*z**5 + 28*z**2 + 4*z - 17*z**4 + 45*z**3 = 0.
-1, -2/7, 0, 1
Factor 9/4*x**2 + 7/4*x - 1/2.
(x + 1)*(9*x - 2)/4
Factor -8/7*n - 2/7*n**2 - 6/7.
-2*(n + 1)*(n + 3)/7
Let d be ((-27)/(-12))/(-3) - (-82)/88. Factor 0*q + 0 - 2/11*q**3 + d*q**4 + 0*q**2.
2*q**3*(q - 1)/11
Suppose -t - 13*o + 15*o + 8 = 0, 4 = 3*t - o. Factor -2/9*w**2 + 4/9*w + t.
-2*w*(w - 2)/9
Let n = 877/165 + -46/11. Let d = n - 4/5. Factor 0*c - d*c**3 + 0 + 0*c**2.
-c**3/3
Let g(l) = -l**2 + 11*l + 17. Let n(v) = -5*v + 2. Let w be n(-2). Let s be g(w). Factor o + s*o - o**2 - 5*o - 2 - 4*o.
-(o + 1)*(o + 2)
Let u = 42 + -38. Let z(s) be the third derivative of -s**2 + 0*s**3 + 0 + 1/420*s**6 + 0*s**5 + 0*s - 1/84*s**u. Factor z(g).
2*g*(g - 1)*(g + 1)/7
Find k, given that -5*k**2 + 5/3*k**4 + 20/3 - 20/3*k + 10/3*k**3 = 0.
-2, 1
Let d(t) be the first derivative of -t**7/70 - 2*t**6/45 - t**5/36 + t**4/36 - t**2 - 2. Let o(i) be the second derivative of d(i). Factor o(w).
-w*(w + 1)**2*(9*w - 2)/3
Suppose -5*c**3 - 1756*c + 1756*c - 5*c**2 = 0. Calculate c.
-1, 0
Suppose -3*y + 9 = -3. Solve 0*n + n**2 + 5 - 5*n - n + y = 0 for n.
3
Suppose -4*d + 48 = -0*d. Suppose -3*k + 0 = -d. Factor -f**2 - 10*f - f**2 + 4*f - k.
-2*(f + 1)*(f + 2)
Let i(x) be the first derivative of -x**4/78 - x**3/39 + 2*x**2/13 - 8*x - 9. Let q(z) be the first derivative of i(z). Solve q(v) = 0.
-2, 1
Find m, given that 15/2*m**3 + 9/2*m**2 - 3*m + 0 = 0.
-1, 0, 2/5
Let w be 2 + 2 + 6/3. Let g be 6/(-4)*(-1)/w. Determine x so that 1/2*x**3 - 3/2*x**2 + 1/4 - 3/4*x**5 + g*x + 5/4*x**4 = 0.
-1, -1/3, 1
Let s(l) be the third derivative of l**9/4320 + l**8/2520 + l**7/4410 + l**5/60 - 3*l**2. Let a(f) be the third derivative of s(f). Factor a(w).
2*w*(7*w + 2)**2/7
Suppose -4*c + 9*c = 25. Factor 0 + 3/2*g**2 - 3/2*g**4 - 3/2*g**c + 3/2*g**3 + 0*g.
-3*g**2*(g - 1)*(g + 1)**2/2
Suppose -1 - 11 = -3*v. Suppose 3*u - v*u = -2. Solve 2/3*l**u - 2/9*l**3 + 2/9 - 2/3*l = 0.
1
Let f = -1 - 0. Let i = 3 + f. Let 1/5*r**i + 0 - 1/5*r = 0. What is r?
0, 1
Suppose -v - 3*j + 6*j = -2, 0 = 2*v + 5*j - 4. Let g(l) be the first derivative of -2 + 1/2*l**v + 0*l + 1/6*l**3. Factor g(k).
k*(k + 2)/2
Let h(v) be the second derivative of -v**6/15 - v**5/10 + v**4/6 + v**3/3 - 2*v. Solve h(n) = 0.
-1, 0, 1
Factor -16*s**4 + 2*s + s - 7*s - 24*s**2 - 36*s**3.
-4*s*(s + 1)**2*(4*s + 1)
Determine o, given that -3/4*o**2 - 1/4*o**4 + 3/4*o**3 + 0 + 1/4*o = 0.
0, 1
Suppose 2*g - 10 = 0, -3*t - 1 + 3 = g. Let l be (-1)/(-2) + t/(-4). Factor l*u**3 + 3/4*u**4 + 0 - 3/4*u**2 - 3/4*u.
3*u*(u - 1)*(u + 1)**2/4
Suppose -5*o = -4*y + 26, -3*y - 4*o = -o - 6. Let q = y - 1. Find w such that 1/4*w**5 - 1/4*w**2 + 3/4*w**q + 0 + 0*w - 3/4*w**4 = 0.
