**2 - 1/6*b - k*b**4 + 0 = 0.
-1/2, 0, 1
Let b(z) be the first derivative of 8*z + 3 - 4*z**2 + 2/3*z**3. Factor b(s).
2*(s - 2)**2
Factor -1/4*v**5 + 1/4*v**2 + 0 + 1/4*v**3 + 0*v - 1/4*v**4.
-v**2*(v - 1)*(v + 1)**2/4
Let i(l) be the first derivative of -1/12*l**4 + 0*l + 0*l**3 - 8/9*l**6 + 8/15*l**5 + 0*l**2 + 1. Factor i(w).
-w**3*(4*w - 1)**2/3
Suppose -306*d + 298*d = -16. What is n in 2/3*n**d + 8/9*n - 8/9 = 0?
-2, 2/3
Suppose 0 = 3*c - c + 14. Let h(i) = 2*i**2 + 16*i + 17. Let r be h(c). Determine m, given that -4/5*m**2 + 2/5*m + 2/5*m**r + 0 = 0.
0, 1
Let z(q) be the second derivative of -q**7/840 - q**6/180 - q**5/120 - q**3/3 + 2*q. Let n(u) be the second derivative of z(u). Factor n(b).
-b*(b + 1)**2
Let q be ((-1)/2)/(2/(-24)). Suppose 2*n = -n + q. What is w in 4*w**2 + 0*w**n - 2*w**2 = 0?
0
Let u(v) be the third derivative of -v**5/20 + v**4/4 + 9*v**2. What is x in u(x) = 0?
0, 2
Suppose 0 = -2*k + 5*h + 10, 0 = 2*k + 4*h + 4 + 4. Let u(q) be the second derivative of k*q**2 + 0*q**4 + 1/20*q**5 - q + 0 - 1/6*q**3. Factor u(x).
x*(x - 1)*(x + 1)
Let m(h) be the second derivative of -h**5/5 + 2*h**3 - 4*h**2 - 13*h. Factor m(u).
-4*(u - 1)**2*(u + 2)
Let z(b) be the first derivative of 0*b + 1/4*b**6 + 2*b**3 + 9/4*b**4 + 3 + 6/5*b**5 + 3/4*b**2. Factor z(w).
3*w*(w + 1)**4/2
Let o(c) = c**3 + c**2. Let a be o(0). Suppose -5 = -0*t + 3*t - 5*g, 2*g - 2 = a. Factor t + 0*i - 1/3*i**2 - 1/3*i**3.
-i**2*(i + 1)/3
Let i be (-12)/(-6)*3/24. Let b(d) be the first derivative of -i*d**2 + 1/8*d**4 + 0*d**3 + 1 + 0*d. Factor b(t).
t*(t - 1)*(t + 1)/2
Let i = 64 + -61. Factor 0*c**i + 0 + 2/5*c**5 - 2/5*c - 4/5*c**4 + 4/5*c**2.
2*c*(c - 1)**3*(c + 1)/5
Find k, given that -10*k**5 - 73/2*k**3 + 127/6*k**2 + 2/3 - 6*k + 92/3*k**4 = 0.
2/5, 1/2, 2/3, 1
Let l(u) = 4*u**3 + 30*u**2 - 30*u + 10. Let f(r) = 6*r + 2*r**2 - 7*r**2 - r**3 - 5 + 3 - r**2. Let k(x) = 14*f(x) + 3*l(x). Solve k(y) = 0.
1
Find w, given that -1 - 2*w**2 + 0*w**2 + 3*w - 5*w + w**2 = 0.
-1
Determine p, given that 4*p**5 + 2*p**4 + 4*p**3 - 5*p**3 + 5*p**5 - 10*p**5 = 0.
0, 1
Let i be (-2)/(-1) + (-4)/(-4). Suppose 5*b - 10 = -5*y, 0*b + b = -i*y + 6. Suppose -2/5*m + 0 - 2/5*m**3 + 4/5*m**y = 0. What is m?
0, 1
Let q(k) be the first derivative of 2/3*k**3 + 0*k**2 + 3 + 6/5*k**5 - 3/2*k**4 - 1/3*k**6 + 0*k. Let q(d) = 0. What is d?
0, 1
Let f(q) = 0 - 1 - 3*q**2 + 0*q**2 + 4*q**2. Let k(l) = -3*l**2 + 3. Let t(a) = 9*f(a) + 2*k(a). Factor t(s).
3*(s - 1)*(s + 1)
Suppose 3*s + 4*l - 22 = -0*s, -12 = -2*s - 2*l. Factor 2/9*o + 2/9*o**s - 4/9.
2*(o - 1)*(o + 2)/9
Let i(z) be the second derivative of -z**6/540 - z**5/90 - z**4/36 - z**3/3 + 4*z. Let p(v) be the second derivative of i(v). Factor p(h).
