y**2 - 21*y**5 - 81*y**3 - 30*y**4 + y - 42*y**4 - x*y + 3*y**4 = 0?
-1, -2/7, 0
Let n(m) be the third derivative of 0*m + 1/900*m**6 + 1/1575*m**7 + 0 - 1/180*m**4 + 0*m**3 - 22*m**2 - 1/450*m**5. Find i such that n(i) = 0.
-1, 0, 1
Factor 345*s**4 - 336*s**4 + 237*s**2 + s**3 + 108 + 288*s + 77*s**3.
3*(s + 2)*(s + 3)**2*(3*s + 2)
Let n = -2009 + 6031/3. Factor -14/3*j**3 - 22/3*j - 32/3*j**2 - n.
-2*(j + 1)**2*(7*j + 2)/3
Let x be (20 + -4)*(1 + 28/(-32)). Solve -2/5*k**4 + 8/5*k - 4/5*k**3 + 6/5*k**x - 8/5 = 0.
-2, 1
Let k(s) be the first derivative of 0*s - 1/8*s**4 - 1/4*s**2 - 1/3*s**3 + 13. Factor k(c).
-c*(c + 1)**2/2
Determine t so that 3*t + 6/5 + 12/5*t**2 + 3/5*t**3 = 0.
-2, -1
Factor -5*r - 4*r**3 - 12*r**2 + 3*r + 2*r.
-4*r**2*(r + 3)
Let c(t) be the first derivative of 2*t**3/15 + 53*t**2/5 - 2. Determine i, given that c(i) = 0.
-53, 0
Let l(h) be the second derivative of -h**4/2 - h**3/3 + 3*h - 2. Suppose l(r) = 0. Calculate r.
-1/3, 0
Let a(j) be the second derivative of -j**6/120 - j**5/16 + 11*j**4/48 + 11*j**3/8 + 9*j**2/4 - j + 353. Factor a(b).
-(b - 3)*(b + 1)**2*(b + 6)/4
Let u(k) be the first derivative of -k**6/1980 - 3*k**5/220 - 2*k**4/33 - 29*k**3/3 - 45. Let z(h) be the third derivative of u(h). Let z(b) = 0. What is b?
-8, -1
Suppose -4*r - 89 = -5*o - 0, 3*r + 5*o = -23. Let w = 19 + r. Factor -3*p**3 + p**2 - w*p**4 - 4*p**2 + 3*p + 6*p**2.
-3*p*(p - 1)*(p + 1)**2
Let f(s) be the third derivative of 5*s**8/336 + 13*s**7/21 + 193*s**6/24 + 26*s**5 + 30*s**4 + 98*s**2. Solve f(y) = 0.
-12, -1, 0
Let w(u) = -41*u**2 - 10*u + 9. Let l be w(1). Let x be -1 - 4/(-6) - 32/l. Let -9/7*k**4 - 6/7*k + 6/7*k**3 - x + 12/7*k**2 = 0. What is k?
-1, -1/3, 1
Factor 2/5*w**3 + 18/5 + 22/5*w**2 + 38/5*w.
2*(w + 1)**2*(w + 9)/5
Suppose 2*m = -l + 9, -18 = -m + l - 21. What is d in 8/9 + 8/9*d + 2/9*d**m = 0?
-2
Let s(k) be the second derivative of 5*k**7/42 - 5*k**6/6 + 5*k**5/4 + 25*k**4/12 - 5*k**3 - 163*k. What is z in s(z) = 0?
-1, 0, 1, 2, 3
Let x be 1188/(-121) + 1*10. Factor 2/11*o**3 + 0 + 0*o**2 - x*o**4 + 0*o.
-2*o**3*(o - 1)/11
Let g(q) = -2*q**2 - 18*q + 20. Let v(o) = -8*o**2 - 53*o + 61. Let d(x) = -14*g(x) + 4*v(x). Determine m so that d(m) = 0.
1, 9
Let x(b) be the second derivative of b**6/10 - 3*b**5/10 - b**4/4 + b**3 + 105*b. Find i such that x(i) = 0.
-1, 0, 1, 2
Let s be (-2 - -4) + (-11)/((-33)/(-4)). Suppose -3*w + 5 = 5*f + 1, -w + 8 = 5*f. Factor 2*a - 2/3 + s*a**3 - f*a**2.
2*(a - 1)**3/3
Let v(z) be the third derivative of -z**8/504 + z**7/63 - 2*z**6/45 + 2*z**5/45 - 156*z**2. Factor v(k).
-2*k**2*(k - 2)**2*(k - 1)/3
Let s = -52 + 54. Let a be (-3)/s + (-62)/(-36). Factor -a*o**4 + 16/9*o + 0 + 4/3*o**3 - 8/3*o**2.
