5*(r - 195)*(r - 1)*(r + 1)
What is k in 204*k - 1/2*k**2 - 20808 = 0?
204
Factor -1/7*r**4 + 0 + 69/7*r + 71/7*r**3 - 139/7*r**2.
-r*(r - 69)*(r - 1)**2/7
Suppose 4*m + 827*x = 830*x + 45, 4*x + 53 = 3*m. Determine z, given that 0 + 0*z + 1/2*z**2 + 1/3*z**m = 0.
-3/2, 0
Let j = 1355 - 120. Let w = j - 1235. Suppose w + 0*l + 2/3*l**3 - 4/3*l**2 = 0. Calculate l.
0, 2
Let o be (50/(-30))/((-1)/51). Suppose -90*a + 5*a**2 - o*a + 150*a = 0. What is a?
0, 5
Suppose -4*d = 3*u + 40, -19*d = -20*d + 4*u + 9. Let g be 255/(-85) - (1 + d + 0). Factor 21/2*j**2 - 3/2*j**g - 33/2*j + 15/2.
-3*(j - 5)*(j - 1)**2/2
Let x = 234168/5 + -86407387/1845. Let l = x - -2/369. Factor -l*n**2 - 5/3*n - 1 + 1/3*n**3.
(n - 3)*(n + 1)**2/3
Let c = 170 - -278. Let d = 450 - c. Let -1/3*i**d + 1/3*i + 2/3 = 0. What is i?
-1, 2
Let -3*q**3 + 4*q**2 + 4*q**2 - 2*q**2 - q**2 - 2*q**3 = 0. What is q?
0, 1
Let l = -9 + 38. Suppose 3*u + l = -j + 344, 2*j + 4*u = 630. Determine d so that -315 + 4*d**2 + j = 0.
0
Suppose -p = g - 10, -4*p - 14 = 333*g - 338*g. Let -14/11*b**3 + 2/11*b**p - 12/11 + 14/11*b + 10/11*b**2 = 0. Calculate b.
-1, 1, 6
Let f be 9/(-27) + ((-1)/(-3) - -1). Let q(r) = 6*r**2 + 221*r + 2419. Let d(i) = i**2 + i - 1. Let p(a) = f*q(a) - d(a). Find m, given that p(m) = 0.
-22
Factor -6*c - 80/11 + 14/11*c**2.
2*(c + 1)*(7*c - 40)/11
Find a such that -6948*a**2 - 253741 - 4*a**3 - 3020640*a - 1645700 + 470937 - 1585192 = 0.
-868, -1
Let g(t) = 19*t**3 - 3*t**2 - 5*t + 20. Let u be g(4). Let c = u - 4667/4. Factor 3/4*k**2 + c - 9/4*k + 1/4*k**3.
(k - 1)**2*(k + 5)/4
Let f(i) be the second derivative of -i**6/10 - 14*i**5/5 - 3*i**4 - i - 386. Let f(r) = 0. Calculate r.
-18, -2/3, 0
Let p be ((-12)/14 + -2)/((-26 + 14)/168). Let j(g) be the third derivative of -1/150*g**6 + p*g**2 + 2/3*g**3 + 0 + 7/75*g**5 + 0*g - 11/30*g**4. Factor j(s).
-4*(s - 5)*(s - 1)**2/5
Let t(l) = 9*l**3 - 29*l**2 + 342*l + 350. Let d(y) = -11*y**3 + 33*y**2 - 343*y - 351. Let q(s) = 5*d(s) + 6*t(s). Factor q(k).
-(k - 15)*(k + 1)*(k + 23)
Let u(v) = -v**3 + 2*v**2 + v - 5. Let y(k) = -6*k**3 - 3867*k**2 - 7734*k - 3882. Let j(b) = 3*u(b) - y(b). Factor j(s).
3*(s + 1)**2*(s + 1289)
Let b = 12078 + -12072. Let r(f) be the second derivative of 7/36*f**b + 1/12*f**5 + 0 + 0*f**2 + 5/84*f**7 + 0*f**3 + 0*f**4 - 12*f. What is l in r(l) = 0?
-2, -1/3, 0
Let 3/7*f**4 + 17/7*f**2 - 1/7*f**5 + 15/7*f**3 + 0 + 6/7*f = 0. Calculate f.
-1, 0, 6
Let g(m) be the first derivative of -m**4/54 - 4*m**3/27 + 5*m**2/9 + 41*m + 87. Let a(r) be the first derivative of g(r). Factor a(p).
-2*(p - 1)*(p + 5)/9
Let n(y) = -12*y**4 + 918*y**3 - 2583*y**2 + 36*y. Let p(g) = 9*g**4 - 689*g**3 + 1937*g**2 - 28*g. Let z(x) = -7*n(x) - 9*p(x). Factor z(u).
