/60*k**5 + 0*k**3 + o*k**7 + 0*k**2 + 1/18*k**6. Factor v(g).
g**3*(g + 1)*(4*g + 1)/3
Let u(n) be the second derivative of 8*n**4/27 + 248*n**3/27 + 961*n**2/9 + 435*n. Solve u(q) = 0 for q.
-31/4
Factor 5/2*k**4 + 0*k**3 - 20*k**2 + 40 + 0*k.
5*(k - 2)**2*(k + 2)**2/2
Let w = 18 + -15. Let c(q) be the third derivative of -q**2 - 1/120*q**4 + 0 + 1/100*q**5 + 0*q**w + 0*q. Factor c(u).
u*(3*u - 1)/5
Let w = 86 - -616. Let i = w + -4902/7. What is h in -2*h**4 + 2/7 + 6/7*h**5 + 4/7*h**3 - 10/7*h + i*h**2 = 0?
-1, 1/3, 1
Suppose 4*s + 71 + 137 = 0. Let t = -46 - s. Let 6*d**4 + 3/2*d**5 - 3 - 15/2*d + t*d**3 - 3*d**2 = 0. Calculate d.
-2, -1, 1
Let o = 2647 + -2637. Factor o*z**2 + 32/3*z**3 + 13/3*z + 2/3 + 16/3*z**4 + z**5.
(z + 1)**3*(z + 2)*(3*z + 1)/3
Factor 4/3*o**3 - 1/3*o**5 - 2/3*o**2 + 0*o**4 + 2/3 - o.
-(o - 1)**3*(o + 1)*(o + 2)/3
Factor -1746*f**3 + f**4 - 246*f + 20*f**2 + 46*f + 1778*f**3 + 3*f**4.
4*f*(f - 2)*(f + 5)**2
Let -3*p**2 - 3/2*p - 3/4*p**4 - 1/4 - 5/2*p**3 = 0. Calculate p.
-1, -1/3
Factor 4*g**2 - 37 - 3 + 16 + 20*g.
4*(g - 1)*(g + 6)
Let y(r) be the first derivative of r**5/3 - 25*r**4/24 + 5*r**3/6 - 9*r**2/2 - 1. Let v(k) be the second derivative of y(k). What is g in v(g) = 0?
1/4, 1
Let d be (11 + -12)*-3*1. Let a be ((-1505)/(-45))/7 - d. Determine o so that a*o + 32/9 + 2/9*o**2 = 0.
-4
Let x(t) be the first derivative of -t**6/4 + 6*t**5/5 + 3*t**4/8 - 2*t**3 + 209. Let x(j) = 0. What is j?
-1, 0, 1, 4
Let t(a) = -a**2 - 18*a - 25. Let b(l) = 18*l + 24. Suppose 2*q = -5*u - 14, 2*q + q - 3*u = 21. Let w(v) = q*t(v) + 2*b(v). Factor w(j).
-3*(j + 3)**2
Let v = -521/5 + 4173/40. Factor 0 - 1/4*d + v*d**2.
d*(d - 2)/8
Factor -36*t - 80*t**3 - 504*t**2 - 18*t - 730*t - 4*t**4 + 1372.
-4*(t - 1)*(t + 7)**3
Let f be (-57)/54 - (-33)/22. Find c, given that f*c + 0 + 2/3*c**2 = 0.
-2/3, 0
Let w be 9/(-2)*22/(-33). Suppose 5 - 5*y**4 + 25*y - 50*y**w + 29*y**5 - 5*y + 5*y**5 - 4*y**5 = 0. What is y?
-1, -1/2, -1/3, 1
Find l, given that 29/5*l - 1/5*l**2 + 0 = 0.
0, 29
Let q = 23 + -21. Let k be 12 + -10 - (q + (-42)/8). Factor -45/4*c - 3/4*c**3 + 27/4 + k*c**2.
-3*(c - 3)**2*(c - 1)/4
Suppose -1135*t + 1138*t = 3*l - 12, -4*t - 5*l + 38 = 0. Factor -1/5*f**3 + 0*f + 0 - 2/5*f**t.
-f**2*(f + 2)/5
Let y(t) be the third derivative of 0*t**4 + 0 + 0*t**5 - 1/40*t**6 + 0*t - 10*t**2 + 0*t**3 + 1/140*t**7. Factor y(j).
3*j**3*(j - 2)/2
Let w be 42 + 254/(-6) + (0 - 1)*-1. Solve w*m + 2/9*m**3 + 2 - 10/9*m**2 = 0 for m.
-1, 3
Let a(b) be the third derivative of b**8/3192 + 4*b**7/665 + b**6/228 - 89*b**5/285 + 24*b**4/19 - 128*b**3/57 + 289*b**2. Suppose a(z) = 0. What is z?
-8, 1, 2
Let p(x) be the third derivative of x**8/112 + 9*x**7/70 - 27*x**5/5 + 2*x**2 + 4*x. Factor p(b).
