251217045*c**2 - 6841192812849/2 + 92699089605/2*c = 0. What is c?
369
Suppose -42*w - 9 = -39*w. Let u be 32/36*w/(-24). Factor 0*m**2 + 0*m + 0 + 0*m**3 - 1/9*m**5 - u*m**4.
-m**4*(m + 1)/9
Let r = 1697 + -1697. Suppose -12 = -2*t - 2*t. Solve r*l**3 + 132*l - 132*l + 3*l**t = 0 for l.
0
Determine h, given that 5891*h - 693 - 432 - 6517*h**2 - 10678*h**2 + 2784*h + 1805*h**3 = 0.
5/19, 9
Suppose 5*n - 9 = -2*t, 2*t + 0 = 3*n - 15. Let b(r) be the first derivative of 0*r**2 - 1/12*r**4 + 2/9*r**n + 3 + 0*r. Factor b(s).
-s**2*(s - 2)/3
Let b(a) be the third derivative of -5*a**5/12 + 1985*a**4/24 - 645*a**3 + 494*a**2 + 9. Solve b(v) = 0.
2, 387/5
Let v(n) be the third derivative of -n**5/180 + 49*n**4/12 + 99*n**3/2 - 886*n**2 - n + 1. Factor v(k).
-(k - 297)*(k + 3)/3
Let g = 32203/42948 + 2/10737. Let f(a) be the first derivative of -5 - a - g*a**2 - 1/6*a**3. Factor f(o).
-(o + 1)*(o + 2)/2
Factor -27 - 85 - 17 + 10*y**2 - 26 - 5 - 880*y + 55*y**3.
5*(y - 4)*(y + 4)*(11*y + 2)
Suppose -4*b = -4*g - 74 - 86, -5*g = 2*b - 73. Let n = -35 + b. Factor -9*h - n + 29*h - 12*h - 4*h**2.
-4*(h - 1)**2
Let y(r) be the second derivative of -r**4/102 - 167*r**3/51 - 652*r**2/17 + 4405*r. Find g such that y(g) = 0.
-163, -4
Suppose -2*w = 5*x + 16, 32*w - 29*w + 2*x = -2. Factor 10/11 + 118/11*l - 72/11*l**3 + 336/11*l**w.
-2*(l - 5)*(6*l + 1)**2/11
Let g be (-1)/8 + 12/(-128)*-6476. Find h, given that -g + 96*h - 4*h**2 - h**4 - 3*h**4 + 687 - 24*h**3 = 0.
-5, -2, -1, 2
Let x(b) = 137 + 114*b**2 - 111*b**2 + 43*b - 17*b + 66. Let z(i) = -i**2 - 8*i - 68. Let u(r) = 4*x(r) + 11*z(r). What is a in u(a) = 0?
-8
Let c = 110281/15564 - 3/1297. Let p(y) be the second derivative of -36*y + 3/4*y**5 + 15/2*y**3 - c*y**4 + 0 + 25/2*y**2. Factor p(j).
5*(j - 5)*(j - 1)*(3*j + 1)
Suppose 7*c + 91 = 105. Determine x so that -3*x**5 - 511*x**2 + 22*x**3 - 12*x**4 - 200*x + 0*x**5 + 631*x**c + x**5 = 0.
-5, 0, 2
Let t(u) be the third derivative of u**5/150 - 13*u**4/60 + 4*u**3/5 - 125*u**2 - 9*u. Factor t(n).
2*(n - 12)*(n - 1)/5
Let 3064*s**3 - 101622*s + 45188*s - 98*s**4 + s**5 - 25840*s**2 - 86910*s - 157216 = 0. What is s?
-2, 34
Let d(x) be the second derivative of 0 - 1/126*x**7 + 1/10*x**5 + 5/18*x**4 - 7/6*x**3 - 1/30*x**6 + 3/2*x**2 - 71*x. Factor d(i).
-(i - 1)**3*(i + 3)**2/3
Let o(z) be the third derivative of 2/135*z**5 + 0 - 1/1512*z**8 + 2/27*z**4 - 50*z**2 - 1/189*z**7 - 1/90*z**6 + 0*z**3 + 3*z. Factor o(u).
-2*u*(u - 1)*(u + 2)**3/9
Let s = 401 + -399. Let c(g) = 57*g - 114. Let t be c(s). Factor t + 0*a**2 + 2/7*a**3 + 0*a + 2/7*a**4.
2*a**3*(a + 1)/7
Let j(l) be the first derivative of -5 + 0*l - 1/56*l**4 + 4/3*l**3 + 0*l**5 + 0*l**2 + 1/840*l**6. Let c(f) be the third derivative of j(f). Factor c(w).
3*(w - 1)*(w + 1)/7
Let -480/11*q - 138/11*q**2 - 6/11*q**3 - 456/11 = 0. What is q?
