
Determine f so that 30*f + 64*f**2 - 27*f - 56 + 24*f - 12*f**3 + 121*f = 0.
-2, 1/3, 7
Let p(k) be the first derivative of k**6/2 - 9*k**4/4 + 2*k**3 - 110. What is x in p(x) = 0?
-2, 0, 1
Let d(f) be the second derivative of f**4/3 - 10*f**3/3 + 12*f**2 - 28*f. Solve d(q) = 0 for q.
2, 3
Suppose 3*p + 9 = -3*n, -3*p - 17 = -4*n - 43. Solve 0 + 3/8*o - 3/8*o**p = 0 for o.
0, 1
Suppose 45*i - 32*i - 31*i = -36. What is m in -10/3*m + 35/6*m**i + 5/3*m**3 + 0 = 0?
-4, 0, 1/2
Suppose -168*b - 1128 = -166*b. Let g = b - -2271/4. Factor g*h - 7/4*h**2 - 9/4 + 1/4*h**3.
(h - 3)**2*(h - 1)/4
Let s(u) be the second derivative of 1/48*u**4 + 7*u - 1/2*u**2 - 1/6*u**3 + 1/80*u**5 + 0. Factor s(m).
(m - 2)*(m + 1)*(m + 2)/4
Factor -12*t**2 - 36 + 39*t + 3/4*t**3.
3*(t - 12)*(t - 2)**2/4
Suppose 3 + 5 = 4*m. Let r = 18 - 15. Factor -8*o**3 + 16 - 2*o + 2*o**r + 2*o**4 + 6*o**m - 16.
2*o*(o - 1)**3
Let h(r) be the first derivative of -3/2*r**2 + 0*r + 1/720*r**6 - 1/180*r**5 + 4 + 1/144*r**4 + 0*r**3. Let p(s) be the second derivative of h(s). Factor p(v).
v*(v - 1)**2/6
Let n = -11 + 11. Suppose 0 = -4*b - w + 17, n = 5*b + 2*w - 24 - 1. Suppose -50*x**5 + 8*x**5 - 4*x + 110*x**4 - 29*x**3 + 34*x**2 - 69*x**b = 0. Calculate x.
0, 2/7, 1/3, 1
Suppose 44*w = -4851 + 5071. Let 0*d + 0*d**2 + 5*d**3 + 2*d**4 + 0 + 1/5*d**w = 0. What is d?
-5, 0
Let d(s) be the third derivative of s**7/11340 - s**5/540 + 23*s**4/24 - 21*s**2. Let q(v) be the second derivative of d(v). Factor q(z).
2*(z - 1)*(z + 1)/9
Let t(d) = 24*d**4 - 14*d**3 + 80*d**2 + 34*d - 98. Let p(a) = -a**4 + a**3 - a**2 - a + 1. Let s(r) = -52*p(r) - 2*t(r). Factor s(k).
4*(k - 9)*(k - 1)*(k + 2)**2
Let h(o) be the third derivative of 0*o - 1/30*o**5 - 9*o**2 + 1/60*o**6 - 1/315*o**7 + 0*o**3 + 0 + 1/36*o**4. Factor h(j).
-2*j*(j - 1)**3/3
Let w(v) = v**2 - 10*v + 13. Let h be ((-4)/(-2))/(6/27). Let j be w(h). Let -27/4*d + 21/4*d**j + 27/4*d**3 - 3/2 - 15/4*d**2 = 0. What is d?
-1, -2/7, 1
Let g(c) be the first derivative of -c**5/25 - 11*c**4/10 - 7*c**3/5 - 63. Suppose g(m) = 0. Calculate m.
-21, -1, 0
Let -38*n**3 + n**4 - 5*n**2 + 124*n**3 - 42*n**3 - 40*n**3 = 0. What is n?
-5, 0, 1
Determine r so that -2/3*r**5 - 8/3*r**3 + 0*r - 8/3*r**4 + 0*r**2 + 0 = 0.
-2, 0
Let x(r) be the third derivative of -r**6/24 - r**5/6 + 5*r**4/6 + 20*r**3/3 + 61*r**2. Determine h, given that x(h) = 0.
-2, 2
Let z(a) be the third derivative of -a**5/30 - 13*a**4/4 + 40*a**3/3 + 19*a**2 + a. Factor z(o).
-2*(o - 1)*(o + 40)
Suppose 45*t - 102 = -61 + 49. Find c such that 2/3*c**3 - 14/9*c**t + 0 + 4/9*c = 0.
0, 1/3, 2
Suppose -40*w = 36 - 36. Let t(u) be the second derivative of 9*u + 0 + 3/80*u**5 + 0*u**3 + w*u**2 + 1/16*u**4. Factor t(i).
