et z(c) be the first derivative of -c**6/1080 + c**5/360 + c**4/36 + 4*c**3 + 56. Let x(q) be the third derivative of z(q). Factor x(n).
-(n - 2)*(n + 1)/3
Factor 1116/5 + 3/5*u**2 + 129/5*u.
3*(u + 12)*(u + 31)/5
Determine d so that 361/6*d + 1/6*d**2 - 181/3 = 0.
-362, 1
Let b(l) be the third derivative of -l**5/90 - 1175*l**4/108 + 392*l**3/27 + 3*l**2 + 175*l. Factor b(a).
-2*(a + 392)*(3*a - 1)/9
Factor 372*x**2 - 16845*x**4 + 33682*x**4 - 159*x**3 - 180*x - 16828*x**4.
3*x*(x - 15)*(x - 2)*(3*x - 2)
Let o(g) = -44*g**2 - 280*g - 389. Let j(y) = -42*y**2 - 280*y - 388. Suppose 0 = 9*u - 212 + 248. Let i(r) = u*o(r) + 3*j(r). Factor i(t).
2*(5*t + 14)**2
Let x(l) = 2*l**3 + 9*l**2 - 5*l - 16. Let c be x(-4). Solve -46 + 5*d**5 + 88 - 42 - c*d**4 = 0 for d.
0, 4
Let o = -262 + 262. Let c be o/(12/3*-1 - -1). Determine f so that 2/3*f**3 - 2*f**2 - 2/3*f + 2*f**4 + c = 0.
-1, -1/3, 0, 1
Let k(a) be the second derivative of -55*a - 1/170*a**5 + 0*a**4 + 0 + 0*a**2 + 0*a**3. Suppose k(r) = 0. What is r?
0
Let s = -15869/369 - -6547/123. Determine u, given that -352/9*u**2 + 0 - 308/9*u**3 - 64/9*u - s*u**4 - u**5 = 0.
-4, -2, -2/9, 0
Let y = -8257 - -8262. Let j(h) be the second derivative of 0*h**4 - 5/2*h**3 + 15*h - 5*h**2 + 0 + 1/4*h**y. Factor j(f).
5*(f - 2)*(f + 1)**2
Let s(h) be the third derivative of -h**7/1680 - 23*h**6/960 + h**5/160 + 67*h**4/192 - 23*h**3/24 + 2*h**2 - 1210*h. Factor s(v).
-(v - 1)**2*(v + 2)*(v + 23)/8
Let o(s) = -39*s**2 - 1182*s - 22839. Let k = -635 + 630. Let f(u) = 16*u**2 + 473*u + 9136. Let z(i) = k*o(i) - 12*f(i). Find m such that z(m) = 0.
-39
Let k(y) be the first derivative of 4*y**5 - 53*y**4 + 512*y**3/3 + 120*y**2 - 1857. Factor k(b).
4*b*(b - 6)*(b - 5)*(5*b + 2)
Let d be 0/(-2) + (-744)/1116 + (-10)/(-9). Suppose 8/9*m**3 + 56/9*m - 16/3*m**2 - 20/9 + d*m**4 = 0. Calculate m.
-5, 1
Let s(q) = 27*q**3 - 5*q**2 - 4*q - 7. Let g(a) = 4*a**3 - a**2 - a - 1. Let m(v) = -21*g(v) + 3*s(v). Factor m(p).
-3*p*(p - 3)*(p + 1)
Suppose -3*u = -5*w + 23, -5*w - 93 + 140 = 3*u. Solve -4/9*n + n**5 - 25/9*n**2 + 7/3*n**u + 4/9 - 5/9*n**3 = 0 for n.
-2, -1, -2/3, 1/3, 1
Let u(l) be the third derivative of 3/20*l**5 + 13*l**2 + 0*l**4 - 1 - 1/480*l**6 + 0*l**3 + 0*l. Let u(y) = 0. Calculate y.
0, 36
Suppose 0 = 9*p - 3192 + 3165. Let m(b) be the second derivative of 0*b**2 + 0*b**p + 3/25*b**6 + 2/15*b**4 - 6/25*b**5 - 6*b + 0. Find o, given that m(o) = 0.
0, 2/3
Suppose 2*g + 4*t - 8 = 0, -2*t + 7 = 3*g - 17. Solve -84*o**3 + 121*o**2 + 16*o**4 - 31 + 120*o - g + 9 - 69*o**2 = 0.
-1, 1/4, 2, 4
Let y(u) be the third derivative of 1/80*u**5 + 0 - 139*u**2 + 9/4*u**3 + 0*u + 21/64*u**4 - 1/960*u**6. Factor y(f).
