2 - 2/3*o**4 - 4/3*o + 0 - 8/3*o**f.
-2*o*(o + 1)**2*(o + 2)/3
Let a(y) be the third derivative of -y**8/1176 + 2*y**7/245 + y**6/28 + 4*y**5/105 + 40*y**2. What is r in a(r) = 0?
-1, 0, 8
Let s be 0*(319/(-22) + 14). What is t in 4/7*t**4 + 0 - 1/7*t**3 - 3/7*t**2 + s*t = 0?
-3/4, 0, 1
Let f be 3*14/(-945)*-1. Let s(q) be the first derivative of -f*q**3 + 0*q**2 + 0*q - 6. Factor s(o).
-2*o**2/15
Let z be ((-2)/(-1))/6*(34 + -55). Let n be z/2 - 15/(-4). Let 1/4*u**2 + 0 - n*u**3 + 0*u = 0. Calculate u.
0, 1
Suppose -2*p = 4*p - 42. What is d in 3 + 4*d**3 - 3*d**3 - 1 + 14*d**2 - 10*d - p*d**3 = 0?
1/3, 1
Factor 5/2*j**2 + 29/4*j + 5 + 1/4*j**3.
(j + 1)*(j + 4)*(j + 5)/4
Let o(n) be the third derivative of n**8/672 - n**7/60 + n**6/16 - 3*n**5/40 - n**2 - 46*n. Find r such that o(r) = 0.
0, 1, 3
Factor 8/9 - 38/9*y + 8/9*y**3 + 22/9*y**2.
2*(y - 1)*(y + 4)*(4*y - 1)/9
Let n(w) be the third derivative of w**8/504 - w**6/45 + 11*w**2 - 3*w. Factor n(g).
2*g**3*(g - 2)*(g + 2)/3
Suppose 5 = j - 0. Solve 6*a**2 - 22*a**3 - 2*a**j + 6*a**3 + 2*a**2 + 10*a**4 = 0 for a.
0, 1, 2
Let r(t) be the first derivative of t**6/240 + t**5/80 - t**4/8 - 20*t**3/3 - 21. Let g(i) be the third derivative of r(i). Find l such that g(l) = 0.
-2, 1
Let i(n) be the first derivative of -5*n**4/14 - 2*n**3/3 + 8*n**2/7 + 8*n/7 + 123. Factor i(h).
-2*(h - 1)*(h + 2)*(5*h + 2)/7
Let x = -69 + 269. Let v be 4/6 + x/24. Factor v*c**2 - 20*c**2 + 6*c**2.
-5*c**2
Let n(w) = -41*w**3 - 85*w**2 + 117*w - 12. Let c(q) = -39*q**3 - 84*q**2 + 117*q - 12. Let v(f) = 7*c(f) - 6*n(f). Determine u, given that v(u) = 0.
-4, 1/9, 1
Let r be (1 - 0)*(-81)/9*-11. Let p = -99 + r. Factor -3/2*s + 0 + p*s**2 + 3/2*s**3.
3*s*(s - 1)*(s + 1)/2
Let p be 5/(-20) + 58/8. Suppose -p*o + 432 = -3*o. Factor -90*y**2 - 31 - o*y + 7 + 29*y**3 + 46*y**3.
3*(y - 2)*(5*y + 2)**2
Let o(j) be the third derivative of -j**6/180 - j**5/60 + j**4/6 + j**3 + 10*j**2. Let l(q) be the first derivative of o(q). Find r, given that l(r) = 0.
-2, 1
Let m(u) be the third derivative of u**7/1260 - u**6/180 + u**5/60 + u**4/12 + 13*u**2. Let y(r) be the second derivative of m(r). Factor y(h).
2*(h - 1)**2
Factor 3*m**2 + 96*m - 4*m**4 + 7*m**4 - 45 + 79*m**3 + 231*m**2 - 339 - 28*m**3.
3*(m - 1)*(m + 2)*(m + 8)**2
Let v(s) be the third derivative of 0 - 1/12*s**6 + 7/12*s**5 - 5/12*s**4 + 0*s**3 + 0*s - 22*s**2 - 1/14*s**7. Factor v(i).
-5*i*(i - 1)*(i + 2)*(3*i - 1)
Let u(k) = 6*k + 12. Let h be u(-3). Let q be h*(-2)/8 + 1. Factor 0*c - q*c**3 - c**2 - 3/2*c**4 + 0.
-c**2*(c + 1)*(3*c + 2)/2
Suppose 4*p - 2*f = 24, 2*f + 2*f - 7 = -3*p. Let c be 12/5 - 2/p. Factor 2*s - 8*s + 32 + 14*s + c*s**2 + 8*s.
