n**3 - 8/13 - 2/13*n**4 + 8/13*n + 10/13*n**2 + 2/13*n**5 = 0.
-2, -1, 1, 2
Let s(n) be the second derivative of 0 + 4/21*n**3 - 1/14*n**4 + 4/7*n**2 + n. Determine q so that s(q) = 0.
-2/3, 2
Let c = 23 - 20. Factor 7*q**2 + c*q**3 + 12*q**2 + 9 + 21*q - 7*q**2 + 3*q**2.
3*(q + 1)**2*(q + 3)
Let m(g) be the first derivative of g**4/8 + 4*g**3/3 - 9*g**2/4 - 103. Factor m(z).
z*(z - 1)*(z + 9)/2
Let u = -7655/4 + 1915. Find d such that 0 - 1/4*d + 1/4*d**2 + u*d**3 + 3/4*d**4 = 0.
-1, 0, 1/3
Solve -192*d**2 + 96*d**2 - 48 + 98*d**2 - 4*d = 0 for d.
-4, 6
Let k(s) be the first derivative of -3*s**4/4 + 2*s**3 + 15*s**2/2 - 18*s - 613. Determine d so that k(d) = 0.
-2, 1, 3
Let m = -1501/4 - -373. Let n = -65/36 - m. Suppose -14/9*b**2 - n*b - 14/9*b**3 + 0 - 4/9*b**4 = 0. What is b?
-2, -1, -1/2, 0
Let v(m) = -4*m**3 + 3*m**2 - 5*m - 3. Let d(r) be the first derivative of -r**3 + 3*r**2 + 4*r - 1 + 5/4*r**4. Let l(f) = 3*d(f) + 4*v(f). Factor l(k).
-k*(k - 2)*(k - 1)
Let w be (-2)/(-52) + 17630/122980. Find t, given that 0*t - 8/11 + w*t**2 = 0.
-2, 2
Factor 77*d**2 - d**3 - 2*d**3 - 74*d**2 + 3*d + 2*d**4 - 5*d**4.
-3*d*(d - 1)*(d + 1)**2
Let s be (-25)/(-6) + 1*(-2)/12. Let f be s/18*9/6. Solve c**2 + 1/3*c**3 - 1/3*c - f*c**4 - 2/3 = 0.
-1, 1, 2
Let o(m) = -3*m - 3. Let t(z) be the third derivative of 0 + 1/6*z**3 + 0*z + 1/60*z**5 - 8*z**2 - 1/24*z**4. Let p(y) = o(y) + 3*t(y). Factor p(a).
3*a*(a - 2)
Let g = 4/309 + 83/1545. Let c(n) be the third derivative of 0*n**3 - n**2 + g*n**5 + 0 + 0*n - 1/120*n**6 - 1/6*n**4. Factor c(i).
-i*(i - 2)**2
Suppose -5*o + 60 = -5*t, 2*t + 5 = 3*o - 26. Suppose o*h - 4*h = -h. Solve -j**5 + j**3 + 1/2*j**4 + h*j + 0 - 1/2*j**2 = 0.
-1, 0, 1/2, 1
Let y(m) be the third derivative of 0*m + 0 + 9/40*m**5 + 11/80*m**6 + 30*m**2 + 0*m**3 - 1/8*m**4. Suppose y(w) = 0. What is w?
-1, 0, 2/11
Let z(a) = 8*a**4 - 32*a**3 + 52*a**2 - 52*a + 12. Let p(d) = -7*d**4 + 30*d**3 - 52*d**2 + 51*d - 13. Let r(j) = -4*p(j) - 3*z(j). Factor r(q).
4*(q - 2)**2*(q - 1)**2
Find b such that 12*b + 579*b**3 - 162*b**2 - 507/2*b**5 - 351/2*b**4 + 0 = 0.
-2, 0, 2/13, 1
Suppose -v + 15 = 4*v. Factor -3*r**2 - 3*r - v*r**4 - 6*r**2 - 19*r**3 + 10*r**3.
-3*r*(r + 1)**3
Factor -20/9*p**3 - 2/9*p**5 + 0*p - 14/9*p**4 + 0*p**2 + 0.
-2*p**3*(p + 2)*(p + 5)/9
Let l be -4 - 333/(-81) - 1/9. Let v(z) be the third derivative of 0*z + 1/420*z**6 + l*z**4 - 7*z**2 + 1/105*z**5 + 0 + 0*z**3 - 1/735*z**7. Factor v(o).
-2*o**2*(o - 2)*(o + 1)/7
Let o(f) be the second derivative of f**4/24 + 53*f**3/12 + 13*f**2 + 3*f - 4. Factor o(b).
(b + 1)*(b + 52)/2
Let r(l) be the third derivative of -37*l**5/12 - 675*l**4/8 + 55*l**3/3 - 406*l**2. Factor r(u).
