5)*1500/(-400). Find m, given that 16/3*m + 32/15*m**3 - f*m**4 - 28/5*m**2 - 26/15 = 0.
1, 13
Factor -o + 6*o**3 - 40*o**2 + 61*o**2 - 3*o**4 - 24*o**3 + o.
-3*o**2*(o - 1)*(o + 7)
Let x(q) be the second derivative of q**9/20160 - q**8/1280 - q**7/420 + 7*q**4/3 - 18*q. Let f(j) be the third derivative of x(j). Factor f(k).
3*k**2*(k - 8)*(k + 1)/4
Let d(z) be the first derivative of 7/15*z**3 - 24/5*z + 4 - 41/5*z**2. Let d(t) = 0. Calculate t.
-2/7, 12
Let q(p) be the first derivative of p**4/4 + p**3 - 20*p**2 - 84*p - 1172. Solve q(x) = 0 for x.
-7, -2, 6
Let l(p) be the second derivative of p**6/60 - 37*p**5/40 + 451*p**4/24 - 605*p**3/4 + 2258*p. Factor l(i).
i*(i - 15)*(i - 11)**2/2
Let f(z) = -3*z - 91. Let a be f(-31). Factor -n**2 + 4*n**4 + 6*n**2 - 14*n**3 + 25*n + 23*n + 11*n**a - 14*n**3.
4*n*(n - 6)*(n - 2)*(n + 1)
Let q(b) be the first derivative of -b**4/2 - 8*b**3/3 + 51*b**2 - 180*b - 545. Factor q(n).
-2*(n - 3)**2*(n + 10)
Let v(i) be the third derivative of i**6/420 - 529*i**5/210 + 1055*i**4/84 - 527*i**3/21 + 4155*i**2. Factor v(a).
2*(a - 527)*(a - 1)**2/7
Let p = -48 - -30. Let g(a) = a**3 + 17*a**2 - 24*a + 2. Let f be g(p). Suppose 8*q**4 - 53*q**4 + 16*q - 120*q**3 - 5 - f*q**2 - 56*q = 0. What is q?
-1, -1/3
Let k be -2 - (-5)/750 - (-8 + 6). Let p(j) be the third derivative of k*j**5 + 4/15*j**3 + 1/15*j**4 + 0 + 0*j - 8*j**2. Determine s, given that p(s) = 0.
-2
Let x = 7567 + -7563. Let c(j) be the first derivative of -1/6*j**x + 22 + 2/15*j**5 - j**2 + 0*j - 10/9*j**3. Factor c(w).
2*w*(w - 3)*(w + 1)**2/3
Let b(y) be the third derivative of 1/35*y**7 - 1/30*y**6 + 0*y - 1/168*y**8 + 33*y**2 + 0*y**4 + 0 + 0*y**3 + 0*y**5. Suppose b(n) = 0. Calculate n.
0, 1, 2
Let k be (-8670)/(-3689) + 4/(-62) - (-2)/(-7). Find o, given that 16/9 + 49/9*o**k + 56/9*o = 0.
-4/7
Suppose -3*x + 5*h = 56, -24*x + 25*x - 3*h + 24 = 0. Let v be (x/(-26))/(280/910). Factor -3 + v*t**3 - 3/2*t + 3*t**2.
3*(t - 1)*(t + 1)*(t + 2)/2
Let a(m) be the second derivative of -m**5/90 + m**4/54 + 82*m**3/27 + 80*m**2/9 + 14*m - 2. Suppose a(c) = 0. What is c?
-8, -1, 10
Let x(v) = 2*v**4 - 78*v**3 - 140*v**2 + 219*v + 6. Let l(z) = 3*z**4 - 155*z**3 - 281*z**2 + 438*z + 10. Let a(n) = 3*l(n) - 5*x(n). Factor a(r).
-r*(r - 1)*(r + 3)*(r + 73)
Let a(h) be the first derivative of h**3/3 - 17*h**2 - 35*h + 1565. Factor a(o).
(o - 35)*(o + 1)
Let b(m) be the first derivative of -5*m**4 - 268*m**3/3 - 528*m**2 - 1008*m + 1418. Factor b(t).
-4*(t + 6)**2*(5*t + 7)
Let p = -32 + 34. Suppose -p*f = -5*k - 32, 0 = 2*f + 3*k - 2*k - 8. Factor -3*q**3 - 10*q**5 - 7*q**5 + f*q**4 + 14*q**5.
-3*q**3*(q - 1)**2
Let o(u) be the second derivative of -1/14*u**7 + 148*u - 11/10*u**6 + 21/10*u**5 + 0*u**2 + 6*u**4 + 0 + 0*u**3. Suppose o(x) = 0. What is x?