3*u**2*(u - 72)*(u - 3)
Suppose 139*u + 18 = 145*u. Factor -28*b + 32*b - 4*b**2 - 4*b**2 - b**4 + 5*b**u.
-b*(b - 2)**2*(b - 1)
Suppose 5*m = 3515*v - 3518*v + 25, v = -5*m + 15. Factor 2/7*u**3 - 8/7*u + 24/7 - 6/7*u**m.
2*(u - 3)*(u - 2)*(u + 2)/7
What is r in 0 - 1636/5*r - 2/5*r**2 = 0?
-818, 0
Solve -8178/11*o**2 - 2/11*o**4 + 26398/11*o - 17956/11 - 262/11*o**3 = 0 for o.
-67, 1, 2
Let -411/4*n**2 - 99/2 - 111/4*n**3 - 3/4*n**4 - 501/4*n = 0. What is n?
-33, -2, -1
Let i(q) be the first derivative of 4*q**3/3 - 876*q**2 + 191844*q + 597. Let i(b) = 0. Calculate b.
219
Let h(o) = -o - 5. Let a(r) = 5*r**2 - 400*r - 745. Let z(k) = a(k) + 25*h(k). Solve z(b) = 0 for b.
-2, 87
Factor 7182*g**2 - 502*g + 285*g**3 + 3*g**4 + 9823*g + 14243*g - 3968*g + 12696.
3*(g + 1)*(g + 2)*(g + 46)**2
Let i be (-102)/(-153)*30/4. Factor d**3 + 3*d**3 - 11*d**5 + 9*d**5 - 2*d**i.
-4*d**3*(d - 1)*(d + 1)
Suppose 0*q - 39*q + 2496 = 0. Suppose 50*b + q = 264. What is o in 0 - 3/10*o**b - 1/5*o + 1/10*o**3 + 1/10*o**5 + 3/10*o**2 = 0?
-1, 0, 1, 2
Let p(v) be the second derivative of -v**5/10 + 10*v**4/3 + 4*v**3/3 - 80*v**2 - 1180*v. Solve p(k) = 0 for k.
-2, 2, 20
Let w(m) be the second derivative of 3*m**5/100 + 7*m**4/10 - 2*m**3/5 - 84*m**2/5 - m + 59. Factor w(d).
3*(d - 2)*(d + 2)*(d + 14)/5
Factor 1640 + 1238*z + 138*z**2 + 83*z**2 - 215*z**2.
2*(z + 205)*(3*z + 4)
Factor 7357*k - 3847299 + 4*k**2 - 1376*k + 8795*k + 17492935.
4*(k + 1847)**2
Factor -38*r + 31*r**2 - 33*r**2 - 84 + 4*r**2.
2*(r - 21)*(r + 2)
Let v = 363 - 402. Let u be ((-130)/v)/((-95)/(-15)). Factor 2/19*s**2 + 12/19 + u*s.
2*(s + 2)*(s + 3)/19
Let b(k) be the second derivative of -1/3*k**6 + 2/3*k**4 + 0*k**2 + 40*k - 8/3*k**3 + 3/5*k**5 + 0 + 1/21*k**7. Solve b(o) = 0.
-1, 0, 2
Suppose 2*b - 5 = -1. Let w be 987/147 + b/7. Solve -g**2 - 2*g + 10*g + g - w*g = 0 for g.
0, 2
Let g = -2359864/5 + 471978. Factor 62/3*l - 8/15*l**2 + g.
-2*(l - 39)*(4*l + 1)/15
Suppose 5*n - 36 = 39. Suppose 0 = 11*t - n*t + 12. Let -4*c**5 + 21*c**2 - 4*c**4 + 12*c**t - 9*c + 17*c - c**2 = 0. Calculate c.
-1, 0, 2
Let f be ((-3)/2)/((-6)/8). Let l(n) = -347*n + 1739. Let r be l(5). What is a in -a**3 + f*a + 2*a**2 + 3*a**3 - r*a**3 - 2*a**4 = 0?
-1, 0, 1
Let i be 4*-1*((-1536)/80 - -19). Let -182/5*n**3 - i - 116/5*n**2 + 62/5*n = 0. What is n?
-1, 1/13, 2/7
Let r(g) = -3*g**2 + 84*g + 67. Let u(i) = -4*i**2 + 86*i + 65. Let y(c) = -5*r(c) + 4*u(c). What is j in y(j) = 0?
-75, -1
Let i(w) be the third derivative of -w**5/90 + 119*w**4/12 - 356*w**3/9 + 12*w**2 - 193*w + 2. Determine n so that i(n) = 0.
1, 356
Let z(f) be the second derivative of -9/5*f**2 + 3/20*f**4 - 2*f + 7/10*f**3 + 50. Let z(s) = 0. Calculate s.
