-f - 1/5*u**2 + 6/5*u = 0. Calculate u.
1, 5
Let g = -840 + 576. Let b = g + 1057/4. Suppose 1/2*o**2 - 3/4*o**3 + 0*o + 0 + b*o**4 = 0. Calculate o.
0, 1, 2
Factor -4/7*q**3 + 5164/7*q - 1712/7*q**2 - 3448/7.
-4*(q - 2)*(q - 1)*(q + 431)/7
Let y(t) be the first derivative of 5*t**2 - 28*t + 2/3*t**3 - 28. Factor y(a).
2*(a - 2)*(a + 7)
What is f in 0 - 2/11*f**2 + 56/11*f = 0?
0, 28
Suppose -1375*p = -1346*p. Let t(b) be the third derivative of 1/90*b**5 + 0 + p*b**3 + 14*b**2 + 0*b + 1/720*b**6 + 0*b**4. Find h such that t(h) = 0.
-4, 0
Let f = 2855/126 + 103/42. Suppose -14/9*c**3 - 332/9*c**2 - f*c + 92/9 = 0. What is c?
-23, -1, 2/7
Let o(v) = v**4 - v**3 + 2*v. Let l(i) = -4*i**5 - 760*i**4 - 35320*i**3 + 111356*i**2 - 75264*i. Let d(p) = l(p) - 4*o(p). Find n, given that d(n) = 0.
-97, 0, 1, 2
Let j(a) be the second derivative of a**4/4 - 28*a**3 + 1176*a**2 - 2*a + 1550. Suppose j(c) = 0. What is c?
28
Let i = 4330 + -30166/7. Suppose 4*v - 9 = -2*m + 9, -v - 2*m + 12 = 0. Solve -4/7*u**v - i + 48/7*u = 0.
6
Let z be (178/890 + 2/15)/(6/4). Factor 0 + 0*p - 4/9*p**2 + 2/9*p**4 + z*p**3.
2*p**2*(p - 1)*(p + 2)/9
Factor -97/3*a**3 + 0 + 0*a + 98/3*a**4 - 1/3*a**5 + 0*a**2.
-a**3*(a - 97)*(a - 1)/3
Let g = -2 + 4. Let s(j) = -2*j + 3*j - 2*j**g + 8*j**2 - 4*j - 10. Let c(i) = 5*i**2 - 2*i - 9. Let n(u) = -7*c(u) + 6*s(u). Factor n(v).
(v - 3)*(v - 1)
Let y(r) be the third derivative of r**8/11200 + 3*r**7/1400 - r**6/120 - 17*r**4/4 - r**3/6 - r**2 + 5. Let p(d) be the second derivative of y(d). Factor p(s).
3*s*(s - 1)*(s + 10)/5
Solve -26/5*m**2 + 2/5*m**3 - 72/5 + 16*m = 0.
2, 9
Let w(z) = -116*z**2 + 137*z + 12. Let h(m) = -580*m**2 + 684*m + 72. Let a(f) = -3*h(f) + 16*w(f). Let a(r) = 0. Calculate r.
6/29, 1
Suppose -3*o - 27 = 0, -3*a - 5*o = -42 + 45. Let n(s) be the first derivative of a*s - 2/3*s**3 - 20 + 6*s**2. Factor n(h).
-2*(h - 7)*(h + 1)
Let u(m) be the third derivative of 0*m - 1/120*m**5 - 131*m**2 - 675/4*m**3 + 0 - 15/8*m**4. Solve u(g) = 0.
-45
Solve -25/2*y**3 + 257/2*y - 93/2*y**2 - 70 + 1/2*y**4 = 0.
-5, 1, 28
Let b be (11 - 13)/(6/(-159)). Suppose -10*j = b*j - 189. Find p, given that -12/11*p + 0 + 2/11*p**j + 2/11*p**2 = 0.
-3, 0, 2
Let q(a) = 1140*a - 18195. Let v be q(16). Let f(x) be the second derivative of 0 + 12*x**2 - 14/3*x**3 + 0*x**4 + 1/5*x**5 + v*x. Determine i so that f(i) = 0.
-3, 1, 2
Let 217*k**4 + 343*k - 2*k**5 + 367*k - 628*k**2 - 170 - 171*k**4 - 80 + 124*k**3 = 0. What is k?
-5, 1, 25
Let p(g) be the second derivative of -g**6/240 + 211*g**5/160 + 425*g**4/96 + 71*g**3/16 + 49*g + 2. Suppose p(d) = 0. What is d?
-1, 0, 213
Let x(k) = 8*k**3 - k**2 + 2. Let z be x(2). Let q = -57 + z. Factor -53*w**2 - q*w**4 - 47*w**2 + 90*w**2 + 15*w**3.
