, 0
What is i in 27/4 - 51/8*i**2 - 33/8*i**3 - 3/8*i**4 + 33/8*i = 0?
-9, -2, -1, 1
Let k(h) be the second derivative of -h**6/105 - 3*h**5/70 + h**4/42 + h**3/7 + 217*h. Find y such that k(y) = 0.
-3, -1, 0, 1
Let h(y) = 9*y**3 + 57*y**2 + 87*y + 39. Let k(o) = o**3 + 7*o**2 + 11*o + 5. Let u(g) = -4*h(g) + 33*k(g). Find f such that u(f) = 0.
-1, 3
Let a(n) be the third derivative of n**5/30 + 19*n**4/6 + 361*n**3/3 - 5*n**2 + 4*n. Factor a(c).
2*(c + 19)**2
Suppose 9*b - 50 = 283. Let k = b + -71/2. What is r in 1/2*r**3 + k*r**2 + 0 + r = 0?
-2, -1, 0
Let f(g) be the second derivative of g**7/16 - 41*g**6/240 - 9*g**5/80 + 3*g**4/8 - g**3/6 + 95*g. Suppose f(m) = 0. Calculate m.
-1, 0, 2/7, 2/3, 2
Let y = 249/46 + -701/138. Solve 1/3*s**2 + 0*s - y = 0 for s.
-1, 1
Let s(j) = -4*j**3 - 55*j**2 - 108*j - 57. Let k(y) = 2*y**3 + 28*y**2 + 54*y + 28. Let m(t) = -10*k(t) - 4*s(t). Solve m(w) = 0 for w.
-13, -1
Let v(q) be the second derivative of q**5/5 + 2*q**4/3 - 10*q**3/3 - 12*q**2 + 62*q - 2. What is u in v(u) = 0?
-3, -1, 2
Let -3*u + 2*u**4 + 16*u**2 + 49/3*u**3 - 14/3 = 0. Calculate u.
-7, -1, -2/3, 1/2
Let c(r) be the second derivative of -r**5/4 - 35*r**4/4 + 55*r**3/3 + 77*r. What is t in c(t) = 0?
-22, 0, 1
Let q(f) be the third derivative of 1/2520*f**8 + 0*f**5 + 0*f**7 - 1/900*f**6 + 0*f - 11*f**2 + 0 + 0*f**4 + 0*f**3. Factor q(n).
2*n**3*(n - 1)*(n + 1)/15
Let u(s) = -3*s - 34. Let q be u(-12). Suppose -q*j = -5*j + 6. Factor -3/7*i + 3/7*i**j + 0.
3*i*(i - 1)/7
Let m(u) be the second derivative of -u**7/168 + u**6/8 - 7*u**5/40 - 85*u - 1. Determine a so that m(a) = 0.
0, 1, 14
Let o(m) be the first derivative of m**4/48 - 4*m + 10. Let w(d) be the first derivative of o(d). Let w(z) = 0. What is z?
0
Suppose -q - 3 = -2*i, -5*i = 2*q - 8 - 22. Let c(u) be the first derivative of 0*u - 2 + 2/3*u**3 - 2*u**2 + 1/2*u**i. Find m, given that c(m) = 0.
-2, 0, 1
Let s be 6/4 + (-156)/(-8). Let d be ((-6)/s)/((-4)/28). Suppose i**2 + i + i + 0*i**d + 0*i**2 = 0. Calculate i.
-2, 0
Let s be (-6)/(-5)*((-20)/6 - -5). Let g(h) be the second derivative of 4*h - 25/42*h**4 - 4/7*h**s + 0 - 20/21*h**3. Factor g(q).
-2*(5*q + 2)**2/7
Let s = 1895/24 + -12497/168. Let 8/7*x + 4/7*x**2 - s = 0. What is x?
-4, 2
Factor 2/3*k**2 - 8/3*k + 0 + 1/3*k**3.
k*(k - 2)*(k + 4)/3
Suppose -8*p - 12 = -14*p. Let f(q) be the second derivative of 3*q - 1/30*q**3 + 0*q**p + 1/60*q**4 + 0. Suppose f(o) = 0. Calculate o.
0, 1
Let z(v) be the second derivative of 5*v**7/42 + 7*v**6/6 + 9*v**5/2 + 25*v**4/3 + 20*v**3/3 - 26*v. Let z(b) = 0. What is b?
-2, -1, 0
Let q(s) = -s**2 + 310*s + 2223. Let u be q(-7). Factor 55/2*d**3 - 27/2*d**u - 53/2*d**2 - 2 + 5/2*d**5 + 12*d.
(d - 2)*(d - 1)**3*(5*d - 2)/2
Let t(f) be the first derivative of 0*f**2 + 0*f + 1/9*f**4 - 1/27*f**6 + 0*f**3 - 2/45*f**5 + 27. Factor t(y).
