Factor -2/15*n - 6/5*n**i - 8/15*n**4 - 22/15*n**3 + 2/15.
-2*(n + 1)**3*(4*n - 1)/15
Suppose -9*f = 15*f. Let g(x) be the second derivative of 5*x + 0*x**2 - 1/4*x**4 - 3/10*x**5 - 1/10*x**6 + f + 0*x**3. Factor g(i).
-3*i**2*(i + 1)**2
Suppose 2*g + 12 = -24*i + 29*i, 24 = 4*i + 2*g. Let n(s) be the third derivative of 0 - 3*s**2 + 8/9*s**3 + 2/9*s**i + 1/45*s**5 + 0*s. Factor n(b).
4*(b + 2)**2/3
Let q(f) be the second derivative of 2*f + 0*f**2 - 1/70*f**5 + 1/105*f**6 - 1/42*f**4 + 0*f**3 + 23 + 1/147*f**7. Factor q(z).
2*z**2*(z - 1)*(z + 1)**2/7
Let c(s) be the first derivative of -6*s - 1/2*s**3 + 15/4*s**2 - 31. Solve c(y) = 0.
1, 4
Let i(f) be the third derivative of -f**7/7560 + f**5/90 - 17*f**4/24 - 14*f**2. Let a(w) be the second derivative of i(w). Suppose a(g) = 0. What is g?
-2, 2
Factor -43*o + 5*o + o**2 - 17*o + 17*o.
o*(o - 38)
Let u(o) be the third derivative of o**6/60 + 7*o**5/15 - 17*o**4/4 - 308*o**2. Factor u(w).
2*w*(w - 3)*(w + 17)
Let y(t) be the third derivative of t**5/330 + t**4/11 + 20*t**3/33 - 5*t**2 - 23*t. Solve y(a) = 0.
-10, -2
Suppose -1/7*g**2 + 0 + 16/7*g = 0. Calculate g.
0, 16
Let w(q) be the first derivative of -1/33*q**3 - 1/44*q**4 + 1/11*q + 4 + 1/22*q**2. Factor w(d).
-(d - 1)*(d + 1)**2/11
Let f(g) be the first derivative of 0*g**3 + 4 - 3/80*g**5 + 0*g**2 - 1/80*g**6 + 10*g + 3/32*g**4. Let s(w) be the first derivative of f(w). Factor s(a).
-3*a**2*(a - 1)*(a + 3)/8
Let j = -84 + 254/3. Solve 0*s**4 + 2/3*s**5 - 4/3*s**3 + 0*s**2 + 0 + j*s = 0.
-1, 0, 1
Suppose 0 = -5*b - 6*w + 3*w + 63, 0 = 5*b - w - 59. Suppose -5*o + o + b = 0. What is d in -2*d**3 + 2*d**3 - d**3 - d + o*d + d**2 = 0?
-1, 0, 2
Let p be (2*6)/1 - -2. Suppose -2*x - 2 = 3*d, -d - 2*x - 2*x = p. Let 6*b + 9*b**d - 6 - 11*b + 8*b = 0. What is b?
-1, 2/3
Let x(o) be the third derivative of o**8/2352 - o**7/105 + 3*o**6/70 - 17*o**5/210 + 11*o**4/168 - 77*o**2 + 3. Suppose x(b) = 0. Calculate b.
0, 1, 11
Let a(n) be the second derivative of 2/21*n**7 + 0*n**2 + 4/3*n**4 - 6/5*n**5 + 2*n - 2/15*n**6 + 16/3*n**3 + 0. Factor a(p).
4*p*(p - 2)**2*(p + 1)*(p + 2)
Let q(p) be the third derivative of -p**7/105 + 11*p**6/60 - p**5/3 + 19*p**2 + 2. Solve q(u) = 0.
0, 1, 10
Let p(r) be the second derivative of r**4/72 + 2*r**3/9 - 5*r**2/3 + 247*r - 2. Factor p(m).
(m - 2)*(m + 10)/6
Let m(t) be the first derivative of -19/4*t**5 - 139/16*t**4 - 97/12*t**3 - 4*t**2 - 8 - t - 25/24*t**6. Factor m(i).
-(i + 1)**3*(5*i + 2)**2/4
Factor 2/11*w**2 - 28*w + 1078.
2*(w - 77)**2/11
Factor 2521*d**2 - 2521*d**2 - 2*d**5 + 8*d**3 - 6*d**4.
-2*d**3*(d - 1)*(d + 4)
Let w(h) be the third derivative of 0 - 13/80*h**6 + 1/35*h**7 - 6*h**2 + 5/4*h**4 + 3/224*h**8 - 2*h**3 - 3/20*h**5 + 0*h. Determine v so that w(v) = 0.