3*i**2*(i + 1)/4
Let q(t) = 4*t**3 + 58*t**2 - 5*t + 5. Let p(h) = -2*h**3 - 30*h**2 + 3*h - 3. Let s(r) = 5*p(r) + 3*q(r). Solve s(n) = 0.
-12, 0
Let p(f) be the second derivative of f**7/245 + f**6/210 - f**5/210 + 25*f**2/2 - 19*f. Let v(t) be the first derivative of p(t). Factor v(m).
2*m**2*(m + 1)*(3*m - 1)/7
Let p(w) be the first derivative of -4*w**5/15 - 11*w**4/3 - 44*w**3/3 - 74*w**2/3 - 56*w/3 + 213. What is r in p(r) = 0?
-7, -2, -1
Let r(p) be the second derivative of p**5/210 - p**4/84 - 4*p**2 - 16*p. Let z(l) be the first derivative of r(l). Factor z(u).
2*u*(u - 1)/7
Let v = -1/22374 + 9665575/156618. Determine s so that 216/7*s + 36/7*s**2 + 2/7*s**3 + v = 0.
-6
Suppose -5*a + 21 - 1 = 0, 4*q = 5*a. Let 14*d**3 - 38*d**3 - 2*d**q - 6*d**2 - 12*d**2 - 14*d**4 - 6*d**3 = 0. Calculate d.
-3, -1, 0
Suppose -25*a - 5 = -26*a. Let m be 2*a/(-8) + (-44)/(-22). Factor -m*k**2 + 7/4*k - 1/2.
-(k - 2)*(3*k - 1)/4
Let m be 33*4/21 + (-3 - 3). Factor m - 4/7*l - 6/7*l**2.
-2*(l + 1)*(3*l - 1)/7
Let i(n) = -3*n - n + 2*n + n**2 - 33 + 1. Let k be i(-5). Factor -2/3 + 1/3*g + g**2 - 1/3*g**4 - 1/3*g**k.
-(g - 1)**2*(g + 1)*(g + 2)/3
Let h(a) be the third derivative of a**7/630 + a**6/10 + 27*a**5/10 - a**4/24 + 32*a**2. Let w(z) be the second derivative of h(z). Solve w(d) = 0 for d.
-9
Let d(z) be the first derivative of 24*z**2 - 16 - 69/4*z**4 - 40*z**3 - 9/5*z**5 + 0*z. Factor d(s).
-3*s*(s + 4)**2*(3*s - 1)
Let j(u) be the third derivative of u**5/12 - 145*u**4/24 + 70*u**3/3 - 32*u**2. Factor j(t).
5*(t - 28)*(t - 1)
Let t be (-1)/((2 + 1)/3). Let d be 4/(14 - (t + 1)). Find y, given that -2/7 - 2/7*y**3 + 2/7*y + d*y**2 = 0.
-1, 1
Let j(y) be the third derivative of -y**6/30 + y**4/6 + 43*y**2 + y. Let j(b) = 0. Calculate b.
-1, 0, 1
Let u(s) = -2*s**3 + 4*s**2 + 2*s + 2. Let c(w) = -9*w**2 - 31*w**3 + 0 + 35*w**3 - 5*w - 5. Let i(m) = 2*c(m) + 5*u(m). Factor i(n).
-2*n**2*(n - 1)
Let a be (-8)/(-12)*3/8. Let u be 1455/120 - (-1 - -13). Determine h, given that a*h + u*h**2 + 1/8 = 0.
-1
Let g(m) be the third derivative of -30*m**2 + 0*m + 0 - 49/2*m**3 + 63/8*m**4 - 3/4*m**5 + 1/40*m**6. Determine k, given that g(k) = 0.
1, 7
Let p be (17 - -7)/3 + -5. Let l(a) be the first derivative of 14 + 0*a + 1/8*a**4 + 0*a**2 + 0*a**p. Factor l(b).
b**3/2
Let q(u) be the second derivative of u**7/5040 - u**6/288 + u**5/60 - 2*u**4/3 + 41*u. Let r(z) be the third derivative of q(z). Factor r(j).
(j - 4)*(j - 1)/2
Let g(s) be the second derivative of s**4/3 + 286*s**3/3 + 284*s**2 + 4*s - 51. Suppose g(h) = 0. What is h?
-142, -1
Let t(v) = -315*v**3 - 4915*v**2 - 10915*v + 3475. Let j(p) = 35*p**3 + 546*p**2 + 1213*p - 386. Let z(i) = 35*j(i) + 4*t(i). Factor z(q).
-5*(q + 3)*(q + 13)*(7*q - 2)
Let i(b) = -578*b + 4048. Let o be i(7). Factor -2/9*u**4 + 0 - 2/3*u**o + 2/3*u**3 + 2/9*u.