-2*y**3*(y - 1)*(y + 2)/9
Let i = -10223 + 10226. Determine h, given that -3/2*h**3 + 3*h**2 + 3/2*h - i = 0.
-1, 1, 2
Let w(z) be the first derivative of z**5/540 + z**4/27 - 33*z**2/2 - 12. Let i(c) be the second derivative of w(c). Solve i(m) = 0 for m.
-8, 0
Let z = 22213 + -155490/7. Find h, given that -2/7*h**3 - h**2 + z*h**4 - 4/7*h + 0 = 0.
-1, 0, 4
Let i(z) = -16*z**2 + 18*z - 16. Let r(q) = q**2 - q + 1. Suppose -f - 10 = -6*f. Let y be (-84)/(-10)*(-30)/(-9). Let l(w) = f*i(w) + y*r(w). Factor l(s).
-4*(s - 1)**2
Let p(y) = -y**3 - 3*y**2 + 17*y + 7. Let z be p(3). Determine n, given that 0 + 3*n**2 - 2*n - 3/2*n**3 + 1/4*n**z = 0.
0, 2
Find d such that -20*d - 25*d**4 + 10*d**4 - 176*d + 120*d**3 + 71*d - 35*d**4 + 50*d**2 + 5*d**5 = 0.
-1, 0, 1, 5
Determine m so that 9*m**3 - 15*m**2 - 4*m**3 + 5 + 70 - 65*m = 0.
-3, 1, 5
Let l(n) be the first derivative of 14*n**6/15 - 26*n**5/25 - n**4/10 + 116. Factor l(a).
2*a**3*(a - 1)*(14*a + 1)/5
Let i = -796/11 + 850/11. Let t = -248/55 + i. Let 0 - 8/5*f**2 + t*f**3 + 8/5*f = 0. Calculate f.
0, 2
Let c(j) = -4*j**3 + 58*j**2 - 279*j + 220. Let h(z) = 2*z**3 - 30*z**2 + 140*z - 110. Let v(m) = -2*c(m) - 5*h(m). Factor v(r).
-2*(r - 11)*(r - 5)*(r - 1)
Let -5*k**5 - 99*k**2 - 6633*k**3 + 6178*k**3 - 85*k**4 - 636*k**2 = 0. Calculate k.
-7, -3, 0
Let d(c) be the third derivative of -c**3 - 13*c**2 + 0 - 1/30*c**6 + 0*c + 1/6*c**4 + 2/15*c**5 - 1/105*c**7. Let d(g) = 0. Calculate g.
-3, -1, 1
What is h in -6*h**2 - 8*h + 3*h**2 - 5*h**2 + 86 - 334*h = 0?
-43, 1/4
Let y(z) be the first derivative of -z**4/5 + 4*z**3/3 - 500. Factor y(g).
-4*g**2*(g - 5)/5
Suppose -3*b + 5 = a, -3*b + 5*a = 4 + 21. Let n(s) be the second derivative of 3/20*s**5 + 0*s**3 + 1/10*s**6 + 0*s**4 + b + 0*s**2 - s. Factor n(h).
3*h**3*(h + 1)
Let v(i) be the first derivative of 2/9*i**3 + 4/3*i - i**2 - 5. Factor v(s).
2*(s - 2)*(s - 1)/3
Suppose 2/5*f**4 - 22/5*f**2 - 9/5*f**3 + 24/5 + 4/5*f + 1/5*f**5 = 0. Calculate f.
-2, 1, 3
Factor -29/2 + 31/4*o - 1/4*o**2.
-(o - 29)*(o - 2)/4
Let z(g) = -g**3 + 9*g**2 - 5*g - 2. Let f be z(7). Suppose -h + 4 = -f. Factor -x - h*x**3 + 4*x**4 + x + 61*x**3.
4*x**3*(x - 1)
Factor -2/9*q**3 - 2/9*q**2 + 8/9 + 8/9*q.
-2*(q - 2)*(q + 1)*(q + 2)/9
Let j(f) be the second derivative of 1/40*f**6 + 3*f + 0 - 2/3*f**3 + 0*f**4 - 1/40*f**5 + 0*f**2. Let m(o) be the second derivative of j(o). Factor m(q).
3*q*(3*q - 1)
Let z = -21 + 21. Find h, given that h**3 - 8*h + 6*h**2 + z*h**3 + 5*h - 4*h**3 = 0.
0, 1
Suppose u - 39 = -35. Let -4/3*d - u - 1/9*d**2 = 0. Calculate d.
-6
Let f(d) be the third derivative of 0*d - d**3 + 15*d**2 + 0 + 1/20*d**5 - 1/8*d**4. Factor f(i).