-2*(h + 1)**2/3
Let v = -3 + 6. Let s(l) be the first derivative of -2/27*l**v + 0*l + 0*l**2 - 1. Determine q so that s(q) = 0.
0
Let q(h) = h**5 - h**4 + h**3 - h**2 + 1. Let a(w) = -679*w**5 - 881*w**4 + 449*w**3 + 871*w**2 + 224*w + 13. Let f(b) = -a(b) - 3*q(b). Solve f(x) = 0 for x.
-1, -2/13, 1
Let w be (-21)/45 + (-8)/(-12). Let h = 48/265 + 1/53. Factor 1/5*c + w*c**2 - h - 1/5*c**3.
-(c - 1)**2*(c + 1)/5
Factor 17 + 20*x - 9 - 2*x**2 + 6*x**2 + 8.
4*(x + 1)*(x + 4)
Let a(x) = -16*x**2 - 67*x - 65. Let z(w) = -11*w**2 - 44*w - 43. Let o(l) = 5*a(l) - 7*z(l). Factor o(n).
-3*(n + 1)*(n + 8)
Let x(h) = -h**3 + 7*h**2 + 7*h - 7. Let q(t) = t**2. Let i(f) = 4*f**2 - f + 1. Let w(d) = i(d) - 5*q(d). Let r(g) = 28*w(g) + 4*x(g). Solve r(k) = 0 for k.
0
Let f = -161 - -161. Factor -3/2*p + 3/2*p**3 + 0*p**2 + f.
3*p*(p - 1)*(p + 1)/2
Let n be ((-36)/48)/((-42)/184) + -3. Factor 0 - 4/7*w + 2/7*w**2 + 4/7*w**3 - n*w**4.
-2*w*(w - 2)*(w - 1)*(w + 1)/7
Suppose 0 = k - o - 3, 2*k + o - 1 = 5. Let l(i) be the first derivative of -2*i + 1/3*i**k + 1 - 1/2*i**2. Factor l(v).
(v - 2)*(v + 1)
Suppose -3 - 9/2*v + 3/2*v**2 + 9/2*v**3 + 3/2*v**4 = 0. What is v?
-2, -1, 1
Suppose 2*a = -2*n + 5*n, 3*a = 3*n. Let w = 10 + -5. Factor 1/2*k**w + 1/2*k**2 + n + 3/2*k**4 + 3/2*k**3 + 0*k.
k**2*(k + 1)**3/2
Let x = -13 - -17. Suppose x - 12 = 4*i - 2*k, -5*k = -5*i - 20. Suppose 0 + i*c**2 + 2/3*c**3 - 2/3*c = 0. Calculate c.
-1, 0, 1
Factor 16/5*i + 6/5 + 2*i**2.
2*(i + 1)*(5*i + 3)/5
Let s = 73/20 - 17/5. Factor 0*g + 1/2*g**3 - s*g**4 - 1/4*g**2 + 0.
-g**2*(g - 1)**2/4
Factor 0*n**2 + 2/3*n - 1/3 + 1/3*n**4 - 2/3*n**3.
(n - 1)**3*(n + 1)/3
Suppose u = 1, 5*k - 3*u = -4*u + 1. Factor -1/4*j - 1/4*j**5 + k*j**4 + 0 + 0*j**2 + 1/2*j**3.
-j*(j - 1)**2*(j + 1)**2/4
Let a be 1 + ((-12)/(-8))/(-3). Let 1/2*m**4 - a*m**2 + 0 - 1/2*m**3 + 1/2*m = 0. Calculate m.
-1, 0, 1
Suppose 3*w - 46 = -20*w. Determine n so that 1/4*n**3 + 0 + 3/4*n**w + 0*n = 0.
-3, 0
Suppose 4 - 2 = 4*i - c, 3*i + c = -2. Let f(x) be the third derivative of 1/24*x**4 - 1/60*x**5 + 0 + i*x**3 + 0*x + x**2. Factor f(h).
-h*(h - 1)
Factor 0 + 9/8*c**3 + 3/8*c - 3/8*c**4 - 9/8*c**2.
-3*c*(c - 1)**3/8
Let v be (-1)/(-3) - 77/(-21). Let y = -4 + v. Factor -2*m + 7*m**3 + m**3 - 6*m**2 + y*m**2.
2*m*(m - 1)*(4*m + 1)
Let t be (-2 + 10/2)/(24/16). Let b(x) be the third derivative of 0 + 3*x**t + 0*x - 1/8*x**4 - 1/60*x**5 - 1/3*x**3. Factor b(h).
-(h + 1)*(h + 2)
Let n(r) be the third derivative of -r**7/13860 + r**5/660 + r**4/8 + 3*r**2. Let y(l) be the second derivative of n(l). Factor y(f).
-2*(f - 1)*(f + 1)/11
Suppose 3*n - s + 3 = 5*n, -8 = -5*n - 2*s. Factor 2*j**3 + 2*j + 0*j**4 - 4*j - 2*j**4 + 2*j**2 + 0*j**n.
