*y**2 + 8 = 0. Calculate y.
3, 8
Let o be (18/21)/((-4)/28) - (13 + -21). Let -15*r**o - 24*r - 48/5 = 0. What is r?
-4/5
Let y = -24 - -27. Let k(w) = -w**2 - 9*w + 10. Let n be k(-9). Let y*v + 4 - 9*v - 10*v - n*v**2 + 4 = 0. Calculate v.
-2, 2/5
Let i(b) = -b**2 + 711*b + 9416. Let o be i(-13). Find y such that 0 + 0*y**2 - 2/5*y**o + 0*y - 4/5*y**3 = 0.
-2, 0
Let o(t) be the first derivative of -t**7/315 + t**6/90 - t**4/18 + t**3/9 + 19*t**2/2 - 35. Let u(k) be the second derivative of o(k). Factor u(v).
-2*(v - 1)**3*(v + 1)/3
Let d(f) be the third derivative of -1/30*f**4 + 0 - 2/15*f**3 + 5*f**2 - 1/300*f**5 + 0*f. Suppose d(g) = 0. What is g?
-2
Let h(y) be the second derivative of -y**6/432 + 11*y**5/144 + y**3/6 + 19*y**2/2 + y - 7. Let c(m) be the second derivative of h(m). Factor c(z).
-5*z*(z - 11)/6
Factor h**3 + 24 + 42*h - 588*h**2 + 101*h + 563*h**2 + 145.
(h - 13)**2*(h + 1)
Let k = 3384 + -3382. Factor 8/3*o - k - 2/3*o**2.
-2*(o - 3)*(o - 1)/3
Suppose 72*t = 313 - 25. Let 4/5*x**3 - 4/5*x**5 + 0 + 0*x**t + 0*x + 0*x**2 = 0. What is x?
-1, 0, 1
Suppose 31*z - 1137 = -1044. Find c such that 1/5*c**5 + 24/5*c**z - 32/5*c**2 + 0 - 8/5*c**4 + 16/5*c = 0.
0, 2
Let g(a) = 2*a**2 - 19*a + 11. Let o be g(9). Solve 4*c**4 + 308*c**3 + 3*c**o - 313*c**3 - 2*c**2 = 0 for c.
0, 1/4, 1
Let r(y) be the third derivative of -y**5/15 + 73*y**4/3 - 10658*y**3/3 + 121*y**2. Factor r(b).
-4*(b - 73)**2
Let s(b) be the first derivative of 4*b**5/35 + 6*b**4/7 - 64*b**2/7 + 295. Let s(a) = 0. What is a?
-4, 0, 2
Let m(j) = 7*j**2 - 201*j - 58. Let s be m(29). Let f(k) be the second derivative of -1/100*k**5 + 1/60*k**4 + s - 5*k + 3/10*k**2 + 1/6*k**3. Factor f(g).
-(g - 3)*(g + 1)**2/5
Let x = 2105/7343 + -1/1049. Let p(g) = -g**3 + 9*g**2 - g + 11. Let a be p(9). Determine i so that x*i + 0 + 2/7*i**a = 0.
-1, 0
Let -497 - 231*g**2 + 66*g - 17*g**3 + 521 + 14*g**3 - 27*g**3 + 9*g = 0. What is g?
-8, -1/5, 1/2
Let b(h) = 5*h - 120. Suppose 24*x - 357 = 219. Let u be b(x). Factor -8/13 + u*s + 2/13*s**2.
2*(s - 2)*(s + 2)/13
Suppose -4*z + 22 = 3*i, i + 13 = 3*z + 3. Suppose z*v + 8*v = 15*v. Factor -2/3*r**3 + 1/3*r**2 + 1/3*r**4 + v*r + 0.
r**2*(r - 1)**2/3
Let w(f) be the second derivative of -9/20*f**5 + 0*f**2 - 4*f + 0*f**3 + 0 + 1/10*f**6 + 1/2*f**4. Let w(b) = 0. Calculate b.
0, 1, 2
Let z = -101 - -107. Let p be (-1 - (-7)/z) + 51/18. Find u such that 1 + 3/2*u + 0*u**2 - 1/2*u**p = 0.
-1, 2
Let i(u) = u + 11. Let h(f) = -f - 12. Let t(z) = 6*h(z) + 7*i(z). Let d be t(-2). Let -12 - 3*r - 3*r + 12 - d*r**2 = 0. What is r?
-2, 0
Let t(c) be the second derivative of -c**6/30 - 21*c**5/20 + 11*c**4/6 + c - 87. Factor t(d).
-d**2*(d - 1)*(d + 22)
Let m(y) = -y**2 + 5*y - 3. Let d(a) = -a**2 + 8*a - 9. Let q be d(6). Let f be m(q). Let 3 + 21*s**f + 27*s**2 - 17 - 36*s + 2 = 0. What is s?