-19, -2
Let c(x) be the first derivative of x**4/2 + 818*x**3/3 + 42024*x**2 + 83232*x - 827. Factor c(a).
2*(a + 1)*(a + 204)**2
Let l(k) be the second derivative of 3*k**5/10 - 28*k**4/3 + 77*k**3 - 130*k**2 - 2900*k. Suppose l(q) = 0. Calculate q.
2/3, 5, 13
Let f = 136/6533 + 182516/19599. Solve -272/3 + 944/3*u + f*u**2 = 0.
-34, 2/7
Let a(z) = 10*z**2 - 1122*z + 4785. Let l(n) = n**2 - 102*n + 435. Let u(j) = 2*a(j) - 23*l(j). Find w, given that u(w) = 0.
5, 29
Suppose -3*y + 64 = -32. Suppose -4*r = -y + 16. Factor b - 4*b**3 - 4*b**4 + 9*b**4 + r*b - b**3 - 5*b**2.
5*b*(b - 1)**2*(b + 1)
Let o(l) = 2*l**3 - 18*l**2 + 44*l + 3. Let p be o(9). Let d = -2783/7 + p. Suppose 8/7*a + 2/7*a**2 - d = 0. Calculate a.
-5, 1
Let z(s) = s**3 + 9*s**2 + 8*s + 3. Let d be z(-8). Suppose -2*n - d*n = -60. Solve -10*r**3 + 14*r**2 - 7*r**3 - n*r**3 + 49*r + 30*r**3 = 0 for r.
-7, 0
Let m(u) be the second derivative of u**4/6 + 212*u**3/3 + 11236*u**2 + 1162*u. Factor m(l).
2*(l + 106)**2
Let v be (19 - (18 - 4)) + -3. Let l = -13 - -27. Factor -3 - 6*p + l*p - 9*p**v + 4*p.
-3*(p - 1)*(3*p - 1)
Let z(m) be the second derivative of -m**6/30 + 31*m**4/12 - 5*m**3 + 674*m. Factor z(g).
-g*(g - 5)*(g - 1)*(g + 6)
Let d be (-13)/39*(-16101)/66. Let k = 163/2 - d. Factor 0 + k*m**2 - 6/11*m.
2*m*(m - 3)/11
Suppose -t + 208 = z - 866, 4*z + 5397 = 5*t. Let s = t - 1077. Factor 0*c**2 + 4/9*c**4 + s*c + 2/9*c**3 + 2/9*c**5 + 0.
2*c**3*(c + 1)**2/9
Solve 305*p**3 + 217*p**2 + 5*p**5 - 156*p**2 - 85*p**4 - 810*p + 524*p**2 = 0.
-2, 0, 1, 9
Let j = 251 + -218. Factor -j*u**2 - 36*u**2 - 2*u**3 + 65*u**2.
-2*u**2*(u + 2)
Let u be (-40)/(-70)*(-33)/(-264). Let s(b) be the first derivative of 0*b - u*b**4 + 0*b**2 - 1 + 2/21*b**3. Let s(c) = 0. What is c?
0, 1
Let h(x) = x**2 + 17*x. Let y(w) = -4*w**2 - 213*w + 252. Let o(j) = 20*h(j) + 4*y(j). Let o(k) = 0. What is k?
2, 126
Let r(m) be the third derivative of 133*m**2 + 1/32*m**4 + 0 + 1/320*m**6 + 3/160*m**5 + 0*m**3 + 0*m. Find t such that r(t) = 0.
-2, -1, 0
Let n(b) = -56*b + 34. Let u be n(-1). Let j be (-4)/(-14)*-8*(-63)/u. Factor -4/5*o**3 - j - 6/5*o**2 + 16/5*o + 2/5*o**4.
2*(o - 2)*(o - 1)**2*(o + 2)/5
Let p be 16/(-88) - 90/(-11). Suppose 3*g - p*g + 10 = 0. Factor g*s**2 + 3*s**2 + 98 - 88 + 15*s.
5*(s + 1)*(s + 2)
Let y(z) = z**2 + 2030*z - 1020108. Let o(k) = -2*k**2 - 2035*k + 1020112. Let p(r) = -4*o(r) - 6*y(r). Determine t, given that p(t) = 0.
1010
Let s(y) be the third derivative of 1/100*y**6 + 0*y**3 - 2/15*y**4 - 1/840*y**8 + 1/15*y**5 + 0 - 4/525*y**7 + 0*y + 29*y**2. Find n, given that s(n) = 0.
-4, -2, 0, 1
Let l(g) be the third derivative of 14*g**2 + 0 + 1/2*g**4 - 1/4*g**3 + 9/40*g**5 - 3*g. Factor l(i).
