 0, 1/2
Let d(s) be the first derivative of 2*s**3/3 - 5*s**2 + 12*s + 29. Find u such that d(u) = 0.
2, 3
Factor 0*q**2 - 64*q**3 + 52*q**3 - 4*q**5 + 0*q**2 + 16*q**4.
-4*q**3*(q - 3)*(q - 1)
Let f(u) be the first derivative of -u**7/189 + 2*u**6/135 + u**5/30 - 2*u**4/27 - 4*u**3/27 + 8*u + 7. Let o(z) be the first derivative of f(z). Factor o(p).
-2*p*(p - 2)**2*(p + 1)**2/9
Let m = 9 + -10. Let q be (m/5)/((-18)/60). Factor -2/3*u**2 + q*u**4 - 2/3*u + 2/3*u**3 + 0.
2*u*(u - 1)*(u + 1)**2/3
Let j = 59 - 41. Factor 2*i**2 - i + 10*i**2 + 7*i**2 - j*i**2.
i*(i - 1)
Let c(s) be the third derivative of 2*s**2 - 1/100*s**5 + 0 + 1/10*s**3 + 1/200*s**6 + 0*s - 1/40*s**4. Factor c(m).
3*(m - 1)**2*(m + 1)/5
Let l(i) be the first derivative of 7*i**6/90 + i**5/30 - 7*i**4/36 - i**3/9 + 7*i - 9. Let y(w) be the first derivative of l(w). Factor y(b).
b*(b - 1)*(b + 1)*(7*b + 2)/3
Let s(i) be the first derivative of 3*i**4/4 - i**3 - 3*i**2/2 + 3*i + 6. Factor s(n).
3*(n - 1)**2*(n + 1)
Let f(k) = k**4 + k**3 - 1. Let l(a) = -8*a**4 - 13*a**3 - 9*a**2 + 7. Let t(o) = -35*f(o) - 5*l(o). Factor t(x).
5*x**2*(x + 3)**2
Solve -2*o - 2*o**4 - 5 - 3*o**3 + 2*o**3 + 3*o**3 + 6*o**2 + 1 = 0.
-1, 1, 2
Find w such that -3/5*w**5 + 6/5*w**3 + 24/5*w**2 - 6/5*w**4 + 21/5*w + 6/5 = 0.
-1, 2
Let b(s) be the second derivative of 9*s**5/5 - 17*s**4 + 80*s**3/3 + 200*s**2 - 42*s. Factor b(v).
4*(v + 1)*(3*v - 10)**2
Suppose -3*b + 4*r - 1 = 3*r, -4*r + 4 = 0. What is p in b*p**2 - 2*p**2 + 4*p**3 - 3*p**3 = 0?
0, 2
Suppose -2*f + h + 0*h - 2 = 0, -2 = -h. Suppose -2/3*t - 2/3*t**3 + f - 4/3*t**2 = 0. What is t?
-1, 0
Let d be 1 + -1 + (-31)/(-93). Solve -1/3*r**3 - 1/3*r**2 + d*r + 1/3 = 0.
-1, 1
Solve 0 - 2/3*m**4 - 7/3*m**2 - 7/3*m**3 - 2/3*m = 0 for m.
-2, -1, -1/2, 0
Let a(o) be the first derivative of o**7/4200 + o**6/450 + o**5/120 + o**4/60 + o**3/3 + 1. Let t(w) be the third derivative of a(w). Solve t(m) = 0 for m.
-2, -1
Let m be ((-1)/2)/(2/(-12)). Let f = 11 - m. Let -f*b**2 + 4*b**3 + 3*b**2 + 3*b**2 - 2*b**4 = 0. Calculate b.
0, 1
Let s(g) = 3*g**4 + 3*g**3 - 3*g**2 + 3*g + 3. Let r(a) = -3*a**4 - 3*a**3 + 2*a**2 - 4*a - 4. Let h(k) = -3*r(k) - 4*s(k). Factor h(y).
-3*y**2*(y - 1)*(y + 2)
Let p(l) = -l**4 - l**2 + 1. Let j(m) = 2*m**3 + 1. Let o(a) = 2*j(a) - 2*p(a). Let o(y) = 0. What is y?
-1, 0
Let h(l) be the third derivative of 0*l**5 + 0*l + 0*l**7 - 2*l**2 + 0 + 0*l**3 + 0*l**6 - 1/840*l**8 + 0*l**4. Let h(v) = 0. What is v?
0
Let u be 5 + -7 - (0 + -6). Suppose -6 = -2*k + 5*i, 2*i = u*k - 8 - 4. Factor -5*b**2 - b + 2*b**k - b**5 + 5*b**2.
-b*(b - 1)**2*(b + 1)**2
Let j(v) = v**3 + 2*v**2. Let b be j(-2). Suppose q + 4*q = b. Factor w + 1/2*w**2 + q.
w*(w + 2)/2
Factor 0 + 1/6*a**2 - 1/6*a**3 + 0*a.
