1, 0, 1
Let v(f) be the third derivative of -f**7/10080 + f**6/1440 - f**4/2 + 33*f**2 - 1. Let z(j) be the second derivative of v(j). Solve z(b) = 0 for b.
0, 2
Let n be 19 - 0/(-2*1). Let q(r) = r**3 + 9*r**2 + 13*r + 16. Let c be q(-6). Solve 22*m - 4*m - c - 3*m**2 + n = 0 for m.
3
Let r(v) = -v - 4. Let z be r(-6). Solve -11*p**2 - 44*p + 12 - 9*p**z + 4*p**2 = 0.
-3, 1/4
Factor -93*s**3 - 3*s - 28 + 30 + 94*s**3.
(s - 1)**2*(s + 2)
Let j = -155 + 160. Suppose -17 = -3*y + j*q, -2*q - 6 - 16 = -5*y. Suppose 0*o - 3*o**3 + 0 + 3/4*o**y + 3*o**2 = 0. Calculate o.
0, 2
Suppose h + 214 - 218 = -w, 2*w - 8 = 3*h. Determine v, given that 4*v**2 - 2/5*v**5 + 2/5 + 2*v**4 - 2*v - w*v**3 = 0.
1
Let m(z) be the first derivative of -2/33*z**3 + 0*z + 5/11*z**2 + 20. Factor m(o).
-2*o*(o - 5)/11
Factor -1/6*s**4 + 0 + 8/3*s**3 + 2/3*s**2 - 32/3*s.
-s*(s - 16)*(s - 2)*(s + 2)/6
Let y be 117/104*(-2 - (-56)/(-6)). Let f = 13 + y. Determine h so that 1/4*h**2 + f + 1/2*h = 0.
-1
Let s(o) be the first derivative of -1/16*o**4 - 1/20*o**5 + 0*o**2 + 0*o + 22 + 1/12*o**3 + 1/24*o**6. Factor s(a).
a**2*(a - 1)**2*(a + 1)/4
Let v(w) be the third derivative of -w**5/15 - w**4/6 + 4*w**3 - 54*w**2 - 2*w. Suppose v(q) = 0. What is q?
-3, 2
Let p = 26 - 24. Factor -2*y**2 - 2439 + 0*y**p + 2439 - 2*y**3.
-2*y**2*(y + 1)
Let f = -118 - -132. Let i be 8/5*f/56. Factor -6/5*o**2 + 4/5*o + i*o**3 + 0.
2*o*(o - 2)*(o - 1)/5
Let t be (119/49 + -2)*4. Factor t*v + 4/7 + 4/7*v**3 + 12/7*v**2.
4*(v + 1)**3/7
Suppose 4*z - 2*x + 4 = -6, 5*z - 3*x = -15. Solve z*u**2 - 28*u + 6*u**2 - 3*u**2 + 10*u + 15 = 0 for u.
1, 5
Factor 165*k**2 + 2*k + 4*k**3 + 4*k**4 - 5*k**4 - 170*k**2.
-k*(k - 2)*(k - 1)**2
Suppose -z - 9 = 5. Let y = z - -19. Factor -2*t**3 + 2*t**4 - 2*t**2 - 3*t**y + t**5 + 4*t**3 + 0*t**5.
-2*t**2*(t - 1)**2*(t + 1)
Let j = -19041 - -19044. Let -32/9*v - 2/9*v**j - 8/3 - 14/9*v**2 = 0. Calculate v.
-3, -2
Let -2/15*v - 4/15*v**2 + 0 - 2/15*v**3 = 0. Calculate v.
-1, 0
Let j be (-339)/565 + (-82)/(-70). Let j - 18/7*i**2 + 2/7*i**3 + 6/7*i**4 + 6/7*i = 0. What is i?
-2, -1/3, 1
Let g(w) be the second derivative of w**7/420 - 13*w**6/300 + 23*w**5/200 - 11*w**4/120 + 131*w. What is a in g(a) = 0?
0, 1, 11
Let t = 49/156 - -1/52. Suppose 0*g + 0*g = -11*g. Factor g*v - t*v**5 + 0*v**2 + 2/3*v**4 + 0 - 1/3*v**3.
-v**3*(v - 1)**2/3
Let r(f) be the second derivative of 7*f**7/75 + 77*f**6/300 + 16*f**5/75 + f**4/15 - 21*f**2 + 5*f. Let l(a) be the first derivative of r(a). Factor l(y).
2*y*(y + 1)*(7*y + 2)**2/5
Solve 6/7*l**2 - 2*l + 4/7 = 0 for l.
1/3, 2
Let g(z) be the second derivative of z**7/210 - z**6/40 + z**5/30 - 29*z**2/2 + 18*z. Let i(b) be the first derivative of g(b). Suppose i(p) = 0. What is p?
