
Let c = 3/21250 + 535497/21250. Determine r so that c*r - 3/5*r**2 - 1323/5 = 0.
21
Let b(f) = 2*f**2 - 2. Let p(a) = -8*a**2 + 64*a + 376. Let w(h) = 6*b(h) + 2*p(h). Factor w(q).
-4*(q - 37)*(q + 5)
Suppose -5*v + v - 5*r + 67 = 0, 0 = 5*v + 2*r - 71. Factor s - 75 + v*s - 24*s + 5*s**2.
5*(s - 5)*(s + 3)
Let k = 2/9871 + 4836784/29613. Let m = 168 - k. Let m*c**3 + 0 - 2*c**5 + 8/3*c**2 - 8/3*c - 8/3*c**4 = 0. What is c?
-2, -1, 0, 2/3, 1
Let y be (-21)/(-105) + 9/5. Factor 4 + 28*d**y + 1258*d - 12 - 1406*d - 348*d**2.
-4*(5*d + 2)*(16*d + 1)
Suppose 0 = -3*u + 2*l + 73, -l = 5*u + 4*l - 105. Suppose 0 = 18*j - u*j + 10. Factor -5 + 6*b**2 - 9*b - 7 - 3*b**j.
3*(b - 4)*(b + 1)
Let s(u) be the first derivative of -2*u**3/9 - 16*u**2 - 184*u/3 - 1650. Factor s(q).
-2*(q + 2)*(q + 46)/3
Suppose -2*p + 4*p = 60. Let x be (-78)/(-20) - p/20. Factor x*a**2 - 3/5*a**3 + 12/5*a - 3/5*a**4 + 0.
-3*a*(a - 2)*(a + 1)*(a + 2)/5
Let f = 455829/182332 + 1/182332. Let f*g**5 + 0 - 25/2*g**2 - 15*g + 25/2*g**3 + 25/2*g**4 = 0. Calculate g.
-3, -2, -1, 0, 1
Suppose -238*y**4 + 16/3 - 436/3*y**3 + 436/3*y + 698/3*y**2 = 0. Calculate y.
-1, -4/7, -2/51, 1
Let f(r) be the first derivative of -2*r**6/27 + 4*r**5/3 + 2*r**4/3 - 328*r**3/27 - 26*r**2 - 20*r + 5849. What is c in f(c) = 0?
-1, 3, 15
Factor 372/7*y + 44/7*y**2 - 216/7.
4*(y + 9)*(11*y - 6)/7
Let x(o) be the first derivative of 8/9*o**3 + 2/3*o + 1/18*o**6 - 7 - 1/6*o**4 - 7/6*o**2 - 2/15*o**5. Let x(p) = 0. Calculate p.
-2, 1
Let g = 164/69 + 8/345. Let i = 113/35 + -10/7. What is n in g*n**2 + 0 + i*n + 3/5*n**3 = 0?
-3, -1, 0
Let a(j) be the third derivative of j**5/270 - 311*j**4/108 - 104*j**3/9 + 81*j**2 - 2. Factor a(n).
2*(n - 312)*(n + 1)/9
Suppose -2*o + 7 = -3*o. Let t be o/(-2)*(-4)/(-7). Factor -5*u - 26*u**t + 21*u**2 + 3 - 3.
-5*u*(u + 1)
Let p(l) = 40969*l - 81934. Let z be p(2). Factor 39/7*r - 1/7*r**5 - 6/7*r**z - 10/7 + 34/7*r**3 - 8*r**2.
-(r - 1)**4*(r + 10)/7
Let i(a) be the first derivative of a**3 - 17*a**2/2 + 12*a - 389. Let b be i(5). Factor 4/5*m + 2/5*m**b + 0.
2*m*(m + 2)/5
Suppose 56*q = -565 + 845. Determine y so that 0*y + 0*y**3 + 0 - 3/5*y**q + 9/5*y**4 - 12/5*y**2 = 0.
-1, 0, 2
Let z be -3*(2014/(-57))/(2/(-6)). Let j = z - -321. What is b in b**2 - 1/7*b**j + 9/7 - 15/7*b = 0?
1, 3
Solve 1281007856/3 + 1724*t**2 + 1486088*t + 2/3*t**3 = 0 for t.
-862
Let v(n) be the second derivative of 74*n**4/15 - 11*n**3/15 - 12*n**2/5 - 2049*n. What is y in v(y) = 0?
-1/4, 12/37
Let d be (-12951)/27*(3 - 2/1). Let l = 482 + d. Factor -l*j**2 - 8/3 + 6*j - j**3.
-(j - 1)*(j + 4)*(3*j - 2)/3
Let 8/7*n**2 + 0 + 10/7*n**3 + 0*n + 2/7*n**4 = 0. Calculate n.
