+ 1)**2*(7*g - 2)**2/5
Suppose 2*a + 2 = 3*a. Find z, given that 12*z + 3*z**a - 3 + 5 - 14 - 6*z**2 = 0.
2
Let z(i) be the third derivative of 1/300*i**6 + 0*i + 0*i**3 - i**2 - 1/75*i**5 + 0 + 8/525*i**7 + 0*i**4 + 1/168*i**8. Factor z(y).
2*y**2*(y + 1)**2*(5*y - 2)/5
Factor -2*r**3 - 3/4*r**4 + 3/4*r**2 + 0*r + 0.
-r**2*(r + 3)*(3*r - 1)/4
Let i(x) = -x**2 - 5*x + 8. Suppose 2*y - 10 = 2*p, -5*y + 3*y = 2*p + 14. Let s be i(p). Factor -4/3*f**4 + 1/3*f - 4/3*f**2 + s*f**3 + 0 + 1/3*f**5.
f*(f - 1)**4/3
Let c = -59/4 + 15. Let -c*t + 1/4*t**2 - 1/4 + 1/4*t**3 = 0. What is t?
-1, 1
Let o be (-14)/(-6) + 4/6. Let a(i) = i**2 + i + 2*i**3 - 2*i**2 - 1 - o*i**3. Let j(b) = b**3 - 3*b**2 - 7*b + 3. Let k(r) = -3*a(r) - j(r). Factor k(l).
2*l*(l + 1)*(l + 2)
Let m = 907/763 + -5/109. Factor -8/7*x - 2/7*x**2 - m.
-2*(x + 2)**2/7
Let -6*a**2 + 76*a - 76*a + 2*a**3 + 8 = 0. Calculate a.
-1, 2
Factor -32/3*g**2 - 4/3*g**3 + 0*g + 0.
-4*g**2*(g + 8)/3
Let v be 2 - (6 - 4 - 5). Let b(j) be the third derivative of 1/21*j**3 + 1/420*j**6 + 0*j - 2*j**2 - 1/84*j**4 - 1/210*j**v + 0. Find i such that b(i) = 0.
-1, 1
Let k(z) be the first derivative of -z**4/3 - 13. What is l in k(l) = 0?
0
Let v = 5 + -9. Let i be 6*1/(-8)*v. Factor 1/3*x**i + x - 1/3 - x**2.
(x - 1)**3/3
Factor 2/5*t**3 + 2*t**2 + 14/5*t + 6/5.
2*(t + 1)**2*(t + 3)/5
Solve -32/9*d**2 - 2 - 14/3*d - 8/9*d**3 = 0 for d.
-3/2, -1
Let w(c) be the second derivative of c**10/75600 + c**9/37800 - c**8/16800 - c**7/6300 + c**4/4 + 2*c. Let b(o) be the third derivative of w(o). Factor b(z).
2*z**2*(z - 1)*(z + 1)**2/5
Solve 19 - 48*z - 24*z**3 - 3 + 58*z**4 - 54*z**4 + 52*z**2 = 0.
1, 2
Let j(b) be the third derivative of -1/20*b**5 + 0 - 5*b**2 + 1/8*b**4 + 0*b + b**3. Factor j(z).
-3*(z - 2)*(z + 1)
Let n(s) be the second derivative of -s**4/4 - 2*s**3 - 6*s**2 + 12*s. Let n(k) = 0. What is k?
-2
Let q = -10 + 20. Suppose q = 4*t - 2. Factor -2/7*x**4 + 0*x + 0 - 2/7*x**t + 0*x**2.
-2*x**3*(x + 1)/7
Let d be (-14)/56 + (-1)/(-4). Solve -2/7 + d*z + 2/7*z**2 = 0 for z.
-1, 1
Let m(w) be the second derivative of -1/16*w**4 + 1/8*w**3 + 1/40*w**6 + 2*w - 3/80*w**5 + 0*w**2 + 0. What is a in m(a) = 0?
-1, 0, 1
Let -1/2*m**3 + 0 + 3/2*m**2 - m = 0. Calculate m.
0, 1, 2
Find r such that -2/5*r**2 + 6/5 + 4/5*r = 0.
-1, 3
Suppose 2/3*w + 1/3 + 1/3*w**2 = 0. Calculate w.
-1
Suppose -3*n + 3*i + 27 = 0, -4*n - 4*i + 3 + 1 = 0. Let s(b) be the second derivative of -1/10*b**n + 1/6*b**4 + 0 - b + 1/3*b**3 - b**2. Factor s(d).
-2*(d - 1)**2*(d + 1)
Let k(c) be the third derivative of c**5/20 - c**4/8 - c**3 - 3*c**2. Solve k(u) = 0 for u.
