8*c - 5200. Let v(l) = 20*k(l) - 5*p(l). Determine a, given that v(a) = 0.
-12, -1, 3
Let d = -241103 - -241105. Solve 9/7*q + 0 - 1/7*q**d = 0.
0, 9
Let a(c) = -120*c**2 - 4*c. Let l be a(3). Let v be 4/22 - l/286. Factor 45*i**5 + 20*i**v + 3*i**3 - 49*i**5 - 27*i**3.
-4*i**3*(i - 3)*(i - 2)
Let d(p) be the second derivative of -1/11*p**4 + 7*p - 4/33*p**3 - 1/66*p**5 + 0 - 9/2*p**2. Let u(j) be the first derivative of d(j). Factor u(i).
-2*(i + 2)*(5*i + 2)/11
Let y(o) = 3*o - 52. Let v be y(16). Let h = v + 6. Let 6*i**2 - 162 - 8*i**h + 9*i + 27*i = 0. What is i?
9
Let h(c) be the first derivative of -c**6/1980 + 7*c**5/660 - c**4/22 + 47*c**3/3 - 75. Let q(y) be the third derivative of h(y). Suppose q(m) = 0. What is m?
1, 6
Let v(b) be the third derivative of 0*b + 0 - 11/60*b**6 - 3/4*b**4 + 19/30*b**5 - 150*b**2 + 0*b**3 + 1/105*b**7. Factor v(o).
2*o*(o - 9)*(o - 1)**2
Let p(h) = -12*h**2 - 48*h + 3. Let w be p(-4). Let f(m) be the first derivative of 6*m**2 - 3/2*m**3 - 3/4*m**4 - w - 6*m + 3/10*m**5. Factor f(v).
3*(v - 2)*(v - 1)**2*(v + 2)/2
Let p(i) be the third derivative of 0 - 3*i**2 - 1/5*i**3 + 1/30*i**4 + 1/150*i**5 - 15*i. What is h in p(h) = 0?
-3, 1
Suppose -4*y + 5 = j, 2*y + 2 + 9 = -5*j. Let v be y/(-3)*(-693)/385. Find i such that 4/5*i + 0 + v*i**2 + 2/5*i**3 = 0.
-2, -1, 0
Let j = 4232 - 4232. Let h(y) be the third derivative of -1/60*y**6 + 0*y - 1/40*y**5 + 0 + 0*y**4 - 8*y**2 + j*y**3 - 1/420*y**7. Factor h(b).
-b**2*(b + 1)*(b + 3)/2
Let v(j) be the first derivative of 5*j**6/6 + 27*j**5 + 425*j**4/2 + 1790*j**3/3 + 1545*j**2/2 + 475*j - 2667. Let v(r) = 0. Calculate r.
-19, -5, -1
Suppose 20 = 2*w - 68. Let f(m) = -2*m**3 - 26*m**2 + 6*m. Let n(b) = -b**2. Let p(o) = w*n(o) - 2*f(o). Factor p(j).
4*j*(j - 1)*(j + 3)
Let v(o) be the second derivative of -o**7/168 - o**6/80 + o**5/20 - o**4/6 + 7*o**2/2 + 2*o. Let d(l) be the third derivative of v(l). Factor d(n).
-3*(n + 1)*(5*n - 2)
Let g(x) be the second derivative of x**5/90 + 247*x**4/54 + 485*x**3/9 + 241*x**2 - 136*x - 12. Determine y, given that g(y) = 0.
-241, -3
Let z(o) be the third derivative of o**7/35 - 19*o**6/6 + 953*o**5/30 - 731*o**4/6 + 232*o**3 + 3*o**2 + 1077. Solve z(w) = 0.
1, 4/3, 3, 58
Let v(w) = w**3 + 20*w**2 + 38*w + 36. Let p be v(-18). Suppose p = -15*n + 42 + 18. Suppose -9/2*a - 1/2*a**2 - n = 0. Calculate a.
-8, -1
Let z(s) = s**3 + 3*s**2 - 9*s - 20. Let r be z(-2). Factor 12*a**3 - 12*a - 2*a**4 + 6 - 19 + 18*a**2 - r - a**4.
-3*(a - 5)*(a - 1)*(a + 1)**2
Let t(x) be the third derivative of x**7/2520 - x**6/540 - x**5/90 - 71*x**4/24 + 2*x**2 + 65. Let v(r) be the second derivative of t(r). Factor v(l).
(l - 2)*(3*l + 2)/3
Let m = 72162 - 288645/4. Determine x so that 5/4*x**2 + 1/4*x**5 - m*x**3 + 0 - 1/4*x**4 - 1/2*x = 0.
-2, 0, 1
Factor 0 - 1/8*m**4 + 0*m - 31/2*m**2 + 125/8*m**3.