-2*u*(u - 1)**3/9
Suppose -3*m + 0*m - 2*c - 8 = 0, -2*m - 3*c = 2. Let k be m + 9 - 1*3. Suppose q - q**3 + 0*q - q - q**k = 0. Calculate q.
-1, 0
Let x(s) = -s - 4. Let p be x(5). Let d be (-1)/((-33)/p - 4). Let 2*h**4 - 5*h**4 - 6*h**2 - 4*h**d - 5*h**3 = 0. What is h?
-2, -1, 0
Let u = 119/60 + -29/60. Factor 0 + 3*q**2 + 0*q - u*q**3.
-3*q**2*(q - 2)/2
Let f(a) be the third derivative of a**7/2100 + a**6/40 + 3*a**5/8 - 63*a**2 + 3. Factor f(b).
b**2*(b + 15)**2/10
Let h be (6/(-20) - 0) + 69/230. Factor -8/7*c**3 - 4/7 + h*c + 12/7*c**2.
-4*(c - 1)**2*(2*c + 1)/7
Let b(x) be the first derivative of x**6/18 - 2*x**5/3 - x**4 + 10*x**3/9 + 11*x**2/6 + 5. What is c in b(c) = 0?
-1, 0, 1, 11
Let r(g) be the first derivative of -12 + 6*g - 5/2*g**2 + 1/4*g**4 - 2/3*g**3. Factor r(v).
(v - 3)*(v - 1)*(v + 2)
Let l(u) = 15*u**3 + 77*u**2 + 43*u - 32. Let k be (-110)/(-33)*(-3)/1. Let g(t) = -8*t**3 - 38*t**2 - 22*t + 16. Let o(d) = k*g(d) - 4*l(d). Factor o(q).
4*(q + 2)**2*(5*q - 2)
Suppose 0 - 3/2*o**3 + 147/2*o**2 + 0*o = 0. Calculate o.
0, 49
Let k(p) be the third derivative of 5/24*p**3 + 5/96*p**4 + 0 + 0*p - 1/96*p**6 - 1/48*p**5 + 3*p**2. Factor k(c).
-5*(c - 1)*(c + 1)**2/4
Suppose 0 - 18/5*g - 8/5*g**2 = 0. Calculate g.
-9/4, 0
Let i(t) be the third derivative of 0*t**4 + 0*t + 0 + 1/100*t**5 + 13*t**2 - 1/350*t**7 + 0*t**3 + 0*t**6. Factor i(k).
-3*k**2*(k - 1)*(k + 1)/5
Determine c, given that -43*c**2 + 100 + 60*c + 106*c**2 - 58*c**2 = 0.
-10, -2
Suppose 5*p = -4*v - 2, 16 = 5*p - 5*v + 3*v. Let f(i) be the first derivative of -3/8*i**p + 0*i - 5 - 1/4*i**3. Factor f(o).
-3*o*(o + 1)/4
Find k, given that -18*k**2 - k - 26*k**2 - k**3 + 26*k**2 - 16*k = 0.
-17, -1, 0
Let q(g) be the second derivative of g**7/6300 - g**6/2700 - g**5/225 + g**4/45 + g**3 + 2*g. Let x(d) be the second derivative of q(d). Solve x(u) = 0.
-2, 1, 2
Let i(z) = z**2 + 8*z + 2. Let s be i(-8). Suppose s*y = 48 + 10. What is t in y*t + t**2 - 15*t - 14*t = 0?
0
Suppose 0 = -g - 0*g + 16. What is u in -51*u**4 - 9 + 28*u + g*u**3 + 1 + 4*u**3 + 47*u**4 - 36*u**2 = 0?
1, 2
Factor -3*t**2 - 44 + 3*t**3 - 49 + 0*t - 3*t + 96.
3*(t - 1)**2*(t + 1)
Let g(i) be the third derivative of i**4/8 - i**3/2 - 6*i**2. Let r be g(2). Factor 5*z**2 + 4*z**3 - 4*z**2 - 2*z**4 + 0*z**r - 3*z**2.
-2*z**2*(z - 1)**2
Let m be (3 + -2)/((-104)/108 - -1). Suppose m*g = 35*g - 16. Factor 2/5*q**g - 2/5*q + 0.
2*q*(q - 1)/5
Let x = 29 + -6. Suppose y + 5*w + x = 0, -2*y - 3 - 3 = 2*w. Let -2*l**3 + 0*l**3 + 2*l**y - 4*l**2 + l**3 = 0. Calculate l.
-2, 0
Suppose -6*k - 37*k + 86 = 0. Factor 3*y**3 - 3/2*y + 0*y**k + 0*y**4 + 