3*(i - 2)*(i + 1)
Let n be 29/(-5 + (-528)/(-102)). Let x = n - 164. Factor -x*p**3 + 0*p + 0 + 1/3*p**2.
-p**2*(p - 1)/3
Let q(w) be the first derivative of -w**6/45 - 2*w**5/25 - w**4/10 - 2*w**3/45 - 38. Factor q(h).
-2*h**2*(h + 1)**3/15
Let g(w) be the third derivative of w**8/224 + 13*w**7/140 + 29*w**6/40 + 53*w**5/20 + 85*w**4/16 + 25*w**3/4 + 6*w**2 + 7. What is k in g(k) = 0?
-5, -1
Suppose -4 = -2*g - 2*g + 2*j, g + 4*j + 8 = 0. What is z in -20*z + g + 5*z**2 - 7 - 13 + 5*z**3 = 0?
-2, -1, 2
Let m = -216 + 218. Let f(t) be the second derivative of 0*t**4 - 1/50*t**6 - t + 0*t**3 + 0 - 3/100*t**5 + 0*t**m. Factor f(d).
-3*d**3*(d + 1)/5
Let -10*b**4 - b**5 - 5*b**3 + 24*b + 3*b**5 + 2*b**4 - 21*b**3 + 8*b**2 = 0. Calculate b.
-2, -1, 0, 1, 6
Let x(g) be the first derivative of g**5/55 + 23*g**4/22 + 529*g**3/33 + 52. Factor x(l).
l**2*(l + 23)**2/11
Let d = -32 - -42. Suppose -3*s + 0*m + 4*m - d = 0, 2*m = s + 6. Factor 0 + 0*y**3 - 1/2*y + 1/2*y**5 + y**s - y**4.
y*(y - 1)**3*(y + 1)/2
Let j(c) be the third derivative of -c**8/672 - 13*c**7/210 - 193*c**6/240 - 13*c**5/5 - 3*c**4 - 2*c**2 - 73*c. Factor j(q).
-q*(q + 1)**2*(q + 12)**2/2
Let z = 2/14497 - -217451/28994. Solve -11/2*r + 1 + z*r**2 = 0 for r.
1/3, 2/5
Let f(w) be the first derivative of 0*w**4 - 1/12*w**6 + 1/5*w**5 + 8 - 1/3*w**3 + 0*w + 1/4*w**2. Factor f(n).
-n*(n - 1)**3*(n + 1)/2
Let w(h) be the first derivative of -4*h**5 - 20/3*h**3 + 5/6*h**6 + 22 + 0*h + 5/2*h**2 + 15/2*h**4. Factor w(g).
5*g*(g - 1)**4
Let b(s) be the second derivative of 11*s**7/42 - 13*s**6/30 - 15*s**5/4 + 25*s**4/12 + 32*s**3/3 - 6*s**2 + 31*s - 9. Suppose b(r) = 0. What is r?
-2, -1, 2/11, 1, 3
Factor -334 - 27*c**2 + 334 - 8*c + 2*c.
-3*c*(9*c + 2)
Factor 0*z + 0 - 4/5*z**2 + 2/5*z**4 - 2/5*z**3.
2*z**2*(z - 2)*(z + 1)/5
Let m(v) be the first derivative of v**3/3 - 53*v**2/2 + 52*v + 585. Find k such that m(k) = 0.
1, 52
Suppose 3*b + 3*k + 30 = 0, 5*k = -5*b + 2*b - 38. Let v be 5/15*(3/b + 2). Determine j so that -1/2 - j - v*j**2 = 0.
-1
Let q = 48 + -58. Let g be (-4)/q - (-52)/20. Factor 0 + 4/7*z**2 - 4/7*z**g + 8/7*z.
-4*z*(z - 2)*(z + 1)/7
Let u(i) = -i - 15. Let y be u(-11). Let t be y - (-7)/1 - -1. Solve 12 - 32*m - 2*m**5 - 8*m**t - 38*m**3 - 20 - 50*m**2 - 6*m**4 = 0 for m.
-2, -1
Let b(m) = 14*m - 36. Let i be b(4). Let k be (18/i)/(12/10). Factor 3/4*v**3 - k*v + 1/4*v**2 - 1/4.
(v - 1)*(v + 1)*(3*v + 1)/4
Solve -24/17 + 98/17*q**4 + 184/17*q + 140/17*q**3 - 398/17*q**2 = 0.
-3, 2/7, 1
Let q(c) be the second derivative of 5*c**4/12 + 65*c**3/3 + 845*c**2/2 + c + 55. Solve q(p) = 0.
-13
Suppose 5*l - 2*o = 0, 0*o = -3*l - 2*o + 16. Factor 91*g**2 - 179