*2 + 1/45*h**4 + 0. Factor j(q).
2*q**2*(q + 2)/15
Let v(x) be the second derivative of 0 - 16*x - 1/6*x**4 - 4*x**2 + 4/3*x**3. Find h such that v(h) = 0.
2
Let d(j) = -10*j**4 - 12*j**3 - 129*j**2 - 136*j - 36. Let g(w) = -w**4 + 4*w**3 + w**2 + 1. Let c(l) = -2*d(l) + 18*g(l). Factor c(v).
2*(v + 1)**3*(v + 45)
Let n = -1/9016 - -9019/27048. Let 0 - 1/3*s**2 + 7/9*s**4 - n*s**5 + 2/9*s - 1/3*s**3 = 0. What is s?
-2/3, 0, 1
Let f(g) be the first derivative of -5/2*g**2 - 4*g + 4 - 1/3*g**3. Factor f(d).
-(d + 1)*(d + 4)
Let a(w) be the first derivative of 32 + 8*w - 2*w**2 + 4/5*w**5 + 1/6*w**6 - 10/3*w**3 + 1/4*w**4. Factor a(j).
(j - 1)**2*(j + 2)**3
Let w(r) be the first derivative of -10*r**4 - 32/3*r**3 + 0*r - 44 + 0*r**2 - 17/10*r**5 - 1/12*r**6. Factor w(a).
-a**2*(a + 1)*(a + 8)**2/2
Let l(o) be the third derivative of -o**8/420 - o**7/70 - o**6/30 - o**5/30 + 4*o**3/3 + 5*o**2. Let a(f) be the first derivative of l(f). Factor a(p).
-4*p*(p + 1)**3
Suppose 4*k + 12 = 0, 0 = -10*r + 7*r + 2*k + 63. Suppose -11*x = r - 52. Factor 0 + 0*i - 4/7*i**2 + 4/7*i**x.
4*i**2*(i - 1)/7
Let g be ((-84)/3)/(-6 + 4). Let d be ((-124)/28 - -5)*g/12. Let -1/3 + 0*b**2 + d*b**3 - 2/3*b + 1/3*b**4 = 0. What is b?
-1, 1
Suppose -14 = 2*f + 5*n, -f + 4*n + 4 = -5*f. Suppose -6*c = -f*c - 18. Factor 0*p**2 - 3*p**4 + c*p**2 - 3*p**5 - 7 + 6*p**3 + 4 - 3*p.
-3*(p - 1)**2*(p + 1)**3
Let b(n) be the second derivative of -n**4/12 + 113*n**3/3 - 12769*n**2/2 - 3*n - 28. Solve b(p) = 0 for p.
113
Let h(f) be the second derivative of f**6/6 + 2*f**5 + 5*f**4/2 - 100*f**3/3 + 125*f**2/2 - 329*f. Factor h(z).
5*(z - 1)**2*(z + 5)**2
Let c(g) = -g**3 - 8*g**2 - 15*g - 18. Let s be c(-6). Let p(i) be the second derivative of 0 + 1/80*i**5 - 1/48*i**4 + 0*i**3 + s*i**2 - 6*i. Factor p(k).
k**2*(k - 1)/4
Let x(i) = -i**3 + 8*i**2 - 6*i - 3. Let z be x(7). Suppose 0 = -0*k + 2*k - z*w + 4, 4*k - 2*w - 4 = 0. What is j in -2/3*j**k + 2/3*j + 2/9*j**3 - 2/9 = 0?
1
Factor 1/4*n**2 + 441 - 21*n.
(n - 42)**2/4
Let t be (-86)/(-30) - 3 - (-3233)/5. Let o = 647 - t. Factor -8/15 - o*r - 2/15*r**2.
-2*(r + 2)**2/15
Let k(j) be the third derivative of j**6/30 - 5*j**5/12 + 13*j**4/12 - 5*j**3/6 - 7*j**2 + 8. Determine o, given that k(o) = 0.
1/4, 1, 5
Solve 121 - 1760*l**4 + 112*l + 1764*l**4 - 40*l**3 - 41 - 12*l**2 = 0 for l.
-1, 2, 10
Let b = 9539 + -9534. Determine u, given that -12/7*u - 132/7*u**2 - 291/7*u**3 + 0 - 108/7*u**b + 396/7*u**4 = 0.
-1/6, 0, 2
Let l be 0/12 - (-36)/102. Factor 8/17 - l*j - 2/17*j**2.
-2*(j - 1)*(j + 4)/17
Let r be (-3 - 20)*(-9 + 14). Let y = r - -235/2. Factor y*m**3 + 0*m + m**2 + 0.
m**2*(5*m + 2)/2
Let p(y) = y**4 + y**3 + y**2 - 1. Let g(d) = -d**5 - 3*d**4 - 13*d**3 - 3*d**2 - d + 7. Let t(w) = -5*g(w) - 35*p(w). Factor t(u).