-m**2*(m - 124)*(m - 1)/8
Let z be (1 + -61)/6*(-272)/96. Let w(q) be the first derivative of -5*q**5 - 45/2*q**4 + 20*q + 0*q**2 - z*q**3 + 12. Solve w(d) = 0 for d.
-2, -1, 2/5
Suppose 5*b - 9*b + 12 = 0. Let p be 1/(-2)*b/((-3)/4). Solve 5*z + 4*z**p + 3 - 1 + z = 0.
-1, -1/2
Solve 704/3*d + 1/3*d**2 - 235 = 0.
-705, 1
Solve 41*o**2 + 49*o**3 - 61*o + 363*o - 94*o**3 + 448 + 46*o**3 = 0 for o.
-32, -7, -2
Let m be (-3 - -5)/2*-1 - -1. Suppose 20 = 5*q, m*f - 4 = f - q. Factor 2/3*n**2 - 1/3*n + f.
n*(2*n - 1)/3
Let x(p) be the first derivative of -4*p**3 + 86*p**2 + 624*p + 1676. Suppose x(h) = 0. What is h?
-3, 52/3
Suppose 2*f + z - 27 = -30, 0 = 3*f + 5*z + 29. Let n(p) be the first derivative of 1/14*p**4 + 2/7*p**3 + 0*p - 29 - 4/7*p**f. Let n(i) = 0. Calculate i.
-4, 0, 1
Let b(g) be the second derivative of 0 - 1/5*g**5 + 173*g - 8/3*g**3 + 0*g**2 + 4/3*g**4. Factor b(d).
-4*d*(d - 2)**2
Suppose 3*h + 14 = -5*n + 39, 0 = 5*n - h - 45. Factor -n*c**5 + 5*c**4 - 11*c**4 - 2*c**3 + 16*c**4.
-2*c**3*(c - 1)*(4*c - 1)
Let s(n) = 6*n**2 + 16*n + 4. Let f be s(-6). Suppose -472 - 144 - 99 - 5 + f*w**2 - 24*w**3 + 624*w - 4*w**4 = 0. What is w?
-6, 1, 5
Let z(a) be the third derivative of -a**8/36960 + a**7/6930 + a**6/1320 - 13*a**4/12 - a**3/6 + 44*a**2. Let l(w) be the second derivative of z(w). Factor l(o).
-2*o*(o - 3)*(o + 1)/11
Let p(x) = -29*x**3 + 271*x**2 - 971*x + 54. Let b(f) = 7*f**3 - 68*f**2 + 243*f - 12. Let t(z) = -9*b(z) - 2*p(z). Factor t(l).
-5*l*(l - 7)**2
Solve 513/2 + 3/4*c**2 - 141/4*c = 0.
9, 38
Let d = 59098/5 - 11819. Determine f so that 2/5 - d*f - 4*f**2 = 0.
-2/5, 1/4
Factor -116*l**2 - 95*l + 2*l**4 + 6*l**3 - 161*l - 224*l.
2*l*(l - 8)*(l + 5)*(l + 6)
Let x(y) be the second derivative of -y**4/3 - 60*y**3 + 182*y**2 + 289*y. Factor x(p).
-4*(p - 1)*(p + 91)
Let n = -31 - -41. Suppose -20 = -2*x + 2*w, -x + w = 4*w + n. Find k, given that -53*k**2 + 5*k**3 + 2*k**x + 58*k**2 - 5*k**4 - 7*k**5 = 0.
-1, 0, 1
Factor -3/7*h**2 + 216/7 - 9*h.
-3*(h - 3)*(h + 24)/7
Factor 3*r**3 + 24*r + 195*r**2 - 30*r + 198*r.
3*r*(r + 1)*(r + 64)
Determine q, given that 2/5*q**4 + 0 + 374/5*q**2 + 186/5*q + 38*q**3 = 0.
-93, -1, 0
Let s be 10 - 39/4 - 583/620. Let h = 40/31 + s. Factor 0 + h*z**5 + 0*z + 6/5*z**3 - 9/5*z**4 + 0*z**2.
3*z**3*(z - 2)*(z - 1)/5
Let w = 22 + 104. Suppose -5*o - w = -11*o. Suppose -24*p + 1 + 5*p**5 + o*p**4 - 2*p**5 + 19 + 28 + 21*p**3 - 69*p**2 = 0. Calculate p.
-4, -1, 1
Let r be (-5)/(18 + -8)*(-88)/33. Solve r*j**5 - 32/3*j**4 - 103/3*j**2 + 17*j - 3 + 89/3*j**3 = 0 for j.
1/2, 1, 3
Let s(q) be the first derivative of q**5/100 + q**4/5 + 8*q**3/5 + 32*q**2/5 + 168*q - 54. Let d(z) be the first derivative of s(z). Factor d(h).