-2, -2/7, 1
Factor 9/4*n + 3*n**2 - 27/2 - 3/4*n**3.
-3*(n - 3)**2*(n + 2)/4
Let t be (-21)/(105/40)*-1. Let m(n) be the first derivative of -2/3*n**2 - 49/15*n**5 - 32/9*n**3 + 0*n - 77/12*n**4 + t. Solve m(w) = 0 for w.
-1, -2/7, 0
Let a(f) = -f + 29. Let s be a(23). Let q be (7 - 2)/(8*3/s). What is b in 1/2*b**4 + 1/4*b**2 - 1/2*b + 0 + q*b**3 = 0?
-2, -1, 0, 1/2
Let l = 426 + -426. Let c(r) be the third derivative of -2/75*r**5 - 1/60*r**4 + l*r + 0 + 0*r**3 + 7*r**2. Factor c(n).
-2*n*(4*n + 1)/5
Let s be ((-9)/3)/(3/(-7)). Suppose s*q - 9 = 2*q - 2*r, -3*r = 2*q + 3. Let 0 + 0*m**q + 8/11*m**2 - 2/11*m**5 + 0*m - 6/11*m**4 = 0. What is m?
-2, 0, 1
Let w = -2099 - -2099. Solve 0*v**2 + 0*v - 2/11*v**5 - 2/11*v**4 + 0*v**3 + w = 0 for v.
-1, 0
Let j(i) = 3*i**3 + i. Let m(o) = -34*o**3 + 38*o**2 - 372*o. Let y(x) = -22*j(x) - 2*m(x). Factor y(s).
2*s*(s - 19)**2
Find t, given that 3768/11*t + 4740/11*t**2 + 752/11 + 50/11*t**3 = 0.
-94, -2/5
Let f(v) = -v - 2. Let r be f(-4). Factor 4*c**r - c + 4*c**3 - 13*c + 4*c + 2*c.
4*c*(c - 1)*(c + 2)
Solve -24/7*v**4 - 48/7*v**2 + 0 + 15/7*v + 54/7*v**3 + 3/7*v**5 = 0 for v.
0, 1, 5
Factor -3/2*f**3 - 3/2*f**2 + 15/2*f - 9/2.
-3*(f - 1)**2*(f + 3)/2
Let u = -36683/3 + 12233. Factor -u - 8/3*j - 1/3*j**2.
-(j + 4)**2/3
Let k(b) be the second derivative of b**5/60 - 35*b**4/36 + 16*b**3 + 54*b**2 - b - 134. Factor k(u).
(u - 18)**2*(u + 1)/3
Let w(z) = -z**3 - 8*z**2 + 22*z + 24. Let i be w(-10). Suppose -i*p = -0*o + 4*o - 20, 4*p - 11 = -o. Factor -2/7*x**p - 2/7*x**3 + 0 + 4/7*x.
-2*x*(x - 1)*(x + 2)/7
Let z(s) = s**4 - s**3 - s - 1. Let v(g) = 5*g**4 + 7*g**5 - 20 - 2*g**2 + 82 + 10*g**3 + 7*g - 27 - 28. Let h(y) = -5*v(y) - 35*z(y). Factor h(k).
-5*k**2*(k + 1)**2*(7*k - 2)
Determine f so that -1449 - f**4 - 24*f + 24*f**3 - 3*f**2 + 4*f**4 + 1449 = 0.
-8, -1, 0, 1
Let c(y) be the third derivative of -y**5/20 - y**4 - 7*y**3/2 - 136*y**2. Find x, given that c(x) = 0.
-7, -1
Let u(v) = -2*v**3 - 14*v**2 - 12*v. Suppose -4*h - 5*s = -27 + 90, 3*h - s + 33 = 0. Let i(r) = r**2 + r. Let j(c) = h*i(c) - u(c). Factor j(n).
2*n**2*(n + 1)
Suppose -4*h + 8 = d, -66*d = -2*h - 63*d - 24. Factor h - 162/13*q + 32/13*q**4 - 92/13*q**3 - 2/13*q**5 - 288/13*q**2.
-2*q*(q - 9)**2*(q + 1)**2/13
Let m(x) be the first derivative of 0*x**2 + 14 + 0*x**4 - 1/21*x**6 + 0*x + 0*x**5 + 0*x**3. Let m(a) = 0. What is a?
0
Let q be -2 + (2 - (2 + -2)). Let o = q + 0. Factor -5*s**2 + 2*s + o*s + 3*s**2 - 5*s**2.
-s*(7*s - 2)
Let b(l) be the first derivative of 2*l**3/27 + 47*l**2/9 - 32*l/3 + 116. Factor b(g).
