y**2 + 0 = 0.
0, 1/2
Let t be (4 - 7) + (-9)/(-2) + -1. Let n(m) be the first derivative of -1/6*m**3 + 3/8*m**4 + 0*m - t*m**2 - 6. Solve n(o) = 0 for o.
-2/3, 0, 1
Let o(f) = f**2 - 10*f + 3. Let u be o(10). Suppose 0 = k + k - 6. Solve 7*s**4 + 39*s**u - 2*s**5 - 39*s**k - 3*s**4 = 0 for s.
0, 2
Let t = -2507/38 + 1263/19. Solve 1/2 + t*i**2 - i = 0 for i.
1
Let k(j) be the third derivative of j**5/12 + 5*j**4/8 + 5*j**3/3 - 40*j**2. Solve k(b) = 0 for b.
-2, -1
Let k be (-4 + 1385/345)*6/(-4). Let y = 43/138 - k. Determine o, given that y*o + 0 - 1/3*o**3 + 1/3*o**2 - 1/3*o**4 = 0.
-1, 0, 1
Solve 120/7*k - 12*k**2 - 6/7*k**3 + 3600/7 = 0 for k.
-10, 6
Let t be 27/(972/48) + (-2)/15. Let k(q) be the first derivative of -12 + 2/5*q**2 - t*q - 2/45*q**3. Factor k(n).
-2*(n - 3)**2/15
Let i(o) be the second derivative of -1/14*o**3 + 0 + 1/84*o**4 - 14*o + 1/7*o**2. Factor i(r).
(r - 2)*(r - 1)/7
Suppose 0 = 3*h - 5*f - 705, -218 = -h - 3*f - f. Let q = h + -228. Factor 1/3*d**q + 1/3*d - 2/3.
(d - 1)*(d + 2)/3
Let m = -173/14 + 90/7. Let t(h) be the second derivative of -1/6*h**3 + 0 - 1/42*h**7 + 1/30*h**6 - 2*h + m*h**2 + 1/10*h**5 - 1/6*h**4. Factor t(v).
-(v - 1)**3*(v + 1)**2
Let a be 57/(-27) + 2 - 8400/(-36720). Solve 20/17 - a*y**2 - 6/17*y = 0.
-5, 2
Let u(q) be the first derivative of -q**4 + 7*q**3/6 + q**2/4 + 906. What is o in u(o) = 0?
-1/8, 0, 1
Let z(l) be the third derivative of -l**5/210 + 11*l**4/21 + 11*l**2 + l. Factor z(d).
-2*d*(d - 44)/7
Let j(x) be the first derivative of -3*x**4/20 + 21*x**3/5 - 64. Suppose j(z) = 0. Calculate z.
0, 21
Let z = 24158 - 169079/7. Factor 18/7*t + z + 3/7*t**2.
3*(t + 3)**2/7
Determine m, given that 124/3*m + 0 - 122/3*m**2 - 2/3*m**3 = 0.
-62, 0, 1
Factor 3*t**2 - 3/4*t**4 + 6*t - 3/2*t**3 + 0.
-3*t*(t - 2)*(t + 2)**2/4
Let i = 1430/3 + -474. Suppose 4*f**3 - 20/3*f**2 + i*f + 4/3*f**4 - 4/3*f**5 + 0 = 0. Calculate f.
-2, 0, 1
Let o(b) be the first derivative of -2*b**5/5 + 4*b**3/3 - 2*b + 259. Find p, given that o(p) = 0.
-1, 1
Let j(o) be the third derivative of o**6/160 - 9*o**5/40 + 105*o**4/32 - 25*o**3 + 513*o**2. Factor j(d).
3*(d - 8)*(d - 5)**2/4
Let n(t) = 31*t**2 - t - 1. Let y be n(2). Let q = -117 + y. What is j in 0*j + 0 - 1/3*j**2 - 2/3*j**3 - 1/3*j**q = 0?
-1, 0
What is f in -165/8 + 3/8*f**3 - 171/8*f**2 + 333/8*f = 0?
1, 55
Let x(f) be the third derivative of f**7/5460 - f**6/1170 - 4*f**3/3 + 5*f**2. Let y(z) be the first derivative of x(z). Determine h, given that y(h) = 0.
0, 2
Let m(w) be the third derivative of 0*w**3 + 51*w**2 - 1/270*w**6 + 0*w + 0 - 1/270*w**5 + 1/108*w**4. Suppose m(h) = 0. Calculate h.
-1, 0, 1/2
Let a(c) = c**3 - 13*c**2 + 12*c + 10. Let b be a(12). Suppose -m - 4*w = -b, 6 = 2*m - w + 2*w. Factor -3*g**2 - 6*g**2 + 15*g**m - 3*g**3.
