*t**2*(t + 19)*(3*t + 2)/5
Let g(d) = 3*d - 27. Let l be g(10). Suppose -h**2 + 0 - 5*h**2 + 0 + 2*h**l + 4*h = 0. What is h?
0, 1, 2
Let l(n) be the third derivative of -99*n**8/112 - 1189*n**7/175 - 423*n**6/50 - 102*n**5/25 - 4*n**4/5 - n**2 + 91. Determine p, given that l(p) = 0.
-4, -2/5, -2/9, -2/11, 0
Let s(q) = q**3 + 4*q**2 + 3*q. Let r be s(-2). Let d be (26/(-15) - (-1)/3) + r. Factor 3/5*l**2 + d*l**3 - 3/5*l - 3/5.
3*(l - 1)*(l + 1)**2/5
Let p be 16/20*-2 - 2337/(-570). Factor -8*q + 25/2*q**3 - p*q**2 - 2.
(q - 1)*(5*q + 2)**2/2
Let p(s) = s**3 - 15*s**2 - 31*s - 51. Let k be p(17). Solve 0*z**3 + 3/5*z**2 - 3/5*z**4 + 0 + k*z = 0 for z.
-1, 0, 1
Let u = -2/3553 - -213206/46189. What is t in -2/13*t**3 - 600/13*t - u*t**2 - 2000/13 = 0?
-10
Let h(n) = n**3 - 6*n**2 + 2*n - 7. Let p be h(6). Suppose 0 = p*y + 3*u - 29, -31 = -4*y - 4*u - 3. Factor 0*k**3 + y*k**3 + k**4 - 4 - 2*k - 2*k**3 + 3.
(k - 1)*(k + 1)**3
Let c = -62 - -64. Find z such that 11*z + 4*z**2 + z + 3*z**c - 3*z**2 = 0.
-3, 0
Suppose 4*c - 3*i = -4, 4*c + 1 - 5 = i. Factor 3/4*s**3 + 3*s**c + 0 + 9/4*s.
3*s*(s + 1)*(s + 3)/4
Let h(g) be the third derivative of 13*g**2 + 0*g**4 + 0 + 0*g - 1/240*g**6 + 0*g**3 + 0*g**5. Determine j so that h(j) = 0.
0
Suppose -5 = 4*w - t, 5*w - t + 1 = -4. Let s be -3 - -1 - -6 - 1 - 1 - -1. Find d, given that 0 - 4/5*d**s + w*d - 6/5*d**5 + 0*d**2 + 14/5*d**4 = 0.
0, 1/3, 2
Let k = 11776 + -11776. Factor 4/3*l**2 + k + 8/3*l.
4*l*(l + 2)/3
Let m = 713/5 - 4971/35. Let k(a) be the first derivative of 3 + m*a + 2/35*a**5 + 6/7*a**3 - 5/14*a**4 - a**2. Find c such that k(c) = 0.
1, 2
Let d(s) be the third derivative of -s**5/12 - s**4/12 + 11*s**3/3 - 28*s**2. Let j(w) = 4*w**2 + 3*w - 21. Let k(z) = -5*d(z) - 6*j(z). Factor k(q).
(q - 4)**2
Let r = 8/142895 + 39467407/3429480. Let x = r + -91/8. Solve -x*b - 4/15*b**2 + 0 - 8/15*b**4 + 14/15*b**3 = 0 for b.
-1/4, 0, 1
Suppose 4*v = -v. Suppose -2 = -v*p - p. Factor 6*c**p - c**4 - 4*c**4 - 3 + 2*c**4.
-3*(c - 1)**2*(c + 1)**2
Let g = -13334 + 13336. Factor 3/7*i**g - 6/7 - 3/7*i.
3*(i - 2)*(i + 1)/7
Factor 1/2*o**3 + 3/2*o**2 + o + 0.
o*(o + 1)*(o + 2)/2
Let m(x) = -x**3 - 7*x**2 - 7*x - 3. Let g be m(-6). Let h = 127/468 + -5/234. Let -1/4*l**2 + h*l**g - 1/4*l + 1/4 = 0. Calculate l.
-1, 1
Let d(y) = 2*y + 18. Let i(q) = q**2 + q - 9. Let c be i(0). Let w be d(c). Solve 1/6*j**4 - 1/6*j**2 + w - 1/6*j**3 + 1/6*j = 0.
-1, 0, 1
Let z = -13 - -24. Suppose 4*m - z = 57. Factor -8*b**2 + 0 - 12 + 4*b**2 + b - m*b.
-4*(b + 1)*(b + 3)
Let b be (1/((-3)/186))/(-10) + -6. Factor 4/5 + 4/5*k + b*k**2.
(k + 2)**2/5
Let 6/5*s**4 - 14/5*s**3 - 4/5 + 14/5*s - 2/5*s**2 = 0. Calculate s.