-5*w**2*(w - 2)*(w - 1)
Let 0 - 17/7*a**2 + 1/7*a**3 + 15/7*a + 1/7*a**4 = 0. What is a?
-5, 0, 1, 3
Let v(f) be the third derivative of 0*f - 118*f**2 - 1/2*f**4 + 0 + 2*f**3 + 1/20*f**5. Let v(o) = 0. What is o?
2
Let n(i) be the first derivative of 0*i - 5/4*i**4 - 38 + 0*i**3 + 0*i**2. Factor n(z).
-5*z**3
Let x(u) be the first derivative of u**9/3024 + u**8/420 - u**7/840 - u**6/90 - u**3/3 - 77*u - 151. Let i(l) be the third derivative of x(l). Solve i(b) = 0.
-4, -1, 0, 1
Let c be ((-836)/(-198))/((-3)/(-252)*7) + -8. Factor 400/3*l**2 + c + 560/3*l - 500/3*l**3.
-4*(5*l - 8)*(5*l + 2)**2/3
Let a(s) be the second derivative of -4/35*s**5 + 0*s**3 + 0*s**2 - 8/21*s**4 - 1/105*s**6 - 13 - s. Determine r so that a(r) = 0.
-4, 0
Let u be (-1)/4 + ((-7215)/(-296) - 24). Let z(y) be the first derivative of 0*y**2 + 1/6*y**3 - 1/5*y**5 + 17 + 0*y - 1/16*y**4 + u*y**6. Factor z(d).
d**2*(d - 1)**2*(3*d + 2)/4
Let 486*y**4 + 315*y**3 - 5/2 + 43*y - 467/2*y**2 - 108*y**5 = 0. What is y?
-1, 1/6, 5
Let g(z) = -8*z**4 - 28*z**3 + 61*z**2 - 48*z + 3. Let x(s) = -12*s**4 - 28*s**3 + 60*s**2 - 48*s + 4. Let l(r) = 4*g(r) - 3*x(r). Let l(i) = 0. Calculate i.
0, 2, 3
Let m(o) be the first derivative of 1/3*o**3 - 111 + 7/2*o**2 - 8*o. Factor m(c).
(c - 1)*(c + 8)
Suppose -w - 3 = 0, 3340*c = 3339*c + 5*w + 15. Factor 0 + 2/7*m**3 + c*m + 6/7*m**2.
2*m**2*(m + 3)/7
Solve 2*b**3 + 1/7*b**4 - 1/7*b**2 - 2*b + 0 = 0.
-14, -1, 0, 1
Let n(f) = f**3 + f**2 - f. Suppose -3*l - 5*o = -43, 3*l - o = 2*o + 3. Let c(d) = -27*d**3 + 38*d**2 + 2*d. Let u(i) = l*n(i) + c(i). Factor u(h).
-h*(h - 2)*(21*h - 2)
Let p = 3891 + -3891. Let k(r) be the second derivative of -3/2*r**4 - 9/2*r**3 + 0 + 16*r - 3/20*r**5 + p*r**2. Let k(q) = 0. What is q?
-3, 0
Let n(l) = -l + 6. Let b be n(0). Let a be 4/(20/2 - 9). Factor -6*c - b*c**2 + 8*c**2 + 0*c + a.
2*(c - 2)*(c - 1)
Let f(r) be the third derivative of -5/12*r**3 - 1/72*r**4 + 0*r + 0 + 108*r**2 + 1/360*r**5. Determine k, given that f(k) = 0.
-3, 5
Let o be 4 + 5/(-10)*-40. Find z, given that 3*z**2 + 64 - 61 - 27 - o + 18*z = 0.
-8, 2
Suppose -14*f = 46*f + f. Let o(p) be the second derivative of 7*p + f + 1/3*p**3 - 4/5*p**2 - 1/30*p**4. Factor o(c).
-2*(c - 4)*(c - 1)/5
Let q be (-8 + 584/72)*27. Determine r so that -3*r**3 + 0 + 4*r**3 + 0 + 3*r**q = 0.
0
Let z(v) = 357*v - 1069. Let p be z(3). Let h be (-16 + 15)*(-2)/8. Factor -25/4*t - h*t**3 + 0 + 5/2*t**p.
-t*(t - 5)**2/4
Suppose -56*v - 57*v - 12 = -117*v. Let g(y) be the second derivative of -1/24*y**4 - 12*y - 3/2*y**2 + 0 - 5/12*y**v. Let g(o) = 0. What is o?
-3, -2
Let x(d) be the second derivative of 6*d**2 + 121*d - 6*d**3 - 25/4*d**4 + 0 - 27/20*d**5. Find a such that x(a) = 0.
-2, -1, 2/9
Let s(t) = 5*t**2 - 4*t + 2. Let h be s(1). Solve -8*x + 0*x**3 - 32 - h*x**3 + 20*x**2 + 0*x**3 - x**3 = 0.