-3*g**2*(g - 2)
Let v be (-4)/5 + 552/460. Factor -2/5*b - v*b**2 + 0.
-2*b*(b + 1)/5
Let z(k) = 13*k**3 - k**2 + 3*k - 4. Let w be z(2). Let f = 106 - w. Let 0*o + 1/2*o**3 + 1/4*o**f + 1/4*o**2 + 0 = 0. Calculate o.
-1, 0
Factor 1/6*s**2 + 1/3*s - 1/2.
(s - 1)*(s + 3)/6
Let l(q) = 2*q**3 - 6*q**2 + 18*q + 9. Let f(r) = -2*r**2 - 3. Let j(h) = -3*f(h) - l(h). Factor j(k).
-2*k*(k - 3)**2
Let b = 9387 - 46928/5. Factor -6/5*l**2 - b*l**3 + 32/5*l - 1/5*l**4 + 32/5.
-(l - 2)*(l + 1)*(l + 4)**2/5
Let t(f) = 2 + 0*f**3 - 1 + f**3 - f**4 + 0*f**3. Let c(d) = -6*d**4 - 14*d**3 - 20*d**2 - 8*d + 2. Let m(r) = -c(r) + 2*t(r). Find i, given that m(i) = 0.
-2, -1, 0
Let j(v) be the first derivative of -2*v**6/5 - 2*v**5/25 + 18*v**4/5 + 36*v**3/5 + 26*v**2/5 + 6*v/5 - 590. Determine q, given that j(q) = 0.
-1, -1/6, 3
Let j(z) be the second derivative of 1/30*z**6 - 1/9*z**4 + 0*z**3 - 25*z + 0*z**2 + 0*z**5 + 0 + 1/126*z**7. Solve j(l) = 0.
-2, 0, 1
Let s(u) = -u**3 - u**2 + 2*u + 3. Suppose -40 = -5*z - 50. Let a be s(z). Find g, given that 2/3*g - 1/3*g**5 + 0 + g**a - 1/3*g**4 + 5/3*g**2 = 0.
-1, 0, 2
Let j(d) be the third derivative of -13*d**7/1050 - 11*d**6/600 + d**5/20 + 11*d**4/120 - d**3/15 + 85*d**2. What is h in j(h) = 0?
-1, 2/13, 1
Suppose -3*b - h - 22 = -24, -3*h - 12 = 3*b. Determine w, given that -54/7*w**b + 0 - 48/7*w**2 - 8/7*w = 0.
-2/3, -2/9, 0
Suppose 2/5*w - 2/5*w**2 + 0 = 0. Calculate w.
0, 1
Let w = 9959/5684 + -3/1421. Let b be 108/40 - 2/10. Determine y so that -3/4*y**4 + 1 - w*y**2 - b*y**3 + y = 0.
-2, -1, 2/3
Let n(p) be the first derivative of p**3/3 - 7*p**2 + 33*p - 186. Factor n(w).
(w - 11)*(w - 3)
Let c(n) be the second derivative of -7*n**5/220 + n**4/66 - 170*n. Factor c(a).
-a**2*(7*a - 2)/11
Let y be (48/112)/(2/14). Find o such that 4*o**y - 4*o**3 + 4*o**3 + 4*o**2 = 0.
-1, 0
Let h(d) be the first derivative of -2/9*d + 1/6*d**2 + 0*d**3 + 12 - 1/36*d**4. Factor h(v).
-(v - 1)**2*(v + 2)/9
Let l(k) be the first derivative of -36 - 784*k - 56*k**2 - 4/3*k**3. Factor l(v).
-4*(v + 14)**2
Factor -2*p + 2/5*p**2 + 8/5.
2*(p - 4)*(p - 1)/5
Let j = 503 - 503. Let 0*i + j - 15/2*i**5 - 18*i**2 + 69/2*i**4 - 30*i**3 = 0. Calculate i.
-2/5, 0, 2, 3
Let z = 13934/33 - 2247730/5313. Let b = z - -32/23. Factor 0 + 8/7*p**4 - 2/7*p - b*p**2 + 6/7*p**3 - 8/7*p**5.
-2*p*(p - 1)**2*(2*p + 1)**2/7
Let i(q) = -36*q**4 - 40*q**3 + 20*q**2 + 3*q. Let u(a) = -24*a**4 - 27*a**3 + 14*a**2 + 2*a. Let o(h) = 5*i(h) - 7*u(h). Factor o(c).
-c*(c + 1)*(3*c - 1)*(4*c + 1)
Let n = 175/27 - 166/27. Suppose 0 + 7/6*f**4 + 11/6*f**2 - n*f - 8/3*f**3 = 0. Calculate f.