5*u*(u - 1)**4
Suppose u - 3 + 0 = -3*q, 4*u = 3*q + 12. Let f(y) be the second derivative of 0 + y - 3*y**u - 1/2*y**4 - 1/30*y**5 - 9*y**2. Factor f(r).
-2*(r + 3)**3/3
Suppose 360*c = 2214 - 774. Let m be (2/(-3))/((-1)/3). Factor 5/2*u - 1/2*u**5 - u**m + 2*u**c - 2*u**3 - 1.
-(u - 2)*(u - 1)**3*(u + 1)/2
Let x(k) be the second derivative of 0 + 1/8*k**4 + k + 0*k**2 - 3/80*k**5 - 1/8*k**3. Solve x(f) = 0.
0, 1
Let q(v) = 7*v**2 + 52*v + 77. Let m(y) = 5*y**2 + 35*y + 50. Let r(b) = 8*m(b) - 5*q(b). Factor r(o).
5*(o + 1)*(o + 3)
Let v = 51 + -46. Suppose 2*a - 8 = -0. Solve a*j**3 - 2*j**2 + 13 - v - 4*j - 4*j**2 - 2*j**2 = 0 for j.
-1, 1, 2
Let w(x) = -x**3 + 5*x**2 - 3*x + 5. Let y be w(4). Factor 3*r**2 + y*r**3 + 9*r**4 + 1778*r + 3*r**5 - 1778*r.
3*r**2*(r + 1)**3
Let r(m) be the first derivative of m**5/100 - m**4/15 + m**3/6 - m**2/5 - 5*m + 7. Let k(a) be the first derivative of r(a). Factor k(n).
(n - 2)*(n - 1)**2/5
Let i(b) be the first derivative of -15*b**3 - 400*b**2 + 180*b - 193. Factor i(q).
-5*(q + 18)*(9*q - 2)
Let u(i) be the second derivative of i**7/105 + 4*i**6/75 + i**5/25 - 2*i**4/15 - i**3/5 - 100*i. Let u(j) = 0. What is j?
-3, -1, 0, 1
Suppose -91 = -5*i - 76. Let l(g) be the third derivative of -11/8*g**4 - 7/40*g**6 + 0 + i*g**2 - 4/5*g**5 - g**3 + 0*g. Solve l(v) = 0 for v.
-1, -2/7
Let a(r) = -5*r**4 - 106*r**3 - 709*r**2 - 1092*r - 496. Let v(s) = -s**3 + s**2 - 2*s - 1. Let j(p) = a(p) + 4*v(p). Factor j(y).
-5*(y + 1)**2*(y + 10)**2
Let m(b) = -5*b**5 + 21*b**4 + b**3 - 15*b**2 + 10*b - 6. Let y(h) = -h**4 - h**3 + 1. Let s(r) = -m(r) - 6*y(r). Factor s(a).
5*a*(a - 2)*(a - 1)**2*(a + 1)
Let g(r) be the second derivative of 5*r + 1/105*r**6 + 1/42*r**4 + 0 - 3/70*r**5 + 1/7*r**3 - 2/7*r**2. Solve g(x) = 0 for x.
-1, 1, 2
Suppose -91 = -3*h - 4*a, 3*h - 194 = 5*a - 58. Solve 18*q**2 - 4 + 17*q**2 + 6*q - h*q**2 = 0 for q.
1, 2
Let j be 2/4*(1122/(-85) + 14). Determine f so that -1/5*f**2 + j - 1/5*f = 0.
-2, 1
Let c(g) be the first derivative of 52/9*g**3 + 0*g + g**4 - 64/15*g**5 + 8/3*g**2 + 26 - 8/9*g**6. Solve c(w) = 0 for w.
-4, -1/2, 0, 1
Solve 14*a**3 + 3*a**4 - 5*a**3 - a**4 + 42*a - 19*a**3 - 34*a**2 = 0.
-3, 0, 1, 7
Let o(m) = -5*m**4 - 37*m**3 - 16*m**2 + 8*m + 4. Let h(f) = 5*f**4 + 36*f**3 + 16*f**2 - 9*f - 3. Let u(v) = -4*h(v) - 3*o(v). Let u(z) = 0. What is z?
-6, -1, 0, 2/5
Let y(i) = 7*i - 11. Let s(l) = 4*l**3 - l**2 + 1. Let u be s(1). Let v be y(u). Determine n so that -14*n - 4 + v*n**2 - 9/2*n**3 = 0.
-2/9, 2
Let j be ((-27460)/(-72))/5 - (-6)/27. Let a = -75 + j. Find w such that a - 33/4*w**2 - 27/4*w = 0.