-1, 2
Let s = -2189/4 + 551. Let v = -6 + 9. Factor 3*o**2 - 3/4*o**v - s*o + 3/2.
-3*(o - 2)*(o - 1)**2/4
Factor 0 + 2/13*k**3 + 0*k + 2/13*k**2 - 2/13*k**5 - 2/13*k**4.
-2*k**2*(k - 1)*(k + 1)**2/13
Suppose -u + 1 = -3. Let m(i) be the third derivative of 0*i + 0*i**u + 2*i**2 + 0*i**3 + 0 - 1/300*i**5. Determine q so that m(q) = 0.
0
Factor -2/5*p**3 + 2/5*p**4 - 4/5*p**2 + 0 + 0*p.
2*p**2*(p - 2)*(p + 1)/5
Let b(o) = -o**4 - o**3 - o + 1. Let m(i) = -4*i**4 - i**3 - i**2 - 3*i + 3. Let t be ((-2)/(-7))/(6/42). Let k(l) = t*m(l) - 6*b(l). Factor k(x).
-2*x**2*(x - 1)**2
Let o(t) be the first derivative of t**2 + 0*t + 4/3*t**3 + 2 + 1/2*t**4. Determine m, given that o(m) = 0.
-1, 0
Let u(g) be the second derivative of g**5/60 - g**4/36 - 5*g**3/18 - g**2/2 + 7*g. Factor u(t).
(t - 3)*(t + 1)**2/3
Solve 4*b**4 + 20*b**2 + 8*b - 18 + 16*b**3 + 18 = 0 for b.
-2, -1, 0
What is u in 20/7*u**2 - 8/7*u + 0 = 0?
0, 2/5
Let u(p) = -2*p**3 - 2*p. Let j(t) = -t**4 - 3*t**3 + t**2 - 3*t. Let g(c) = 4*j(c) - 6*u(c). What is a in g(a) = 0?
-1, 0, 1
Suppose 1 + 3 = 2*u, 0 = -2*g - 3*u + 66. Suppose -4*s = -l - 15, -4*l - 2*s + g = -0*l. Factor 2/5*m**l - 2/5*m**2 - 2/5*m**3 + 0*m + 2/5*m**4 + 0.
2*m**2*(m - 1)*(m + 1)**2/5
Let s(d) be the third derivative of 2*d**2 - 2/21*d**3 + 0 - 1/84*d**4 + 1/210*d**5 + 0*d. Determine u, given that s(u) = 0.
-1, 2
Let o(w) = 10*w**5 - 5*w**4 + 25*w**3 - 12*w**2 + 3*w. Let j(d) = -3*d**5 + 2*d**4 - 8*d**3 + 4*d**2 - d. Let n(q) = -7*j(q) - 2*o(q). What is l in n(l) = 0?
0, 1
Suppose 0 = -5*p - 342 + 357. Factor 0 + 0*x**2 - 2/11*x**p + 2/11*x.
-2*x*(x - 1)*(x + 1)/11
Let l(f) = f**3 + 8*f**2 + 6*f - 7. Let o be l(-7). Let 0*b + o + 0*b**4 - 2/5*b**5 + 0*b**3 + 0*b**2 = 0. Calculate b.
0
Suppose -3*g - 4*y - 12 = -0*g, 2*y - 4 = g. Let a = g - -8. Find o, given that -113/3*o**3 + 76/3*o**2 + 24*o**a - 7*o - 16/3*o**5 + 2/3 = 0.
1/4, 1, 2
Let b be (-5 - (-378)/78) + (-184)/(-182). Let -2/7*x**3 + b*x**2 + 2/7 - 6/7*x = 0. Calculate x.
1
Let d(x) be the third derivative of -x**8/2520 - x**3/2 + x**2. Let q(n) be the first derivative of d(n). Solve q(y) = 0 for y.
0
Suppose 0 = 2*v + v - 36. Suppose a - 4*y = -v, 2*y = -2*a - 2*a + 24. Determine g, given that 0*g**5 - 2*g**3 - 2*g**a + 3*g**5 + g**3 = 0.
-1/3, 0, 1
Let f(a) be the second derivative of -a**6/2 - 3*a**5/10 + 5*a**4/4 + a**3 + 8*a. Find u, given that f(u) = 0.
-1, -2/5, 0, 1
Let r = -2 + 7. Factor -r + 3*x + 2*x**2 + 0 + 4*x**2 - 1 - 3*x**3.
-3*(x - 2)*(x - 1)*(x + 1)
Let p(z) = 26*z**2 + 71*z + 56. Let r(w) = 9*w**2 + 24*w + 19. Let y(g) = 4*p(g) - 11*r(g). Factor y(b).
5*(b + 1)*(b + 3)
Suppose 6*k = 2*k + 8. Suppose -k*u = -4*u. Suppose 3*g + u*g**2 - g + g**2 = 0. Calculate g.
