be the third derivative of 0 + 1/240*i**6 - 1/8*i**5 - z*i**3 + 0*i + 21/16*i**4 - 31*i**2. Find j, given that n(j) = 0.
1, 7
Let o(y) be the third derivative of y**5/60 - y**4/2 - 15*y**3/2 - 26*y**2 - 2*y. Let a be o(15). Factor -2/9*w**5 + 0*w + a + 2/9*w**4 - 2/9*w**2 + 2/9*w**3.
-2*w**2*(w - 1)**2*(w + 1)/9
Let d be ((-691383)/(-14))/(-11)*4/(-36). Let z = 499 - d. Suppose 2/3 - z*r**2 + 0*r = 0. Calculate r.
-2, 2
Let d(o) be the first derivative of 3*o**4/4 + 26*o**3 + 216*o**2 - 204. Determine r, given that d(r) = 0.
-18, -8, 0
Factor 8674*g**2 - 3*g + 90 - 8673*g**2 - 20*g.
(g - 18)*(g - 5)
Factor 452 + 354*f**3 - 168 - 572*f + 292*f**2 - 358*f**3.
-4*(f - 71)*(f - 1)**2
Suppose -4*a - 192 = 4*a. Let z = a - -27. Factor 5*m**4 + 10*m**2 - 10*m**3 + 17*m**3 + 8*m**z.
5*m**2*(m + 1)*(m + 2)
Let o(d) be the third derivative of -d**7/42 - 3*d**6/8 - 23*d**5/12 - 25*d**4/8 - 16*d**2 - 29*d. Determine z, given that o(z) = 0.
-5, -3, -1, 0
Let g(o) = 300*o**3 + 590*o**2 + 105*o + 25. Let y(b) = -149*b**3 - 294*b**2 - 52*b - 12. Let j(d) = -12*g(d) - 25*y(d). What is a in j(a) = 0?
-2, -4/25, 0
Let b(o) be the third derivative of -o**7/70 + o**5/2 - 9*o**3/2 - 485*o**2. Solve b(a) = 0.
-3, -1, 1, 3
Suppose 6*u + 7*u + 32*u - 90 = 0. Let -2/7*r**3 + 6/7*r**u + 0*r + 0 = 0. What is r?
0, 3
Let a(v) be the third derivative of 13/54*v**4 - 46*v**2 + 1 + 16/27*v**3 + 1/90*v**5 - 1/945*v**7 + 0*v - 2/135*v**6. Solve a(u) = 0 for u.
-8, -1, 2
Let u(w) be the second derivative of 7*w**5/20 + 5*w**4/4 - 7*w**3/6 - 15*w**2/2 + 2912*w. Find h such that u(h) = 0.
-15/7, -1, 1
Let o(s) = -s**3 - s**2 + 8*s + 3. Let a be o(-3). Let g(m) = -2*m**3 - 3*m**2 + 3*m + 4. Let c be g(a). What is t in 78 + 43 + 0*t - 5*t**2 + 6*t**2 + c*t = 0?
-11
Let x(w) be the first derivative of -w**4/12 + 13*w**3/3 - 24*w**2 + 140*w/3 + 756. Solve x(b) = 0 for b.
2, 35
Let y(m) be the first derivative of -5/3*m**3 + 5/12*m**4 + 10 - 8*m + 5/2*m**2. Let s(k) be the first derivative of y(k). Factor s(a).
5*(a - 1)**2
Let k = 82 - 62. Suppose 4*r - 8 = k. Find d such that -12*d - 24 + r*d**2 + 102*d**3 - d**2 - 99*d**3 = 0.
-2, 2
Let c(q) be the first derivative of q**4/16 + 19*q**3/6 + 9*q**2 - 2643. Factor c(x).
x*(x + 2)*(x + 36)/4
Let g(w) be the first derivative of -w**4/2 - 1648*w**3/3 - 1645*w**2 - 1644*w + 6758. What is f in g(f) = 0?
-822, -1
Factor -4/5*s**3 - 48/5*s**2 + 676/5*s + 144.
-4*(s - 9)*(s + 1)*(s + 20)/5
Let u(j) be the third derivative of -j**6/80 + 49*j**5/40 + j**4/4 - 49*j**3 - 36*j**2 - 2. Find i such that u(i) = 0.
-2, 2, 49
Let n(p) be the first derivative of -19/3*p**2 + 2/9*p**3 - 2 + 12*p. Factor n(q).
2*(q - 18)*(q - 1)/3
Let i = -36299/12 - -3025. Let n(g) be the third derivative of 15/2*g**3 - 5/4*g**4 - 8*g**2 + i*g**5 + 0 + 0*g. Suppose n(d) = 0. What is d?
