/9*x**b + 8/9 - 8/9*x = 0. What is x?
2
Factor 0 + 2/5*i**5 + 2/15*i - 4/3*i**4 + 8/5*i**3 - 4/5*i**2.
2*i*(i - 1)**3*(3*i - 1)/15
Solve 0 - 2/9*n**2 - 2/9*n = 0 for n.
-1, 0
Let i = -1 + 3. Let t = -2 - -3. Factor -s + s**i + s - 2*s + t.
(s - 1)**2
Let i = -308/5 + 62. Suppose 0 - 2/5*c + i*c**3 + 0*c**2 = 0. Calculate c.
-1, 0, 1
Let g(a) = a**2 + 3*a - 5. Let t be g(-5). Suppose -4 = -t*r + 3*f + 3, 11 = 3*r + 5*f. Solve 5*s**2 - 2*s**r + s**3 - 6*s**2 + 2*s**3 = 0.
0, 1
Let i(l) be the first derivative of 8*l + 38*l**2 + 1 + 76*l**3 + 64/5*l**5 + 56*l**4. Find b, given that i(b) = 0.
-2, -1, -1/4
Suppose -3*r - 2*u + 65 = -4*u, -3*u + 83 = 5*r. Suppose 3*s = -3*x - 3, -4*x - 2*s - 2 = -x. Factor r*z**3 + 2*z**3 + 15*z**4 + x*z**3 + 9*z**2 + z + 2*z**3.
z*(z + 1)*(3*z + 1)*(5*z + 1)
Let s be 3 + -5*(6 - 2)/12. Factor -8/9*m**2 - 8/9*m**4 + 0 + 2/9*m + 2/9*m**5 + s*m**3.
2*m*(m - 1)**4/9
Let n(p) be the first derivative of p**5 - 5*p**4/4 - 5*p**3 + 5*p**2/2 + 10*p - 66. Factor n(y).
5*(y - 2)*(y - 1)*(y + 1)**2
Let a(m) = 2*m**2 - 1. Let i be a(-1). Solve -2*o**4 - i - 8*o**3 + 8*o**3 + o**4 + 2*o**2 = 0 for o.
-1, 1
Let f(q) be the first derivative of -1/2*q**2 - 1/20*q**4 + 2/5*q - 3 + 4/15*q**3. What is o in f(o) = 0?
1, 2
Let c(j) be the third derivative of j**7/945 + j**6/540 - 2*j**5/135 - j**4/27 - 15*j**2. Factor c(b).
2*b*(b - 2)*(b + 1)*(b + 2)/9
Let m = 0 - 0. Suppose m = -3*h + 7*h - 12. Find j, given that -2*j - h*j**2 + 4*j**2 + 3*j = 0.
-1, 0
Let i(g) be the second derivative of -3*g**5/20 + 6*g. Factor i(z).
-3*z**3
Suppose -5*p - 3 = -8*p. Let h(a) = -7*a**3 + a**2. Let r be h(p). Let d(m) = m**2 - 1. Let f(c) = 4*c - 4. Let n(o) = r*d(o) + f(o). Solve n(y) = 0.
-1/3, 1
Let j(m) = 4*m**5 - 12*m**3 - 4*m**2 + 4. Let d(t) = -4*t**5 + 12*t**3 + 5*t**2 - 3. Let w = -19 - -16. Let f(l) = w*j(l) - 4*d(l). Factor f(z).
4*z**2*(z - 2)*(z + 1)**2
Let q(f) be the third derivative of 2/3*f**3 - 1/30*f**5 + 0 - 1/12*f**4 + 0*f + 5*f**2. Factor q(z).
-2*(z - 1)*(z + 2)
Suppose 0 + 3/4*b**3 + 1/4*b**4 + 1/4*b + 3/4*b**2 = 0. Calculate b.
-1, 0
Let w = -3/11 - -17/22. Let b be (-1 - -1)/(16/(-16)). Factor b + 1/4*c**2 - w*c.
c*(c - 2)/4
Let z(t) be the second derivative of t**6/135 - t**5/30 + t**4/18 - t**3/27 - t. What is u in z(u) = 0?
0, 1
Let i be (182/(-21) + 4)*(-12)/154. Factor 2/11*z**3 - i + 2/11*z**4 - 6/11*z**2 - 10/11*z.
2*(z - 2)*(z + 1)**3/11
Let y(v) be the third derivative of -v**5/60 - v**4/6 - 5*v**3/6 - 2*v**2. Let t(b) = b + 1. Let o(f) = 5*t(f) + y(f). Suppose o(c) = 0. Calculate c.
0, 1
Solve 0 + 0*w + 3/2*w**2 + 9/2*w**4 - 3/2*w**5 - 9/2*w**3 = 0.
0, 1
Let q be 8 + (-19)/((-1254)/(-516)). Let r be (-2)/(-4) + (-14)/44. Factor 0 - q*p**3 - 2/11*p**4 + 2/11*p**2 + r*p.
