et w(k) = -11*k**3 - 244*k**2 - 4073*k - 21684. Let s(a) = 120*a**3 + 2685*a**2 + 44805*a + 238520. Let p(v) = 6*s(v) + 65*w(v). Find z, given that p(z) = 0.
-19, -12
Let k(b) be the second derivative of -b**6/600 + b**5/150 - 30*b**2 + 147*b. Let m(z) be the first derivative of k(z). Suppose m(n) = 0. Calculate n.
0, 2
Let b(t) be the second derivative of 1/2*t**5 + 0*t**2 + 5/12*t**4 - 1 + 0*t**3 + 7*t. Factor b(o).
5*o**2*(2*o + 1)
Suppose 3*g - 187 = -u, 4*u - 7*u + 5*g = -505. Let a(y) be the first derivative of y**2 - 125*y - 11 - u*y - y**3 + 29*y**2. Factor a(j).
-3*(j - 10)**2
Let -1138*b - 206*b**3 + 942*b**2 + 6/5*b**4 + 2004/5 = 0. Calculate b.
2/3, 1, 3, 167
Let g(s) = s + 3. Let o(u) = -4*u**2 - 36*u - 88. Suppose v + 1 - 4 = 0, 4*t = v + 1. Let x(m) = t*o(m) - 4*g(m). Factor x(d).
-4*(d + 5)**2
Let p(i) be the first derivative of 164*i + 4/3*i**3 - 49 + 84*i**2. Factor p(u).
4*(u + 1)*(u + 41)
Suppose 20 = 5*m - 10. Let v be (-1 - -1)/(4 + -7). Factor 4*o + v*o**2 - o + m*o**2 + 1874*o**3 - 1871*o**3.
3*o*(o + 1)**2
Let s(p) be the third derivative of p**5/12 + 55*p**4/8 + 500*p**3/3 + p**2 - 510*p. Solve s(u) = 0 for u.
-25, -8
Suppose -683*h + 678*h = -15. Let f = 73/414 - 2/207. Find n, given that 2/3*n**2 + 5/6*n + f*n**5 + 0 - 2/3*n**4 - n**h = 0.
-1, 0, 1, 5
Suppose -22*q + 24*q = 4. Determine o, given that -8*o**2 + 11*o**2 - 44*o - o**2 - 6*o**q + 48 = 0.
-12, 1
Let x(f) = 9*f + 57. Let v be x(-6). Suppose 2*r = 2*q, -5*r + v*q = q. Factor -2/11*y**4 + 0*y**2 + 0*y**3 + 0*y + r.
-2*y**4/11
Factor -58/7*s - 1/7*s**2 + 59/7.
-(s - 1)*(s + 59)/7
Let k = 7155/52 - 19853/156. Determine t, given that 10 + 1/3*t**2 - k*t = 0.
1, 30
Let l(f) = -5*f**3 - 3*f**2 + 5*f + 7. Let g be l(-1). Factor -12 + 2 + 4*s**g - 12 - 12*s**2 + 15*s**3 - 2 - 3*s**3 - 44*s.
4*(s - 2)*(s + 1)**2*(s + 3)
Let s(o) be the second derivative of o**4/12 - 17*o**3/6 + 9*o**2 - 7*o. Let d be s(16). Let 16*z**3 - 7*z**2 - 10*z**3 - d*z**4 + 3*z**2 = 0. What is z?
0, 1, 2
Let b(v) be the second derivative of -v**6/15 + 1189*v**5/5 - 1413721*v**4/6 - 4405*v. Factor b(g).
-2*g**2*(g - 1189)**2
Suppose -220 + 80 = 5*p. Let v = -20 - p. Factor 4*n + v*n**2 + 1 - 1 + 0 - 8 - 4*n**3.
-4*(n - 2)*(n - 1)*(n + 1)
Let m(f) = -12*f**4 + 64*f**3 - 92*f**2 + 26*f + 24. Let s(o) = 47*o**4 - 255*o**3 + 368*o**2 - 105*o - 100. Let j(t) = -18*m(t) - 4*s(t). Solve j(p) = 0.
-2/7, 1, 2
Let s(g) = 10*g**2 - 17*g - 354. Let o(z) = 38*z**2 - 61*z - 1418. Let r(a) = 3*o(a) - 11*s(a). Factor r(i).
4*(i - 9)*(i + 10)
Let g = 57 - 55. Solve 5*u**g + 6*u + 11*u + 43*u = 0 for u.
-12, 0
Suppose 11 = -f - 3*n, -n = -5*f - 4*n + 5. Factor 15*r**2 + f*r**2 - 16*r**2 - 2*r - r.
3*r*(r - 1)
Let q be (703 + -703)/(-1 - 13). Let q - 1/3*a**4 - 4*a**2 + 10/3*a**3 - 24*a = 0. Calculate a.
