4, -2, 1
Let x(r) be the second derivative of r**4/4 + 9*r**3/2 + 12*r**2 + r + 204. Find n such that x(n) = 0.
-8, -1
Let s = 81 + -125. Let c = 46 + s. Factor 3/5*r**3 - 3/5 - 3/5*r + 3/5*r**c.
3*(r - 1)*(r + 1)**2/5
Solve -6/5*z**4 + 0*z - 32/5*z**3 - 24/5*z**2 + 2/5*z**5 + 0 = 0.
-2, -1, 0, 6
Let s(v) = -3*v**2 - 10*v + 8. Let z be s(-4). Let b(k) be the third derivative of 1/45*k**5 + 1/45*k**6 + z - k**2 + 0*k + 1/144*k**4 + 0*k**3. Factor b(h).
h*(4*h + 1)**2/6
Suppose 0 = 3*t + t - 4, 5*k + 2*t - 17 = 0. Factor -x - x**4 - x + 2*x**k + 87*x**2 - 86*x**2.
-x*(x - 2)*(x - 1)*(x + 1)
Let a = 122 - 119. Suppose 3*o - o - 2 = -a*v, -o + 2 = 2*v. Solve 0*y - 2/3 + 2/3*y**v = 0 for y.
-1, 1
Let q = 74 + -73. Let a be (42/(-10) + q)*(-4 - -3). Suppose -a*u - 35*u**5 - 448/5*u**3 + 144/5*u**2 + 108*u**4 + 0 = 0. Calculate u.
0, 2/7, 2/5, 2
Let t(c) = -2*c + 12. Let r be t(0). Let u be 186/r + 3/2. Find d, given that -u*d - d**2 + 3*d + 6 + 9*d**2 = 0.
3/4, 1
Let y be (-10)/25 + 126/15. Factor 7*b + 5*b**4 - 20*b**3 - 20 + 5*b + 15*b**2 + y*b.
5*(b - 2)**2*(b - 1)*(b + 1)
Let t(r) be the second derivative of r**7/168 + r**6/18 - 13*r**3/6 + 8*r. Let j(i) be the second derivative of t(i). Factor j(v).
5*v**2*(v + 4)
Factor j**4 - 69*j**2 + 0*j**5 - j**5 + j**3 + 138*j**2 - 70*j**2.
-j**2*(j - 1)**2*(j + 1)
Let v(i) = -i**2 + 8*i - 5. Let w be v(7). Suppose 5 = -w*o + 3*p - 3, 4*o - 2*p = 0. Factor -34*c**2 - 3*c**4 - 3*c + 3*c**3 + 17*c**o + 20*c**2.
-3*c*(c - 1)**2*(c + 1)
Let n be (-5)/15*(5/(-2) - -1). Suppose -b**2 + 1/2*b**3 + n*b**4 + 0 + 0*b = 0. What is b?
-2, 0, 1
Suppose -19*g + 5*g = 56. Suppose 0*h = 3*h - 33. Let x(m) = -m**2 + 3*m. Let i(d) = -2*d**2 + 9*d. Let t(y) = g*i(y) + h*x(y). Factor t(r).
-3*r*(r + 1)
Let x be 11/((-495)/(-10)) - 32/(-18). Suppose -125 + 2*q**2 - 3*q**2 + 50*q - 3*q**2 - q**x = 0. Calculate q.
5
Let y(c) be the second derivative of 2*c**7/63 + 4*c**6/15 - 8*c**5/15 - 2*c**4/3 + 14*c**3/9 + c - 19. Find z, given that y(z) = 0.
-7, -1, 0, 1
Suppose -245*i - 59 = -151 - 643. Factor -1/2*r + 1/4*r**4 - 3/4*r**2 + 0 + 0*r**i.
r*(r - 2)*(r + 1)**2/4
Let i = -14464 - -14468. Solve -164/7*w**2 + 0 - 64/7*w**i + 20/7*w + 352/7*w**3 = 0 for w.
0, 1/4, 5
Suppose -11*p + 160 = -16. Let 24*o**3 + 2*o + p*o**2 + 2*o - 2*o**5 + 6*o**5 + 8*o**4 + 8*o**4 = 0. Calculate o.
-1, 0
Let f(m) be the third derivative of -m**5/20 + 9*m**4/8 - 4*m**3 + 180*m**2. Determine x so that f(x) = 0.
1, 8
Let l(v) be the second derivative of 8/9*v**3 + 2/3*v**4 + 1/15*v**5 - 1/63*v**7 - 1/15*v**6 + 0 + 0*v**2 - 7*v. Determine a, given that l(a) = 0.
-2, -1, 0, 2
Let g be (5 - (-35)/(-5))*13/(-6) + -4. Determine o so that 1/6 + 1/6*o**2 + g*o = 0.