-2*p*(p - 1)*(p + 1)**2/11
Suppose x = 2*x - 18. Let b(c) = -c**2 + 3*c + 2. Let u(j) = j**3 - 5*j**2 + 11*j + 8. Let y(s) = x*b(s) - 4*u(s). Factor y(f).
-2*(f - 2)*(f + 1)*(2*f + 1)
Let z**3 - 2*z**2 + 6*z + 1 - 3*z + 1 - 4*z = 0. Calculate z.
-1, 1, 2
Let l = 13 + -11. Let h be 2/(-6) - (l - 3). Factor 0*g + 2/3*g**4 + 4/3*g**3 + 0 + h*g**2.
2*g**2*(g + 1)**2/3
Let t = 486/23 - 4037/92. Let r = t + 23. Factor 1/4*x**3 + 0*x - r*x**2 + 0.
x**2*(x - 1)/4
Let d(x) be the third derivative of -x**5/15 + x**4/12 + x**3/3 + 8*x**2. Factor d(f).
-2*(f - 1)*(2*f + 1)
Suppose -2*b + 5*b + 5*m = 51, 4*b - 39 = 3*m. Factor 32/7*z**4 + b*z + 16*z**3 + 146/7*z**2 + 18/7.
2*(z + 1)**2*(4*z + 3)**2/7
Let z(i) be the second derivative of -3*i**4/4 + 11*i**3/6 - i**2 - 32*i. Factor z(p).
-(p - 1)*(9*p - 2)
Let s(u) = -u**3 - 20*u**2 - u - 17. Let a be s(-20). Suppose -a*d = -t - 7, 0 = 2*d + 3*d - 15. Suppose -5/2*w**3 + w - 3/2*w**t + 0 = 0. Calculate w.
-1, 0, 2/5
Let f = 3 + -3. Factor f*q**5 + 0*q**3 - 6*q**5 - 2*q**5 + 2*q**3 - 6*q**4.
-2*q**3*(q + 1)*(4*q - 1)
Let b(g) be the second derivative of 4*g + 0*g**3 + 0*g**2 - 1/75*g**6 - 1/30*g**4 - 1/25*g**5 + 0. Let b(l) = 0. What is l?
-1, 0
Let r(c) = -21*c**5 - 57*c**4 - 49*c**3 - 7*c**2 + 10*c. Let x(y) = y**3 + y**2 - y. Let z(h) = -r(h) - 4*x(h). Factor z(o).
3*o*(o + 1)**3*(7*o - 2)
Suppose -25*f**3 + 2*f**3 + 5*f**4 + 20*f + 8*f**3 = 0. Calculate f.
-1, 0, 2
Let z = 23 - 14. Let l = -4 + z. Let 2/7*q**l - 2/7 + 4/7*q**2 - 2/7*q**4 + 2/7*q - 4/7*q**3 = 0. Calculate q.
-1, 1
Solve -8/5 + 2/5*t**3 + 16/5*t - 2*t**2 = 0 for t.
1, 2
Factor 108*u**2 - 92*u**3 - 9*u + 29*u**4 + 8 - 43*u - 4*u**4 + 3*u**4.
4*(u - 1)**3*(7*u - 2)
Let y(w) be the third derivative of 0*w**3 + 0 + 0*w + 1/4*w**4 - 2*w**2 - 1/20*w**5. Factor y(t).
-3*t*(t - 2)
Let l be (-2*3)/(-1 + -1). Suppose -2*p + l*p = 0. Factor 2*w**3 + w + p*w**3 - w**3 - 2*w**2.
w*(w - 1)**2
Factor -59/4*l + 15/4 + 14*l**2 + l**3.
(l + 15)*(2*l - 1)**2/4
Let q(d) be the second derivative of 0 + 1/80*d**5 + 0*d**2 + 3*d + 1/24*d**4 + 1/24*d**3. Factor q(s).
s*(s + 1)**2/4
Let t = 19 - 14. Suppose -5*y - 4*p - 10 = 0, p - 4*p = 5*y + t. Let 0*i + 2/5*i**4 + 0 - 4/5*i**3 + 2/5*i**y = 0. Calculate i.
0, 1
Let v = -8 + 10. Suppose 0 = -v*n - 0 + 4. Find l such that -1/3*l**n + 0 - 1/3*l**4 + 2/3*l**3 + 0*l = 0.
0, 1
Let n be 260/32 + 1/(-8). Find x, given that 8*x**2 - 2*x**2 - 2*x**2 - n - 6*x**2 + 8*x = 0.
2
Let w(o) be the third derivative of o**5/150 - o**4/20 + 2*o**3/15 + o**2. Determine j so that w(j) = 0.
1, 2
Let d(s) be the second derivative of -s**4/4 - 5*s**3 - 24*s**2 - 48*s. Factor d(f).