3*b**2*(b - 3)*(b + 6)**2
Suppose -17*j**2 - 13*j**2 + 64*j**2 + j**3 - 15*j**2 + 11*j - 11*j**2 - 20 = 0. Calculate j.
-5, -4, 1
Factor -21*d**4 - 4*d**2 + 6658*d - 3*d**5 - 6706*d - 12 - 71*d**2 - 57*d**3.
-3*(d + 1)**3*(d + 2)**2
Factor -3/7*f**4 - 108/7*f**2 - 6*f**3 - 33/7 - 102/7*f.
-3*(f + 1)**3*(f + 11)/7
Let d(i) = 60*i**3 + 245*i**2 + 440*i + 220. Let b(c) = c**4 + c**2 - 4*c + 1. Let w(a) = 5*b(a) + d(a). Find y such that w(y) = 0.
-5, -3, -1
Solve 16/3*i - 8 - 2/3*i**3 + 2/3*i**2 = 0.
-3, 2
Suppose 4*p - 58 = 4*m - 14, 3 = p + 3*m. Let x be (-12)/(-10)*(-5)/p*-6. Factor 23/2*h**3 - 7/2*h**x + 0 + 2*h - 10*h**2.
-h*(h - 2)*(h - 1)*(7*h - 2)/2
Let l(k) = -3*k + 18. Let n be l(5). Suppose -n*j - 5*m = -6*j + 20, -4*m - 16 = -j. Determine d, given that j*d + 0 + 1/4*d**2 = 0.
0
Let w(i) be the second derivative of -i**7/210 - 11*i**6/150 - 9*i**5/50 + i**4/30 + 19*i**3/30 + 9*i**2/10 + 108*i. Suppose w(v) = 0. What is v?
-9, -1, 1
Let a = 40 - 39. Let w be 2 + a - (4 - 6). What is n in 0*n + 0 - 3/2*n**w + 0*n**4 + 0*n**3 + 0*n**2 = 0?
0
Let s = -5 - -7. Suppose -4*f = 4*p - 103 + 7, s*p = 2*f - 28. Let 0*y**3 - 3*y**3 + f*y - 16*y = 0. Calculate y.
-1, 0, 1
Let x be ((-12)/(-105))/((-4)/(-5610)). Let z = x + -160. Factor -2/7*t**2 + 4/7 - z*t.
-2*(t - 1)*(t + 2)/7
Let p = 4642 + -4642. Solve -z**4 - 1/2*z + z**2 + p*z**3 + 1/2*z**5 + 0 = 0 for z.
-1, 0, 1
Let n(y) = -23*y + 1. Let g be n(-3). Let b = g - 70. What is t in b*t**3 + 4/3*t**2 - 2/3*t**5 + 2/3*t - 4/3*t**4 + 0 = 0?
-1, 0, 1
Let n(q) be the second derivative of 0 + 27*q - 4*q**3 - 1/3*q**4 + 0*q**2. Factor n(g).
-4*g*(g + 6)
Factor -16/3*v**2 - 4/3*v**4 - v - 17/3*v**3 + 0.
-v*(v + 1)*(v + 3)*(4*v + 1)/3
Let s(v) = 3*v**4 - 18*v**3 - 15*v**2 + 18*v + 3. Let g(t) = -2 + 2*t**4 - 8*t**2 - 8*t**3 - t**3 + 3 + 2*t + 7*t. Let h(x) = 9*g(x) - 5*s(x). Factor h(q).
3*(q - 1)*(q + 1)**2*(q + 2)
Let x be 2/(-16)*(-256)/12. Solve -x*v - 1/6*v**3 + 0 + 4/3*v**2 = 0 for v.
0, 4
Let a(t) be the second derivative of t**4/3 + 2*t**3 - 9*t**2 + 10*t. Let m(k) = k**2. Let r(p) = -a(p) + 6*m(p). Let r(w) = 0. Calculate w.
3
Let b = -1/2943 + 54955/55917. Let q = b - 6/19. Solve q*x**4 + 1/3*x**5 + 0*x**3 + 0 - 2/3*x**2 - 1/3*x = 0 for x.
-1, 0, 1
Let f(p) be the third derivative of -p**9/189 + p**8/56 + 5*p**7/168 + p**6/72 - 4*p**4/3 + 16*p**2. Let h(d) be the second derivative of f(d). Factor h(z).
-5*z*(z - 2)*(4*z + 1)**2
Let f(u) be the third derivative of -u**5/150 + u**4/12 - 2*u**3/5 - u**2 - 4. Factor f(n).
-2*(n - 3)*(n - 2)/5
Suppose -m + 2 = -5*q, 394*m + 5*q - 2 = 393*m. Determine d so that -3/2*d**m + 0 - 3/2*d**5 + 3/2*d**3 + 0*d + 3/2*d**4 = 0.
-1, 0, 1
Factor 0 - 3/5*b**3 + b - 3/10*b**2 - 1/10*b**4.