-5*(u + 11)*(37*u - 2)
Let q(b) = 55*b**5 - 315*b**4 - 190*b**3 + 15*b - 30. Let z(s) = -8*s**5 + 45*s**4 + 27*s**3 - 2*s + 4. Let c(j) = 2*q(j) + 15*z(j). Factor c(y).
-5*y**3*(y - 5)*(2*y + 1)
Let c(z) = -5*z**2 + 1. Let o(s) = -s**2 + 6*s - 2. Let d be o(6). Let w(u) = -16*u**2 + u + 3. Let i(l) = d*w(l) + 7*c(l). Suppose i(x) = 0. What is x?
-1, 1/3
Factor 4/3*v**2 - 4/3 + 4/3*v**3 - 4/3*v.
4*(v - 1)*(v + 1)**2/3
Let t be (88/(-24) + 2)*-3. Let w(g) be the first derivative of -1/4*g**4 + t - 1/3*g**3 + 0*g + 1/2*g**2 + 1/5*g**5. Factor w(x).
x*(x - 1)**2*(x + 1)
Let r(y) be the first derivative of y**2/2 - 2*y - 4. Let c be r(2). Factor 0 + 0*u**2 + 1/5*u**5 + c*u**4 - 1/5*u**3 + 0*u.
u**3*(u - 1)*(u + 1)/5
Let w(j) be the second derivative of -6*j + 3/2*j**2 + 0 + 5/16*j**4 + j**3 + 3/80*j**5. Let w(l) = 0. Calculate l.
-2, -1
Let t(z) = z**2 - 15*z - 21. Let g(x) = 4*x**2 - 76*x - 104. Let c(o) = -5*g(o) + 24*t(o). Factor c(k).
4*(k + 1)*(k + 4)
Suppose 0 = 4*b - 7*b + 9. Let v be -1 - (-2 + (-2 - -1)). Factor 2 - 12*i**2 + b*i + 5*i + v*i**2.
-2*(i - 1)*(5*i + 1)
Let w(o) be the first derivative of -o**4/38 - 92*o**3/19 - 6348*o**2/19 - 194672*o/19 - 98. Factor w(b).
-2*(b + 46)**3/19
Let a = 526 - 1577/3. Let b(c) be the first derivative of 0*c + a*c**3 + 1/12*c**4 - 2 + 1/3*c**2. Solve b(n) = 0 for n.
-2, -1, 0
Let d(u) be the second derivative of -8*u + 0 + 5/12*u**4 - 1/8*u**5 + 1/72*u**6 - 1/3*u**3 + 0*u**2. Let z(y) be the second derivative of d(y). Factor z(r).
5*(r - 2)*(r - 1)
Factor -132 + 4 + 41*b**2 - 17*b**2 - 32*b + b**4 + 10*b**3.
(b - 2)*(b + 4)**3
Let v = 86 - 62. Let k be v*(-10)/(-135) + (-2)/(-9). Factor -4/7 + 4/7*m**k - 6/7*m.
2*(m - 2)*(2*m + 1)/7
Let p(v) be the first derivative of -v**5/90 - 13*v**2/2 - 34. Let m(f) be the second derivative of p(f). Find h, given that m(h) = 0.
0
Suppose -83 + 2 = -27*l. Let r(m) be the second derivative of 0*m**2 - 1/96*m**4 + 0 - 1/24*m**l - 7*m. Suppose r(c) = 0. What is c?
-2, 0
Let l = 1057 + -1055. Let d(a) be the second derivative of 4*a + 0 + 1/10*a**5 - 27*a**l + 9*a**3 - 3/2*a**4. Factor d(f).
2*(f - 3)**3
Let q(j) = j**2 + 10*j + 4. Let o be q(-10). Factor 13*b**5 + 2*b**3 - b**3 - o*b**5 - 10*b**5.
-b**3*(b - 1)*(b + 1)
Let v be -6 + 267/45 - (-222)/630. Suppose v*u + 1/7*u**5 - 1/7*u**4 + 1/7*u**2 + 0 - 3/7*u**3 = 0. What is u?
-1, 0, 1, 2
Suppose -8*q - 13 = -9*q. Suppose q*s + 24*s**4 - 22*s + 32*s**3 + 4*s**5 - 27*s - 24*s**2 = 0. Calculate s.
-3, -1, 0, 1
Determine v so that -4*v**2 - 2 - 7 - 3*v**2 + 11*v + 17 - 12 = 0.
4/7, 1
Factor 25*l - 65/3*l**2 + 0 + 5/3*l**4 - 5*l**3.
5*l*(l - 5)*(l - 1)*(l + 3)/3
Let b(d) be the third derivative of 0*d + 0 + 1/40*d**5 - 1/140*d**7 + 1/16*d**4 - 10*d**2 + 0*d**3 - 1/80*d**6. Factor b(f).
-3*f*(f - 1)*(f + 1)**2/2
Factor 39/4 + 10*x + 1/4*x**2.
