.
-28, 1/3, 2
Let j(n) = -n**3 - 7*n**2 - 4*n + 40. Let v be j(-5). Factor 11*s**2 - 9 - 16*s**2 + 24 - v*s.
-5*(s - 1)*(s + 3)
Let m be 4/9 + 1270/(-3195). Let p = m - -782/1491. Determine f so that -20/7*f + p*f**2 + 0 = 0.
0, 5
Let -606*g**5 - 24*g**4 + 301*g**5 + 90*g**2 + 314*g**5 - 93*g - 12*g**3 + 30 = 0. Calculate g.
-2, 1, 5/3
Let b(d) = -4*d**2 + 1844*d - 1924. Let t(j) = 3*j**2 - 1226*j + 1283. Let f(h) = -5*b(h) - 7*t(h). Let f(v) = 0. What is v?
-639, 1
Let g(h) be the first derivative of -19*h**4/4 + 79*h**3/3 + 83*h**2/2 - 15*h + 34. What is i in g(i) = 0?
-1, 3/19, 5
Let o = -858103 - -858106. Factor 10/3*r**2 - 17/3*r - 1/3*r**o + 8/3.
-(r - 8)*(r - 1)**2/3
Let g = 4/7625 + 15238/22875. Let q(h) be the first derivative of -13 + 20*h + 7*h**2 + g*h**3. Solve q(c) = 0.
-5, -2
Let k be (0/((10 - 10) + 2))/(2 + -1). Let j(c) be the third derivative of 0*c + 10/3*c**4 + 1/24*c**6 + k*c**3 + 2/3*c**5 + 6*c**2 + 0. Factor j(m).
5*m*(m + 4)**2
Let m(s) be the second derivative of 30*s**2 + 2 + 10/3*s**3 + 5*s - 5/12*s**4. Suppose m(l) = 0. Calculate l.
-2, 6
Let b(g) = -4*g**4 - 8*g**3 - 156*g**2 - 336*g - 24. Let j(d) = d**4 + 2*d**3 + 31*d**2 + 67*d + 5. Let f(t) = -5*b(t) - 24*j(t). Factor f(k).
-4*k*(k - 3)*(k + 2)*(k + 3)
Let t be 15 - 1547/(-52) - 3/(-8)*-2. Let s(l) be the first derivative of -20*l**5 + 36*l - 30*l**4 + t + 60*l**2 + 64/3*l**3. Let s(g) = 0. What is g?
-1, -3/5, 1
Let 1016189*d**2 + d - 1016187*d**2 - 25*d - 10*d + 60 = 0. Calculate d.
2, 15
Let r = 68 - 68. Suppose 8*y - 2*y - 12 = r. Determine k, given that 104*k**3 + k**4 + y*k**4 - 7*k**2 + 16*k**2 - 116*k**3 = 0.
0, 1, 3
Let z(g) be the third derivative of -g**8/84 + g**7 - 5*g**6/2 - 31*g**5/6 + 17*g**4/2 - 4*g**2 + 8*g - 33. Determine p, given that z(p) = 0.
-1, 0, 1/2, 2, 51
Let w be (-4085)/76 - (-41 - 15). Solve -w*z**4 + 0 + 7/4*z**3 + 0*z + 1/2*z**2 = 0 for z.
-2/9, 0, 1
Let r(b) be the second derivative of b**7/2520 + 7*b**6/1080 - b**5/36 - 2*b**4/9 + 7*b**3/2 + 3*b. Let p(j) be the second derivative of r(j). Factor p(h).
(h - 2)*(h + 1)*(h + 8)/3
Let z(a) be the second derivative of 289*a**2 + 170/3*a**3 - 185*a + 0 + 25/6*a**4. Factor z(v).
2*(5*v + 17)**2
Solve -1824/5*a + 6/5*a**3 - 192/5*a**2 - 768 = 0.
-4, 40
Find k such that 152/13 - 2/13*k**2 + 72/13*k = 0.
-2, 38
Let k = -149 + 152. Suppose 8*o**2 + 7*o**3 - 22*o**2 - 10*o**2 + 36*o + k*o**4 - 10*o**3 = 0. What is o?
-3, 0, 2
Let c = 2893/18 - 1442/9. Factor c*o**3 + 11/2*o - 13/4*o**2 - 2.
(o - 4)*(o - 2)*(2*o - 1)/4
What is z in 333/2*z - 165/2*z**2 - 167/2 - 1/2*z**3 = 0?
-167, 1
Let f(v) be the first derivative of -4*v**5/5 + 11*v**4 + 8*v**3 - 280*v**2 - 800*v - 8488. Determine k so that f(k) = 0.
-2, 5, 10
Let b(p) be the first derivative of -p**4/3 + 16*p**3/3 - 32*p**2 - 141*p + 92. Let g(i) be the first derivative of b(i). What is k in g(k) = 0?