2*(s + 4)**2
Let j(y) = y**3 + 16*y**2 + 15*y - 17. Let x be j(-15). Let c = x - -20. Factor -2*g - 75 + 16*g**2 - 32*g**c + 75.
-2*g*(4*g - 1)**2
Let x be (-3 - 4/(-2))*0. Let b(u) be the third derivative of x*u + 1/350*u**7 - 1/50*u**5 + 0 + 0*u**4 - 1/200*u**6 + 3*u**2 + 0*u**3. Factor b(v).
3*v**2*(v - 2)*(v + 1)/5
Factor -62*h**2 + 10*h**3 + 15*h - 54*h**2 + 11*h**3 - 3*h**4 + 139*h**2 - 56*h**2.
-3*h*(h - 5)*(h - 1)**2
Suppose 0 = -5*n + 2*n - 4*q - 16, 20 = -5*n - 5*q. Determine i, given that -168*i**4 - 96*i**2 - 234*i**3 - 12*i - 147/4*i**5 + n = 0.
-2, -2/7, 0
Let q = 21154/79215 + -2/5281. Suppose 26/15*d**2 - 2*d**4 - 22/15*d**3 + q + 22/15*d = 0. What is d?
-1, -2/5, -1/3, 1
Let f(y) be the third derivative of -y**6/960 - y**5/60 + y**4/192 + y**3/6 + 143*y**2 - 2. Factor f(l).
-(l - 1)*(l + 1)*(l + 8)/8
Suppose -15 = -i - 13. Let o be -2 - (-2 + 1)*4. Suppose o*s + 4*s**2 + 2*s - s**2 + 2*s**3 + 3*s**i = 0. What is s?
-2, -1, 0
Let y(p) be the second derivative of 3*p**7/70 + p**6/50 - 9*p**5/25 - p**4/5 - 107*p. Determine s so that y(s) = 0.
-2, -1/3, 0, 2
Let x(g) = -g**2 - 8*g + 2. Let d be x(-8). Factor 3*f + 10*f**4 - 14*f**d + 2*f - 9*f**5 + 4*f**5 + 4*f**2.
-5*f*(f - 1)**3*(f + 1)
Let w be (-15)/9 - (-50)/30. Find o such that w + 0*o - 1/4*o**2 - 3/4*o**4 - o**3 = 0.
-1, -1/3, 0
Let g(m) = m + 23. Let w = -74 + 56. Let s be g(w). Solve 2/3*k**4 + 2*k**3 - 4/3*k**2 - k - k**s + 2/3 = 0 for k.
-1, 2/3, 1
Let n(s) be the third derivative of s**7/105 + s**6/20 - 19*s**5/30 - s**4/4 + 6*s**3 - 136*s**2. What is m in n(m) = 0?
-6, -1, 1, 3
Factor 3/5*o**2 + 24/5 + 18/5*o.
3*(o + 2)*(o + 4)/5
Let w(y) be the first derivative of 1/12*y**2 + 1/2*y - 1/6*y**3 + 31 - 1/24*y**4. Factor w(g).
-(g - 1)*(g + 1)*(g + 3)/6
Let m(i) be the first derivative of 1/18*i**3 + 8/3*i + 2/3*i**2 - 16. Solve m(y) = 0.
-4
Let a(i) be the second derivative of i**9/2520 - i**8/840 + i**7/1260 + i**4/6 + 13*i**2 + 23*i. Let f(v) be the third derivative of a(v). Factor f(s).
2*s**2*(s - 1)*(3*s - 1)
Suppose 2*y = -3*q + 8, y + 2*y - 2*q + 1 = 0. Let k be (y/10)/(81/15 + -5). Factor 0 + 0*n + k*n**3 - 1/4*n**2.
n**2*(n - 1)/4
Let -3/5*m**3 + 6/5*m**2 + 3*m - 18/5 = 0. What is m?
-2, 1, 3
Determine d, given that -2/5*d**3 - 84/5 + 106/5*d - 4*d**2 = 0.
-14, 1, 3
Let d(v) be the second derivative of -v**4/84 - 20*v**3/21 - 38*v**2/7 - 472*v. Factor d(l).
-(l + 2)*(l + 38)/7
Suppose 0 = x - 46 + 41. Let y(o) = 2*o**3 - 2*o**2 - o - 2. Let i be y(2). Factor -1/2 - 5*k**2 + 1/2*k**x - 5/2*k**i + 5/2*k + 5*k**3.