-1, 2, 4
Let b = -2664735/7 - -380677. Factor b*y + 4/7*y**2 + 0.
4*y*(y + 1)/7
Factor 4*m**2 - 4*m**2 + 5*m**2 + 106165*m - 97895*m.
5*m*(m + 1654)
Let k(z) be the third derivative of -z**7/10080 - z**6/240 - z**4/12 + z**3/3 + 52*z**2. Let l(i) be the second derivative of k(i). Factor l(r).
-r*(r + 12)/4
Let v = -239 + 243. Suppose -v*c + 1 = -7. Factor -1/2*k**4 + 5/8*k**3 + 0*k + 1/8*k**5 - 1/4*k**c + 0.
k**2*(k - 2)*(k - 1)**2/8
Let l(o) = -6*o**2 - 2*o - 2. Let y(g) = 6 + 3*g - 4*g - 5 + g**2. Let w = -66 - -67. Let z(m) = w*l(m) + 2*y(m). Factor z(p).
-4*p*(p + 1)
Let 1/5*i**2 - 37/5*i - 164/5 = 0. What is i?
-4, 41
Let f(w) be the second derivative of w**6/10 + 31*w**5/10 - 401*w**4/12 + 68*w**3 + 234*w**2 + 166*w - 1. Factor f(l).
(l - 3)**2*(l + 26)*(3*l + 2)
Let l(c) = -2*c**3 + 6*c**2 + 7*c + 6. Let y be l(4). Factor 4*n**3 + 13 - 8*n**3 - y*n - 10*n**2 - 9.
-2*(n + 1)*(n + 2)*(2*n - 1)
Solve 941*o - 146533*o**4 + 146534*o**4 + 540 - 142*o**3 + 5*o**3 + 263*o**2 = 0 for o.
-1, 4, 135
Let c be 976/4636*38/22. Factor c*u**2 + 0 - 3/11*u - 1/11*u**3.
-u*(u - 3)*(u - 1)/11
Let k(w) be the third derivative of -3087/22*w**5 - 1/22*w**7 + 1/3696*w**8 - 1361367/22*w**3 + 0*w + 147/44*w**6 - 180 + 324135/88*w**4 - w**2. Factor k(i).
(i - 21)**5/11
Let s(v) = v**2 - 20*v - 136. Let r be s(-13). Suppose -294*p + r*p + 4 = 0. Determine i so that 0 - 3/8*i**p + 0*i**2 + 0*i + 3/8*i**3 = 0.
0, 1
Let -20/3*n**4 + 0*n + 2/9*n**5 + 0 + 0*n**2 + 32*n**3 = 0. Calculate n.
0, 6, 24
Factor -5/8*l**4 + 12*l**2 + 13/8*l**3 + 9/2*l + 0.
-l*(l - 6)*(l + 3)*(5*l + 2)/8
Let i(k) = 37 + 2*k - k - 6*k. Let w be i(7). Factor -20 + 25*z + 60*z**2 + 65*z**w - 130*z**2.
-5*(z - 4)*(z - 1)
Suppose 22*v - 21*v - 6 = -2*i, -44 = -5*v + 4*i. Factor -747*c**2 - 1 + 746*c**2 + v*c + 1.
-c*(c - 8)
Let b(h) = -62*h**2 + 273*h + 33. Let l(j) = 21*j**2 - 91*j - 12. Let k(f) = 6*b(f) + 17*l(f). Factor k(g).
-(g - 6)*(15*g - 1)
Suppose 0 = 4*d + 12 - 20. Factor -43 - 151*m - 7 + 166*m + 5*m**d.
5*(m - 2)*(m + 5)
Let z(f) be the first derivative of -2*f**3/3 - 149*f**2 - 588*f - 4281. Solve z(k) = 0.
-147, -2
Let j(v) = -5*v**3 + 165*v**2 - 500*v + 400. Let t(q) = -3*q**3 + 110*q**2 - 334*q + 266. Let c(d) = -7*j(d) + 10*t(d). Solve c(o) = 0.
2, 7
Let y(a) be the first derivative of -a**3 + 2820*a**2 + 5422. Factor y(q).
-3*q*(q - 1880)
Let j(p) = -30*p**4 + 82*p**3 - 29*p**2 - 23*p. Let x(l) = 147*l**4 - 411*l**3 + 144*l**2 + 117*l. Let k(q) = -29*j(q) - 6*x(q). Solve k(n) = 0 for n.
-1/2, 0, 5/6, 7
Factor -8*i**4 + 42*i**4 - 2*i**5 + 72702*i**2 - 286*i**3 - 180*i**4 - 72844*i**2.
-2*i**2*(i + 1)**2*(