-a**2*(a - 1)/6
Let x(a) be the third derivative of 1/210*a**6 - 1/70*a**5 + 1/21*a**3 + 0 + 7*a**2 + 0*a**4 + 0*a. Factor x(v).
2*(v - 1)**2*(2*v + 1)/7
Factor -7*d**3 - 3*d - 5*d**3 + 4*d**4 + 12*d**2 - d.
4*d*(d - 1)**3
Suppose 3*q - 7 + 1 = 0. Let j be 0 + 1 + 3/(-6). Factor 0 + j*d**q + 1/2*d.
d*(d + 1)/2
Let s = -3/16 + 17/48. Let f(k) be the second derivative of -3*k - s*k**3 - 1/12*k**4 + 0 + 0*k**2. Determine y so that f(y) = 0.
-1, 0
Let m = 9/40 + 29/10. Let v = m + -5/8. Determine i, given that 1/2 - 1/2*i - v*i**2 - 3/2*i**3 = 0.
-1, 1/3
Let r be ((-1)/2)/((-1)/16). Suppose r = 4*k - 0*k. Factor 4*o**2 + o - k - o**5 - o**2 + 4*o**4 + 4*o - 4*o**3 - 5*o**2.
-(o - 2)*(o - 1)**3*(o + 1)
Suppose 0 = -2*q + 4. Factor -2*y**2 - q - 71*y**3 + y + 2 + 72*y**3.
y*(y - 1)**2
Let k = 29 - 26. Factor 0 + 10/9*p**5 + 0*p + 2*p**k - 8/3*p**4 - 4/9*p**2.
2*p**2*(p - 1)**2*(5*p - 2)/9
Let r(f) be the third derivative of f**8/2240 + f**7/420 + f**6/240 - f**4/6 + 5*f**2. Let j(t) be the second derivative of r(t). Factor j(d).
3*d*(d + 1)**2
Let z(i) be the first derivative of -i**7/4200 - i**6/900 - i**5/600 + 2*i**3/3 - 3. Let f(r) be the third derivative of z(r). Determine m, given that f(m) = 0.
-1, 0
Let l(k) = -12*k**4 + 45*k**3 + 48*k**2 - 3*k - 36. Let p(d) = 3*d**4 - 11*d**3 - 12*d**2 + d + 9. Let t(r) = -5*l(r) - 21*p(r). Factor t(b).
-3*(b - 3)*(b - 1)*(b + 1)**2
Let g = 193/651 - 1/93. Factor g - 2/7*q**2 + 2/7*q - 2/7*q**3.
-2*(q - 1)*(q + 1)**2/7
Let q(w) be the third derivative of -w**6/20 - 7*w**5/30 + 4*w**3/3 - w**2. Factor q(p).
-2*(p + 1)*(p + 2)*(3*p - 2)
Let i be (-10 + 12)/(2/36). Factor -i*q**3 + 11*q**2 + 4*q**2 - 3*q**2 - 16 + 32*q.
-4*(q + 1)*(3*q - 2)**2
Let u be (-91)/(-42) + 1/(-6). Let 8/5*d - 12/5*d**u + 8/5*d**3 - 2/5 - 2/5*d**4 = 0. Calculate d.
1
Let a(g) = -14*g**3 - 24*g**2 - 24*g + 2. Let i(o) = o**3 - o**2 + 1. Let c(q) = a(q) + 6*i(q). Let c(p) = 0. Calculate p.
-2, 1/4
Let a(r) = r - 2. Let c be a(2). Let b = -2/183 + 124/183. Factor 1/3*y**2 - b*y + c.
y*(y - 2)/3
Let o(a) be the third derivative of a**8/1120 + a**7/280 + a**6/240 + a**4/12 + 5*a**2. Let v(f) be the second derivative of o(f). Suppose v(w) = 0. What is w?
-1, -1/2, 0
Let h(j) be the third derivative of -j**6/40 + j**5/5 - j**4/2 + 4*j**2. Suppose h(c) = 0. Calculate c.
0, 2
Let z(a) be the first derivative of -a**5/35 - 3*a**4/28 - a**3/21 + 3*a**2/14 + 2*a/7 + 15. Factor z(n).
-(n - 1)*(n + 1)**2*(n + 2)/7
Factor -2*f**4 - 25*f**2 - 22*f**2 + 49*f**2.
-2*f**2*(f - 1)*(f + 1)
Suppose c - 4*c + 9 = 0, n = 4*c - 9. Suppose 0 = 5*y + 2*b - 6, -n*b + 3 = 9. Factor 0*w**2 + 2*w**4 + 4*w**3 - 8*w**3 + 2*w**y.
2*w**2*(w - 1)**2
Suppose 363*o**4 + 0*o**3 + 2*o**2 - o**3 - 364*o**4 = 0. What is o?