-2, 2/3, 1
Let h(k) = -k**2 + 7*k + 5. Let p be h(6). Let l(d) = -d**2 + 12*d - 7. Let x be l(p). Factor 3*f - 4 + 30*f**3 - 20*f**2 - 25*f**x - 15*f + 31*f**2.
-(f - 1)**2*(5*f + 2)**2
Let c(y) be the third derivative of y**7/1470 - 3*y**6/140 + 97*y**5/420 - 6*y**4/7 + 32*y**3/21 - 13*y**2 + 5*y. Factor c(o).
(o - 8)**2*(o - 1)**2/7
Let o(w) be the second derivative of w**5/20 - 19*w**4/12 + w + 26. Let o(c) = 0. Calculate c.
0, 19
Let r be 8/(-2) + 9 + 2. Suppose 2*w - 2*o + o = r, 9 = -3*o. Let 2/5*k**w - 6/5*k + 0 = 0. Calculate k.
0, 3
Suppose -61*v + 74 + 109 = 0. Let c(m) be the third derivative of 0*m + 0 - 1/360*m**5 + 1/36*m**4 + v*m**2 + 0*m**3. Suppose c(l) = 0. Calculate l.
0, 4
Let g(h) be the second derivative of h**8/20160 - h**6/540 + 17*h**4/12 - 9*h. Let r(f) be the third derivative of g(f). What is o in r(o) = 0?
-2, 0, 2
Let y(d) be the second derivative of d**4/42 - d**3 + 20*d**2/7 + 45*d. Factor y(h).
2*(h - 20)*(h - 1)/7
Let w(u) be the first derivative of -5*u**4/4 - 195*u**3 - 22815*u**2/2 - 296595*u - 37. Suppose w(r) = 0. Calculate r.
-39
Suppose 3*i = -52 - 29. Let z be 0 + (-129)/i - 26/(-117). Factor 0*u + 0*u**2 + 0*u**4 + 0 + 0*u**3 + 2/15*u**z.
2*u**5/15
Let w = -41 + 63. Let q = w - 20. Suppose 4/7 + 6/7*l - 2/7*l**3 + 0*l**q = 0. Calculate l.
-1, 2
Let x(v) be the second derivative of -5/6*v**4 - 10*v**2 - 35/6*v**3 + 1/4*v**5 + 15*v - 2. Factor x(k).
5*(k - 4)*(k + 1)**2
Let y(t) = t**2 - 24*t - 1701. Let g be y(-31). Suppose 128/13*q**3 + 50/13*q**5 - 190/13*q**g + 32/13 + 176/13*q**2 - 160/13*q = 0. What is q?
-1, 2/5, 2
Suppose 8*w - 29 = -29. Let i(v) be the third derivative of 5*v**2 + 0*v + 1/60*v**6 + 1/3*v**4 + 2/15*v**5 + 0 + w*v**3. Factor i(h).
2*h*(h + 2)**2
Let k(q) = 12*q**2 + 42*q + 7. Let r(s) = -13*s - 10*s**2 - 3 - 8*s + 4*s**2. Let x(f) = 6*k(f) + 11*r(f). Factor x(u).
3*(u + 3)*(2*u + 1)
Factor 4*h**5 + 8*h**3 + 6*h**4 - h**5 - 5*h**3 + 0*h**5.
3*h**3*(h + 1)**2
Let f(u) = -u**3 - u - 1. Let h(r) be the second derivative of 5*r**4/4 - 5*r**3/6 + 5*r**2/2 - 2*r. Let d(g) = -5*f(g) - h(g). Factor d(c).
5*c*(c - 2)*(c - 1)
Let k(u) be the third derivative of -u**7/1155 - 7*u**6/165 - 24*u**5/55 - 68*u**4/33 - 16*u**3/3 - 66*u**2 + 3. Factor k(b).
-2*(b + 2)**3*(b + 22)/11
Let d(c) be the first derivative of -2*c**3/3 + 2*c**2 + 6*c - 22. Factor d(q).
-2*(q - 3)*(q + 1)
Let o(i) = 2*i**2 - 15*i + 7. Let a be o(7). Let f(m) be the second derivative of 9*m + 1/8*m**2 + 1/40*m**5 + 0 + a*m**3 - 1/16*m**4. Factor f(g).
(g - 1)**2*(2*g + 1)/4
Suppose 10/13*w**4 + 0*w**3 + 0 + 2/13*w**5 - 32/13*w - 40/13*w**2 = 0. What is w?
-4, -2, -1, 0, 2
Let w be 3 + 4/(48/978). Let u = 85 - w. Solve f - u*f**2 + 0 = 0 for f.