-3, 2/3
Factor -19/3*l**2 + 1/6*l**5 + 4/3*l**4 + 0 + 5/6*l**3 + 4*l.
l*(l - 1)**2*(l + 4)*(l + 6)/6
Let y(q) be the third derivative of -4*q**7/35 + 11*q**6/8 - 24*q**5/5 - 45*q**4/8 + 81*q**3 - 1548*q**2. Determine u so that y(u) = 0.
-9/8, 2, 3
Let m = -678 + 676. Let q be m*(-165)/308 - 1/2. Factor -q*i**4 + 8/7*i**2 + 0 + 0*i - 4/7*i**3.
-4*i**2*(i - 1)*(i + 2)/7
Suppose 1 = 30*g - 59. Let t be (-1624)/(-420) + (-1)/5. Factor -t + 4*m - 1/3*m**g.
-(m - 11)*(m - 1)/3
Let r(n) be the third derivative of n**6/30 + 802*n**5/15 + 160801*n**4/6 + 43*n**2 - 3*n. Factor r(d).
4*d*(d + 401)**2
Let k(r) be the third derivative of r**5/390 - 319*r**4/78 + 101761*r**3/39 + 137*r**2 - 7*r + 2. Factor k(l).
2*(l - 319)**2/13
Let a(o) be the third derivative of -o**8/336 + o**7/105 + o**6/30 - o**5/30 - o**4/8 - 110*o**2. Find v, given that a(v) = 0.
-1, 0, 1, 3
Factor 126*b**2 + 208 - 393*b**3 - 10*b**2 - 109*b - 397*b**3 - 211*b + 786*b**3.
-4*(b - 26)*(b - 2)*(b - 1)
Let z(x) be the third derivative of -x**7/315 + 61*x**6/180 - 143*x**5/10 + 11495*x**4/36 - 37268*x**3/9 + 101*x**2 - 11. Let z(b) = 0. What is b?
11, 28
Let u(w) = -62*w**2 - 29518*w - 8431. Let n(j) = -153*j**2 - 73797*j - 21078. Let y(d) = 5*n(d) - 12*u(d). Factor y(c).
-3*(c + 703)*(7*c + 2)
Let t = -47873/117 - -4610/13. Let m = t + 55. Factor -8/9*n**2 - 2/9*n + m*n**3 + 8/3*n**4 - 2*n**5 + 0.
-2*n*(n - 1)**2*(3*n + 1)**2/9
Let l(d) = -4*d**2 + 18*d - 10. Let o(x) = 5 - 20*x + x**2 + 4 + 3*x**2 + 4*x**2 - 3*x**2. Let k(v) = -3*l(v) - 2*o(v). Factor k(f).
2*(f - 6)*(f - 1)
Let -2/11*h**2 - 70/11*h - 588/11 = 0. Calculate h.
-21, -14
Let d(l) = l**3 - 14*l**2 - 15*l - 13. Let n be d(15). Let y = n - -48. Factor -48*x + 64 - 28 + 28 - 36*x**3 + y*x**3 + 12*x**2.
-(x - 4)**3
Let m be 61/(-6)*((-182)/77)/13. Let h = m + 9/11. Factor 0 + 4/3*s**3 - h*s**2 - 2/9*s**4 + 16/9*s.
-2*s*(s - 2)**3/9
Let g = -452 + 457. Let u be 78/(-36) + (-9)/6 + g. Determine k so that u*k**3 + 0 + 100/3*k + 40/3*k**2 = 0.
-5, 0
Let h(z) be the first derivative of z**6/40 - 2*z**5/3 + 49*z**4/24 - 2*z**3 - 3*z**2/2 + 4*z + 39. Let g(j) be the second derivative of h(j). Factor g(q).
(q - 12)*(q - 1)*(3*q - 1)
Let c(s) be the third derivative of -s**6/180 + 29*s**5/6 + 437*s**4/18 + s**2 - 758*s. Factor c(j).
-2*j*(j - 437)*(j + 2)/3
Let n = -8862 - -8865. Suppose 3*o + 2*i - 27 = -i, 2*i = -o + 14. Solve -4*q + 6*q**2 - q**3 - o*q**n + 3*q**3 = 0 for q.
0, 1, 2
Let x = 5437/56 + -763/8. Factor 6/7*r + x*r**2 + 6/7*r**3 + 0.
6*r*(r + 1)**2/7
Let z(r) = r**3 + 6*r**2 - r - 1. Let k(b) = -b**4 + 6*b**3 + 11*b**2 - 8*b - 2. Let w(f) = -2*k(f) + 4*z(f). Factor w(x).
2*x*(x - 3)*(x - 2)*(x + 1)
Let a(s) be the third derivative of s**6/100 + 7*s**5/150 - 7*s**4/6 - 8*