-2, 0, 6
Factor 2/3*d**3 - 128/3*d**2 + 1202/3*d - 636.
2*(d - 53)*(d - 9)*(d - 2)/3
Let y be -3 + (2 - 2) + -1 + -6. Let g be -4*15/y - 0. Solve 2 - g*x**4 + 11*x**4 + 5*x**3 - 2 = 0.
-1, 0
Suppose -4*x - 6*m = -4*m - 8, 20 = 4*x + 5*m. Suppose 5*u - b - 18 = x, 6*u + 18 = 7*u - 5*b. Factor -2/13*k**2 - 2/13*k**5 - 6/13*k**4 + 0 - 6/13*k**u + 0*k.
-2*k**2*(k + 1)**3/13
Let i = 1157 + -1162. Let z be (-90)/(-126)*(-3)/i. Determine s, given that 3/7*s**3 + z*s**2 + 0 + 0*s = 0.
-1, 0
Let t(u) = u**3 - 8*u**2 + 9*u - 12. Let n be t(7). Suppose 7*y + n = 30. Factor -2*o**2 - 6*o**3 + 0*o - 205*o**4 + y*o + 2*o**5 + 207*o**4.
2*o*(o - 1)**2*(o + 1)*(o + 2)
Let v = 454 - 451. Factor 144*m**5 - 3*m + 4*m**2 - 4*m**4 - 139*m**5 - 24*m**2 - 26*m**v.
m*(m - 3)*(m + 1)**2*(5*m + 1)
Let w(r) be the second derivative of -r**5/20 - r**4 + 19*r**3/6 + 39*r**2 - 473*r. Find m such that w(m) = 0.
-13, -2, 3
Suppose -2*m = -10, 3*m = -10*l + 6*l + 31. Find y such that -45*y**2 - 181 - 2*y**4 + 171 - 3*y**l - 35*y - 25*y**3 = 0.
-2, -1
Let u(x) = -2*x**3 + x**2 + 18*x - 7. Let q be u(3). Let 3*k**3 - 1685*k**q - k**4 + 846*k**2 + 848*k**2 + 5*k = 0. Calculate k.
-1, 0, 5
Let o be -4*(-54)/(-2016)*12/27*-2. Determine t so that o*t**2 - 6/7 - 16/21*t = 0.
-1, 9
Let w(v) be the third derivative of 1/20*v**5 + v + 0*v**3 + 32*v**2 - 1/120*v**6 + 0 + 1/6*v**4. Suppose w(b) = 0. Calculate b.
-1, 0, 4
Let o(u) be the third derivative of -u**6/300 - 67*u**5/75 + 732*u**2 - 2. Let o(m) = 0. What is m?
-134, 0
Let y(v) be the second derivative of 22*v + 1/36*v**4 + 0 + 361/6*v**2 - 19/9*v**3. Factor y(z).
(z - 19)**2/3
Let b(l) be the first derivative of -3/10*l**2 + 0*l - 1/15*l**3 + 72. Find k, given that b(k) = 0.
-3, 0
Let d = 517330/7 - 74582. Let k = 678 + d. Factor 0 - 2/7*l**4 - k*l**2 + 0*l + 4/7*l**3.
-2*l**2*(l - 1)**2/7
Let v = 8554 + -8554. Let b(i) be the third derivative of 0*i + v*i**4 - 1/20*i**5 + 1/2*i**3 + 0 - 21*i**2. Factor b(y).
-3*(y - 1)*(y + 1)
Let j be ((-20)/(-35))/(2/7). Suppose 0 = 4*o + 2*m + 13 - 17, 4*o - 8 = -m. Factor 8/5*q**j + 2/15*q**o + 32/5*q + 128/15.
2*(q + 4)**3/15
Suppose -3*l + 398 = 3*i + 140, -15 = 3*i. Let b = -89 + l. Solve 0*r**b + 2*r**2 - 166*r + 162*r = 0.
0, 2
Let i be ((-480)/18)/(-16) - ((-8)/28 + (-4)/84). Let x(l) = l**3 - 3*l**2 + l. Let n be x(3). Factor -4/5*m**i + 0 + 14/5*m**4 + 2*m**n + 0*m.
2*m**2*(m + 1)*(7*m - 2)/5
Determine q, given that -14/3*q**2 - 4*q + 0 - 16/9*q**3 - 2/9*q**4 = 0.
-3, -2, 0
Let a = -15776 + 9923106/629. Let m = 633/1258 - a. Let m*s**4 - 3*s**3 + 6*s**2 + 0 - 4*s = 0. Calculate s.