3
Let u be ((-5)/2)/(1105/(-1326)). Determine x so that 0 - 2*x**2 + 2*x**4 + 5/2*x - 3*x**u + 1/2*x**5 = 0.
-5, -1, 0, 1
Let v = 2 + -1. Let i(y) = y**2 - y - 1. Let g(o) = 21*o + 2 + 247*o**2 + 4 - 223*o**2 - o**3 + 6*o**3. Let u(m) = v*g(m) - 4*i(m). Let u(c) = 0. Calculate c.
-2, -1
Let n(a) = 13*a**4 + 314*a**3 - 1271*a**2 + 1468*a - 580. Let q(r) = -8*r**4 - 209*r**3 + 844*r**2 - 979*r + 387. Let m(i) = 5*n(i) + 8*q(i). Factor m(c).
(c - 98)*(c - 2)*(c - 1)**2
Let a = 4762151/5 - 952429. Factor 0 + a*z**4 + 3/5*z**3 + 0*z**2 + 0*z + 3/5*z**5.
3*z**3*(z + 1)**2/5
Let w(i) = -63*i - 441. Let m be w(-7). Suppose v + 0 = 2. Solve -28*d**3 + 19*d**4 + 28*d - v - 68*d**4 + m + 6 + 45*d**2 = 0.
-1, -2/7, 1
Let y = -77936357/3798410 + -1/34531. Let v = 207/10 + y. Factor 2*s**3 + 128/11 - v*s**4 + 32/11*s - 72/11*s**2.
-2*(s - 4)**3*(s + 1)/11
Factor -100*q + 15*q**3 + 2*q**4 - 64 + 2567*q**2 - 2573*q**2 + 17*q**3.
2*(q - 2)*(q + 1)**2*(q + 16)
Let n be (-170)/(-13) - (5828/94 - 50). Suppose 2/13*i**3 - 12/13 + 0*i**2 - n*i = 0. What is i?
-2, -1, 3
Let s(n) be the first derivative of -n**6/75 + n**5/50 + n**4/30 - n**3/15 - 70*n - 58. Let a(g) be the first derivative of s(g). Factor a(p).
-2*p*(p - 1)**2*(p + 1)/5
Let n(q) be the second derivative of -15/2*q**3 - 1/8*q**4 + 93/4*q**2 + 72 - 2*q. Factor n(j).
-3*(j - 1)*(j + 31)/2
Let y = -13802 + 13804. Suppose -3/5 + 28/5*z**y + z = 0. Calculate z.
-3/7, 1/4
Factor -121/4*h**3 - 122*h + 485/4*h**2 + 1.
-(h - 2)**2*(121*h - 1)/4
Let z(y) be the first derivative of 3*y**5/25 - 27*y**4/10 - y**3/5 + 27*y**2/5 + 1134. What is k in z(k) = 0?
-1, 0, 1, 18
Let u(t) be the third derivative of t**8/1344 + t**7/840 - t**6/96 - t**5/48 + t**4/24 + t**3/6 - 10119*t**2. Find a, given that u(a) = 0.
-2, -1, 1, 2
Let k(a) be the third derivative of a**5/12 + 135*a**4/2 + 8*a**2 + 60*a. Factor k(q).
5*q*(q + 324)
What is c in 2/5*c**4 + 48*c**3 - 242/5*c**2 + 0 + 0*c = 0?
-121, 0, 1
Let a(s) be the first derivative of -s**3/21 - 172*s**2 - 207088*s + 4200. Factor a(p).
-(p + 1204)**2/7
Let d(j) = 17*j - 53. Let n be d(-22). Let h = 431 + n. Factor -1024*a**3 + 1/2 + 2048*a**h - 16*a + 192*a**2.
(8*a - 1)**4/2
Suppose 0 = 23*k - 35*k + 144. Factor -k + n**2 - n - n + 10*n - n**3.
-(n - 2)**2*(n + 3)
Let r(z) = -z**3 - 5*z**2 + z - 7. Let i be r(-5). Let g be (1/3)/((-50)/i - 4). Determine d so that 8*d - 4*d**g - 16 - 20*d - 8*d = 0.
-4, -1
Let m be (606/707)/((-99)/(-231)). Factor -18/5*t - 3/5*t**m + 0.
-3*t*(t + 6)/5
Let o(m) be the first derivative of -3*m**5/5 - 9*m**4 + 27*m**3 + 729*m**2 + 3804. Factor o(q).
-3*q*(q - 6)*(q + 9)**2
Let x(r) = 18 - 32*r + 28*r + 0 - r**3 - 6*r**2. Let w be x(-4). What is o in 8/5*o + 52/5*o**w - 77/5*o**4 + 0 + 66/5*o**3 - 49/5*o**5 = 0?