0, 2/7, 1
Let v(g) be the third derivative of g**7/945 + g**6/45 + 11*g**5/270 - 37*g**2. Factor v(h).
2*h**2*(h + 1)*(h + 11)/9
Let p be 58/145*7/14. Let 5 - 9/5*q**2 + p*q**3 + 3*q = 0. What is q?
-1, 5
Let v(q) = 2*q**2 - 68*q + 5. Suppose 28*x = 5*x + 782. Let t be v(x). What is g in 9/4*g**5 + 13/4*g**3 + 0 + t*g**4 + 1/2*g**2 + 0*g = 0?
-1, -2/9, 0
Suppose 0*i**2 - 16*i**2 - 200 - 53224*i + 52420*i = 0. Calculate i.
-50, -1/4
Find p, given that 6/5 + 21/5*p + 27/5*p**2 + 3*p**3 + 3/5*p**4 = 0.
-2, -1
Let l(u) be the third derivative of u**8/1680 + u**7/2520 - u**6/180 - u**5/120 - u**4/8 + 14*u**2. Let i(c) be the second derivative of l(c). Factor i(h).
(h - 1)*(h + 1)*(4*h + 1)
Let g(q) = -q**4 + q**3 - q**2 - q - 2. Let w(b) = -4*b**4 + 44*b**3 - 12*b**2 - 44*b - 16. Let p(v) = 8*g(v) - w(v). What is c in p(c) = 0?
-9, -1, 0, 1
Let u(f) be the first derivative of 20/3*f**3 - 27 - 5/2*f**2 + 4*f**5 - 5/6*f**6 - 15/2*f**4 + 0*f. Determine y so that u(y) = 0.
0, 1
Let v(k) be the second derivative of -1/28*k**7 - 2*k + 1/2*k**3 + 9/40*k**5 - 5/8*k**4 + 1/20*k**6 + 0*k**2 + 0. Factor v(w).
-3*w*(w - 1)**3*(w + 2)/2
Let g be (12/(-4) - -5)/(44/(-11170)). Let i = -507 - g. Factor 8/11 - 30/11*n - i*n**2.
-2*(n + 4)*(4*n - 1)/11
Let z(g) be the first derivative of -1/12*g**4 - 5 + 0*g + 5/9*g**3 - 2/3*g**2. Factor z(i).
-i*(i - 4)*(i - 1)/3
Suppose 0 = 4*c - 5*z - 25, -13*c + 10*c + z = -16. Let b(v) be the second derivative of -3/20*v**c + 1/4*v**4 + 0 + 0*v**3 + 0*v**2 - 2*v. Factor b(x).
-3*x**2*(x - 1)
Let k(f) be the first derivative of -f**8/14280 + f**7/2380 - f**6/1530 - 3*f**3 + 9. Let b(v) be the third derivative of k(v). Factor b(q).
-2*q**2*(q - 2)*(q - 1)/17
Let u(d) be the first derivative of -d - 25 + 1/2*d**2 + 1/3*d**3 - 1/4*d**4. Let u(p) = 0. What is p?
-1, 1
Let h(a) = -13*a**2 - 21*a - 17. Let y(r) = 3*r**2 + 5*r + 4. Suppose 0 = -k, n - 2*k = 3*k + 2. Let b(v) = n*h(v) + 9*y(v). Find i, given that b(i) = 0.
-2, -1
Let j = 565 + -79099/140. Let g(f) be the third derivative of 0 + 10*f**2 + 0*f + j*f**5 + 0*f**4 + 1/98*f**7 + 0*f**3 + 1/70*f**6 + 1/392*f**8. Factor g(w).
3*w**2*(w + 1)**2*(2*w + 1)/7
Let t(k) = 7*k**3 + 284*k**2 + 567*k + 290. Let z(n) = -10*n**3 - 285*n**2 - 565*n - 290. Let r(a) = 5*t(a) + 4*z(a). Determine s so that r(s) = 0.
-1, 58
Let z(m) = m**2 - 3*m - 1. Let b be z(-2). Factor -15 + b*t**2 + 4*t**2 + 18*t - 16*t**2.
-3*(t - 5)*(t - 1)
Let v(q) = q**2 - 175*q + 7534. Let y be v(75). Factor 145/2*r**2 + y*r + 2.
(5*r + 2)*(29*r + 2)/2
Suppose 5*p = u + 15, 2*u + 3*u = 2*p - 6. Suppose p*k = 21 - 15. Determine m, given that 8/7*m + 2/7*m**k + 8/7 = 0.
-2
Factor -51/2*v - 6*v**2 + 21/2*v**3 - 9.
3*(v - 2)*(v + 1)*(7*v + 3)/2
Let y(k) be the second derivative of 121*k**5/20 + 352*k**4/3 - 262*k**3/