0, 2
Let o = 2949 - 2949. Let r(x) be the third derivative of 0*x + 0 + 0*x**3 + 37*x**2 + 1/45*x**5 - 1/90*x**6 + o*x**4. Find m such that r(m) = 0.
0, 1
Let w(f) = -29*f**2 - 860*f - 4435. Let t be w(-23). Find a, given that -12/13*a**t - 32/13*a + 48/13*a**2 - 2/13*a**5 + 0 - 2/13*a**3 = 0.
-4, 0, 1
Suppose 2*w + 10 = 2, 0 = -r + 2*w - 17. Let b be (40/r)/((-2 - 0) + 1). What is k in 0 - b*k - 4/5*k**2 = 0?
-2, 0
Determine c, given that -451*c**5 - 1488*c + 351*c**5 + 3400*c**2 + 1197*c**4 - 3116*c**3 - 117*c**4 + 224 = 0.
2/5, 1, 2, 7
Let k be ((-3)/(-20))/((-1331)/242). Let a = k - -1517/165. Let a + 35/3*w + 5/2*w**2 = 0. Calculate w.
-11/3, -1
Let c(f) be the second derivative of f**6/180 - f**5/8 - 37*f**4/72 + 97*f**3/12 + 60*f**2 - 3499*f. What is q in c(q) = 0?
-3, 5, 16
Factor 218*t - 105*t - 3*t**2 - 1109*t - 3535 + 574.
-3*(t + 3)*(t + 329)
Let y(s) be the second derivative of s**6/75 - 9*s**5/25 + 47*s**4/30 - 2*s**3 - 1871*s. Factor y(u).
2*u*(u - 15)*(u - 2)*(u - 1)/5
Let j = 140671/131865 + -1/8791. Find f, given that -2/15*f**5 - 4/5 - 14/15*f + 0*f**4 + j*f**3 + 4/5*f**2 = 0.
-2, -1, 1, 3
Let p(c) = 2*c**3 + 2*c**2. Let o(a) = a**2 - 5*a - 62. Let w be o(11). Let g(t) = t**3. Let y(f) = w*g(f) - p(f). Determine l so that y(l) = 0.
0, 1
Let h(k) be the second derivative of 1/140*k**5 + 0 + 3/28*k**4 + 49*k + 0*k**3 - 54/7*k**2. Suppose h(q) = 0. What is q?
-6, 3
Let z = 304604/9 + -33840. Let 2048/9 - 2/9*m**4 - z*m**3 - 256/9*m - 32*m**2 = 0. Calculate m.
-8, 2
Let 54/7*s**3 + 2/7*s**4 - 384/7 + 132/7*s**2 - 304/7*s = 0. Calculate s.
-24, -4, -1, 2
Suppose 700*u - 2667*u = -3934. Suppose -2/3*i**u - 100/3*i - 1250/3 = 0. What is i?
-25
Suppose -404 = -o - 27. Let c = -374 + o. Factor 2/3*b**5 - 10/3*b - 4/3*b**2 - 4/3 + 8/3*b**4 + 8/3*b**c.
2*(b - 1)*(b + 1)**3*(b + 2)/3
Let q = -1020 + 1234. Suppose -o = -5*y - 67, -3*o = -0*o - 2*y - q. Factor -o*m + 96 - 3/2*m**3 - 45/2*m**2.
-3*(m - 1)*(m + 8)**2/2
Let f(x) be the third derivative of x**5/30 + x**4/4 + 5*x**3/6 + 20*x**2. Let b be f(5). Let 85*n - 33*n**3 - b*n - 6*n**2 = 0. What is n?
-2/11, 0
Let o(n) be the second derivative of -n**6/15 + 2*n**5 + 33*n**4/2 - 18*n**3 - 432*n**2 - 64*n - 14. Factor o(u).
-2*(u - 24)*(u - 2)*(u + 3)**2
Let f(l) = -4*l**3 + 6*l + 4. Let o be f(4). Let d = o + 576. What is v in -4*v - 81*v**3 - 36*v**5 + d*v**2 - 21*v**4 - 72*v**4 - 375*v**2 + v = 0?
-1, -1/3, -1/4, 0
Let g(d) be the first derivative of -d**5/20 + 1111*d**4/16 - 68635*d**3/2 + 12765925*d**2/2 - 12663250*d + 2927. Let g(c) = 0. Calculate c.
1, 370
Suppose -2*g - 2*m = -7*m + 12, 5*m - 8 = 3*g. Factor -68*a - 33*a**3 + 17*a**3 - 24*a - 49 - 20*a - 78*a**2 - a**4 + 0*a**g.
-(a + 1)**2*(a + 7)**2
Let y(v) be the third derivative of v**7/1575 - 37*v**6/225 + 71*v**5/6 + 125*v**4/2 + 3*v**2 - 19. Supp