
-3*(m - 6)*(m - 5)
Let i(k) be the first derivative of k**3 + 9*k**2 - 561*k + 8153. Factor i(x).
3*(x - 11)*(x + 17)
Let o be (-86)/30 + -57 + 60. Let v = o + 2/3. Suppose -4/5*g + v*g**3 - 22/5*g**4 + 0 + 22/5*g**2 = 0. Calculate g.
-1, 0, 2/11, 1
Let l = 1899 + -1893. Let n(b) be the third derivative of -1/24*b**l - 25/24*b**4 - 5/3*b**3 + 0*b + 0 - 1/3*b**5 - 9*b**2. Factor n(g).
-5*(g + 1)**2*(g + 2)
Suppose -228*t - 23*t - 1 = 87*t - 1. Determine x, given that 0*x + t - 4/5*x**2 + 8/5*x**3 - 3/5*x**4 = 0.
0, 2/3, 2
Let n(r) be the second derivative of 61*r - 10/3*r**2 - 11/9*r**3 - 1/18*r**4 + 0. Factor n(t).
-2*(t + 1)*(t + 10)/3
Let m(w) be the second derivative of -w**6/72 + w**5/24 + 5*w**4/4 + 34*w**3/3 + 108*w. Let b(h) be the second derivative of m(h). Let b(y) = 0. Calculate y.
-2, 3
Suppose s = 1, 0 = -3*q - 2*q - 3*s + 43. Let k be 1*(5 - (-3)/(-1)). Let -8*v + q*v + 4*v**k - 8*v = 0. What is v?
0, 2
Let s(c) = -c**5 - c**4 - c**3 - 4. Let x(w) = 28*w**4 + 24*w**3 - 264*w**2 + 128*w + 400. Let a(q) = -4*s(q) - x(q). Find m, given that a(m) = 0.
-3, -1, 2, 4
Suppose 0 + 90*u - 64*u**2 - 132/5*u**3 + 0*u**4 + 2/5*u**5 = 0. Calculate u.
-5, 0, 1, 9
Factor -423*i - 2*i**2 - 31*i - 1273*i - 278*i - 2000 - 3*i**2.
-5*(i + 1)*(i + 400)
Suppose 1/2*r**4 - 4*r**2 + 6*r - 3/2*r**3 + 8 = 0. Calculate r.
-2, -1, 2, 4
Suppose 1725*l**2 - 888*l - 892 - 3447*l**2 + 1726*l**2 = 0. What is l?
-1, 223
Suppose 3*h - 13*a - 84 = 0, 5*h - 5*a + 0*a - 40 = 0. Let f(n) be the first derivative of -16/3*n + h - 1/9*n**3 - 4/3*n**2. Factor f(m).
-(m + 4)**2/3
Suppose -54*l - 262169 = -262277. Find x such that 10/3*x**4 + 44/3*x**3 + 0 + 46/3*x**l + 4*x = 0.
-3, -1, -2/5, 0
Let q(b) be the second derivative of -1/960*b**6 + 19/6*b**3 + 21*b - 1/4*b**4 + 0 + 0*b**2 - 1/40*b**5. Let x(k) be the second derivative of q(k). Factor x(u).
-3*(u + 4)**2/8
Let y(q) be the third derivative of -q**6/900 - 8*q**5/75 - 145*q**3/6 + 253*q**2. Let z(u) be the first derivative of y(u). Determine o, given that z(o) = 0.
-32, 0
Suppose 60 = v + 56. Let i = 6 - v. Factor -9*k**3 + 1 + 7*k**2 + 6*k - 1 - 10*k**i.
-3*k*(k + 1)*(3*k - 2)
Let j(l) be the third derivative of l**5/40 - 33*l**4/32 + 45*l**3/8 - 3805*l**2. Find i, given that j(i) = 0.
3/2, 15
Let l(f) be the second derivative of 2*f**7/21 - 6*f**6/5 + 32*f**5/5 - 56*f**4/3 + 32*f**3 - 32*f**2 + 571*f. Solve l(y) = 0 for y.
1, 2
Let v(o) be the second derivative of o**4/28 + 85*o**3/14 + 249*o**2/7 + 4880*o. Let v(l) = 0. What is l?
-83, -2
Let t be (-1 - (-6)/10) + 528/220. Find z, given that -z**2 + 4*z**2 - 12 - 5*z**t + z + 3*z**2 - 12*z = 0.
-1, 12
Suppose -429 + 117 = -95*k + 17*k. Let t(a) be the third derivative of 1/12*a**5 + 30*a**3 + 0*a + 5/2*a**k + 0 - 19*a**2. Factor t(g).
5*(g + 6)**2
Factor -4*g + 21*g**2 - 40*g**2 - 52*g + 384 - 48*g + 21*g**2.