0, 1
Factor -11 + 92 + 19*d**2 + d**3 + 144*d - 45*d.
(d + 1)*(d + 9)**2
Let n(m) = 7*m**3 - 8*m**2. Let b(p) = -13*p**3 + 16*p**2. Let f(w) = -3*b(w) - 5*n(w). Suppose f(h) = 0. Calculate h.
0, 2
Let u(t) be the third derivative of 0*t**4 + 3*t**2 - 1/336*t**8 + 0*t**3 + 0*t**6 + 0*t**5 - 1/210*t**7 + 0 + 0*t. Factor u(o).
-o**4*(o + 1)
Let l(i) be the third derivative of -7*i**8/16 - i**7/2 + 13*i**6/40 - i**5/20 + 14*i**2. Factor l(q).
-3*q**2*(q + 1)*(7*q - 1)**2
Let s = -3 + 6. Factor x + x - x + x**2 - 1 - x**s.
-(x - 1)**2*(x + 1)
Let z(l) = -l + 1. Suppose 0 = 3*t - 2*o - 7, 7 = 4*t - 3*o - 4. Let m be z(t). Factor 4*v**3 + 6/7*v**5 - 2/7 - 2/7*v + 22/7*v**4 + 12/7*v**m.
2*(v + 1)**4*(3*v - 1)/7
Let w(t) be the third derivative of 0 + 0*t + 0*t**3 - 1/12*t**4 - 3*t**2 - 7/60*t**5. Factor w(m).
-m*(7*m + 2)
Let k be (16 - 16)*2/(-6). Factor 2/3*a**2 - 1/3*a + k.
a*(2*a - 1)/3
Let p(x) be the first derivative of -x**6/3 + 6*x**5/5 - x**4/2 - 2*x**3 + 2*x**2 + 6. Suppose p(g) = 0. Calculate g.
-1, 0, 1, 2
Factor -4/3*m**3 + 5/3*m**2 + 0 - 2/3*m + 1/3*m**4.
m*(m - 2)*(m - 1)**2/3
Factor 10*l**2 + 0*l - 4*l**2 + 2*l - 4*l**2.
2*l*(l + 1)
Suppose -2*t = t - 6. Solve 36*b + 2 - 3 + 81*b**t + 5 = 0.
-2/9
Determine b, given that -2/5*b**2 - 16/5*b - 14/5 = 0.
-7, -1
Let h be 9/26 + 4/26. Factor 1/4*b**3 + h*b**2 + 0 + 1/4*b.
b*(b + 1)**2/4
Let u(w) be the second derivative of -w**8/630 - w**7/1260 + w**3/6 + 2*w. Let f(o) be the second derivative of u(o). Factor f(y).
-2*y**3*(4*y + 1)/3
Let p be 3*1 + 298/(-116). Let k = p + 2/29. Factor -n**2 + k*n**3 + 0 + n**4 - 1/2*n.
n*(n - 1)*(n + 1)*(2*n + 1)/2
Let d be 12/4*1 - 0. Find a such that -11*a**4 - 5*a**3 + 4*a**3 + 16*a**5 + 5*a**d - 5*a**4 = 0.
0, 1/2
Solve -14/5*n**4 - 24/5*n - 8/5 + 24/5*n**3 + 22/5*n**2 = 0 for n.
-1, -2/7, 1, 2
Let w(o) be the first derivative of o**7/35 - o**6/12 - o**5/15 + 2*o**2 - 4. Let z(f) be the second derivative of w(f). Factor z(d).
2*d**2*(d - 2)*(3*d + 1)
Let w(g) be the third derivative of -g**9/30240 - g**8/25200 + g**7/2520 + g**6/900 + g**5/30 + 2*g**2. Let d(y) be the third derivative of w(y). Factor d(o).
-2*(o - 1)*(o + 1)*(5*o + 2)/5
Let a(p) be the second derivative of 0*p**4 + 0*p**5 + 1/480*p**6 + 0*p**3 + p + 0 - p**2. Let h(n) be the first derivative of a(n). Factor h(k).
k**3/4
Suppose -249 = -5*m + 5*j + 576, 849 = 5*m + 3*j. Let u be 2/(-7) - (-272)/m. Factor -u + 4/3*z - 1/3*z**2.
-(z - 2)**2/3
Let s(d) be the second derivative of -2*d**7/21 + 2*d**6/5 - 2*d**5/5 + 3*d. Factor s(l).
-4*l**3*(l - 2)*(l - 1)
Let p = 3 + -1. Solve 3*z**2 + z**4 - 2*z**2 + 4*z**p - 6*z**2 = 0.