-1
Let h(p) be the first derivative of 5*p**3 + 27/4*p**2 + 0*p + 17 + 3/8*p**4. Find i, given that h(i) = 0.
-9, -1, 0
Let o(y) be the first derivative of y**7/1260 - y**5/120 - y**4/72 + 7*y**2 - 12. Let c(h) be the second derivative of o(h). Factor c(r).
r*(r - 2)*(r + 1)**2/6
Let m(n) be the first derivative of -5/3*n**3 - 6 + 0*n**4 + n**5 + 0*n**2 + 0*n. Factor m(p).
5*p**2*(p - 1)*(p + 1)
Let o(u) be the second derivative of -u**4/4 + u**3/2 - u**2 - 36*u. Let b(a) = -10*a**2 + 8*a - 4. Let c(h) = 2*b(h) - 7*o(h). Let c(m) = 0. Calculate m.
2, 3
Let z be (5/(-10))/((-3)/(-42)). Let g = 11 + z. Suppose 9*o - 2*o**3 - 4*o - o**g - o**2 - 5*o = 0. Calculate o.
-1, 0
Let h(n) be the third derivative of -n**5/90 - 11*n**4/36 - 2*n**2 + 6. Find q such that h(q) = 0.
-11, 0
Let s(j) = 7*j**2 + 9*j - 3. Let i(a) = -16*a - 11*a - 20*a**2 - 1 + 9 + a. Let t(k) = 5*i(k) + 14*s(k). Find x such that t(x) = 0.
-1
Let r(p) = -p**5 - 4*p**4 - p**3. Let n(a) = -10*a**5 + 2*a**4 - 38*a**3 + 20*a**2 - 4*a. Let x(t) = -n(t) + 5*r(t). Suppose x(m) = 0. What is m?
0, 2/5, 1, 2
Let o = -19915 + 219093/11. Factor -98/11 - 2/11*n**2 - o*n.
-2*(n + 7)**2/11
Let h(u) be the third derivative of 13*u**2 + 0*u + 0 + 1/540*u**6 + 1/180*u**5 + 0*u**4 + 4/3*u**3. Let q(i) be the first derivative of h(i). Factor q(j).
2*j*(j + 1)/3
Let o(r) be the third derivative of -r**5/12 - 5*r**4/8 + 10*r**3/3 - 283*r**2. Factor o(d).
-5*(d - 1)*(d + 4)
Let u = -1703 + 1706. Factor 0 - 3/8*s**2 + 3/8*s**4 + 3/8*s - 3/8*s**u.
3*s*(s - 1)**2*(s + 1)/8
Let s(g) be the first derivative of 4*g**5/15 - 13*g**4/6 + 2*g**3 + 40*g**2/3 + 32*g/3 + 128. Solve s(h) = 0.
-1, -1/2, 4
Let v(x) be the second derivative of -1/9*x**3 + 1/18*x**4 - 1/3*x**2 + 0 + 4*x + 1/30*x**5. Factor v(b).
2*(b - 1)*(b + 1)**2/3
Let v(j) be the first derivative of -4*j**3/3 + 50*j**2 - 184*j - 46. Factor v(w).
-4*(w - 23)*(w - 2)
Factor -2*k - 36*k**2 - 21*k + 18*k**3 - 9*k - 22*k**3.
-4*k*(k + 1)*(k + 8)
Factor 0 + 169/5*n - 26/5*n**2 + 1/5*n**3.
n*(n - 13)**2/5
Let r(i) be the first derivative of 4*i**5/25 - 8*i**4/5 - 136*i**3/15 + 16*i**2/5 + 132*i/5 + 47. Find o such that r(o) = 0.
-3, -1, 1, 11
Let d be -4 + (-2 - 1 - -1). Let m = -1 - d. Factor -b**2 - 5*b**m + 3*b**2 + 8 - 2*b**4 - 7*b**5 - 10*b**3 + 14*b**5 + 16*b.
2*(b - 2)**2*(b + 1)**3
Suppose c + 15 = -k, -2*c + 0*k - 26 = k. Let x = c - -13. Factor 6*j - 4*j**x - 9*j + 7*j**2.
3*j*(j - 1)
Let a(j) be the second derivative of -3/40*j**5 + 0 + 1/4*j**3 + 1/40*j**6 - 11*j + 0*j**4 - 3/8*j**2. Let a(f) = 0. Calculate f.
-1, 1
Suppose i + 9*u - 11*u - 246 = 0, 4 = 4*u. Determine o so that -i*o + 4 - 4*o**4 + 8*o**3 + 0 + 240*o = 0.
-1, 1
Let q be -13*14/(-30) + -6. Let m(s) be the second derivative of -2*s + 0 - 1/18*s**4 - 1/45*s**6 + q*s**5 + 0*s**3 + 0*s**2. Factor m(w).