4
Factor 64144 + 28761*k**2 + 37916 - 58016*k**2 - 10800*k - 5*k**3 + 28750*k**2.
-5*(k - 7)*(k + 54)**2
Let q(c) = -116*c**3 + 40*c**2 - 20*c - 216. Let z(v) = 5*v**3 - v**2 - 2*v - 1. Let b(d) = q(d) + 24*z(d). Factor b(s).
4*(s - 4)*(s + 3)*(s + 5)
Let x(y) = -19*y + 80 - 9*y - 38*y + 6*y**2. Let k = 23 + -20. Let c(v) = -v**2 + 13*v - 16. Let o(b) = k*x(b) + 14*c(b). Let o(m) = 0. Calculate m.
2
Let k = 127 + -101. Suppose k = 21*d - 8*d. Determine x so that -75*x + 4*x**2 - x**d + 1 + 78*x + 4*x**3 - 3*x**3 = 0.
-1
Suppose 0 = -5*z - 67 + 242. Let k = z - 33. Solve 4*u**2 - 2*u**k - 5*u + 4*u**2 - u**2 = 0.
0, 1
Let j(b) be the first derivative of -b**5/480 + 23*b**4/192 - 11*b**3/24 - 7*b**2 - 23. Let w(u) be the second derivative of j(u). Solve w(t) = 0 for t.
1, 22
Let g = -4464403/30 - -148834. Let s = -109/6 + g. Factor -9/5*u**3 + 6/5 + 3/5*u - s*u**2.
-3*(u + 1)**2*(3*u - 2)/5
Suppose 7*k - 1 = 6*k, 2*a - k = 5. Let t(l) be the first derivative of -3/14*l**4 + 0*l**a + 0*l - 6/35*l**5 + 6 + 0*l**2. Determine q, given that t(q) = 0.
-1, 0
Suppose -66*d + 16659 = -7827. Suppose -d*u + 376*u = 15. Factor -7/10*v**u + 16/5 + 29/5*v**2 - 64/5*v.
-(v - 4)**2*(7*v - 2)/10
Let i(l) be the third derivative of l**7/140 - 31*l**5/40 - 15*l**4/8 - 538*l**2. Factor i(w).
3*w*(w - 6)*(w + 1)*(w + 5)/2
Let z be (-5)/((-5)/2 - 0). Let g be 103/4 - 1/(-4). Suppose -g + c**3 - c**z + 27 + c - 2*c = 0. What is c?
-1, 1
Factor 1/5*d**5 + 4/5*d**3 + 14/5 + 26/5*d**2 - 8/5*d**4 - 37/5*d.
(d - 7)*(d - 1)**3*(d + 2)/5
Let c be 12/(-42) + (37/7 - 2). Suppose -c*m - 2 + 26 = -5*f, -f - 6 = -m. Suppose -163*s**2 - 108*s**m + 12 + 12*s - 54*s**2 + 4*s**2 = 0. What is s?
-2, -2/9, 1/4
Suppose -29/2*a + a**4 + 15*a**3 + 20*a**2 - 21 - 1/2*a**5 = 0. What is a?
-3, -2, -1, 1, 7
Factor -2/5*h**4 - 844/5*h**3 - 89882/5*h**2 - 35448*h - 17640.
-2*(h + 1)**2*(h + 210)**2/5
Let d(v) = 2*v**2 - 2. Let o be d(-3). Suppose 0*m - o = -4*m - 3*t, 4*t - 4 = -m. Let 12*y**m + 3*y**5 - 30*y**3 - 4*y + 42*y**3 + 4*y = 0. What is y?
-2, 0
Suppose 151*m**3 + 195*m**3 + 0*m**5 - 345*m**4 - 3*m**5 - 2*m**5 + 4*m**3 = 0. What is m?
-70, 0, 1
Let r(p) be the third derivative of 2 - 1/15*p**5 + 6*p**3 + 0*p + 53*p**2 - 4/3*p**4. Factor r(z).
-4*(z - 1)*(z + 9)
Let k be (-412)/(-309) - 60/(-27)*9/(-24). Find v, given that -2*v - 3/2*v**2 + 2*v**3 + 2 - k*v**4 = 0.
-1, 1, 2
Let g(f) be the first derivative of 0*f + 3/5*f**5 + 3/10*f**4 - f**3 + 45 - 3/5*f**2. Suppose g(m) = 0. Calculate m.
-1, -2/5, 0, 1
Factor -540 - 3/2*t**3 + 807*t - 531/2*t**2.
-3*(t - 2)*(t - 1)*(t + 180)/2
Let a be 5/(-5) - (-69 - 14). Suppose a*x - 69*x = 39. Factor 0 - 8/7*