-b*(b - 1)*(b + 2)*(b + 5)/10
Let k(u) be the first derivative of -2*u**3 + 0*u + 12 - 21/4*u**4 + 0*u**2. Factor k(x).
-3*x**2*(7*x + 2)
Let w(j) be the first derivative of 25 + 4/9*j - 5/9*j**2 - 8/45*j**5 + 4/27*j**3 + 1/27*j**6 + 2/9*j**4. Factor w(y).
2*(y - 2)*(y - 1)**3*(y + 1)/9
Let v = -16 + -16. Let r = v - -35. Factor -r*z**2 + 4 - 31*z - z**2 + 23*z + 5*z**3 - 3*z**2.
(z - 2)*(z + 1)*(5*z - 2)
Suppose -4*f - 3*j - 5 = 0, 1 + 7 = 5*f - j. Let v be (5 + f)/(15 - 2). Factor 6/13*b + 2/13*b**3 + 2/13 + v*b**2.
2*(b + 1)**3/13
Let w be ((-3)/12)/(2/(-24)). Suppose 0 = 3*l, w*n - 8*n + 10 = -l. Find c such that -n*c**3 + 10*c**4 + 4*c**3 - 2*c - 13*c**4 + 3*c**2 = 0.
-1, 0, 2/3, 1
Suppose -16 = -4*o, -3*f + 8*f + 4*o = 41. What is v in 12*v - 6*v**4 + 0*v**3 + 9*v**3 + 15*v**2 + 3*v**4 - 3*v**f - 6*v = 0?
-1, 0, 2
Suppose 5*y - 3*b = 8, 0*b + 32 = 3*y + 5*b. Suppose -z - 4*z + 7 = y*u, 0 = u - 2*z - 5. Factor 2*r**2 - 32*r + u*r**2 + 29*r - 2*r**2.
3*r*(r - 1)
Factor -4/3*y**2 - 1936/3 - 176/3*y.
-4*(y + 22)**2/3
Let i(g) = 19*g**2 + 4*g - 3. Let a(w) = 54*w**2 + 11*w - 9. Let t(y) = 6*a(y) - 17*i(y). Find q, given that t(q) = 0.
-1, 3
Let w be (-3)/(12/(-8)) - (-408)/4. What is k in -3*k**2 - 110*k**3 + 35*k**4 + 5 + w*k**2 - 50*k + 19*k**2 = 0?
1/7, 1
Factor 15/2*o - 3/2*o**2 + 0.
-3*o*(o - 5)/2
Let o(w) = w**4 + w**3 - w**2 - 3*w - 1. Let a(q) = -3*q**4 + 11*q**3 + 15*q**2 + 3*q + 1. Let g(y) = -2*a(y) - 2*o(y). Find h, given that g(h) = 0.
-1, 0, 7
Let y(m) be the second derivative of -8*m**4/3 - 6*m**3 - 2*m**2 + 106*m - 2. Factor y(z).
-4*(z + 1)*(8*z + 1)
Suppose 5*x - 4 = 4*z, -5*x + 4*z + z = -5. Let u = 4 + x. Factor -2*o**u + 2 - 2 - 4*o**4 - 2*o**5 - 4*o**3.
-2*o**3*(o + 1)*(o + 2)
Factor 5*i**5 - 12*i**3 - 16*i**3 + 13*i**3 - 5*i**4 + 10*i + 5*i**2.
5*i*(i - 2)*(i - 1)*(i + 1)**2
Suppose -4*b - 285 = -b - 4*q, b - q + 95 = 0. Let k = 98 + b. Factor g**2 - 1/2*g - 1/2*g**k + 0.
-g*(g - 1)**2/2
Let 40/7 + 32/7*k**2 + 4/7*k**3 + 68/7*k = 0. What is k?
-5, -2, -1
Let h(f) = f**3 - 22*f**2 - 37*f - 14. Let q(v) = v**3 - 45*v**2 - 73*v - 27. Let r(t) = -5*h(t) + 3*q(t). Factor r(p).
-(p + 1)*(p + 11)*(2*p + 1)
Suppose 0 = 5*r - 61 - 134. Let p = r - 36. Solve -1/4 + 1/4*x - 1/4*x**p + 1/4*x**2 = 0.
-1, 1
Let h be 1 + 100/(-80)*10/25. Let -1/4 + 0*z**2 + 1/2*z + 1/4*z**4 - h*z**3 = 0. Calculate z.
-1, 1
Let q(g) = 3*g + 3. Let u be q(-3). Let h be (u/(-24))/(1/8). Factor 0*n**h + 1/5*n**4 - 1/5 - 2/5*n + 2/5*n**3.
(n - 1)*(n + 1)**3/5
Let m(r) be the second derivative of 3 + 3*r**3 - 27/2*r**2 - 1/4*r**4 + 9*r. Suppose m(s) = 0. What is s?
3
Let w(i) be the second derivative of i**4/96 - 47*i**3/48 - 328*i. Let w(v) = 0. Calculate v.
0, 47
Let u = -235 + 238. Let h(f