-2*o*(o - 2)**3/9
Let i(m) = -251 + 80 + 4*m + 103 + 5*m. Let h be i(8). Solve 54*j**h - 261/2*j**3 - 3 + 42*j**2 + 15/2*j = 0 for j.
-1/4, 1/3, 2
Let t(z) be the first derivative of -81*z**5/5 - 1071*z**4/2 - 940*z**3/3 - 52*z**2 - 777. Determine d so that t(d) = 0.
-26, -2/9, 0
Let w(p) = -p**3 + 6*p**2 + 11*p - 23. Let d be w(7). Let n be 9*(30/27)/d. Suppose -1/4*q + 1/4*q**4 + 3/4*q**n - 3/4*q**3 + 0 = 0. What is q?
0, 1
Let v(n) be the first derivative of n**3/6 - 17*n**2/2 - 111*n/2 - 752. Determine t so that v(t) = 0.
-3, 37
Factor 0*k + 8*k - 5*k**2 - 11 - 9 + 17*k.
-5*(k - 4)*(k - 1)
Factor -135 + 14*j**4 + 468*j - 501*j**2 - 28*j**4 + 62*j**4 + 120*j**3.
3*(j - 1)*(j + 5)*(4*j - 3)**2
Let p be 140/(-2)*(-24)/48. Solve -87*w**2 - 120*w - 45*w**4 - 95*w**3 + 192*w**2 + p*w**5 + 178 - 158 + 100*w**2 = 0 for w.
-2, 2/7, 1
Factor 0 - 3/2*h - 3/2*h**2 + 3/2*h**3 + 3/2*h**4.
3*h*(h - 1)*(h + 1)**2/2
Let v(i) = i - 1. Let n(h) = 5*h**2 + 24*h + 31. Let q = 49 - 50. Let t(y) = q*n(y) - 6*v(y). Suppose t(s) = 0. What is s?
-5, -1
Let d(s) = s**3 + 10*s**2 - 25*s - 8. Let r be d(-12). Let z(a) be the second derivative of 0 - 4*a + 1/6*a**r + 1/3*a**3 + 0*a**2. Factor z(g).
2*g*(g + 1)
Let n be 4 + (315/(-84) - (-2)/8). Solve -n*k**2 + 1/2*k + 1 = 0.
-1, 2
Let f be (-132)/(-720)*2 - 2/12. What is p in -f*p**3 + 1/5*p**4 + p - 2/5 - 3/5*p**2 = 0?
-2, 1
Let b(i) be the second derivative of 0 + 1/45*i**6 - 1/60*i**5 + 0*i**3 + 0*i**4 - 1/126*i**7 + 20*i + 0*i**2. Suppose b(v) = 0. What is v?
0, 1
Let x(d) = 2*d**2 - 12*d - 10. Let t be x(7). Factor 41*c**3 + 6*c**4 - 4*c**4 + c**t - 38*c**3 - 18*c**2.
3*c**2*(c - 2)*(c + 3)
Let x(k) = -k + 20. Let n be x(0). Let 3*p + 6*p**3 - p - p**3 - 10 + 23*p - n*p**2 = 0. What is p?
1, 2
Let g be ((-18)/7)/((-15)/1890*20). Factor -g + 18/5*b - 1/5*b**2.
-(b - 9)**2/5
Let z be (-57)/(-7) + 12 + (5 - 24). Suppose 0 + z*f**2 + 4/7*f + 4/7*f**3 = 0. What is f?
-1, 0
Let j = 36 + -25. Suppose -4*z + j + 1 = 0. Factor 26*f**4 + 15*f**5 - 2*f**4 + 33*f**5 + 3*f**z.
3*f**3*(4*f + 1)**2
Suppose 30 = 26*m - 20*m. Let s(y) be the second derivative of 0*y**2 - 1/15*y**6 - 1/3*y**3 + 1/6*y**4 - y + 1/10*y**m + 0. Determine r, given that s(r) = 0.
-1, 0, 1
Let n = -981/4 + 246. Let o(c) be the first derivative of -1/16*c**4 + 5/8*c**2 - 1/12*c**3 - n*c - 3. What is j in o(j) = 0?
-3, 1
Let r(c) = -c**4 + c**2 - 1. Let y(g) = -34*g**4 + 116*g**3 + 118*g**2 - 32*g + 2. Let w(j) = 2*r(j) + y(j). What is t in w(t) = 0?
-1, 0, 2/9, 4
Let f(t) = 6*t**3 - 255*t**2 - 4346*t - 24543. Let p(w) = -w**3 + 51*w**2 + 869*w + 4909. Let g(v) = -2*f(v) - 11*p(v). Suppose g(h) = 0. What is h?
-17
What is l in 7 + 1850*l**3 - 1855*l**3 - l + 6*l + 3 - 10*l**2 = 0?