(x + 1)*(x + 39)/4
Let w(h) = 2*h**3 + 52*h**2 + 43*h - 173. Let p be w(-25). Suppose -1/4*m**3 + 0*m**p + 3/4*m - 1/2 = 0. Calculate m.
-2, 1
Determine h, given that 22/23*h - 12/23 + 2/23*h**3 - 12/23*h**2 = 0.
1, 2, 3
Let g(n) = n**3 + 6*n**2 - 8*n - 45. Let x be g(-6). Let p(z) be the first derivative of 0*z**2 - 2*z**x - 3/4*z**4 + 2 + 0*z. Find m, given that p(m) = 0.
-2, 0
Suppose 3*h - j + 161 = 0, 5*j = 4*h - 2*h + 103. Let z be (-8)/(-14)*(-21)/h. Factor -2/9*q**2 + 2/9*q**3 + z*q**4 + 0 - 2/9*q.
2*q*(q - 1)*(q + 1)**2/9
Determine t, given that -152/3*t + 8/3 + 722/3*t**2 = 0.
2/19
Suppose 3*i + u = 8*i - 16, -20 = -i + 3*u. Determine a, given that -6/5*a**i + 8/5 - 24/5*a + 6/5*a**4 + 16/5*a**3 = 0.
-2, 1/3, 1
Let c be -4 - (6 + (-4 - -5)). Let r be (c + 15)*(-1)/(-9). Suppose 10/9*h + 2/9*h**3 - r - 8/9*h**2 = 0. What is h?
1, 2
Suppose 0 = -58*r - 2*r + 144 + 36. Find i such that 8/5*i**2 + 22/5*i**4 - 4*i**5 + 0*i + 32/5*i**r + 0 = 0.
-1/2, -2/5, 0, 2
Let s(l) be the first derivative of -l**3/3 - 7*l**2/2 + 8*l + 127. Factor s(v).
-(v - 1)*(v + 8)
Let v(q) be the first derivative of 0*q**2 - 2/5*q**5 + 0*q - 1/2*q**4 + 2/3*q**3 + 1/3*q**6 - 14. Solve v(i) = 0.
-1, 0, 1
Let w = 2/2473 + 37091/4946. Factor 24*m**5 + 75/2*m**3 + 3/2 + 60*m**4 - 15/2*m**2 - w*m.
3*(m + 1)**3*(4*m - 1)**2/2
Let n be (-10)/15 - (-517)/(-12). Let a = 44 + n. Suppose 1/2*m**4 + 0 + 0*m + a*m**3 + 1/4*m**5 + 0*m**2 = 0. What is m?
-1, 0
Suppose -7*y = -10 - 25. Suppose -6 + 11*l**2 - l**2 - y*l**4 + 1 = 0. What is l?
-1, 1
Factor 17/6*h**3 + 0*h - 1/6*h**5 + 0 - 3/2*h**2 - 7/6*h**4.
-h**2*(h - 1)**2*(h + 9)/6
Let w(c) be the second derivative of -c**7/35 - 9*c**6/50 + 3*c**5/20 - 40*c. Factor w(t).
-3*t**3*(t + 5)*(2*t - 1)/5
Let u(q) = -2*q + 32. Let c be u(0). Determine o so that 35*o**2 - 108 - c*o**3 + 4*o**4 + 38*o**2 - o**2 = 0.
-1, 3
Factor 0 - 82/3*y - 2/3*y**2.
-2*y*(y + 41)/3
Let z(r) = -r**3 + 7*r**2 - 4*r - 27. Let x be z(5). Suppose 3*g - 2*l = 0, -6*g - x*l = -5*g. Factor 2/5*p**3 + 2/5*p**2 - 4/5*p + g.
2*p*(p - 1)*(p + 2)/5
Let i(c) be the second derivative of -2/195*c**6 - 1/39*c**3 + 1/273*c**7 + 17*c + 0*c**2 + 0 + 0*c**5 + 1/39*c**4. Suppose i(h) = 0. What is h?
-1, 0, 1
Let b(i) = -32*i + 66. Let x be b(2). Let l(g) be the third derivative of -4*g**x + 0*g**3 - 1/180*g**6 - 1/30*g**5 + 0 + 0*g - 1/18*g**4. Factor l(h).
-2*h*(h + 1)*(h + 2)/3
What is z in -1/3 - 8/3*z**4 - 1/3*z**3 + 1/3*z + 5/3*z**2 - 4/3*z**5 = 0?
-1, 1/2
Let k be (2 + -7)*(-9)/3. Suppose -2*q - k = -5*q. Factor -47*r - 16*r + 32*r**2 - r + 4*r**q - 7*r**3 + 71*r**3 + 28*r**4 - 64.
4*(r - 1)*(r + 2)**4
Let -4/9*z**3 - 20/9*z**4 + 4/3*z**5 - 8/9*z + 20/9*z**2