-4, -1, 0
Let g = 84 + -175. Let x be 35/25 - g/(-65). Find j such that 1/2*j**3 - 1/8*j**4 + 0*j - 1/2*j**2 + x = 0.
0, 2
Let t be ((-3130)/(-35))/((-36)/105). Let f = t - -261. Factor 1/3*k**4 + 1/6*k - f*k**5 + 0 - 1/3*k**2 + 0*k**3.
-k*(k - 1)**3*(k + 1)/6
Let l be (3/(-6))/(4/8) + -3. Let h be l + (12 - 1 - 5). Factor -12 + 25*k - 9*k + k**h - 8*k - 2*k**2.
-(k - 6)*(k - 2)
Let z(n) be the first derivative of 2/27*n**3 + 20/9*n**2 + 38/9*n + 42. Solve z(a) = 0.
-19, -1
Suppose 0 = 3*k - 6, -2*k + 24 = -5*l + l. Let c be (-2)/(-4)*l*-4 - 0. Let 2*p**3 + 11 + p - 2*p - p**3 - c - p**2 = 0. Calculate p.
-1, 1
Let h(f) be the third derivative of 2*f**7/105 + 77*f**6/15 - 157*f**5/5 + 2*f**4/3 + 1256*f**3/3 - 5545*f**2. Find a, given that h(a) = 0.
-157, -1, 2
Let k be (300/160)/(-5)*(-8)/6. Let g(j) be the first derivative of -k*j**2 + 1/20*j**4 + 3/5*j + 1/15*j**3 + 1. Find p such that g(p) = 0.
-3, 1
Let i = -2161 + 2160. Let f be (7*i/(-7))/(4/6). Determine z so that -9/4*z**3 + 0 + 0*z - 3/4*z**4 - f*z**2 = 0.
-2, -1, 0
Suppose 90*q**4 + 5041*q**3 + 20*q**5 - 5133*q**3 - 18*q**5 = 0. What is q?
-46, 0, 1
Let c(r) be the first derivative of r**7/1260 + 7*r**6/180 + 19*r**5/90 + 73*r**3/3 + 150. Let o(l) be the third derivative of c(l). Solve o(x) = 0.
-19, -2, 0
Let c(r) be the second derivative of r**6/45 - 13*r**5/10 + 55*r**4/2 - 225*r**3 + 2245*r. Factor c(t).
2*t*(t - 15)**2*(t - 9)/3
Let p = 1309 + -1289. Suppose -p*q = 18 - 58. Factor 2/5*a**5 - 12/5*a**3 + 0*a**q + 2/5*a**4 + 0*a + 0.
2*a**3*(a - 2)*(a + 3)/5
Let l = -5144647/60 - -428721/5. Factor -2*o + l*o**2 + 12.
(o - 12)**2/12
What is w in 14*w**2 + 8*w**2 + w**3 - 46 + 38522*w - 38547*w = 0?
-23, -1, 2
Suppose 10*x - 15*x = 6*x + 2*x. Let f(s) be the second derivative of 15*s + 1/96*s**4 + 0 - 1/16*s**2 + x*s**3. Factor f(n).
(n - 1)*(n + 1)/8
Let h(t) be the third derivative of t**5/12 - 1705*t**4/8 - 4233*t**2. Let h(w) = 0. What is w?
0, 1023
Let y be ((-186)/36)/(3/(-6)) - (-11 + 28)/(-17). Factor -1/3*g**2 - y*g - 289/3.
-(g + 17)**2/3
Let k(f) be the second derivative of -5*f**7/168 + 3*f**6/8 - 19*f**5/16 - 35*f**4/16 + 35*f**3/3 + 30*f**2 + 2822*f - 2. Determine x, given that k(x) = 0.
-1, 3, 4
Let p(y) be the third derivative of y**7/105 - 41*y**6/30 - 17*y**5/6 + 83*y**4/6 - 70*y**2 + 7. Suppose p(k) = 0. Calculate k.
-2, 0, 1, 83
Let d(y) be the second derivative of y**5/60 + 29*y**4/12 + 841*y**3/6 - 32*y**2 - 33*y. Let z(a) be the first derivative of d(a). Factor z(o).
(o + 29)**2
Let b(v) be the second derivative of -1/50*v**5 - 1/45*v**4 + 0 - 17*v + 0*v**2 - 1/225*v**6 + 0*v**3. Solve b(s) = 0 for s.
-2, -1, 0
Let y = -191219/6 + 95617/3. Determine q so that q**3 - 2*q - 8*q**2 + y + q**5 + 11/2*q**4 = 0.
-5, -1, 1/2, 1
Determine j so that 3600 + 3*j**3 - 1453*j + 141*j**2 + 33*j**2 + 2968*j = 0.