0, 1, 2
Let l = 68781/7 + -9825. What is h in 0 + l*h**2 + 6/7*h = 0?
-1, 0
Let y(z) be the first derivative of -4*z**3/9 + z**2 - 2*z/3 + 31. Factor y(t).
-2*(t - 1)*(2*t - 1)/3
Let n(r) be the third derivative of 1/240*r**6 + 1/40*r**5 + 0*r**3 - 6*r**2 + 0 + 0*r + 1/24*r**4. Suppose n(q) = 0. What is q?
-2, -1, 0
Let o(p) = p**3 - 18*p**2 - 2*p + 38. Let d be o(18). Let m(n) be the second derivative of -5*n + 0 + 7/6*n**3 - 5/12*n**4 - n**d. Suppose m(q) = 0. What is q?
2/5, 1
Factor g**2 + 0 + 2/3*g + 0*g**3 - 1/3*g**4.
-g*(g - 2)*(g + 1)**2/3
Let a be 3 + 3 + 132/(-33). Suppose 12/11*c + 16/11 + 2/11*c**a = 0. Calculate c.
-4, -2
Suppose 0 = 2*t - 6. Factor -12*q + q**2 - q**2 + t*q**2 + 9.
3*(q - 3)*(q - 1)
Let c(m) = -m**2 + 5*m - 2. Let b be c(5). Let u be (0 + b/4)*(-4)/9. Let 0 - 2/9*s**2 - u*s = 0. Calculate s.
-1, 0
Let d be (39/(-117))/(7/(-2)). Solve 0*c - 2/21*c**5 + d*c**3 - 2/21*c**2 + 2/21*c**4 + 0 = 0 for c.
-1, 0, 1
Let x = -1/4710 - -4717/32970. Determine y so that 0*y + 3/7*y**4 + 1/7*y**2 - 3/7*y**3 - x*y**5 + 0 = 0.
0, 1
Let u(j) = j**2 - 42*j - 852. Let x be u(-15). Factor 4/3*d**x + 2*d**2 - 2/3*d**4 - 8/3 - 8/3*d.
-2*(d - 2)**2*(d + 1)**2/3
Factor -6590*m**3 + 6614*m**3 + 2*m**4 + 0 + 0 - m**5.
-m**3*(m - 6)*(m + 4)
Let n(w) = 6*w**5 + 16*w**4 + 18*w**3 + 8*w**2 + 4*w. Let c(k) = 5*k**5 + 15*k**4 + 19*k**3 + 9*k**2 + 3*k. Let q(g) = -4*c(g) + 3*n(g). Solve q(s) = 0 for s.
-3, -2, -1, 0
Let d(a) be the first derivative of a**7/980 - a**6/630 - a**5/420 + 7*a**3/3 + 18. Let s(f) be the third derivative of d(f). Factor s(v).
2*v*(v - 1)*(3*v + 1)/7
Let p(l) = -6*l**5 + 400*l**4 - 20004*l**3 - 8*l**2. Let i(g) = g**5 + g**3 + 2*g**2. Let x(z) = 4*i(z) + p(z). Factor x(o).
-2*o**3*(o - 100)**2
Let r(p) be the first derivative of p**4/4 - 31*p**3/3 + 159*p**2/2 - 225*p - 324. Factor r(q).
(q - 25)*(q - 3)**2
Solve 784 + 57*l**2 - 158*l + 3362*l**3 + 998*l - 3361*l**3 = 0.
-28, -1
Let y(l) be the first derivative of -l**5/80 - 7*l**4/32 + l**3 - 5*l**2 - 27. Let o(j) be the second derivative of y(j). Suppose o(b) = 0. Calculate b.
-8, 1
Let u be ((-66)/88)/((-36)/72). Factor 21/4*c**2 + u*c - 27/4*c**3 + 0.
-3*c*(c - 1)*(9*c + 2)/4
Factor -2/5*f**2 - 1/5*f**3 + 11*f + 40.
-(f - 8)*(f + 5)**2/5
What is i in -2/3*i**2 - 16/3 - 6*i = 0?
-8, -1
Let t(g) = -34 + 8*g + 59 - g**2 - 31. Let a(d) = -d**2 + 9*d - 7. Let j(v) = 6*a(v) - 7*t(v). Factor j(y).
y*(y - 2)
Suppose 7 = -5*r + 4*r + 2*o, -r - 17 = -4*o. Let v(j) be the first derivative of 0*j - 3/4*j**4 + 3/5*j**5 + 1/2*j**6 - j**r + 0*j**2 + 6. Factor v(u).
3*u**2*(u - 1)*(u + 1)**2
Let r(o) be the second derivative of o**6/20 - 9*o**5/10 + 23*o**4/4 - 15*o**3 + 75*o**2/4 - 7*o. Factor r(n).