0, 2
Let x(u) = -u**2 - 7*u - 8. Let q be x(-5). Factor -11*t + 3*t + 28*t**q - 32*t**2.
-4*t*(t + 2)
Let x = -2/4143 + 1391/20715. Let t(k) be the third derivative of 0*k - 1/6*k**4 + 0 + 10*k**2 - x*k**5 + 2/3*k**3 + 1/30*k**6. Factor t(y).
4*(y - 1)**2*(y + 1)
Let q(k) be the second derivative of -2*k**6/105 + k**4/21 + 46*k. Factor q(b).
-4*b**2*(b - 1)*(b + 1)/7
Suppose 35*m - 96 = -13*m. Let z(q) be the first derivative of -8/5*q + 6/5*q**3 - 8 + 16/5*q**m. Factor z(i).
2*(i + 2)*(9*i - 2)/5
Let v(b) be the third derivative of 1/2*b**4 + 1/30*b**5 + 0*b + 0 + 3*b**3 + 3*b**2. Find c such that v(c) = 0.
-3
Let l(t) = -t**3 + 9*t**2 - 16*t + 12. Let c be l(6). Let f = c + -22. Factor f*d**2 + 7 + 0*d + 5*d - 1 + 3*d.
2*(d + 1)*(d + 3)
Let x(w) = -w**2 + 9*w + 38. Let k be x(12). Factor -5*l - 10 + 109*l**2 - 220*l**k + 116*l**2.
5*(l - 2)*(l + 1)
Suppose -15 = -m - 4*o, -3*m = -23*o + 24*o - 12. Factor -3/2 - 3/4*y**m + 3/2*y**2 + 3/4*y.
-3*(y - 2)*(y - 1)*(y + 1)/4
Suppose 64*m - 14 = -5*k + 62*m, -2*k = -5*m - 23. Factor 0 - 4/19*v**2 + 6/19*v**3 - 2/19*v**5 + 0*v**k + 0*v.
-2*v**2*(v - 1)**2*(v + 2)/19
Factor 4*b + 41*b**2 - 91*b**2 + 51*b**2 + 4.
(b + 2)**2
Let d(j) be the second derivative of j**5/5 + 14*j**4/3 - 98*j**3/3 + 68*j**2 + 173*j. Suppose d(a) = 0. Calculate a.
-17, 1, 2
Suppose -3*d = -2*z - 16, 8*d = 10*d - 5*z - 29. Let -4/17 + 2/17*l**3 - 8/17*l**d + 10/17*l = 0. Calculate l.
1, 2
Let f(l) be the third derivative of -l**8/168 - 4*l**7/315 + l**6/90 + 2*l**5/45 + l**4/36 - 74*l**2. Suppose f(z) = 0. Calculate z.
-1, -1/3, 0, 1
Let i(m) be the third derivative of -2/315*m**7 + 45*m**2 + 0 + 0*m**3 + 1/18*m**4 + 0*m + 1/30*m**6 - 1/15*m**5. Factor i(l).
-4*l*(l - 1)**3/3
Let x(n) be the second derivative of n**7/18900 - n**5/900 - n**4/4 - 3*n. Let y(u) be the third derivative of x(u). What is f in y(f) = 0?
-1, 1
Determine m so that -410*m + 92*m**3 - 27*m**3 - 5*m**4 + 570*m + 230*m**2 = 0.
-2, -1, 0, 16
Factor -1/4*y**2 - 441/4 - 21/2*y.
-(y + 21)**2/4
Let j(y) = -y**3 - 6*y**2 - 11*y - 10. Let g = 75 + -79. Let o be j(g). Factor 24/11*q**o + 8/11*q + 0 - 14/11*q**3.
-2*q*(q - 2)*(7*q + 2)/11
Factor 4/3*l + 34/9*l**2 - 2/3*l**3 + 0.
-2*l*(l - 6)*(3*l + 1)/9
Let t(f) = -13*f**5 + 13*f**4 + 30*f**3 + 5*f**2 + 1. Let m(c) = -c**5 - c**4 - c**2 - 1. Let p(g) = m(g) + t(g). Solve p(w) = 0.
-1, -1/7, 0, 2
Let w = 200 + -195. Let l(v) be the second derivative of 2/15*v**6 + 0*v**2 + 0*v**3 + 0*v**4 + 6*v + 0 + 1/10*v**w + 1/21*v**7. Suppose l(c) = 0. What is c?
-1, 0
Let x(v) = -v**3 + 4*v**2 - 11*v + 14. Let y(t) = 1. Let a(z) = x(z) + 3*y(z). Let u be a(2). Factor -6/7 + 46/7*i - 80/7*i**2 - 32/7*i**u.
-2*(i + 3)*(4*i - 1)**2/7
Let i(c) be the third derivat