2*i = 20. Find f, given that 2*f**3 - 9*f + n*f**2 - 6*f**3 - 3*f**4 - 2*f**3 + 2*f**5 + f**3 + 2 = 0.
-2, 1/2, 1
Let 3*l**2 - 4 + l + 7 - 10*l + 3 = 0. What is l?
1, 2
Let k(u) be the second derivative of 2*u**6/195 - 3*u**5/130 - u**4/39 + 7*u. Factor k(b).
2*b**2*(b - 2)*(2*b + 1)/13
Let a(t) be the first derivative of 2*t**6/3 - 4*t**5/5 - t**4 + 4*t**3/3 + 12. Factor a(r).
4*r**2*(r - 1)**2*(r + 1)
Let k(x) be the second derivative of -x**5/28 + x**4/7 + 11*x**3/42 - 3*x**2/7 - 15*x. Let k(c) = 0. What is c?
-1, 2/5, 3
Let q(w) be the first derivative of 0*w + 0*w**4 - w**2 - 4/5*w**5 + 4/3*w**3 + 1/3*w**6 + 1. Let q(g) = 0. Calculate g.
-1, 0, 1
Let i(p) be the first derivative of -2*p**6/15 + 2*p**4/5 - 2*p**2/5 + 8. What is z in i(z) = 0?
-1, 0, 1
Let y be (-3)/(2 + 153/(-75)). Determine n, given that 57*n**3 + 43*n + 25*n + 10*n**4 + 3*n**5 + 12 - 20*n + y*n**2 + 11*n**4 = 0.
-2, -1
Let n = -2 + 2. Suppose -6*a + 5*a = n. Let a*q + 2/5*q**5 + 0*q**2 + 2/5*q**3 + 4/5*q**4 + 0 = 0. What is q?
-1, 0
Let t be 5/2*((-341)/55 - -7). Factor 3/2 + 9/4*l + 3/4*l**t.
3*(l + 1)*(l + 2)/4
Suppose 2 - 12 = -5*u. Suppose 9 = u*o + o. Factor -2/7*r**4 - 2/7*r**2 + 0*r + 0 - 4/7*r**o.
-2*r**2*(r + 1)**2/7
Solve -12 + 2*h**2 + 23*h**3 - 47*h**2 - 3*h**4 - 3*h**3 + 39*h + h**3 = 0 for h.
1, 4
Let w(v) be the third derivative of 0*v**3 - v**2 + 0 + 1/60*v**4 + 1/300*v**5 + 0*v. Factor w(c).
c*(c + 2)/5
Factor 0*w + 0*w**2 + 2/15*w**4 + 0 + 2/15*w**3.
2*w**3*(w + 1)/15
Let h(u) be the third derivative of -u**6/80 - u**5/40 - 2*u**2 - 19*u. Factor h(y).
-3*y**2*(y + 1)/2
Let i be 0 + 4 + -2 - 9. Let y(d) = -9*d**2 + 25*d. Let v(h) = -3*h**2 + 8*h. Let z(g) = i*v(g) + 2*y(g). Factor z(a).
3*a*(a - 2)
Determine h so that 0*h**2 - 8/9*h**3 + 0*h**4 + 4/9*h + 0 + 4/9*h**5 = 0.
-1, 0, 1
Let y = 19 - 15. Suppose -2 = 2*t - 2*h - 6, 4*t + y*h = -8. Factor 0 + 1/2*w**3 + t*w + 0*w**2.
w**3/2
Suppose -2*t + 21 = 5*u - 5, -3*u - 3*t + 21 = 0. Suppose -2/9*f**2 - 8/9 - 10/9*f**3 + 2/9*f**u + 2/9*f**5 + 16/9*f = 0. Calculate f.
-2, 1
Factor 4/9*i**3 + 2/9 - 4/9*i + 0*i**2 - 2/9*i**4.
-2*(i - 1)**3*(i + 1)/9
Find d, given that 2/17*d**5 - 10/17*d**4 + 4/17*d**3 - 6/17*d - 18/17 + 28/17*d**2 = 0.
-1, 1, 3
Let f(w) be the third derivative of -w**5/150 + w**4/15 - 11*w**2. Factor f(h).
-2*h*(h - 4)/5
Let b(x) be the third derivative of -x**6/1260 - x**5/210 - x**4/84 + x**3/2 + 2*x**2. Let g(t) be the first derivative of b(t). What is u in g(u) = 0?
-1
Let s(m) be the first derivative of -2*m**3 - 3/2*m**2 + 3/4*m**4 + 5 + 6*m. Let s(d) = 0. Calculate d.