-2*j*(j - 1)**2*(j + 1)
Let f(d) = -d**4 + d**2 + 3*d - 3. Let l(s) = -s + 1. Let g = -15 + 18. Let m(p) = g*l(p) + f(p). Factor m(c).
-c**2*(c - 1)*(c + 1)
Let s(j) be the third derivative of -j**5/12 + 5*j**4/6 - 10*j**3/3 - 3*j**2. Factor s(c).
-5*(c - 2)**2
Let z(g) = -2*g + 16. Let m be z(7). Let i(a) be the first derivative of -5/2*a**m - 2*a - 1/3*a**3 + 5/4*a**4 + 3/5*a**5 - 1. Factor i(j).
(j - 1)*(j + 1)**2*(3*j + 2)
Let q(i) be the second derivative of -i**4/78 + 4*i**3/39 - 4*i**2/13 - 5*i. Find r such that q(r) = 0.
2
Find z such that -432/7*z - 324/7 - 216/7*z**2 - 4/7*z**4 - 48/7*z**3 = 0.
-3
Let o(x) be the third derivative of x**5/60 - x**4/12 + x**3/6 - 4*x**2. Let t be o(3). Factor 32/11*d**2 - 8/11*d - 10/11*d**3 - 50/11*d**t + 0.
-2*d*(d + 1)*(5*d - 2)**2/11
Let a(o) be the first derivative of 2/3*o**5 - 7/6*o**4 + 8/3*o**2 - 1/9*o**6 - 2/9*o**3 - 1 - 8/3*o. Solve a(z) = 0 for z.
-1, 1, 2
Determine g, given that -4/9*g - 8/9*g**2 + 4/9*g**3 + 2/9*g**4 + 2/3 = 0.
-3, -1, 1
Suppose -32*g = -2*g - 60. Factor 0 + 3/7*p**3 - 1/7*p**5 - 4/7*p + 4/7*p**g - 2/7*p**4.
-p*(p - 1)**2*(p + 2)**2/7
Let g(i) be the first derivative of 0*i**3 - 2 + 0*i + 1/14*i**4 + 0*i**2 - 2/35*i**5. Factor g(f).
-2*f**3*(f - 1)/7
Suppose 0*y - 3*y - m + 25 = 0, 0 = -m - 5. Suppose 4*w + 2*p = 22, 0*p - 2*p = -y. Factor 0*g - 1/4*g**5 + 0 - 1/4*g**2 - 3/4*g**4 - 3/4*g**w.
-g**2*(g + 1)**3/4
Let t(y) be the first derivative of y**6/180 - y**5/10 + 3*y**4/4 + 2*y**3/3 + 5. Let u(g) be the third derivative of t(g). Factor u(l).
2*(l - 3)**2
Let v(d) be the second derivative of -d**4/6 - d**3 + 4*d**2 + 3*d. Factor v(o).
-2*(o - 1)*(o + 4)
Factor 2/11 + 0*a - 2/11*a**2.
-2*(a - 1)*(a + 1)/11
Factor 0 + 0*w + 8/17*w**4 - 2/17*w**5 + 4/17*w**2 - 10/17*w**3.
-2*w**2*(w - 2)*(w - 1)**2/17
Let m = -2669/15 - -178. Let i(v) be the second derivative of -3/20*v**4 - m*v**3 + 3*v - 7/100*v**5 + 0*v**2 + 0. Find f, given that i(f) = 0.
-1, -2/7, 0
Let o = 3 - 1. Factor 0*q + q - 1 - 2*q**2 + 0*q + o.
-(q - 1)*(2*q + 1)
Factor 3*c**3 - 4*c**3 + 3*c**4 - c**2 + 5*c - 4*c - 2*c**4.
c*(c - 1)**2*(c + 1)
Let m(u) be the first derivative of -3*u**3 - 1/5*u**5 - 2 - 5/4*u**4 - 7/2*u**2 - 2*u. Find p, given that m(p) = 0.
-2, -1
Let m(a) = -a + 15. Let h be m(9). Let j(q) be the first derivative of -1/2*q**2 - 2/3*q**3 + 2/5*q**5 + 0*q + 0*q**4 + 2 + 1/6*q**h. Factor j(i).
i*(i - 1)*(i + 1)**3
Let v(l) be the first derivative of -l**3/9 + l**2/6 + 2*l/3 + 32. Factor v(n).
-(n - 2)*(n + 1)/3
Let m(p) be the first derivative of 4/5*p**5 + 0*p**2 + 0*p**4 + 0*p + 0*p**3 - 3. Factor m(z).
4*z**4
Let k(c) be the second derivative of c**4/9 - 32*c**3/9 - 34*c**2/3 - c - 28. Suppose k(h) = 0. What is h?
-1, 17
Let x be (1 - -1)*9/(-711). Let w = 75