2*(g - 48)*(g - 4)
Let t(b) be the first derivative of b**4/32 + 8*b**3/3 + 125*b**2/16 + 31*b/4 - 1282. Solve t(w) = 0.
-62, -1
Let x = 89 + -85. Suppose n + v = -1, -x*n + v + 0*v = -11. Factor -9*t + 11*t + 20*t + 3*t**2 + n*t.
3*t*(t + 8)
Let q = -25634 + 384524/15. Factor -2/3*d**2 - q*d - 2/5 - 2/15*d**3.
-2*(d + 1)**2*(d + 3)/15
Let i be 36/102*(-221)/(-39). Factor 1 + 7*v**3 + 9/2*v + 1/2*v**5 + 8*v**i + 3*v**4.
(v + 1)**4*(v + 2)/2
Let d be ((-15)/2)/((-15)/10). Suppose 5*u + 2*w = 78 - 5, -u + d*w = -20. Factor -4 + u*a - 7/2*a**2.
-(a - 4)*(7*a - 2)/2
Factor 80*m**3 - 120*m**2 + 1019*m**2 + 0 + 2*m**4 + 0 + 3468*m + 87*m**2.
2*m*(m + 6)*(m + 17)**2
Let u(d) = 2*d + 28. Let v be u(16). Solve 155*t**2 + 110*t**3 + 91*t**3 - v*t - 336*t**3 - 6*t**5 + 28*t**4 + t**5 + 17*t**4 = 0 for t.
0, 1, 3, 4
Let a = -222 + 224. Factor 4*t - 3*t**3 - 3*t**2 + 17*t - 13*t**a - 2*t**2.
-3*t*(t - 1)*(t + 7)
Let v(t) = -2*t**2 - 14*t - 16. Let m be v(-5). Suppose -3*x = -4*w + m, 2*x - 163 + 167 = 4*w. Factor 0*n - 3/2*n**3 + 3*n**2 + x - 3/2*n**4.
-3*n**2*(n - 1)*(n + 2)/2
Let m(o) = o**3 + 6*o**2 - 3*o + 2. Let j be m(-6). Let b be ((-5)/5)/(28/(-56)). Factor -2*u + 0*u**b - j - 4*u**2 + 6*u**3 + 20.
2*u*(u - 1)*(3*u + 1)
Let p(n) be the second derivative of 5/12*n**4 + 64*n + 5/6*n**3 + 0 - 5/2*n**2 - 1/4*n**5. Determine c, given that p(c) = 0.
-1, 1
Factor -28/5*q + 0 + 214/5*q**3 - 1494/5*q**2.
2*q*(q - 7)*(107*q + 2)/5
Let k(g) be the third derivative of -g**7/18900 - g**6/600 - 2*g**5/225 - 19*g**4/6 + 69*g**2. Let q(v) be the second derivative of k(v). Factor q(h).
-2*(h + 1)*(h + 8)/15
Find s, given that -195 + 177*s**3 - 570*s**2 - 3/2*s**5 + 9*s**4 + 1161/2*s = 0.
-10, 1, 13
Let y(s) = 11*s**2 - 33*s + 25. Let h(n) be the third derivative of 2*n**5/15 - 4*n**4/3 + 13*n**3/3 - 11*n**2 - 4. Let a(q) = -3*h(q) + 2*y(q). Factor a(l).
-2*(l - 14)*(l - 1)
Let t(l) be the second derivative of -55*l**4/6 + 58*l**3/3 - 3*l**2 + 2306*l + 1. Find a, given that t(a) = 0.
3/55, 1
Let o be (1/(-6)*162/(-9))/(14/24). Factor 40/7*f - o - 4/7*f**2.
-4*(f - 9)*(f - 1)/7
Let q(r) be the third derivative of -r**6/60 + 209*r**5/10 - 43681*r**4/4 + 9129329*r**3/3 - 1078*r**2. Factor q(j).
-2*(j - 209)**3
Let k = 17957 - 17957. Let q(n) be the first derivative of -18 - 1/5*n**5 + k*n**2 + 0*n - 1/4*n**4 + 1/6*n**6 + 1/3*n**3. Factor q(r).
r**2*(r - 1)**2*(r + 1)
Let o = -313 - -309. Let i(n) = 2*n**3 + 13*n**2 + 20*n + 3. Let x be i(o). Determine z so that 1/5*z - 1/5*z**x - 1/5*z**2 + 1/5 = 0.
-1, 1
Let m(w) be the second derivative of w**4/60 + 107*w**3/30 - 54*w**2/5 + 5082*w. Find l such that m(l) = 0.