-2*w**2*(w - 1)**2/3
Let m be 2 + (-569)/(-2) - (-24)/48. Let r = m - 283. Solve 1/2*u + 0 - 1/4*u**5 - 1/4*u**3 - 3/4*u**r + 3/4*u**2 = 0.
-2, -1, 0, 1
Let g(q) be the second derivative of 0 + q**3 - q**2 + 1/10*q**5 - 1/2*q**4 + 8*q. Factor g(m).
2*(m - 1)**3
Let l(a) be the second derivative of 3*a**5/20 + 11*a**4/12 + 4*a**3/3 - 2*a - 22. Find m, given that l(m) = 0.
-8/3, -1, 0
Let j(l) be the second derivative of l**7/1008 + l**4/3 - l. Let s(t) be the third derivative of j(t). Suppose s(w) = 0. Calculate w.
0
Let l(d) = d + 1. Let f(y) = y**3 - 28*y**2 + 24*y + 25. Let x(z) = -f(z) - 2*l(z). Let g be x(27). Determine v so that 2/3*v**3 + g + 2/3*v**2 + 0*v = 0.
-1, 0
Let u be 1*(13/4 - (19 - 16)). Factor 1/4*q**5 - 1/4*q**2 - u*q**3 + 0 + 1/4*q**4 + 0*q.
q**2*(q - 1)*(q + 1)**2/4
Suppose 4*h - 20 = -4*u, -5*u - 3*h + 23 = -10. Suppose u*w - 7*w = 0. Factor 0*t + 4*t + 6*t**2 - 3*t**3 - t + w*t**2 - 6.
-3*(t - 2)*(t - 1)*(t + 1)
Find d, given that -203*d**3 + 407*d**3 - 12*d**4 - 208*d**3 = 0.
-1/3, 0
Let l be 68/16 + 5/(-20). Let s be 6/l + 8/16. Factor 8*u**2 - u**3 + u**5 + 0*u**5 - 2*u**2 - u**4 - 5*u**s.
u**2*(u - 1)**2*(u + 1)
Let i = 134 - 134. Let b(m) be the second derivative of -1/3*m**3 + 1/5*m**5 + 0*m**4 - 2*m - 1/21*m**7 + 0 + 0*m**2 + i*m**6. Factor b(r).
-2*r*(r - 1)**2*(r + 1)**2
Let a be (-72)/64*(-5)/30*4. Solve -a*m - 1 + 1/4*m**2 = 0 for m.
-1, 4
Let f(n) be the first derivative of -n**4/24 - 2*n**3/3 - 7*n**2/4 - 45*n - 17. Let o(t) be the first derivative of f(t). Find b, given that o(b) = 0.
-7, -1
Determine v so that 6*v**4 + 39/2*v**2 - 37/2*v**3 + 1/2 - 15/2*v = 0.
1/12, 1
Determine w, given that 0 - 26/5*w + 2/5*w**3 + 24/5*w**2 = 0.
-13, 0, 1
Let p(z) be the second derivative of z**5/50 + 3*z**4/10 - 5*z**3/3 - 33*z**2/5 - 2*z + 118. Solve p(k) = 0 for k.
-11, -1, 3
Factor -1/4*p**4 - 64*p + 0 - 56*p**2 + 31/4*p**3.
-p*(p - 16)**2*(p + 1)/4
Find t such that -75/7 + 90/7*t - 27/7*t**2 = 0.
5/3
Let w be 14/(-21) - 112/216*-3. Factor -w*x**3 + 2/9*x**4 - 4/9*x + 10/9*x**2 + 0.
2*x*(x - 2)*(x - 1)**2/9
Let x(v) be the first derivative of 3*v**6/8 - 39*v**5/20 + 45*v**4/16 + 5*v**3/4 - 27*v**2/4 + 6*v - 905. Solve x(u) = 0.
-1, 1, 4/3, 2
Suppose 22 = 5*x + 2. Suppose 0 = x*k + 2 - 2. Solve 2/11*o - 4/11*o**2 + k*o**3 + 4/11*o**4 - 2/11*o**5 + 0 = 0.
-1, 0, 1
Let v be 15 + (-202)/6 - -19. Let v*d**3 - 13/3*d**2 + 35/3*d + 49/3 = 0. What is d?
-1, 7
Let x(w) be the first derivative of w**3/21 + 3*w**2/7 + 5*w/7 - 118. Factor x(o).
(o + 1)*(o + 5)/7
Let s(c) be the first derivative of 23 + 3/4*c**4 + 0*c - 1/5*c**5 + 5/2*c**2 + 3*c**3. Factor s(z).
-z*(z - 5)*(z + 1)**2
Suppose -412 = -6*t + 38. Let z be 12/t*