-1, 1/3, 1, 2
Suppose -x - 1 = 4*u + 3, 5*u = -x - 6. Factor 3*d**x + 0*d**3 - 3*d**5 + 7*d**3 - 7*d**3.
-3*d**4*(d - 1)
Let k(w) be the second derivative of w**7/7 + w**6/2 - 3*w**5/5 - 11*w**4/4 + 2*w**3 + 6*w**2 + 22*w - 1. Determine q so that k(q) = 0.
-2, -1/2, 1
Let n(h) = 2*h**3 - 11*h**2 + 104*h - 491. Let z be n(5). Factor -1/2*c**2 + c - c**3 + 0 + 1/2*c**z.
c*(c - 2)*(c - 1)*(c + 1)/2
Let a(w) be the second derivative of -w**7/2520 + w**6/360 - w**5/180 + 19*w**3/6 - 18*w. Let i(o) be the second derivative of a(o). Factor i(t).
-t*(t - 2)*(t - 1)/3
Let k(q) be the first derivative of q**3/9 + 5*q**2/2 + 44*q/3 - 614. Factor k(x).
(x + 4)*(x + 11)/3
Suppose -h = 3*k + 3 - 18, 107 = 5*h - k. Find j such that 19*j + 29*j + 30 - 13*j + 76*j + h*j**2 = 0.
-5, -2/7
Let v be (-38)/(-33) + 6/33. Let n = 1502 + -1500. Solve -2/3 + v*u - 2/3*u**n = 0.
1
Let r(g) be the third derivative of -g**7/140 - g**6/40 + 11*g**5/40 + 3*g**4/4 + 84*g**2. Suppose r(q) = 0. Calculate q.
-4, -1, 0, 3
Suppose 15*f - 4 - 281 = 0. Suppose -f*n - 4 = -21*n. Suppose 0*y - 1/3*y**n + 1/3 = 0. Calculate y.
-1, 1
Let o(s) = 11 - 10 + 4*s - 5 - 18. Let p be o(6). What is r in 2/9*r - 2/9*r**4 + 2/9*r**p - 2/9*r**3 + 0 = 0?
-1, 0, 1
Let f(h) = -5*h - 1. Let m be f(-1). Solve 8*a + m*a**2 - 5*a - 7*a - 12*a = 0 for a.
0, 4
Let a be (4/(-20))/((-54)/90). Let w be 1 + (-2 - 1) + 2. Suppose -a*s**3 + 2/3*s + w - 1/3*s**2 = 0. Calculate s.
-2, 0, 1
Suppose -4*g - 4*q - 418 = q, -g = -q + 100. Let m = g - -716/7. Factor -1/7*n**2 - m*n + 0.
-n*(n + 2)/7
Suppose 83*p**3 + 4*p**4 + 45*p - 4*p**5 + 65*p**2 - p**4 - 266*p**2 + 2*p**4 = 0. What is p?
-5, 0, 1/4, 3
Factor -2/3*u**2 - 8/3*u - 8/3.
-2*(u + 2)**2/3
Let r(s) be the first derivative of 27*s**5/5 + 141*s**4/4 - 206*s**3 - 72*s**2 - 190. Factor r(g).
3*g*(g - 3)*(g + 8)*(9*g + 2)
Let u(g) be the third derivative of 24*g**2 - 1/360*g**5 + 0*g**3 + 1/144*g**4 + 1/1260*g**7 - 1/720*g**6 + 0 + 0*g. Let u(x) = 0. Calculate x.
-1, 0, 1
Suppose -3*l - 1 = 4*t - 10, -2*t = 0. Let b be l*(-2)/(-60)*4. Determine j, given that b*j**2 + 0 + 0*j = 0.
0
Factor 10/7*z**3 - 6*z + 2/7*z**2 - 36/7 + 2/7*z**4.
2*(z - 2)*(z + 1)*(z + 3)**2/7
Solve 790342*h**2 + h**5 + 8680*h**3 + 3*h**5 + 1334698*h**2 + 964*h**4 + 69081*h**3 + 2067200*h + 512000 = 0 for h.
-80, -1/2
Let u(s) = 3*s**2 + 70*s + 9. Let x(n) = -2*n**2 - 46*n - 6. Let a(c) = -5*u(c) - 8*x(c). Let f be a(-18). Find r, given that 0 + 0*r**2 - 1/4*r + 1/4*r**f = 0.
-1, 0, 1
Suppose 36 + 144 = 60*k. Suppose -4/3*p + 4/3*p**2 + 4/3*p**k - 4/3 = 0. Calculate p.
-1, 1
Let c = -78 - -76. Let n be 16/120*(c - -5). Factor 4/5*t - n*t**2 - 2/5.
-2*(t - 1)**2/5
Let z(y) be the second derivative of -y**5/5 - 8*y**4 + 2*y**3/3 + 48*y**2 - 11*y + 4. Factor z(w).