-1, 1, 2
Let s(w) be the third derivative of w**8/252 - 4*w**7/63 + 5*w**6/18 + 4*w**5/9 - 40*w**4/9 - 128*w**3/9 - 14*w**2. Find r such that s(r) = 0.
-1, 4
Let p(x) be the first derivative of 6*x**2 - 3/4*x**4 - 12*x + 2 + x**3. Suppose p(j) = 0. Calculate j.
-2, 1, 2
Let w(f) be the first derivative of -f**5/20 - f**4/4 - f**3/2 - f**2/2 - f + 1. Let l(a) be the first derivative of w(a). What is n in l(n) = 0?
-1
Suppose -2*p + 17 = -1. Suppose 0 = f - p - 7. Solve -f*u - 2*u**2 + 2*u**4 + 16*u = 0.
-1, 0, 1
Let g(c) be the third derivative of c**8/840 - c**6/75 + c**5/75 + c**4/20 - 2*c**3/15 + 7*c**2. Find d such that g(d) = 0.
-2, -1, 1
Let p(z) be the second derivative of -z**5/180 + z**4/72 - z**2 + 2*z. Let l(y) be the first derivative of p(y). Find v such that l(v) = 0.
0, 1
Suppose 4*x + 2 = -6*i + 4*i, 0 = -3*x - 4*i - 4. Let g = x - -3. Factor 13*k**4 - 4*k**5 - 6*k**3 + 3*k - k - 2*k**2 - g*k**4.
-2*k*(k - 1)**3*(2*k + 1)
Let v(q) be the first derivative of q**4/4 - 2*q**3/15 + 26. Factor v(d).
d**2*(5*d - 2)/5
Let o be (-16)/128*18/(-2). Let y = -7/8 + o. Find w such that 1/4*w**3 - 1/2*w**2 + y*w + 0 = 0.
0, 1
Let p be (-4)/(-18) - (-104)/18. Suppose -x - 5*m + 18 = 0, -x - 9 = -p*x + 2*m. Factor -1/2*z + 1/2*z**x + 1/2*z**2 - 1/2*z**4 + 0.
-z*(z - 1)**2*(z + 1)/2
Find k, given that 2/11 - 2/11*k**2 + 0*k = 0.
-1, 1
Let f be 1/(-2) + 22/28. Let y(c) = -2*c - 58. Let w be y(-30). Factor -f*g**w - 8/7 + 8/7*g.
-2*(g - 2)**2/7
Let x be (-5)/(-4*(-4)/(-16)). Let 1/2*v**x + 1/2*v + 1 - 2*v**2 + v**4 - v**3 = 0. What is v?
-2, -1, 1
Factor 14/11*q**3 + 18/11*q**2 + 4/11*q + 0.
2*q*(q + 1)*(7*q + 2)/11
Solve -3/4*p**2 + 0 - 1/2*p + 1/2*p**3 = 0.
-1/2, 0, 2
Let v(o) be the first derivative of -o**9/1512 + o**7/140 + o**6/90 - o**3 + 2. Let u(i) be the third derivative of v(i). Factor u(a).
-2*a**2*(a - 2)*(a + 1)**2
Let p(g) be the first derivative of -g**4/18 - 2*g**3/27 + 1. Factor p(k).
-2*k**2*(k + 1)/9
Factor -39*y**2 - 6 + 0 - 259*y + 304*y.
-3*(y - 1)*(13*y - 2)
Let c(a) be the second derivative of -a**4/3 + a**3/6 - a**2/2 + a. Let z(w) = -5*w**2 + w - 2. Let i(y) = 4*c(y) - 3*z(y). Find u such that i(u) = 0.
-1, 2
Let l = -6 + 6. Let u(o) = -o**3 + o + 4. Let w be u(l). What is p in -3*p**2 + 3*p**5 - p**5 + p**5 - 2*p**w - 3*p**3 + 5*p**2 = 0?
-1, 0, 2/3, 1
Let q(r) be the third derivative of r**6/50 - 9*r**5/100 + 3*r**4/20 - r**3/10 - 25*r**2. Factor q(a).
3*(a - 1)**2*(4*a - 1)/5
Let g(m) be the first derivative of -m**2 + 4 + 1/2*m**4 + 2/3*m**3 - 2*m. Suppose g(l) = 0. What is l?
-1, 1
Let b(u) be the first derivative of -2*u**3/15 + 4*u**2/5 - 8*u/5 - 2. Let b(p) = 0. Calculate p.
2
Factor 0*g + 1/11*g**4 + 4/11*g**2 + 0 - 4/11*g**3.
g**2*(g - 2)**2/11
Let w(f) be the first derivative of 4*f**3/21 + 8*f**2/7 + 12*f/7 + 36. Determine y so that w(y) = 0.