-48, -5
What is u in -4/7*u**4 - 20/7*u**2 + 144/7 - 96/7*u + 24/7*u**3 = 0?
-2, 2, 3
Let j be 38/152 - (-4)/16. Let w(x) be the second derivative of -3/20*x**5 - 3*x**2 + 0 + 1/2*x**4 - 27*x + j*x**3. Solve w(t) = 0 for t.
-1, 1, 2
Let s(v) be the third derivative of -v**6/240 - 23*v**5/120 - 7*v**4/2 - 33*v**3 + 2*v**2 - 275. Factor s(r).
-(r + 6)**2*(r + 11)/2
Let b = -16 - -17. Let a be 2/(5 - (3 + b)). Factor -3/7*u**a - 27/7 + 18/7*u.
-3*(u - 3)**2/7
Let r be 60/(-280)*8/(-1758). Let s = r + 32806/10255. Factor -73/5*x**3 - s*x**4 + 324/5*x - 1/5*x**5 - 216/5 - 18/5*x**2.
-(x - 1)**2*(x + 6)**3/5
Let g(u) = -5*u**3 + 1072*u**2 - 425*u + 10. Let t(b) = 5*b**3 - 1071*b**2 + 424*b - 12. Let f(w) = 6*g(w) + 5*t(w). Factor f(l).
-l*(l - 215)*(5*l - 2)
Let q = -172420 + 172424. Factor 0 - 8/7*o**3 + 2/7*o**q - 4/7*o + 10/7*o**2.
2*o*(o - 2)*(o - 1)**2/7
What is y in -134*y**2 - 116*y**2 - 108*y + 246*y**2 - 7*y - 69*y + 188 = 0?
-47, 1
Determine t so that 4330/9 - 2/9*t**2 - 4328/9*t = 0.
-2165, 1
Let v(c) = -40*c**4 - 86*c**3 + 137*c**2 + 314*c - 223. Let p(l) = -5*l**4 - 11*l**3 + 17*l**2 + 39*l - 28. Let f(b) = -17*p(b) + 2*v(b). Solve f(t) = 0 for t.
-3, -2, 1
Let w be (1 + 6/(-4))*-6. Let b be -2*97/(-2) - (-2 + w). Factor 36*u - 3*u**2 - 75 + 30*u - b*u.
-3*(u + 5)**2
Let h be (-4)/26 - (-492)/156. Suppose -j - 2 = h, -5*g - 2*j = -350. Find t, given that 16*t**2 - g*t**3 - 24*t - 225 + 27*t**4 + 50*t**2 + 228 = 0.
1/3, 1
Suppose 118 - 214 = -106*h + 222. Let p(v) be the third derivative of -1/12*v**5 + 10/3*v**h - 5/8*v**4 + 0*v + 8*v**2 + 0. Factor p(t).
-5*(t - 1)*(t + 4)
Let p(n) be the first derivative of -4*n**5/5 - 12*n**4 + 460*n**3/3 + 252*n**2 - 3441. Determine i, given that p(i) = 0.
-18, -1, 0, 7
Factor 108/7 + 3/7*d - 3/7*d**3 - 108/7*d**2.
-3*(d - 1)*(d + 1)*(d + 36)/7
Suppose 5*f + 140 = 2*q, f - 2*f - 51 = -5*q. Let m be (-56)/f - 42/273. Factor -3/2 + 0*a + 3/8*a**m.
3*(a - 2)*(a + 2)/8
Suppose -225 - 119 = -84*x - 92. Let c(q) be the first derivative of -2/3*q + 19 + 2/9*q**2 + 2/27*q**x. Factor c(o).
2*(o - 1)*(o + 3)/9
Solve 546*i - 200*i + 507*i + 385*i + 27 + 37*i**2 - 238*i = 0.
-27, -1/37
Find v, given that -9/4*v**4 + 3/2*v + 65/4*v**2 - 14 - 1/4*v**5 - 5/4*v**3 = 0.
-7, -4, -1, 1, 2
Let f(r) be the second derivative of r**4/4 + 7*r**3/2 - 216*r**2 - 1273*r. Determine p so that f(p) = 0.
-16, 9
Let k(f) = 10*f**5 - 10*f**4 - 70*f**3 - 5*f**2 + 30*f + 15. Let c(b) = -b**5 - b**4 + 2*b**3 - b**2 - 2*b - 1. Let h(o) = -15*c(o) - k(o). Solve h(g) = 0.
-2, -1, 0
Let p(i) be the first derivative of -1/8*i**4 + 7/6*i**3 + 17/4*i**2 + 9/2*i - 8. Solve p(m) = 0.
-1, 9
Let o = -380697/4 + 95178. Factor 63/4*c**2 + 18*c**3 +