-2, 0
Let d(l) be the first derivative of l**4/8 + l**3/2 - 2*l - 4. Factor d(s).
(s - 1)*(s + 2)**2/2
Let k(c) be the first derivative of 2/3*c**5 + 7/6*c**4 + 0*c**2 + 0*c - 1 + 4/9*c**3. Factor k(a).
2*a**2*(a + 1)*(5*a + 2)/3
Let r(u) be the second derivative of u**7/420 + u**6/240 - u**2/2 - 2*u. Let n(d) be the first derivative of r(d). Factor n(k).
k**3*(k + 1)/2
Let u(t) = -87*t**2 - 12*t - 9. Let v(i) = 43*i**2 + 6*i + 4. Let h(j) = 4*u(j) + 9*v(j). Suppose h(n) = 0. What is n?
-2/13, 0
Suppose -12 + 0 = -2*s + 2*w, 3*s - 19 = 4*w. Let r = -3 + s. What is v in -4*v**5 + 2*v**5 + 3*v**2 + 2*v**3 - 5*v**r + 2*v**4 = 0?
-1, 0, 1
Suppose -r - 8 = -11. Let f(t) be the second derivative of -1/210*t**7 + 3*t + 1/30*t**4 + 0 + 0*t**5 + 1/30*t**r + 0*t**2 - 1/75*t**6. Factor f(k).
-k*(k - 1)*(k + 1)**3/5
Let l be 12/(-42) - 4/(-14). Solve 2*x**2 + 0 + l = 0.
0
Suppose -4*x = -5*t - 92, 2*t = -t + 2*x - 56. Let f = -16 - t. Solve -2/5*a - 4/5 + 4*a**2 - 16/5*a**f + 2*a**5 - 8/5*a**3 = 0 for a.
-1, -2/5, 1
Let o = -1996 - -111779/56. Let f = o - -215/168. Determine m so that 8*m + f - 49/3*m**3 + 7*m**2 = 0.
-2/7, 1
Factor -2 - 10 + 7 + 6*j - j**2.
-(j - 5)*(j - 1)
Let m(z) be the second derivative of -z**7/14 + z**6/10 + 33*z**5/80 - z**4/4 - 5*z**3/8 + 3*z**2/4 - 12*z. Determine c, given that m(c) = 0.
-1, 1/2, 2
Let z(b) be the first derivative of b**5/15 - b**4/4 + 2*b**3/9 + 3. Find x such that z(x) = 0.
0, 1, 2
Let i(d) be the first derivative of d**3/2 - 3*d**2 + 6*d + 16. Factor i(j).
3*(j - 2)**2/2
Let j(h) be the first derivative of h**6/12 - 3*h**5/10 + 3*h**4/8 - h**3/6 - 4. Solve j(o) = 0 for o.
0, 1
Let u(r) = 3*r**3 - 12*r**2 + 15*r - 17. Let y(q) = -q**3 + 4*q**2 - 5*q + 6. Let x(d) = -4*u(d) - 11*y(d). Suppose x(s) = 0. What is s?
1, 2
Let l(t) be the first derivative of -t**5/40 - t**4/8 - t**3/4 - t**2 + 2. Let f(x) be the second derivative of l(x). Factor f(y).
-3*(y + 1)**2/2
Let v(q) be the third derivative of -q**8/60480 - q**7/7560 + q**5/15 - q**2. Let l(b) be the third derivative of v(b). Find g such that l(g) = 0.
-2, 0
Let c(b) be the third derivative of -b**6/360 - b**5/60 - b**4/36 + 20*b**2. Solve c(f) = 0 for f.
-2, -1, 0
Let m(b) be the first derivative of -2*b**2 + 3*b + 2 + 1/3*b**3. Factor m(l).
(l - 3)*(l - 1)
Let y = -19 + 19. Let j(w) be the third derivative of -1/30*w**4 - w**2 - 1/150*w**5 - 1/15*w**3 + 0*w + y. Factor j(s).
-2*(s + 1)**2/5
Let q(u) be the first derivative of -u**4/12 + 2*u**3/9 + u**2/6 - 2*u/3 + 15. Let q(j) = 0. Calculate j.
-1, 1, 2
Let d(a) = a**3 + 16*a**2 - 4*a - 5. Let h be d(-7). Suppose 4*r = 8*r - h. Factor 29 - 5 + 90*p**2 - 12*p - r*p + 75*p**3 + 20*p.
3*(p + 2)*(5*p - 2)**2
Let m(v) be the first derivative of -1/13*v**4 + 8/39*v**3 - 2/13*v - 7 - 6/65*v**5 + 2/13*v**2. Determine s, given that m(s) = 0.
-1, 1/3, 1
Factor 2/9*v + 0 - 2/9*v