2*(g - 1)*(g + 48)/9
Let f(x) be the first derivative of 3*x**4/4 - 37*x**3 - 231*x**2/2 - 117*x - 21. Determine g, given that f(g) = 0.
-1, 39
Let 18*z**2 + 12 + 7*z + 3*z**3 + 6*z + 28*z - 14*z = 0. What is z?
-4, -1
Factor -17*c**2 + 45*c - 67 + 12*c**2 - 23.
-5*(c - 6)*(c - 3)
Let y(b) = -b + 14. Let n be y(9). Suppose -4*p**5 + 15*p**5 - p**2 - 10*p**n + p**4 + 2*p - 3*p**3 = 0. Calculate p.
-2, -1, 0, 1
Let q(r) be the second derivative of -5/3*r**3 - 1/15*r**6 + 1/10*r**5 + 11*r + 2*r**2 + 1/2*r**4 + 0. Factor q(o).
-2*(o - 1)**3*(o + 2)
Let f(j) be the third derivative of j**6/120 - 29*j**5/60 + 55*j**4/24 - 9*j**3/2 - 38*j**2 + j. Factor f(m).
(m - 27)*(m - 1)**2
Let z(d) be the third derivative of -d**8/1008 - d**7/70 - 13*d**6/180 - d**5/9 + d**4/3 + 16*d**3/9 - 6*d**2 - 2. Factor z(s).
-(s - 1)*(s + 2)**3*(s + 4)/3
Suppose -3*o - 2*m = 23, -4*o - 8 = -3*m - 0*m. Let k be 3/15 + (-19)/o. Solve k - 4*j + 11*j + 6*j**2 + 3*j - 2*j**4 - 2*j**3 = 0 for j.
-1, 2
Let f(c) be the second derivative of -2*c**6/15 - 2*c**5 - 12*c**4 - 36*c**3 - 54*c**2 - 98*c. Find t such that f(t) = 0.
-3, -1
Let r be (-4)/(-22)*((-2024)/(-32))/23. Let a be (-24)/(-14) - 2/(-7). Factor -2*l**2 - a*l**4 + 3*l**3 + 0 + 1/2*l + r*l**5.
l*(l - 1)**4/2
Suppose 19520*m = 19498*m + 66. Factor 0*i**2 + 6/11*i**5 - 12/11*i**m + 0 + 0*i**4 + 6/11*i.
6*i*(i - 1)**2*(i + 1)**2/11
Factor 225/4 - 5/4*u**2 - 15*u.
-5*(u - 3)*(u + 15)/4
Let t(w) be the first derivative of -w**7/189 - 2*w**6/135 - 2*w + 10. Let c(k) be the first derivative of t(k). Factor c(y).
-2*y**4*(y + 2)/9
Let n(v) = v**3 - v - 1. Let t(g) be the third derivative of -g**6/15 + g**5/6 + g**4/8 + g**3/2 - 9*g**2. Let w(k) = -3*n(k) - t(k). Factor w(o).
5*o**2*(o - 2)
Factor 336/11*t**2 + 54/11*t**4 + 288/11*t + 6/11*t**5 + 192/11*t**3 + 96/11.
6*(t + 1)*(t + 2)**4/11
Let f be 6 - (420/230 - -4). Factor -2/23*c**4 + 0*c - 2/23*c**2 + 0 + f*c**3.
-2*c**2*(c - 1)**2/23
Let a be (1/(-10))/(8/(-20)). Suppose -3/4*j - 3/4*j**2 - 1/4*j**3 - a = 0. What is j?
-1
Let s(u) be the second derivative of u**7/105 + 2*u**6/25 - u**5/50 - u**4/5 - 32*u. Suppose s(b) = 0. Calculate b.
-6, -1, 0, 1
Let s be ((-2)/(-8))/((-3 - -5)/(-8 + 24)). Suppose -4/5*g - 2/5*g**s + 0 = 0. What is g?
-2, 0
Let t(o) be the second derivative of 2*o - 1/3*o**4 + 4/3*o**3 + 0*o**2 + 0. Factor t(n).
-4*n*(n - 2)
Let p = -9949/8 + 1249. Let u = p - 41/8. Solve u*w**4 - 1/2*w**2 - 1/4*w + 1/2*w**3 + 1/4 - 1/4*w**5 = 0 for w.
-1, 1
Suppose 0*t - 2*t = -t. Suppose t = -4*s - 3*s. Factor 1/4*k**3 + 0*k**2 - 1/4*k + s.
k*(k - 1)*(k + 1)/4
Let l(d) be the second derivative of -d**5/20 + 19*d**4/12 - 32*d**3/3 + 30*d**2 + 86*d - 2. Solve l(r) = 0 for r.
2, 15
Let u(p) be the first derivative of 3*p**4/4 - 3*p**3/2 + 3*p**2/4 