3*(i + 1)*(9*i - 1)/2
Suppose 2336/5*k + 424/5 + 22/5*k**2 = 0. What is k?
-106, -2/11
Suppose 24 = -f + 29. Determine g so that f*g**2 - 3*g**3 + 12*g**3 - 6*g**3 - 5*g**2 = 0.
0
Let r = 5062 + 518. Factor -924 + r*b - 15*b**3 + 201*b**3 + 3624 + 3063*b**2 + 3*b**4.
3*(b + 1)**2*(b + 30)**2
Let c be (15 - 13) + 0/1. Let k be (4 + -12)/(-2) - c/(-2). Factor 12*y**4 - k*y + 48*y**2 + 13*y**4 - 10*y**4 + 51*y**3 + 17*y.
3*y*(y + 1)*(y + 2)*(5*y + 2)
Let u = -605/63 - -89/9. Let k be -1 + (48/8)/6. Determine s, given that 2/7*s**2 + k*s - u*s**3 + 0 = 0.
0, 1
Suppose 36*n = 42*n - 144. Let l be (n/9 - 3)*-9. Factor -43*z**2 + 23*z**2 + 13*z**3 + 3*z**l - 4*z**4 + 8*z.
-4*z*(z - 2)*(z - 1)**2
Let p be (-12)/21 - 396/(-154). Suppose 5*m - p*h - 6 = 0, 0 = 4*m - 0*m - 4*h - 12. Factor -8/7*w**2 - 12/7*w**3 - 4/7*w**4 + m*w + 0.
-4*w**2*(w + 1)*(w + 2)/7
Factor 0 + 2/5*a**5 + 0*a + 16/5*a**2 - 8/5*a**3 - 4/5*a**4.
2*a**2*(a - 2)**2*(a + 2)/5
Suppose 0*m = -2*m - 4*j - 4, -4*m + 3*j = -14. Let t = -49648/5 + 546208/55. Find p such that -t - 152/11*p - 162/11*p**3 - 36*p**m = 0.
-2, -2/9
Suppose 0 = -3*u + h + 11 + 7, 13 = 2*u - h. Suppose -5*k = -5*n - 5, -7 + u = -5*n - 2*k. Factor 2/7*g**2 - 6/7*g**4 + 8/7*g**3 - 4/7*g + n.
-2*g*(g - 1)**2*(3*g + 2)/7
Solve 376 + 38*j**2 - 1148 + 343 + 389 - 25*j**4 - 76*j + 47*j**3 + 2*j**5 = 0 for j.
-1, -1/2, 2, 10
Let b = -347659 + 1390637/4. Factor b*j**2 - 9 - 4*j.
(j - 18)*(j + 2)/4
Suppose 345*i = 328*i + 68. Factor 1/2*h**i + 0 + 19/2*h**2 + 9/2*h + 11/2*h**3.
h*(h + 1)**2*(h + 9)/2
Let z(k) = k**2 - 11*k - 10. Suppose 7*p = 9*p + 12. Let h(y) = 6*y**2 - 67*y - 60. Let m(w) = p*h(w) + 39*z(w). Factor m(n).
3*(n - 10)*(n + 1)
Let h(r) = -12*r - 58. Let l be 2*90/24*(-2)/3. Let a be h(l). Factor -c**5 - 9*c + 13*c**a + 7*c**3 + 15*c - 5*c**4 + 4*c**4.
-c*(c - 3)*(c + 1)**2*(c + 2)
Let f(q) = -3*q**2 + 47*q - 27. Let m be f(15). Solve s**m + 3545 + 36*s**2 + 324*s - 3545 = 0.
-18, 0
Let c = -7150175/17 + 420607. Factor c + 2/17*a**3 + 120/17*a + 28/17*a**2.
2*(a + 2)*(a + 6)**2/17
Let -13408*a**2 - 3507*a**2 - 33171*a**2 + 20394*a + 7242*a**2 - 20392*a**3 + 42436 - 2*a**5 + 408*a**4 = 0. What is a?
-2, -1, 1, 103
Solve 73*c**2 - 50*c**2 + 3*c**3 - 74*c**2 + 480 - 60*c**2 - 372*c = 0.
-4, 1, 40
Let p = 214 - 212. Factor p*z**2 + 96 - 8*z + 17*z - 66 - 5*z**2.
-3*(z - 5)*(z + 2)
Let t(x) = -x**3 + x**2 + 3. Let d(u) = 4*u**3 - 13*u**2 - 9. Let b(l) = 2*d(l) + 6*t(l). Factor b(n).
2*n**2*(n - 10)
Suppose 120*f + 204 = 222*f. Find q, given that 2/9*q + 0 - 4/3*q**5 - 10/3*q**3 + 34/9*q**4 + 2/3*q**f = 0.
-1/6, 0, 1
Let a(u) be the second derivative of 8*u**7/7 - 44