-4*(w - 1)*(w + 1)*(w + 24)
Let d(t) be the first derivative of t**6/6 - t**5 + 25*t**4/12 - 5*t**3/3 + 4*t + 1. Let a(m) be the first derivative of d(m). Factor a(q).
5*q*(q - 2)*(q - 1)**2
Let h = -18507/2168 - 24/271. Let b = h - -507/56. Factor 6/7*v**3 + 0 + 3/7*v**4 - 6/7*v - b*v**2.
3*v*(v - 1)*(v + 1)*(v + 2)/7
Let b(p) be the second derivative of p**6/80 + 3*p**5/160 - 5*p**4/32 + 3*p**3/16 + 82*p. Factor b(q).
3*q*(q - 1)**2*(q + 3)/8
Let t(x) = -x**3 + 11*x**2 + 12*x + 2. Let q be t(12). Determine p so that p**5 - 2*p**4 + 7*p**4 + q*p**2 - 3*p**3 - 5*p**4 = 0.
-2, 0, 1
Let z be 8/10 + 21/5 + -5. Factor -1/2*s**5 + 3/2*s**3 + s**2 + 0*s**4 + 0 + z*s.
-s**2*(s - 2)*(s + 1)**2/2
Let n(v) be the second derivative of v**7/315 + 2*v**6/75 + 13*v**5/150 + 2*v**4/15 + 4*v**3/45 + 33*v + 1. Factor n(b).
2*b*(b + 1)**2*(b + 2)**2/15
Let q(r) be the first derivative of -28 + 81/2*r**2 + 41/3*r**4 - 41*r**3 - 18*r + 16/3*r**5 - 32/9*r**6. Suppose q(c) = 0. Calculate c.
-2, 3/4, 1
Let a(w) be the third derivative of -1/120*w**6 + 0*w**3 - 31*w**2 + 1/80*w**5 + 0 + 1/840*w**7 + 0*w**4 + 0*w. Factor a(l).
l**2*(l - 3)*(l - 1)/4
Let w(b) be the second derivative of 3*b**5/20 - b**4/2 - 10*b**3 - 36*b**2 + 84*b. Find h, given that w(h) = 0.
-2, 6
Let 51*z + 405*z**3 - 117 - 191*z + 77 - 200*z - 630*z**2 = 0. Calculate z.
-2/9, 2
Let f(u) = 8*u - 46. Let b be f(6). Find s, given that -9 - 5*s**2 - 6*s**2 + 3*s**3 + 21*s - 2*s**b - 2*s**2 = 0.
1, 3
Factor 158/3 + 160/3*i + 2/3*i**2.
2*(i + 1)*(i + 79)/3
Suppose 17 + 7 = -p. Let y(f) = f**2 + 23*f - 21. Let j be y(p). Solve 2/5*x**j + 2*x + 4/5 + 8/5*x**2 = 0 for x.
-2, -1
Let l(a) be the second derivative of -1/9*a**2 + 0 + 1/9*a**3 - 1/18*a**4 + 1/90*a**5 + 19*a. What is t in l(t) = 0?
1
Let b = 25 + -23. Factor -13*o**b - 55*o - 5*o + 18 + 2 - 22*o**2.
-5*(o + 2)*(7*o - 2)
Let f(l) be the second derivative of -l**4/30 + 2*l**3/3 - 16*l**2/5 + 40*l + 3. Factor f(a).
-2*(a - 8)*(a - 2)/5
Let m be ((-1855)/(-56))/(-5) - -10. Factor -15/2*a - 45/4*a**3 + 3/2 + 111/8*a**2 + m*a**4.
3*(a - 1)**2*(3*a - 2)**2/8
Factor 1 + 7/4*o**3 + 2*o - 19/4*o**2.
(o - 2)*(o - 1)*(7*o + 2)/4
Factor -506/9*g**2 - 8/9*g**4 - 18 - 68*g + 136/9*g**3.
-2*(g - 9)**2*(2*g + 1)**2/9
Let f be 190/(-8) + (-2)/(-32)*-4. Let x be ((-78)/f - 4)*(-16)/9. Determine k, given that -6*k**3 - 4/3*k**2 + x + 6*k = 0.
-1, -2/9, 1
Let h(y) = -13*y**2 + 5*y + 20. Let w(b) = -7*b**2 + 3*b + 10. Let a(c) = 6*h(c) - 11*w(c). Factor a(r).
-(r - 2)*(r + 5)
Suppose -4*z = -7*z + 12. Suppose y + y = 0. Find s such that -3*s**4 + y*s**2 + 12*s**z + 9*s**3 + 0*s**4 + 3*s**2 + 3*s**5 = 0.
-1, 0
Factor 3*l**2 - 9 - 3/2*l**3 + 15/2*l.
-3*(l - 3)*(l - 1)*(l + 2)/2
Let k(f) = -7*f**3 - 4*f**2 - 5*f - 8. Let h(