-108, 1
Let v = 436451/480084 + -1/43644. What is i in 14/11*i**3 - 8/11 + v*i**4 - 16/11*i + 2/11*i**5 - 2/11*i**2 = 0?
-2, -1, 1
Suppose -71 = 5*g + 2*t - 61, -t = 2*g + 6. Solve 8 - 16/3*d + 2/3*d**3 - 10/3*d**g = 0.
-2, 1, 6
Let h(c) be the first derivative of -2*c**3 + 177 + 1/4*c**4 + 0*c**2 + 32*c. Find p, given that h(p) = 0.
-2, 4
Let i(c) = 3*c**2 - 3*c. Let j(w) = -32*w**2 + 7*w - 19. Let z(m) = 11*m**2 - 2*m + 7. Let g(r) = -4*j(r) - 11*z(r). Let a(y) = -2*g(y) + 5*i(y). Factor a(s).
(s - 2)*(s - 1)
Let z be 14007/145 - -3 - 74. Suppose 18/5*g**2 + z - 96/5*g - 1/5*g**3 = 0. Calculate g.
2, 8
Let q = 9 + 1. Factor -5*o**3 - 25 + 0*o**3 + 20*o**2 + 5*o**2 - 5*o + q*o**3.
5*(o - 1)*(o + 1)*(o + 5)
Let x(l) be the first derivative of 4*l**2 - 161 + 17/6*l**3 + 5/8*l**4 + 2*l. Factor x(o).
(o + 1)*(o + 2)*(5*o + 2)/2
Let z(j) be the second derivative of j**4/36 + 577*j**3/9 + 332929*j**2/6 - 24*j + 56. Solve z(y) = 0.
-577
Suppose -144*t + 93*t = -306. Let g(j) be the third derivative of 0*j**4 - 9*j**2 + 0 - 1/20*j**5 + 0*j + 0*j**3 + 1/350*j**7 - 1/50*j**t. Factor g(z).
3*z**2*(z - 5)*(z + 1)/5
Factor 522 - 220 - 15*r**2 + 8*r - 286 - 9*r**3.
-(r - 1)*(3*r + 4)**2
Let a(q) = 39*q**4 - 237*q**3 + 357*q**2 - 129*q - 6. Let g(z) = 4*z**4 + 2*z**3 - 2*z**2 + z - 1. Let b(k) = a(k) - 6*g(k). Factor b(p).
3*p*(p - 15)*(p - 1)*(5*p - 3)
Let h(u) be the second derivative of 31/240*u**6 + 319/48*u**4 - 2299/48*u**3 + 0 + 25*u + 1331/16*u**2 + 1/336*u**7 + 149/80*u**5. Factor h(r).
(r - 1)**2*(r + 11)**3/8
Let w(o) be the third derivative of 0*o**3 + 2*o**2 - 9 + 1/600*o**6 + 0*o + 15/2*o**4 - 1/5*o**5. Find f, given that w(f) = 0.
0, 30
Suppose 668*r - 29036 - 98404 = 78*r. Factor r*u - 111/5*u**2 + 3/5*u**3 - 972/5.
3*(u - 18)**2*(u - 1)/5
Let r = -216 - -238. Let y(u) = u**4 - u**2 - 2*u. Let x(i) = -24*i**4 - 144*i**3 + 152*i**2 + 14*i - 20. Let f(o) = r*y(o) - 2*x(o). Let f(m) = 0. Calculate m.
-5, -2/5, 2/7, 1
Suppose 121*f = 1025 - 662. Factor 2/5*d**5 + 0 + 4*d**4 - 46/5*d**f + 24/5*d**2 + 0*d.
2*d**2*(d - 1)**2*(d + 12)/5
Let j(l) = l**3 - 9*l**2 + 7*l + 71. Let h be j(6). Let m(c) be the second derivative of 7/12*c**4 + 7*c - 1/20*c**h + 6*c**2 - 8/3*c**3 + 0. Factor m(g).
-(g - 3)*(g - 2)**2
Factor -36/5*g**4 - 456*g**3 - 18000 - 22800*g - 7940*g**2.
-4*(g + 30)**2*(3*g + 5)**2/5
Let n(m) = -8*m**3 - 30*m**2 - 61*m - 54. Let a(h) = -10*h**3 - 34*h**2 - 60*h - 54. Let o(b) = 5*a(b) - 6*n(b). Factor o(v).
-2*(v - 9)*(v + 1)*(v + 3)
Determine u, given that -4 + 118/3*u - 38/3*u**2 = 0.
2/19, 3
Solve -1/2*c**2 + 54 - 33/2*c = 0 for c.
-36, 3
Let u(w) be the third derivative of 3*w**6/160 + 2077*w**5/240 - 425*w**4/16 + 58*w**3/3 + 2*w**2 + 2069*w - 2. Find b such 