-2, -1, 1
Let -18/5*x**3 + 36/5 + 2/5*x**4 - 78/5*x + 58/5*x**2 = 0. Calculate x.
1, 2, 3
Let i(c) be the third derivative of -3*c**7/350 + 23*c**6/150 - 49*c**5/60 + 5*c**4/12 + 136*c**2 - 2. Solve i(s) = 0 for s.
0, 2/9, 5
Let p(t) = 3*t**2 - 197*t - 212. Let l(x) = 6*x**2 - 393*x - 426. Let d(m) = -4*l(m) + 9*p(m). Determine u, given that d(u) = 0.
-1, 68
Let s(g) be the third derivative of g**8/40320 + g**7/10080 - g**5/60 + 6*g**2. Let w(p) be the third derivative of s(p). What is z in w(z) = 0?
-1, 0
Let r = 35 - 45. Let f(j) = -j**3. Let v(x) = -15*x**3 - 20*x**2 - 20*x. Let w(q) = r*f(q) + v(q). Factor w(m).
-5*m*(m + 2)**2
Let l = -96 + 484/5. Suppose -147*k + 905 - 170 = 0. Factor 0*b + 0 + 24/5*b**4 + 18/5*b**3 + 2*b**k + l*b**2.
2*b**2*(b + 1)**2*(5*b + 2)/5
Solve 9/2*c**2 + 0*c + 1/2*c**4 + 0 - 5*c**3 = 0 for c.
0, 1, 9
Let n(r) = r**4 + 7*r**3 + 4*r**2 - 7*r - 6. Let i(o) = -o**3 + o + 1. Let f(p) = -i(p) - n(p). Factor f(c).
-(c - 1)*(c + 1)**2*(c + 5)
Suppose -7*n = -4*s - 8*n + 4, -4*n + 16 = -4*s. Let -2/5*o**4 + s*o - 4/5*o**3 + 0 + 6/5*o**2 = 0. What is o?
-3, 0, 1
Suppose 9 = 3*n, -6 = 3*j - 2*n - 18. Suppose -6*y = -j*y - 10*y. Solve -2/7*k**5 - 6/7*k**4 + 0 + y*k**3 + 0*k + 8/7*k**2 = 0 for k.
-2, 0, 1
Find d such that -d**5 + 4*d**3 - 265*d**2 + 273*d**2 - 3*d**5 - 8*d**4 + 0*d**5 = 0.
-2, -1, 0, 1
Let 0 - 8*n + 2/3*n**3 + 2/3*n**2 = 0. What is n?
-4, 0, 3
Suppose 3*d + 18 = 2*l, 4*l - 2*d - 2*d = 28. Factor 0*v**3 - 3*v - 2*v**l + 5*v**3.
3*v*(v - 1)*(v + 1)
Let r(v) = -v**3 + 2*v**2 + v. Let j be r(2). Suppose -q + j = 5*n, 2*q - 2*n - 4 = -0*q. What is c in -2/5 + 2/5*c + 2/5*c**q - 2/5*c**3 = 0?
-1, 1
Let s(o) = o**3 + 24*o**2 - 80*o + 30. Let x be s(-27). Let u(m) be the third derivative of 0*m - 8*m**2 - 1/30*m**5 + 1/4*m**4 + 0 + 0*m**x. Factor u(p).
-2*p*(p - 3)
Let j(h) be the first derivative of -3*h**5/25 - 9*h**4/10 + 81*h**2/5 + 243*h/5 - 62. Factor j(v).
-3*(v - 3)*(v + 3)**3/5
Let p(i) be the first derivative of -4*i**5/5 - i**4 + 16*i**3 + 125. Factor p(k).
-4*k**2*(k - 3)*(k + 4)
Let q(n) be the first derivative of -n**4/10 - 162*n**3/5 - 19683*n**2/5 - 1062882*n/5 - 188. Factor q(m).
-2*(m + 81)**3/5
Let x(h) be the second derivative of -h**5/10 + 2*h**4/3 + 52*h**3 + 576*h**2 + 41*h. Factor x(f).
-2*(f - 16)*(f + 6)**2
Let v(o) be the third derivative of -o**6/300 - 13*o**5/75 - 209*o**4/60 - 484*o**3/15 + 230*o**2. Factor v(x).
-2*(x + 4)*(x + 11)**2/5
Let o = 27 + -25. Let -8*d**3 + 11*d**3 - o*d**4 - 2*d**4 + d**3 = 0. What is d?
0, 1
Let s(m) = 485*m**2 + 620*m - 755. Let f(j) = -18*j**2 - 23*j + 28. Suppose 3*a - a - 110 = 0. Let r(p) = a*f(p) + 2*s(p). Determine g, given that r(g) = 0.
-2, 3/4
Factor 3*u**3 + 40*u**4 - 128*u - 30*u**2 - 78*u**4 + 39*u**4 - 96.
(u - 6)*(u