-3, -1
Let q(w) be the third derivative of -w**6/720 - w**5/360 + w**4/72 - 6*w**2. Solve q(c) = 0 for c.
-2, 0, 1
Let c(m) be the second derivative of -3*m**7/70 + 13*m**6/50 - 17*m**5/50 - m**4/6 + 11*m**3/30 + 3*m**2/10 - 9*m. Suppose c(z) = 0. Calculate z.
-1/3, 1, 3
Let u(k) be the third derivative of -k**5/210 - 2*k**4/7 - 48*k**3/7 + 2*k**2 + 8*k. Factor u(l).
-2*(l + 12)**2/7
Suppose -2*f + f = -2. Suppose -5*o - f*q + 10 = 3*q, 4*o - 4 = -2*q. Suppose -6/5*m**4 + 2/5*m**5 + o + 4/5*m**3 + 0*m**2 + 0*m = 0. What is m?
0, 1, 2
Factor 230 - 222 - 37*z + 20*z**2 - 7*z.
4*(z - 2)*(5*z - 1)
Let p(h) be the first derivative of 2*h**4 + 7/3*h**3 + 0*h - 16/5*h**5 + 2 + 1/2*h**2. Let p(o) = 0. What is o?
-1/4, 0, 1
Let g(a) be the second derivative of -2*a**6/25 + a**5/5 - 2*a**4/15 + 14*a. Determine u so that g(u) = 0.
0, 2/3, 1
Suppose 0 = -4*c + 32 - 20. Let o(b) be the second derivative of 1/24*b**3 - 1/120*b**6 - 1/16*b**4 + c*b + 0*b**2 + 3/80*b**5 + 0. Factor o(u).
-u*(u - 1)**3/4
Suppose -5*r + 1 = b + 5, 4*r - 2*b = -6. Let p be (10/(-25))/(r/5). Solve -1/3*g**p + 0 + 0*g = 0 for g.
0
Let n(h) = -h**4 - 5*h**3 - 6*h**2 + 6*h + 6. Let y(q) = -2*q**4 - 9*q**3 - 11*q**2 + 11*q + 11. Let z(j) = 11*n(j) - 6*y(j). Factor z(s).
s**3*(s - 1)
Let y(m) be the second derivative of 0*m**2 + 4*m - 1/180*m**6 - 3/4*m**4 - 1/10*m**5 + 1/2*m**3 + 0. Let r(o) be the second derivative of y(o). Factor r(j).
-2*(j + 3)**2
Let h(g) be the first derivative of g**7/3360 + g**3/3 + 2. Let y(m) be the third derivative of h(m). What is x in y(x) = 0?
0
Let q = -10 - -42. Let x be 2/1 - q/20. Factor -2*f - x*f**3 + 4/5 + 8/5*f**2.
-2*(f - 2)*(f - 1)**2/5
Let n(p) be the second derivative of -p**4/42 + p**2/7 + 11*p. Let n(v) = 0. Calculate v.
-1, 1
Factor f - 1/4*f**4 + 0*f**2 + 0 - 3/4*f**3.
-f*(f - 1)*(f + 2)**2/4
Let c(s) be the first derivative of -2*s**3/33 - s**2/11 - 3. Factor c(y).
-2*y*(y + 1)/11
Let a(h) be the first derivative of -1/30*h**5 - 1 - 1/3*h**3 + h + 1/6*h**4 + 1/3*h**2. Let q(g) be the first derivative of a(g). Factor q(x).
-2*(x - 1)**3/3
Let x(v) be the first derivative of v**7/840 - v**5/120 + 4*v**3/3 + 2. Let b(f) be the third derivative of x(f). Solve b(r) = 0.
-1, 0, 1
Let k(w) be the third derivative of 3*w**8/28 - 2*w**7/35 - 4*w**6/15 + 4*w**5/15 - 8*w**2. Factor k(b).
4*b**2*(b + 1)*(3*b - 2)**2
Let n be (-54)/(-216)*(-1 + 4). What is p in n*p**3 - 1/2*p**2 + 0*p + 0 + 5/4*p**4 = 0?
-1, 0, 2/5
Suppose 3*t + 10 = -2*t. Let a be t/10 - 21/(-5). Let -2*z**4 - 2*z**3 + a*z**4 + 0*z**4 = 0. Calculate z.
0, 1
Solve -99*s**3 + 18*s**4 - 23*s**2 + 42*s**4 - 49*s**2 + 18*s**3 - 12*s = 0 for s.
-2/5, -1/4, 0, 2
Suppose -2*s = -10 - 8. Suppose 4*v = v + s. Find w such that v*w**2 - 6*w**2 - 2*w**2 - 3*w**3 - 2*w = 0.
-1, -2/3, 0
Let r(q) b