-12, -1, 0, 2
Let j = -205 + 208. Suppose -4*u**4 + u - 3*u - 2*u**2 + 16*u**j - 2*u**2 - 22*u = 0. What is u?
-1, 0, 2, 3
Let w = -231 + 220. Let u(o) = 2*o**2 - 48*o + 76. Let t(q) = 5*q**2 - 141*q + 229. Let s(z) = w*u(z) + 4*t(z). Solve s(k) = 0.
-20, 2
Let z(d) be the first derivative of -3*d**5/35 + 11*d**4/14 + 43*d**3/21 + 9*d**2/7 + 1075. Find m, given that z(m) = 0.
-1, -2/3, 0, 9
Let o be 13 + 754/(-104) + 1/4. Let d(q) be the third derivative of -1/48*q**o - 5/6*q**3 + 9*q**2 + 0*q**5 + 0 + 0*q + 5/16*q**4. Find b such that d(b) = 0.
-2, 1
Let h = -2979 + 2983. Let w(l) be the first derivative of -10*l**2 + 25*l**5 + 0*l - 225/4*l**h + 12 + 40*l**3. Factor w(p).
5*p*(p - 1)*(5*p - 2)**2
Let b be 2907/51 - 17885/315. Suppose b*k**3 + 16/3*k + 40/9 + 2*k**2 = 0. What is k?
-5, -2
Let h = 2491/19 + -131. Let v = 171453/814492 + 1/42868. Factor v*d + h - 6/19*d**2.
-2*(d - 1)*(3*d + 1)/19
Let v = 4/1333 - -17321/2666. Let j(f) be the first derivative of 19 + 8/3*f**3 + 4*f**2 + 0*f + 2*f**5 - v*f**4. Factor j(k).
2*k*(k - 2)*(k - 1)*(5*k + 2)
Suppose 4*c = 5*r - 6, -197*r + 195*r - 5*c + 42 = 0. Factor 1/3*n**2 - r*n + 27.
(n - 9)**2/3
Let -76*k**3 + 80*k**3 - 373 + 4565 + 4208*k + 1064*k**2 = 0. What is k?
-262, -2
Factor 81/2*t - 18*t**2 - 1/4*t**4 - 135/4 + 7/2*t**3.
-(t - 5)*(t - 3)**3/4
Suppose -8*a + 31 = -5*f + 2*f, -10 = 5*a + 4*f. Let w(h) = -h**3 + h**2 + 7. Let v be w(a). Solve 0*c**2 - 1/4*c**v + 0*c + 0 = 0 for c.
0
Let a = 19 + -15. Suppose -a*d = -2*d - 6. Factor d*z**2 - 9*z**2 - 1 + 5*z + 2*z**2.
-(z - 1)*(4*z - 1)
Let g = 68/75 + -6/25. Let i be -2 + (-112)/(-80) + (-74)/(-90). Factor 8/9 + g*z**3 - 2/3*z + i*z**4 - 10/9*z**2.
2*(z - 1)**2*(z + 1)*(z + 4)/9
Let c(g) be the third derivative of -g**8/896 + g**7/80 + 5*g**6/64 - 67*g**5/160 + 9*g**4/16 - 13*g**2 - 3. Determine x so that c(x) = 0.
-4, 0, 1, 9
Let b(w) be the first derivative of -3*w**5/5 + 399*w**4/4 - 5805*w**3 + 236925*w**2/2 + 546750*w + 1320. Suppose b(r) = 0. What is r?
-2, 45
Suppose 168 - 40 = 16*m. Let c be -6*(35/220 + (-2)/m). Let -c - 8/11*f - 2/11*f**2 = 0. Calculate f.
-3, -1
Let x(g) = g**3 - 4*g**2 + 3. Let b be x(3). Let m(w) = w**2 + 2*w + 13. Let d be m(b). Factor 3*t**3 + d*t + 2*t**3 - 17 - 23 - 30*t**2 + 23*t.
5*(t - 2)**3
Suppose 0 = -4*y + 4*j + 36, -11*y - j = -13*y + 14. Suppose y*t + 5*k = k + 6, 0 = 2*t + k - 3. Factor -2/7*b**t - 32/7*b - 128/7.
-2*(b + 8)**2/7
Let h(p) be the third derivative of -p**6/840 + 3*p**5/140 + 5*p**4/84 - 1888*p**2. Suppose h(g) = 0. What is g?
-1, 0, 10
Let c be ((-344)/946)/((-1)/(-22)*(17 - 19)). Suppose -6/5*j**c + 21/5*j**5 + 108/5*j**2 - 378/5*j**3 - 486/5 + 1701/5*j = 0. What is j?
