3*h. Let a(t) be the second derivative of d(t). Factor a(n).
-2*n**2*(n + 6)/13
Suppose s + 5*z - 31 - 31 = 0, 2*s - z = 80. Factor 20*f**3 - 6*f - 6*f**2 - 6*f**2 - 6 + s*f**4 + 18*f**5 + 8.
2*(f + 1)**3*(3*f - 1)**2
Suppose -128*c - 6 = -130*c. Factor 8*k + 4*k**4 + 20*k**2 + 38*k**3 - 22*k**c - 3*k + 3*k.
4*k*(k + 1)**2*(k + 2)
Find s such that -161312 + 74089*s - 1124*s**3 + 82295*s - 77256*s**2 - 4*s**4 + 83312*s = 0.
-142, 1, 2
Let w(r) = 28*r**2 - 69*r - 13. Let t(j) be the first derivative of 13*j**3/3 - 17*j**2 - 6*j + 35. Let x(u) = 13*t(u) - 6*w(u). Let x(q) = 0. What is q?
0, 28
Let u(b) be the first derivative of -b**6/12 + 17*b**5/2 - 533*b**4/4 + 2636*b**3/3 - 2872*b**2 + 4544*b - 6883. Determine o, given that u(o) = 0.
2, 4, 71
Suppose 0 = -2*u + 1302 + 370. Factor 6*h**4 - 841*h**3 + u*h**3 - 5*h**5 + 4*h**4.
-5*h**3*(h - 1)**2
Suppose 0 = -0*g + 14*g + 112. Let w = -3 - g. Suppose 2*k + k**w - 2512 + 2512 + k**4 - k**2 - 3*k**3 = 0. What is k?
-2, -1, 0, 1
Let o(q) be the first derivative of 2*q**6/45 - 91*q**5/45 - 119*q**4/18 - 16*q**3/3 + 91*q**2/2 + 4. Let x(i) be the second derivative of o(i). Factor x(g).
4*(g - 24)*(g + 1)*(4*g + 1)/3
Let y(o) be the second derivative of -o**8/560 + 3*o**7/140 + o**6/8 + o**5/5 + 7*o**3 + o**2 + 3*o. Let z(n) be the second derivative of y(n). Factor z(q).
-3*q*(q - 8)*(q + 1)**2
Let u(f) be the first derivative of f**4/6 + 10*f**3 - 64*f**2 + 392*f/3 - 2572. Factor u(c).
2*(c - 2)**2*(c + 49)/3
Let g be 19/((-1881)/(-1100)) - 8. Suppose -g*l**3 + 2/9*l**4 + 0 + 40/3*l**2 - 16*l = 0. What is l?
0, 2, 6
Let p(b) be the second derivative of b**4/32 - 37*b**3/8 + 27*b**2 + 322*b. Solve p(s) = 0 for s.
2, 72
Let y(t) = -10*t - 69. Let q be y(-8). What is g in 13*g + q*g**2 + 13*g**2 + 62*g - 70 + g**2 + 90*g = 0?
-7, 2/5
Let t = 110 + -102. Let w be -6 - (-153)/24 - (-1)/t. Factor -1/2 + w*v**4 + v + 0*v**2 - v**3.
(v - 1)**3*(v + 1)/2
Let s(g) = -2*g**2 + 3*g - 1. Let r(n) be the second derivative of 1/2*n**3 - 1/12*n**4 + 0*n**2 + 0 + 20*n. Let t(m) = -3*r(m) + 2*s(m). Factor t(j).
-(j + 1)*(j + 2)
Let u(n) be the first derivative of -n**4/16 + 49*n**3/12 - 109*n**2/2 + 171*n - 4279. Factor u(d).
-(d - 38)*(d - 9)*(d - 2)/4
Let s = 819386/3 - 273126. Factor 4/3*n**5 + 0 + s*n - 28/3*n**2 + 12*n**3 - 20/3*n**4.
4*n*(n - 2)*(n - 1)**3/3
Let u(t) be the third derivative of 0 + 192/5*t**3 - t**2 - 10*t - 4/5*t**4 + 1/150*t**5. Let u(y) = 0. What is y?
24
Let p be 3*7/(-49) - 4458/(-14). Let y = p + -315. Determine s so that s**2 - 1/2 - 1/2*s**4 + s**y - 1/2*s - 1/2*s**5 = 0.
-1, 1
Find v such that 61*v - 1/2*v**2 - 121/2 = 0.
1, 121
Let z(j) = 951*j - 23770. Let c be z(25). Find d such that -3/11*d**c + 19/11*d**4 + 36/11 - 35/11*d**2 + 48/11*d - 25/11*d**3 = 0.
-1, -2/3, 2, 3
Let v = 499/7 - 71. Suppose 445*w - d = 441*w + 29, 3*w = -d - 8. Factor -10/7*h**2 - 6/7 + v*h**w + 2*h.