-(f - 12)*(f + 3)**2/8
Let l(t) be the first derivative of -t**5/100 - 3*t**4/10 - 27*t**3/10 + 27*t**2 + 319. Let v(x) be the second derivative of l(x). Factor v(k).
-3*(k + 3)*(k + 9)/5
Let t(q) be the first derivative of 2*q**3/27 - 25*q**2/3 - 52*q - 576. Factor t(x).
2*(x - 78)*(x + 3)/9
Let d(p) = -p**2. Let m(x) = -3*x**2 - 3*x - 4. Suppose -8*g - 42 = -2. Let t = -13 - -33. Let k(y) = g*m(y) + t*d(y). Factor k(v).
-5*(v - 4)*(v + 1)
Let u(x) be the second derivative of x**5/15 - 73*x**4/36 + 11*x**3 - 15*x**2/2 + 2*x + 174. Factor u(a).
(a - 15)*(a - 3)*(4*a - 1)/3
Let t be 75/(-50) + (-26)/(-4) + -5. Suppose t = 37*n + 15 - 15. Solve -4/7*y**2 - 4/7*y + n = 0 for y.
-1, 0
Suppose 4*k = -5*p - 124 + 9, 2*k = -3*p - 67. Let s be (-8)/18*(-1 + p - -19). Solve -s + 10/9*u - 4/9*u**2 = 0.
1/2, 2
Let u be -2 - 2606/(-14) - 7. Let p = -176 + u. Let p*m**2 - 16/7*m**4 + 0 - 4/7*m**3 + 0*m + 12/7*m**5 = 0. Calculate m.
-2/3, 0, 1
Let v(b) = -197*b + 6308. Let a be v(32). Let c(t) be the third derivative of -100/3*t**3 + 5/3*t**a - 25*t**2 + 0*t + 0 - 1/30*t**5. Let c(g) = 0. What is g?
10
Suppose -3*n + 1 - 16 = 0, 2*t = -4*n - 28. Let h(p) = 36*p + 144. Let m be h(t). Factor 1/7*u**4 + 1/7*u**5 + 0 - 2/7*u**3 + m*u + 0*u**2.
u**3*(u - 1)*(u + 2)/7
Let w(i) be the first derivative of i**5/2 + 15*i**4/8 - 35*i**3 - 80*i**2 + 1200*i + 3098. Find j, given that w(j) = 0.
-6, -5, 4
Find j, given that -1812/7*j - 3/7*j**2 - 273612/7 = 0.
-302
Determine v, given that -22/3*v**3 + 1/3*v**5 + 0*v**2 + 0*v - 7*v**4 + 0 = 0.
-1, 0, 22
Let m be (20/(-40))/(9/306) + (17 - 0). Determine o so that -7/4*o**3 + 47/4*o**2 + m + 7/2*o = 0.
-2/7, 0, 7
Factor 20/9*b**2 - 50/3*b + 0 + 2/9*b**3.
2*b*(b - 5)*(b + 15)/9
Let v be (-5)/2*1*2 - -526. Let d = 523 - v. Solve 1/7*h**4 + 3/7*h**d - 3/7*h**3 - 1/7*h + 0 = 0.
0, 1
Factor -330*u**2 + 1283 + 1313 - 4068 - 27*u**3 + 1352 - 612*u.
-3*(u + 2)*(u + 10)*(9*u + 2)
Let c(z) be the second derivative of z**9/5040 - z**8/700 - 3*z**7/350 - 121*z**3/3 - 136*z. Let p(k) be the second derivative of c(k). Solve p(m) = 0.
-2, 0, 6
Let i = -12 - -15. Let k(w) = w**3 - 5*w**2 + 2. Let n be k(5). Factor -4 + 17*t + 3 + i - 4*t**n - 6.
-(t - 4)*(4*t - 1)
Let r(g) = -g**2 - 71*g - 97. Let w(f) = -28*f - 1. Let p(o) = r(o) + w(o). Factor p(u).
-(u + 1)*(u + 98)
Let a(p) = -15*p**2 + 164*p + 354. Let l(t) = -13*t**2 + 157*t + 354. Let d(g) = 6*a(g) - 7*l(g). Factor d(q).
(q - 118)*(q + 3)
Let d(q) be the second derivative of -q**4/12 + 1178*q**3/3 - 693842*q**2 + 683*q. Solve d(w) = 0.
1178
Let t(v) = -v**3 - 2*v**2 + v - 4. Let o be t(-3). Suppose -o*a + 2*k = -386, 4*k + 471 + 112 = 3*a. Factor -15*g + 189 - 5*g**2 - a.