3*(n - 5)**2*(n - 1)**2/2
Factor -2/7*x**2 + 34/7*x - 12.
-2*(x - 14)*(x - 3)/7
Let o(b) be the first derivative of b**6/14 - 3*b**5/7 + 3*b**4/4 - 3*b**3/7 + 8. Determine k, given that o(k) = 0.
0, 1, 3
Let s(v) be the second derivative of -3*v - 3/5*v**5 - 2/3*v**3 + 0*v**2 - v**4 + 0 - 2/15*v**6. Determine y so that s(y) = 0.
-1, 0
What is n in -41/4*n**3 + 13/2*n**2 + 0 + 0*n + 3/4*n**4 = 0?
0, 2/3, 13
Let c = -12672 + 12675. Factor 2/3 + 1/3*t**c - 5/3*t - 1/3*t**4 + t**2.
-(t - 1)**3*(t + 2)/3
Let p(v) be the third derivative of -v**6/720 + v**5/72 + v**4/144 - 5*v**3/36 - 6*v**2 + 29*v. Factor p(h).
-(h - 5)*(h - 1)*(h + 1)/6
Let a(y) be the second derivative of -y**5/80 + 5*y**4/4 - 50*y**3 + 1000*y**2 - 401*y - 2. Determine t, given that a(t) = 0.
20
Let j(f) = -f**3 - 3*f**2 + 5*f + 6. Let x be 4/(-10) - 90/25. Let q be j(x). Factor -m + m**q - 1 + 1 + m**3 - 1.
(m - 1)*(m + 1)**2
What is g in -g - 1/2*g**4 + 0 + 1/2*g**2 + g**3 = 0?
-1, 0, 1, 2
Let j(o) = -o**3 - 11*o**2 - 11*o - 10. Let u be j(-10). Suppose u = k - r, -r - r + 3 = -k. Factor k*p + 6*p**2 + 3*p**3 + 1 - 6*p**3 - 4 - 3.
-3*(p - 2)*(p - 1)*(p + 1)
Let m = -119 - -125. Let v(y) be the second derivative of -3/8*y**5 - 1/12*y**7 + 0 + 19/60*y**m + 1/24*y**4 + 1/6*y**3 + 0*y**2 - y. Solve v(k) = 0.
-2/7, 0, 1
Let q(f) be the first derivative of 2*f**3/15 - 16*f**2/5 + 78*f/5 + 195. Factor q(x).
2*(x - 13)*(x - 3)/5
Let v(d) be the first derivative of 3*d**6/11 - 24*d**5/55 - d**4/2 - 4*d**3/33 + 6. Find w such that v(w) = 0.
-1/3, 0, 2
Let c be (-13)/39 + 6/16. Let b(h) be the second derivative of -5*h + 0 + 1/80*h**5 + 0*h**3 + 0*h**2 + c*h**4. Factor b(g).
g**2*(g + 2)/4
Let f(y) = y**3 - y**2 - y - 1. Let w(b) = 4*b**3 - 15*b**2 + 45*b - 67. Let i be 132/(-11)*2/(-8). Let k(a) = i*f(a) - w(a). Factor k(g).
-(g - 4)**3
Let b(g) be the first derivative of -5/3*g**3 - 1/180*g**6 + 0*g + 0*g**5 + 0*g**2 - 5 + 0*g**4. Let y(s) be the third derivative of b(s). Factor y(w).
-2*w**2
Let y(t) be the third derivative of 2*t**7/35 - 3*t**6/40 - 3*t**5/10 + 5*t**4/8 - 739*t**2. Suppose y(k) = 0. What is k?
-5/4, 0, 1
Find x such that -8/5 - 4/5*x**4 - 4/5*x**3 + 4/5*x + 12/5*x**2 = 0.
-2, -1, 1
Let h(b) be the first derivative of 2*b**5/35 + b**4/7 - 2*b**3/21 - 2*b**2/7 + 153. Factor h(l).
2*l*(l - 1)*(l + 1)*(l + 2)/7
Let s(y) be the third derivative of 0 + 0*y + 11/45*y**7 - 17/180*y**6 - 4/9*y**3 - 73/90*y**5 + 7/72*y**8 + 27*y**2 - 8/9*y**4. Solve s(z) = 0 for z.
-1, -2/7, 1
Find f, given that 20/19 - 14/19*f + 2/19*f**3 - 8/19*f**2 = 0.
-2, 1, 5
Let x(f) be the third derivative of f**7/210 + 4*f**6/15 + 181*f**2. Factor x(n).
n**3*(n + 32)
Let -1/2 + z**3 + 3/2*z + 5*z**2 - 9/2*z**4 - 5/2*z**5 = 0. What is z?
-1, 1/5, 1
Suppose 8