(h + 4)**3/5
Let t(p) be the first derivative of p**6/8 + 11*p**5/4 - 41*p**4/16 - 55*p**3/12 + 19*p**2/4 - 1001. Determine u, given that t(u) = 0.
-19, -1, 0, 2/3, 1
Let y(b) = -11*b**5 + 55*b**3 + 71*b**2 - 28*b. Let m(a) = -10*a**5 + 54*a**3 + 70*a**2 - 24*a. Let h(t) = 7*m(t) - 6*y(t). Factor h(p).
-4*p**2*(p - 4)*(p + 2)**2
Factor 3353*v**3 + 3*v**4 + 290*v**3 + 6671880*v**2 + 1921480800*v + 4103*v**3 + 3816336000.
3*(v + 2)*(v + 860)**3
Let w(a) = -a + 0 + 1 - a**3 + 152*a**2 - 151*a**2. Let u(b) = 15*b**5 - 21*b**4 - 81*b**3 - 3*b**2 + 60*b + 30. Let k(j) = -u(j) + 3*w(j). Solve k(x) = 0.
-1, -3/5, 1, 3
Let j(o) be the third derivative of 1/36*o**4 + 0 + 1/630*o**5 + 24*o**2 + 0*o + 0*o**3. Factor j(h).
2*h*(h + 7)/21
Suppose 5*p = -3*j - 12 + 47, -2*j + 14 = 2*p. Suppose 19 = -p*l + 8*l. Let -2*h - 11*h**2 + 7*h + 25 + 0*h - l = 0. Calculate h.
-6/11, 1
Let h be 1 - (-42)/(-48)*1. Let z be (-273)/27 + 10 - (-1 - -2)/(-9). Factor 1/8*n**2 - h*n**4 + 0*n + 1/8*n**3 - 1/8*n**5 + z.
-n**2*(n - 1)*(n + 1)**2/8
Let m(x) = -420*x**2 + 24380*x - 7035. Let y(d) = 35*d**2 - 2032*d + 586. Let g(s) = -2*m(s) - 25*y(s). Determine a so that g(a) = 0.
2/7, 58
Let j be (-6)/(-1) + ((-1545)/(-9))/((-1020)/(-408)). Find r, given that j*r - 98/3*r**5 - 32/3 + 350/3*r**4 - 368/3*r**2 - 176/3*r**3 = 0.
-1, 2/7, 2
Let j(u) = -5*u**2 - 313*u - 209. Let f(q) = -3*q**2 - 162*q - 105. Let s(t) = -11*f(t) + 6*j(t). Factor s(b).
3*(b - 33)*(b + 1)
Let h(t) = t**2 - 640*t + 2709. Let q(v) = 1280*v - 5395. Let g(s) = 5*h(s) + 3*q(s). Let g(r) = 0. What is r?
-132, 4
Let b = 49 + -33. Let g be b/9 + 12/54. Determine i, given that -3*i**2 - 3*i**4 - i - 3*i**g + i**3 + 11*i**2 - 2 = 0.
-1, -2/3, 1
Let m(o) be the second derivative of -2*o**7/21 + 126*o**6/5 - 559*o**5/5 + 61*o**4 + 1120*o**3/3 - 744*o**2 - 22*o - 69. What is c in m(c) = 0?
-1, 1, 2, 186
Let v(u) = 56*u**5 + 24*u**4 + 19*u**3 + 2*u**2 - 49*u - 26. Let q(w) = -13*w**5 - 6*w**4 - 5*w**3 + 12*w + 6. Let x(b) = -26*q(b) - 6*v(b). Factor x(l).
2*l*(l - 1)*(l + 1)*(l + 3)**2
Factor -159 - 143 + 15*x - 141 + 115 + 309*x + 4*x**2.
4*(x - 1)*(x + 82)
Let r(i) be the first derivative of 2/3*i**3 + 0*i**2 + 1/6*i**6 - 30 + 4/5*i**5 + 5/4*i**4 + 0*i. Factor r(o).
o**2*(o + 1)**2*(o + 2)
Suppose 9 = -c + 2*s, -4*s + 4 = 4*c - 2*s. Let r be c - (-7)/5 - (-295)/75. Find u such that -r*u**2 - 16*u - 1/3*u**3 - 12 = 0.
-6, -1
Factor -36 + 201*s + s**4 - 87*s**2 + 18 - 52 - 52*s + 4*s**3 + 3*s**3.
(s - 5)*(s - 1)**2*(s + 14)
Suppose -5*q + 1022 = 2*f, 5*q + 1356 = 5*f - 1164. Determine x, given that 5*x + 2*x**2 - 505 + 1005 - f - x**3 = 0.
-2, 1, 3