-1, 2/11
Let j(k) be the second derivative of k**9/3024 + 11*k**8/3360 - 17*k**7/2520 - k**6/72 + 7*k**4/4 + 9*k. Let u(a) be the third derivative of j(a). Factor u(o).
o*(o - 1)*(o + 5)*(5*o + 2)
Suppose -8*c = -12*c + 20. Suppose -u - 8 - c = 5*d, 5*d = -4*u - 7. Factor 1/2 + 1/2*b**u + b.
(b + 1)**2/2
Let x(q) be the second derivative of -1/4*q**5 + 0 + 5/3*q**4 + 0*q**2 - 5/2*q**3 - 15*q. Let x(m) = 0. Calculate m.
0, 1, 3
Let a be (-6)/(-2)*((-2885)/(-720) - 4). Let c(u) be the third derivative of a*u**4 + 1/240*u**5 + 0*u + 0*u**3 + 0 - 6*u**2. Factor c(k).
k*(k + 2)/4
Factor -85*m - 10*m**2 - 224*m - 27*m**3 - 180 - m**4 + 26*m**2 - 85*m**2 - 86*m**2.
-(m + 1)*(m + 3)**2*(m + 20)
Solve 16*t - 1 - 41*t + 9*t - 2*t**2 + 41 = 0.
-10, 2
Let j(p) be the third derivative of p**7/210 + 2*p**6/45 + 2*p**5/15 + 2*p**3/3 - 15*p**2. Let m(w) be the first derivative of j(w). Factor m(o).
4*o*(o + 2)**2
Let w be (56/16 - 3)*14. Let z(k) be the first derivative of 4/9*k**2 - 2/9*k - w + 10/27*k**3. Factor z(a).
2*(a + 1)*(5*a - 1)/9
Let b(m) be the first derivative of m**5/570 - m**4/114 - 25*m**2/2 + 14. Let d(n) be the second derivative of b(n). Factor d(q).
2*q*(q - 2)/19
Suppose 6*d + 3*d = 0. Suppose -7*v - v + 16 = d. Factor 0 + 1/2*q + 1/2*q**v - 1/2*q**3 - 1/2*q**4.
-q*(q - 1)*(q + 1)**2/2
What is m in -4067*m**2 - 27306 + 3*m**3 + 83360*m + 26900*m + 1102*m**2 - 74 + 17*m**3 = 0?
1/4, 74
Let m be ((-27)/20)/(138/(-30) - -7). Let z = 3/16 - m. Suppose 1/2*o + 1/4*o**2 - z = 0. Calculate o.
-3, 1
Suppose -3*i + 13/4*i**2 + 1 - 3/2*i**3 + 1/4*i**4 = 0. What is i?
1, 2
Let n(a) be the third derivative of -a**9/423360 + a**8/70560 - a**5/3 - 15*a**2. Let b(q) be the third derivative of n(q). Factor b(t).
-t**2*(t - 2)/7
Let q(g) be the first derivative of -4*g**5/5 + 32*g**4 - 120*g**3 + 176*g**2 - 116*g + 722. Find c, given that q(c) = 0.
1, 29
Let l be 948/9954 + 16/126. Factor 2/9*n**3 - 2/9*n + l*n**2 - 2/9.
2*(n - 1)*(n + 1)**2/9
Let s(z) be the second derivative of -z**5/20 + 3*z**4/2 - 10*z**3 + 28*z**2 + 4*z + 2. Determine o so that s(o) = 0.
2, 14
Let n(f) be the first derivative of -f**3/6 - f**2/2 + 3*f/2 - 147. Factor n(s).
-(s - 1)*(s + 3)/2
Let s = -51 + 54. Suppose 2*j + 4*q + 0*q + 4 = 0, 2*q = s*j - 2. Suppose -2/15*h**2 + 2/15*h + 2/15*h**4 - 2/15*h**3 + j = 0. What is h?
-1, 0, 1
Let m(v) be the third derivative of 1/60*v**6 + 0 - 16/3*v**3 - v**4 + 17*v**2 + 0*v + 0*v**5. Factor m(j).
2*(j - 4)*(j + 2)**2
Let z = 37307/11 - 3391. Factor -2/11*n**3 + 0*n**2 + 4/11 + z*n.
-2*(n - 2)*(n + 1)**2/11
Let u be (-3)/27*-3*15. Solve 107 + 5*q**2 + 5*q**3 - u*q**4 - 107 - 5*q = 0.
-1, 0, 1
Factor -45/4*l**3 + 5/4*l**4 + 35/2*l**2 + 0 + 0*l.
5*l**2*(l - 7)*(l - 2)/4
Let a(y) = y + 2. Let c be a(-12). Let n(d) = -4*d**3 + 3*d**2 - 2*d - 3.