-2, -2/7, 0, 1
Let c be (-70 - -68)/(1/(-2)). Suppose o - 2 = -4*v, o - c*v = -9*v + 2. Factor o + 1/2*s**3 + 4*s + 5/2*s**2.
(s + 1)*(s + 2)**2/2
Let d(m) be the first derivative of m**3/5 + 96*m**2/5 + 189*m/5 - 1084. Factor d(n).
3*(n + 1)*(n + 63)/5
Let m(i) be the first derivative of 25/4*i**3 - 27/4*i**2 - 3/20*i**5 - 9/8*i**4 - 198 + 0*i. Solve m(q) = 0.
-9, 0, 1, 2
Let o(p) be the second derivative of -1/3*p**4 + 1/21*p**7 + 0*p**2 + 2/15*p**6 - 57*p - 1/10*p**5 + 0 + 0*p**3. Factor o(j).
2*j**2*(j - 1)*(j + 1)*(j + 2)
Let y(n) be the third derivative of n**6/20 - 541*n**5/360 + 13*n**4/144 + 5*n**3/6 + 2*n**2 - 157*n. Let y(z) = 0. What is z?
-2/9, 1/4, 15
Let k be (0 - 18)/(8564/(-29974)). Factor -k*b - 1323/2 - 3/2*b**2.
-3*(b + 21)**2/2
Let g be -7 - (10 + 364/(-22)). Let d = g + 69/55. Factor -14/5*o**3 - d + 14/5*o + 4/5*o**2.
-2*(o - 1)*(o + 1)*(7*o - 2)/5
Let c be (-1)/(6/(5 + -3) - 4). Let a be (c - 0)*(5 - 2). Factor -91*d**4 - 3*d**a + d**3 - 18*d**5 + 103*d**4.
-2*d**3*(3*d - 1)**2
Suppose 2*x = r - 4, -2662*x + 2661*x - 9 = -4*r. Solve 400/7*n + 4*n**r + 16 = 0.
-14, -2/7
Solve -86*i + 1/3*i**2 + 5547 = 0 for i.
129
Suppose 68*s + 200*s = 41*s + 681. Let o(m) be the first derivative of -4/5*m**5 - 5 + 0*m**2 - 1/3*m**6 + 4/3*m**s + 0*m + 1/2*m**4. Find r such that o(r) = 0.
-2, -1, 0, 1
Let n = 767002 + -766999. Factor -1/3*w**n - 21*w - 27 + 17/3*w**2.
-(w - 9)**2*(w + 1)/3
Factor -48*q**3 + 0 - 3/4*q**5 - 57/4*q**4 + 0*q - 45*q**2.
-3*q**2*(q + 2)**2*(q + 15)/4
Let r(l) = -2*l**3 - 40*l**2 - 181*l - 179. Let w be r(-14). Solve -4/5*d**2 - 1/5*d**4 + 0 + 7/10*d**w + 3/10*d = 0.
0, 1, 3/2
Let o(c) be the third derivative of c**6/24 + 7*c**5/12 - 395*c**4/6 + 770*c**3/3 - 10923*c**2. Factor o(u).
5*(u - 14)*(u - 1)*(u + 22)
Let w be (2 - -7 - (-12 + (-192)/(-9)))*-3. Find b such that 13/4*b**3 + w - 11/4*b**2 + 7/4*b**4 - 5/4*b**5 - 2*b = 0.
-1, 2/5, 1, 2
Let d = 126 - 108. Determine h so that 36*h - 12*h**2 + 116*h**5 + 119*h**5 + d*h**4 - 27*h**3 - 238*h**5 = 0.
-1, 0, 2, 3
Suppose -11*w + 6 + 126 = 0. Suppose 23*h = 26*h - w. Let -2*m**3 - 24/7*m - 32/7*m**2 - 2/7*m**h + 0 = 0. What is m?
-3, -2, 0
Let h(x) be the third derivative of -2*x**5/15 - 313*x**4/60 - 122*x**3/15 + 782*x**2 - 3. Factor h(b).
-2*(4*b + 61)*(5*b + 2)/5
Suppose -5*w - 35 = -2*j, -47*w + 50*w - j = -20. Let g be (2/(-6))/(w - (-120)/27). Factor 2/5*d**2 + 1/5*d**4 + 0 + 0*d + g*d**3.
d**2*(d + 1)*(d + 2)/5
Let y = 735 + -732. Let l be y/((-4)/(-18) - 2849/(-666)). Suppose l*g - 1 + 1/3*g**2 = 0. Calculate g.
-3, 1
Let d(h) = -2*h**2 - 34*h + 6. Let c be d(-17). Determine n, given that