2*(h - 3)*(h - 1)**2/7
Let k = -322 - -345. Determine d, given that -4*d - 31*d**2 - 26*d**2 - k*d**2 + 76*d**2 = 0.
-1, 0
Let c be (136/(-5))/(30394/(-32565)). What is a in -4/7*a**3 + 404/7*a + c + 28*a**2 = 0?
-1, 51
Let l be (5*136/(-255))/(6/(-7)). Factor -12 - 4/9*d**5 + 8*d**2 - 40/9*d**3 + 12*d - l*d**4.
-4*(d - 1)**2*(d + 3)**3/9
Let a(q) be the second derivative of -2/3*q**4 + 21*q + 0*q**2 - 1/10*q**5 - 2 - q**3. Factor a(x).
-2*x*(x + 1)*(x + 3)
Let d be 1 - (10 + 1362/(-12)). Let q = -1017/10 + d. Solve 22/5*k**3 + 4/5 + 2*k**4 - 8/5*k**5 - q*k**2 - 14/5*k = 0 for k.
-1, 1/4, 1, 2
Factor -239/6*y + 305/6 - 1/6*y**3 - 65/6*y**2.
-(y - 1)*(y + 5)*(y + 61)/6
Let w(v) be the third derivative of v**6/60 - 11*v**5/5 + 85*v**4 + 2312*v**3/3 + 2337*v**2. Solve w(g) = 0.
-2, 34
Let q(w) = -w**2 - 655*w - 9600. Let c be q(-15). Factor 4/9*j**2 + c + 46/9*j**3 + 0*j.
2*j**2*(23*j + 2)/9
Let m(n) = -2*n**3 - 6*n**2 + 9*n + 12. Let k(i) = i**3 + 4. Let v(w) = k(w) + m(w). Let z be v(-7). Factor 0 - 4/9*u - 4/9*u**z.
-4*u*(u + 1)/9
Let i(q) = -29*q**2 + 37*q + 103. Let n(p) = -50*p**2 + 75*p + 205. Let y(r) = 5*i(r) - 3*n(r). Factor y(a).
5*(a - 10)*(a + 2)
Let x be (-1)/(-4 - 935/(-235)). Suppose 4*h - 10 = -m, -x*m = -50*m + 2*h + 2. Determine z so that -1/6*z**3 + 0 + 0*z + 1/3*z**m = 0.
0, 2
Suppose -12*y + 13*y - 31 = 0. Suppose 4*j - d - y = 2*d, -5*d = 5*j + 5. Factor -j*x**2 + 9*x - x**2 - 3*x**3 + 11*x**2.
-3*x*(x - 3)*(x + 1)
Let r be 28/8*((-15048)/(-252) + -55). Solve -60*l**2 - 8 + 9/4*l**5 + 46*l**3 + 36*l - r*l**4 = 0.
2/3, 2
Let b(y) = 7*y**2 - 39*y - 10. Let s be b(6). Suppose 2*c + s*c = 8*c. Factor 24/7*v**2 + 6/7*v**3 + 24/7*v + c.
6*v*(v + 2)**2/7
Let m(u) = 52*u + 38 - 2*u**2 + 0*u**2 - 104*u - 3*u - 12*u. Let r be m(-34). Factor -1 - 4*w**2 + w**r - 1/2*w**5 + w**3 + 7/2*w.
-(w - 1)**4*(w + 2)/2
Let z(d) be the third derivative of d**5/270 + 29*d**4/108 + 40*d**3/9 + 6*d**2 - 4*d + 3. Factor z(y).
2*(y + 5)*(y + 24)/9
Let 8*q - 2/11*q**2 - 246/11 = 0. What is q?
3, 41
Suppose -8*v - 207 = -55. Let b be (-8)/6 + (-16 - v). Find r such that 0 - b*r**4 - 17/3*r**3 + 14/3*r**2 + 8/3*r = 0.
-4, -2/5, 0, 1
Let w = 1804367/206212 - 3/51553. Factor -w*q**2 + 81 - 72*q - 1/4*q**3.
-(q - 1)*(q + 18)**2/4
Suppose -94*a - 1057 = -1433. Solve a*i**2 - 16/3 + 44/3*i = 0.
-4, 1/3
Determine o so that 0 + 0*o - 4/7*o**5 + 0*o**2 + 32/7*o**4 + 36/7*o**3 = 0.
-1, 0, 9
Let t(j) = 6*j - 24. Let p(k) = -3*k + 12. Let i(z) = 13*p(z) + 6*t(z). Let a be i(3). Factor -3*u**5 + 7*u**4 - 3*u**a - u**4 + 0*u**5.