-5*g*(g + 3)
Suppose 0 = 2*t - 0*q + q - 7, 4 = 3*t - 5*q. Factor -4*a**t - 4*a**2 - 2*a**4 + 5*a**5 - 3*a**3 + 2*a**2 - 2*a**5.
a**2*(a - 2)*(a + 1)*(3*a + 1)
Suppose 32*k - 4*k - 56 = 0. Let g be 276/120 + k + 27/(-15). Suppose 11/6*p + g*p**3 - 14/3*p**2 + 1/3 = 0. What is p?
-2/15, 1
Let 2/21*n**2 + 12268/21*n + 18812978/21 = 0. What is n?
-3067
Factor -129*y - 1558*y**2 - 191 - 45*y + 1557*y**2 + 18.
-(y + 1)*(y + 173)
Let f = -675 - -723. Let 327*i**3 + f*i**2 + 12*i - 10*i**4 + 4*i**5 - 359*i**3 + 52*i - 2*i**4 = 0. What is i?
-2, -1, 0, 2, 4
Let g(n) = 2*n**4 + n**2. Let b(f) = 3*f**4 - 56*f**3 - 324*f**2 + 824*f - 441. Let l(k) = b(k) - 2*g(k). Factor l(u).
-(u - 1)**2*(u + 9)*(u + 49)
Let y(p) be the second derivative of -2/15*p**5 + 1/3*p**2 + 1/2*p**4 - 10*p - 2/3*p**3 - 7. Factor y(j).
-2*(j - 1)**2*(4*j - 1)/3
Let v be (89/(12015/162))/(20/50). Suppose -34/13*x**2 - 116/13*x + 2/13*x**v - 80/13 = 0. What is x?
-2, -1, 20
Factor -1/5*i**2 - 498/5 - 499/5*i.
-(i + 1)*(i + 498)/5
Suppose 99817*y**2 + 508032*y + 179769*y**2 - y**5 - 58334*y**3 - 27586*y**2 - 196688*y**3 + 1009*y**4 = 0. Calculate y.
-1, 0, 2, 504
Let p = 2758 - 8419/3. Let a = p - -49. Solve -4/3*n**3 + 2 - 8/3*n**2 + 4/3*n + a*n**4 = 0 for n.
-1, 1, 3
Factor -10*k**2 - 54543*k + 27332*k + 132*k**2 + 2*k**3 + 27331*k.
2*k*(k + 1)*(k + 60)
Let f(b) = 7*b**2 + 172*b + 113. Let w be f(-24). Let g(d) be the second derivative of 0 + 2/27*d**3 - 1/9*d**2 - w*d - 1/54*d**4. Factor g(c).
-2*(c - 1)**2/9
Let o(f) = -6*f**2 + 38*f + 688. Let q be o(-8). What is x in -21/5*x**3 - 1/5*x**5 + q*x - 18/5*x**2 - 8/5*x**4 + 0 = 0?
-3, -2, 0
Let f(r) be the third derivative of r**7/8820 + r**6/945 + r**5/1260 - r**4/42 - 86*r**3/3 + r**2 - 49. Let x(g) be the first derivative of f(g). Factor x(z).
2*(z - 1)*(z + 2)*(z + 3)/21
Let m be ((-9)/(-3)*110)/((-8)/20). Let p = m + 3309/4. Factor 0 + 15/4*x**3 - 3/4*x - 3/4*x**2 - p*x**4.
-3*x*(x - 1)**2*(3*x + 1)/4
Let t(i) be the third derivative of i**5/15 + 362*i**4/3 + 262088*i**3/3 + 1340*i**2 - 1. Find m, given that t(m) = 0.
-362
Let l be (22/(-10))/((-72)/50) - 20/(-90). Let g(r) be the first derivative of 3/2*r**2 + 9/32*r**4 - l*r**3 + 0*r + 24. Factor g(o).
3*o*(o - 4)*(3*o - 2)/8
Let s(u) be the first derivative of -u**7/21 - u**6/15 + u**5/5 + u**4/3 - u**3/3 - u**2 - 83*u + 117. Let j(v) be the first derivative of s(v). Factor j(m).
-2*(m - 1)**2*(m + 1)**3
Factor -4*t**2 - 8130*t - 8158*t - 16 + 16262*t - 6*t**2.
-2*(t + 1)*(5*t + 8)
Let u = -166 - -628. Suppose 13*g = 2*g + u. Determine h so that g*h**4 - 8 + 57*h**3 + 16 - 157*h**3 + 10*h**2 + 40*h = 0.
-1/3, -2/7, 1, 2
Let x(j) be the first derivative of j**5/10 - 21*j**4 + 1176*j**3 + 2950. Factor x(k).
k**2*(k - 84)**2/2
Let i(t) be the third derivative of -8/3*t**3 - 85*t**2 + 5/3*t**5 + 0*t + 2*t**4 +