(k - 1)**5/2
Let i = -4173806/69 + 60491. Let r = i - 9/23. Factor 1/3*f**4 + 0 + 5/3*f**2 - r*f - 4/3*f**3.
f*(f - 2)*(f - 1)**2/3
Let p(w) = w**4 - 10*w**3 + 12*w**2 + 2*w - 10. Let i(n) = n**4 - n**3 + n**2 - 2. Let y(t) = 5*i(t) - p(t). Factor y(d).
d*(d - 1)*(d + 2)*(4*d + 1)
Let r(d) be the third derivative of d**6/40 + 7*d**5/10 + 43*d**4/8 + 15*d**3 + 30*d**2. Let r(y) = 0. Calculate y.
-10, -3, -1
Let p(k) be the first derivative of -k**7/168 + k**6/60 - k**5/80 + 19*k + 9. Let f(n) be the first derivative of p(n). Let f(g) = 0. Calculate g.
0, 1
Let c(k) = -7*k**3 + 30*k**2 + 108*k + 56. Let v(q) = -q**3 - q**2. Let a(d) = c(d) - 4*v(d). Find t, given that a(t) = 0.
-2, -2/3, 14
Let k(c) be the first derivative of -c**5/25 - 7*c**4/60 - c**3/15 + 12*c**2 + 26. Let d(f) be the second derivative of k(f). Suppose d(y) = 0. Calculate y.
-1, -1/6
Let g(h) = -6*h**2 - 39*h - 147. Let r(d) = 7*d**2 + 38*d + 147. Let u = 1 + -4. Let y(k) = u*r(k) - 4*g(k). Factor y(l).
3*(l + 7)**2
Let t(m) = -m**3 + 10*m**2 + 9*m - 14. Let f(x) = 7*x - 45. Let i be f(7). Let q(s) = s**3 + s - 1. Let y(h) = i*q(h) - t(h). Factor y(u).
5*(u - 2)*(u - 1)*(u + 1)
Let b(c) be the third derivative of -c**6/3240 + c**5/90 - c**4/6 + 43*c**3/6 - 22*c**2. Let t(a) be the first derivative of b(a). Factor t(r).
-(r - 6)**2/9
Let q(x) be the first derivative of -2*x**3/9 - 9*x**2 + 76. Factor q(t).
-2*t*(t + 27)/3
Suppose 0 = -6*f + 10*f. Suppose f = 5*x + 7 - 17. Factor 1 + 25/4*z**x + 5*z.
(5*z + 2)**2/4
Let y(n) be the first derivative of n**4/36 + n**3/27 - n**2/9 - 11. Factor y(m).
m*(m - 1)*(m + 2)/9
Let t(f) be the second derivative of -f**8/420 + f**7/105 + f**6/30 + 11*f**3/3 + 30*f. Let i(a) be the second derivative of t(a). Solve i(g) = 0.
-1, 0, 3
Suppose -4*u - 92 = 4*y, 0*u + 3*u + 5*y = -79. Let o = u + 21. Factor -21*i - 11*i + 6*i**3 - 16 - 38*i**o - 76*i**3 + 156*i**2.
-4*(i - 1)*(3*i - 2)*(9*i + 2)
Let r = 3461 + -3459. Factor 1/3*l + l**r + 0 + 1/3*l**4 + l**3.
l*(l + 1)**3/3
Let j(s) be the third derivative of -s**5/50 - 13*s**4/40 + 7*s**3/10 - 8*s**2 + 6*s. Find b, given that j(b) = 0.
-7, 1/2
Let a(w) = w**2 - 10*w + 1. Let g(m) = -m - 1. Let u(q) = -5*a(q) + 20*g(q). Solve u(p) = 0.
1, 5
Let a be 209/855*10 - -8*1/(-18). Let 0 + 0*r**a - 2/15*r + 2/15*r**3 = 0. Calculate r.
-1, 0, 1
Let w(k) = -k + 2. Let g(a) = -a**2 - 1. Let x(m) = -g(m) + w(m). Let l = 11 - 13. Let q(t) = -t**2 - 2. Let v(u) = l*x(u) - 3*q(u). Factor v(o).
o*(o + 2)
Let u(g) be the third derivative of g**6/360 + g**5/180 + g**2 + 14. Factor u(b).
b**2*(b + 1)/3
Let w(m) be the first derivative of 2*m**3/51 + 35*m**2/17 - 72*m/17 - 128. What is y in w(y) = 0?
-36, 1
Let c(a) be the first derivative of -a**6/4 - 2*a**5/5 + 25*a**4/8 + 5*a**3/3 - 13*a**2 + 12*a + 113. Solve c(d) = 0 for d.
-3, -2, 2/3, 1, 2
Factor -5/3*w + 8/3 - 7/6*w**2 + 1/6*w**3.
(w - 8)*(w - 1)*(w + 2)/6
Suppose 0 = -2*j - 163 + 175. Let a(i) be the third derivative of 0*i**5 - 7*i**2 