-1, 0, 1
Let s(q) = q + 4. Let d be s(-2). Suppose -1/4*u**4 + 0 + 0*u - 1/4*u**d + 1/2*u**3 = 0. What is u?
0, 1
Factor -3*c + 1 + 4*c - 3*c + c**2.
(c - 1)**2
Let r = -15 + 20. Let l(w) be the third derivative of 0*w + 0 - 1/6*w**4 + 1/30*w**r + 1/3*w**3 - 3*w**2. Solve l(c) = 0 for c.
1
Let c(g) be the first derivative of -g**7/4200 + g**5/200 + g**4/60 + 4*g**3/3 - 2. Let o(l) be the third derivative of c(l). Factor o(u).
-(u - 2)*(u + 1)**2/5
Let o(j) be the first derivative of j**7/35 + 3*j**6/40 + j**5/20 + 2*j**2 - 3. Let v(l) be the second derivative of o(l). Find a such that v(a) = 0.
-1, -1/2, 0
Suppose -9*j = -12*j + 15. Let z(h) be the third derivative of 0*h + h**2 + 0 - 1/90*h**j - 1/540*h**6 - 1/36*h**4 - 1/27*h**3. Solve z(i) = 0 for i.
-1
Let c = -292/3 + 98. Suppose -1/3*n - c + 1/3*n**2 = 0. Calculate n.
-1, 2
Let c(y) = -5*y**2 + 13*y. Let d(k) = -2*k**2 + 6*k. Let w(b) = 3*c(b) - 7*d(b). Factor w(a).
-a*(a + 3)
Suppose 0 = -10*z + 13*z. Find p, given that 2 - 4 - 4 + z + 3*p + 3*p**2 = 0.
-2, 1
Suppose -4*f + 0*f = -8. Determine k, given that 2 - k + 4*k + 0 + k**f = 0.
-2, -1
Let o(u) be the first derivative of 9*u**4/16 - u**3/4 - 11. Find x, given that o(x) = 0.
0, 1/3
Let c(w) be the third derivative of -5*w**6/216 - 29*w**5/108 - 13*w**4/27 - 10*w**3/27 - 7*w**2 - 3*w. Determine g so that c(g) = 0.
-5, -2/5
Let l(d) be the second derivative of 3*d**5/20 + 3*d**4/2 + 6*d**3 + 12*d**2 + 14*d. Factor l(o).
3*(o + 2)**3
Let f(m) = -5*m - 5. Let a be f(-1). Solve 0*v + a*v**3 + 2/5*v**4 + 0 - 2/5*v**2 = 0 for v.
-1, 0, 1
Let o(w) be the first derivative of -w**6/300 + w**5/150 + w**4/30 - 5*w**2/2 - 4. Let d(x) be the second derivative of o(x). Factor d(l).
-2*l*(l - 2)*(l + 1)/5
Let j(x) = x**3 + x**2 + x - 1. Let y(z) = -6*z**3 + 6*z**2 - 18*z + 10. Let q(d) = -4*j(d) - y(d). Suppose q(o) = 0. What is o?
1, 3
Let h(d) = -5*d + 3 - 2 + 4*d - 4. Let y be h(-3). Factor -2/9*m + 2/9*m**2 + y.
2*m*(m - 1)/9
Suppose 2*h = -5*o + 4, 3*h = 3*o - 4*o - 7. Let n be 2 - (-3 + 6/o). Factor -6/7*r**n + 0 + 2/7*r**3 + 4/7*r.
2*r*(r - 2)*(r - 1)/7
Let y(s) be the second derivative of -s**5/240 - s**4/96 + 3*s**2/2 + 2*s. Let w(l) be the first derivative of y(l). Find x, given that w(x) = 0.
-1, 0
Let t(o) be the second derivative of 0*o**4 + 0 + 0*o**2 + 1/100*o**5 + 2*o - 1/30*o**3. Solve t(p) = 0 for p.
-1, 0, 1
Let f(n) = -n**2 - 6*n + 9. Suppose 0 = -2*r - 3 - 11. Let q be f(r). Solve 1/3*o**q - 1/3*o + 0 = 0.
0, 1
Solve -2/3*t**2 + 8/15*t**3 + 0 + 2/15*t**4 + 0*t = 0 for t.
-5, 0, 1
Let g(a) be the first derivative of a**3/3 + 3*a**2/2 - 2*a - 2. Let q be g(-5). Factor 4*d**4 + 4*d**2 - 3*d - d**5 + 2*d + 2*d**3 - q*d**3.
-d*(d - 1)**4
Solve -2/3*z**2 - 4/3*z + 0 = 0 for z.
-2, 0
Determine q so that 6/7*q**2 - 4/7*q - 2/7*q**3 + 0 = 0.
0, 1, 2
What is m in 2/9*m**3 + 0 + 0*m - 4/9*m**2 = 0?
0, 2
Let p(i