-3*(f + 2)*(f + 8)
Factor 2/3*z + 0 - 7/6*z**3 + 2*z**2.
-z*(z - 2)*(7*z + 2)/6
Let s(v) be the first derivative of v**3/6 - 5*v**2/2 - 11*v/2 + 4. Factor s(b).
(b - 11)*(b + 1)/2
Let u(c) = 66*c - 4. Let r be u(5). Let o = r - 2274/7. Factor o*s - 2/7*s**2 - 8/7.
-2*(s - 2)**2/7
Let c = -11759/30 + 392. Let z(f) be the second derivative of 9*f**2 - 2*f - 3*f**3 - c*f**5 + 1/2*f**4 + 0. Factor z(r).
-2*(r - 3)**3/3
Suppose 7*f - 4*f = 24. Suppose -12*o = -f*o. Solve o*d + 0 - 2/7*d**5 - 6/7*d**3 - 6/7*d**4 - 2/7*d**2 = 0 for d.
-1, 0
Suppose a + 3*b + 2 = 0, 0*a - 5*a - 4*b + 23 = 0. Let c be 12/a + (-4)/(-14). Factor c*n + n - n**2 - 4*n.
-n*(n + 1)
Let y(d) be the second derivative of d**7/252 + d**6/180 - d**5/60 - 3*d. Factor y(z).
z**3*(z - 1)*(z + 2)/6
Let a(u) be the third derivative of -u**7/315 + u**6/180 + 9*u**2. Find c, given that a(c) = 0.
0, 1
Let l(a) = -a**3 + a**2 + a. Let w be l(-1). Let s = 81 - 323/4. Factor d + s*d**2 + w.
(d + 2)**2/4
Let v(k) = k**2 + 2*k - 1. Let h be v(-4). Determine z, given that -19*z + 17*z**2 + 8 - h*z**2 + 3*z - 2*z**3 = 0.
1, 2
Let y be (1/(-123 + 3))/(-2). Let q(m) be the third derivative of -1/160*m**6 + 2*m**2 - y*m**5 + 0*m**3 + 0*m + 0*m**4 + 0. Solve q(t) = 0.
-1/3, 0
Factor -4/19*f**2 - 2/19*f**3 + 4/19 + 2/19*f.
-2*(f - 1)*(f + 1)*(f + 2)/19
Suppose 2 = -2*z, -5*o + 3 + 4 = 3*z. Determine w, given that 4*w**2 + 3*w**4 - w**o - 3*w**3 - 3*w**2 = 0.
0, 1
Suppose 3 = f + q, -2*q + q = 0. Let w be (-1)/f + 8/6. Factor 3*i**2 + i**3 + w + 0*i + 0*i**3 + 3*i.
(i + 1)**3
Let k(f) = 17*f**2 - 27*f + 10. Let r(y) = -9*y**2 + 14*y - 5. Let g(u) = 4*k(u) + 7*r(u). Factor g(z).
5*(z - 1)**2
Let k be -4*-2*(-15)/(-24). Factor 0*t**3 + t**k + t**2 - 5*t**4 - t**3 + 4*t**4.
t**2*(t - 1)**2*(t + 1)
Determine o, given that 3/4*o**5 + 0 + 9/4*o**3 + 0*o - 15/4*o**4 + 27/4*o**2 = 0.
-1, 0, 3
Let o(q) = -6*q**5 - 3*q**2 - 3*q. Let r(j) = 5*j**5 - j**3 + 2*j**2 + 2*j. Let x(u) = 2*o(u) + 3*r(u). Factor x(h).
3*h**3*(h - 1)*(h + 1)
Let c(w) = -3*w**3 + 7*w**2 - 6*w + 4. Let k(n) = -n**3 + n**2 + n. Let b(j) = c(j) - 2*k(j). Factor b(y).
-(y - 2)**2*(y - 1)
Let z(q) be the first derivative of q**4/60 + 2*q**3/15 + 3*q**2/10 - 4*q + 6. Let t(v) be the first derivative of z(v). Factor t(i).
(i + 1)*(i + 3)/5
Let k(l) = -9*l**4 + 41*l**3 + 7*l**2 + 8*l - 17. Let a(u) = -u**4 + 5*u**3 + u**2 + u - 2. Let z(b) = -51*a(b) + 6*k(b). Determine i so that z(i) = 0.
-1, 0
Suppose 32 = 3*q + 5*v, -v = 3*q - 10 - 6. Let b(w) be the third derivative of w**2 + 0 - 1/24*w**q + 0*w - 1/60*w**5 + 0*w**3. Let b(j) = 0. What is j?
-1, 0
Let i be (44/(-33))/2 + (-52)/(-42). Suppose -i*w + 2/7*w**2 + 2/7 = 0. Calculate w.
1
Let h(r) be the second derivative of -r**7/4200 + r**6/1800 + r**5/600 - r**4/120 - 2*r**3/3 + r. Let b(s) be the second derivative