-3, 2/7, 3
Find n, given that -114*n + 1/3*n**2 + 341/3 = 0.
1, 341
Determine p so that -324/5*p**3 + 2/5*p**4 + 0 + 13122/5*p**2 + 0*p = 0.
0, 81
Let y(w) be the third derivative of -214*w**2 + 1/504*w**8 - 1/105*w**7 + 0 + 0*w + 1/3*w**5 - 1/18*w**6 + 1/4*w**4 - 3*w**3. Let y(r) = 0. What is r?
-3, -1, 1, 3
Let c = -71 - -74. Suppose -c*z = 4*u - 161, 3*u = 2*u + 2*z + 43. Solve 5*v**2 + 193 + 87 + u*v + 29*v - 35 = 0 for v.
-7
Let l(s) be the third derivative of s**5/180 - 4165*s**4/36 + 17347225*s**3/18 + 14849*s**2. Factor l(c).
(c - 4165)**2/3
Let l(k) be the second derivative of 961*k**4/36 + 310*k**3 + 1350*k**2 + 30*k - 1. Determine v so that l(v) = 0.
-90/31
Factor 252/5*u + 3/5*u**2 + 729/5.
3*(u + 3)*(u + 81)/5
Let z be 355/7 + -1 - (-32)/112. Suppose -z + 19 + 3*y**2 + 27*y - 35 = 0. What is y?
-11, 2
Let k = 223 + -196. Determine y so that -2*y - 8*y**2 + y + 18*y - k*y**2 + 2*y**3 = 0.
0, 1/2, 17
Suppose 4*x = -2*x + 18. Let o = -9 - -15. Factor -22 + 3*c + 10 + o*c + x*c**2.
3*(c - 1)*(c + 4)
Let w(l) = l**2 - 30*l + 31. Let f(x) = 2*x**2 + 12*x + 29. Let v be f(-6). Let n be w(v). Factor -8/5*a + 0 + 2*a**n - 2/5*a**3.
-2*a*(a - 4)*(a - 1)/5
Let v(r) be the second derivative of 3*r**5/4 + 40*r**4/3 + 95*r**3/6 - 25*r**2 + 23*r. Factor v(s).
5*(s + 1)*(s + 10)*(3*s - 1)
Suppose 88 = 31*q - 9*q. Factor -25*z - 5 + 15*z**2 - 4*z**4 + 5*z**3 + 15 - z**q.
-5*(z - 1)**3*(z + 2)
Factor -85 - 90*f**2 - 20 - 695*f - 397 - 98 + 3*f**3 + 2*f**3.
5*(f - 24)*(f + 1)*(f + 5)
Let x(w) = w**3 - w**2 - 12*w + 2. Let h be x(-3). Find f, given that -f**4 - 25*f - 15*f**3 - 125385*f**2 + 125430*f**h - 4*f**4 = 0.
-5, 0, 1
Suppose 0 = 4*w + 3*k - 981, 0 = -0*w - 3*w + 4*k + 742. Suppose 18*i = w - 192. Find m, given that -4/3*m**2 + 2/3*m**4 + 0 + 0*m + 2/3*m**i = 0.
-2, 0, 1
Let h(p) be the first derivative of 23/17*p**2 + 40/51*p**3 - 61 + 12/17*p - 2/17*p**4. Factor h(g).
-2*(g - 6)*(2*g + 1)**2/17
Suppose -12*v**5 + 71*v**3 - 63*v**3 + 10*v**5 - 56*v**2 + 102*v**3 - 43*v**4 - 9*v**4 = 0. Calculate v.
-28, 0, 1
Let p = 1852504 - 9262418/5. Suppose -p*m**3 + 27/5*m**5 - 33/5*m**4 + 0 + 132/5*m**2 - 24/5*m = 0. What is m?
-2, 0, 2/9, 1, 2
Let z(n) be the second derivative of -2*n**7/21 - 2*n**6/5 + 34*n**5/5 - 52*n**4/3 - 16*n**3 + 128*n**2 - 1520*n. Suppose z(t) = 0. What is t?
-8, -1, 2
Let c(u) = 74*u + 198. Let a be c(-3). Let t be a/(-28) - 34*1/56. Let 0 - t*n + 1/4*n**2 + 1/2*n**3 = 0. What is n?
-1, 0, 1/2
What is q in 26912/3 + 1/6*q**2 + 232/3*q = 0?
-232
Let x(w) be the first derivative of -16/3*w - 4/3*w**3 + 1/6*w**4 + 4*w**2 + 334. Factor x(b).
2*(b - 2)**3/3
Let g(f) be the second derivative of f**4/24 - 307*f**3/36 - 103*f**2/6 - 174*f. Factor g(x).
(x - 103)*(3*