-3*u**3*(u - 1)**2
Suppose 22*n = -16*n + 114. Determine k so that 397*k**3 - 129*k**3 + 4*k**4 - 10*k - 129*k**n - 4 - 129*k**3 = 0.
-2, -1, -1/2, 1
Let i be (-3 + 8*2/6)*-3. Suppose 4*j = -v - i, 2*v = -7*j + 4*j + 3. Suppose f**4 - 75*f - 9*f**2 + 0*f**v - 3*f**3 + 70*f = 0. What is f?
-1, 0, 5
Let v(u) be the first derivative of -u**6/1260 + 23*u**5/420 + 19*u**3/3 + 2*u - 128. Let a(b) be the third derivative of v(b). Solve a(h) = 0 for h.
0, 23
Let y = 69 - 65. Suppose -5*u - y + 14 = 0. Factor 19*c**2 - 8*c - 35*c**2 + 18*c**u.
2*c*(c - 4)
Find j such that 11 + 7989*j**2 + 935*j + 1075*j + 42 + 5478*j**2 + 22 = 0.
-5/67
Let z(j) = 44*j + j**2 - 2*j**2 + 3 - 45*j + 0*j**2. Let a be z(0). Factor -3*o + o**3 - 4*o**a + 0*o**3 + 4*o**3 + 2.
(o - 1)**2*(o + 2)
Suppose -38 = -29*x + 10*x. Suppose 196*r**4 - 59*r**x + 29*r**3 + 32*r + 235*r**2 + 283*r**3 + 29*r**5 + 11*r**5 = 0. Calculate r.
-2, -1/2, -2/5, 0
Find d, given that 78*d**5 - 108*d**2 - 6*d**4 + 66*d + 64*d**3 - 12*d**2 - 80*d**5 + 5*d - 7*d = 0.
-8, 0, 1, 2
Factor 142/3*y - 37/3*y**2 + 1/6*y**3 - 140/3.
(y - 70)*(y - 2)**2/6
Let f be ((-22)/(-176))/(-2*1/(-15)). Let t(r) be the first derivative of f*r**4 + 3/2*r**3 + 10 + 3/20*r**5 + 0*r + 0*r**2. Determine x so that t(x) = 0.
-3, -2, 0
Solve 0 + 1/3*c**3 + 24*c + 73/3*c**2 = 0.
-72, -1, 0
Let c(a) be the third derivative of -a**5/150 + 55*a**4/12 + 92*a**3/5 - 167*a**2. Find v, given that c(v) = 0.
-1, 276
Let z(u) be the first derivative of 0*u + 0*u**2 - 36 - 2/5*u**5 - 10/3*u**3 + 3*u**4. What is b in z(b) = 0?
0, 1, 5
Let q be (-1)/((-6)/(-16)) + 660/(-108)*714/(-1309). Solve q*w**3 + 10/3*w - 4/3 - 8/3*w**2 = 0.
1, 2
Let h(z) be the second derivative of -z**4/42 + 166*z**3/21 - 328*z**2/7 + 4*z - 9. Let h(l) = 0. What is l?
2, 164
Let b be 18 - (3*14/6 + -4). Let h be 6/b*5/13. What is y in -h*y - 4/13 + 2/13*y**2 = 0?
-1, 2
Let v(g) be the second derivative of -22/7*g**2 - 4/21*g**4 + 1 + 8*g + 1/70*g**5 - 31/21*g**3. Factor v(q).
2*(q - 11)*(q + 1)*(q + 2)/7
Suppose -10/7*p**4 + 6*p**3 - 200/7*p + 0 + 170/7*p**2 - 2/7*p**5 = 0. Calculate p.
-5, 0, 1, 4
Suppose 19*z = -16*z + 23 + 2 + 45. Factor -8/3*l + 2*l**z + 0*l**3 - 1/3*l**4 + 1.
-(l - 1)**3*(l + 3)/3
Let f be 8 - 2 - 6/3. Suppose 0 = f*h - 5*o - 16 - 11, 4*o = -12. Solve -6*u**2 + 1 - 7 + 3*u + h*u**3 + 12*u**2 - 6*u = 0.
-2, -1, 1
Let h be 6/14 + (-351)/(-63). Let d be -1 - ((-123)/h + (-4 - -1)). Factor 87/2*b**3 - 3 + d*b - 27/2*b**4 - 99/2*b**2.
-3*(b - 1)**3*(9*b - 2)/2
Factor -320/9*g + 2/9*g**2 + 12800/9.
2*(g - 80)**2/9
Let g(p) = -37*p**2 - 5*p + 6. Let t be g(2). Let y = t + 285. Factor -y*n + 2*n**4 - 4*n**4 + 157*n + 12*n**3 - 8 - 26*n**2.
-2*(n - 2)**2*(n - 1)**2
Let l(u) = -5*u**2 - 7891*u + 7906. Let t(g) = -135*g**2 