-2, 0, 1
Let u(r) be the first derivative of -r**6/24 - r**5/20 + 3*r**4/16 + r**3/12 - r**2/4 - 1. Find n, given that u(n) = 0.
-2, -1, 0, 1
Let i(u) be the third derivative of 11/24*u**4 + 0 + 17/120*u**6 + 0*u - 7/20*u**5 + 2*u**2 - 1/3*u**3 - 1/42*u**7. Suppose i(m) = 0. What is m?
2/5, 1
Let n(b) be the first derivative of -2/3*b**2 - 1/9*b**3 + 3 - 4/3*b. Factor n(p).
-(p + 2)**2/3
Determine r so that -2*r**4 + 14/3*r**3 + 2/3*r + 0 - 10/3*r**2 = 0.
0, 1/3, 1
Factor -4/5 - 2/5*d + 4/5*d**2 + 2/5*d**3.
2*(d - 1)*(d + 1)*(d + 2)/5
Let r be 47/2 + (-7)/14. Suppose -23 = -5*b - 2*q, -b + r = 3*q + 2*q. Factor 0*a**b - 2/5*a**2 + 0 - 1/5*a**5 + 2/5*a**4 + 1/5*a.
-a*(a - 1)**3*(a + 1)/5
Let u(q) be the second derivative of 0*q**3 - 3/2*q**2 - 1/60*q**4 + 0 + 1/150*q**5 - 3*q. Let y(b) be the first derivative of u(b). Factor y(x).
2*x*(x - 1)/5
Let g(u) be the second derivative of -5*u**4/102 - 8*u**3/51 - 3*u**2/17 + 13*u. Let g(d) = 0. What is d?
-1, -3/5
Factor -15*h**2 + 34*h**2 + h - 18*h**2.
h*(h + 1)
Let b(z) = -8*z**2 + 20*z + 17. Let n(l) = -3*l**2 + 7*l + 6. Let t(s) = -4*b(s) + 11*n(s). Solve t(f) = 0.
-2, -1
Determine b, given that 0*b - 2/7*b**3 + 0 + 0*b**2 + 5/7*b**4 = 0.
0, 2/5
Let t(q) = 3*q**4 - 2*q**3 - 8*q**2 - 8*q. Let d = -6 - -1. Let v(u) = 2*u**4 - u**3 - 5*u**2 - 5*u. Let g(w) = d*t(w) + 8*v(w). Let g(c) = 0. What is c?
-2, 0
Let h(z) = z - 2. Let q be h(5). Suppose -4*d + 4 = -q*k + 4*k, 0 = 3*k + d - 12. What is p in -p**5 - 5*p**k + 4*p**4 + 3*p**2 + p**3 - 2*p**2 = 0?
-1, 0, 1
Let s(t) be the first derivative of -2/7*t**2 - 4 + 0*t - 2/7*t**3 - 1/14*t**4. Factor s(f).
-2*f*(f + 1)*(f + 2)/7
Suppose -3*s + 5 = -4. Determine r, given that s*r**3 + 4*r**2 + 8 - r**3 - 10*r**2 = 0.
-1, 2
Let n(j) be the second derivative of 2*j**7/21 + 2*j**6/3 + 7*j**5/5 - j**4/3 - 16*j**3/3 - 8*j**2 - 2*j. Solve n(h) = 0 for h.
-2, -1, 1
Suppose 3*v + t = -0*v + 8, -4*t + 22 = 2*v. Let r be (v - 4)*5/(-5). Factor -2 - f**r + 2 + f.
-f*(f - 1)*(f + 1)
Let z(o) be the third derivative of -o**7/105 - o**6/30 + o**5/30 + o**4/6 - 4*o**2 + 8. Let z(s) = 0. Calculate s.
-2, -1, 0, 1
Let c = 1 - -4. Let d(t) be the third derivative of 0*t + 2*t**2 + 1/120*t**6 + 0*t**3 + 0 - 1/30*t**c + 1/24*t**4. Solve d(j) = 0.
0, 1
Let n be (-2)/(-3) + (-21)/(-9). Let v(w) = w + 2. Let h be v(n). Let 8/7*t - 6/7*t**3 + 0 + 2/7*t**h + 8/7*t**2 - 4/7*t**4 = 0. What is t?
-1, 0, 2
Let d(z) be the first derivative of 7*z**4/4 - 2*z**3/3 + z**2/2 + 2. Let m be d(1). Let -2*x**3 - 2 + 2*x**2 - m*x**2 + 2 - 2*x = 0. Calculate x.
-1, 0
Let i(n) = n**4 + n**2 - n. Let q(c) = -6*c**4 - 20*c**3 - 21*c**2 + c. Let f(w) = -i(w) - q(w). Factor f(x).
5*x**2*(x + 2)**2
Let q(s) be th