4 + 11*v**3 + 6*v**2 - 6*v - 6. Let l(u) = u**5 - u**4 - u**3 - u**2 + u + 1. Let g(r) = -6*l(r) - z(r). Factor g(k).
5*k**3*(k - 1)*(10*k + 1)
Let d = 25748/15 - 8566/5. Factor -34/3*q**4 - 22/3*q**2 - 14*q**3 + 0 - d*q**5 - 4/3*q.
-2*q*(q + 1)**3*(5*q + 2)/3
Let o(n) be the second derivative of -n**7/1890 + n**6/270 - n**5/135 + 2*n**3/3 - 2*n. Let t(u) be the second derivative of o(u). Let t(a) = 0. What is a?
0, 1, 2
Let z(w) be the first derivative of 8*w**6/3 - 116*w**5/5 - 25*w**4 + 32*w**3/3 + 262. Determine o so that z(o) = 0.
-1, 0, 1/4, 8
Let g(a) be the second derivative of 0 - 1/15*a**6 + 3*a**2 + a**4 - 8/3*a**3 - 15*a + 0*a**5. What is d in g(d) = 0?
-3, 1
Let w(l) be the first derivative of -l**3/6 + 3*l**2/2 - 9*l/2 - 98. Factor w(t).
-(t - 3)**2/2
Suppose 5*q - 30 = -5*c, -4*c - q = 12 - 27. Factor -11*k**c - 9/2*k - 75/4*k**2 - 7/4*k**4 + 0.
-k*(k + 3)**2*(7*k + 2)/4
Let r(x) be the third derivative of -1/120*x**6 + 0 + 0*x**4 + 0*x**3 + 11*x**2 + 0*x + 0*x**5. Factor r(b).
-b**3
Suppose -25*c = -24*c - 3. Let 4*z**3 + z**c + 278*z**2 - 263*z**2 = 0. What is z?
-3, 0
Let x = 9713 + -38851/4. Factor -1/2*r**2 + 1/2 + x*r**3 - 1/4*r.
(r - 2)*(r - 1)*(r + 1)/4
Let a(x) be the first derivative of 2*x**6/3 - 16*x**5/5 + 4*x**4 + 102. Solve a(w) = 0.
0, 2
What is d in 0*d - 15/2*d**3 - 5/6*d**4 - 20/3*d**2 + 0 = 0?
-8, -1, 0
Let u(l) be the second derivative of -l**7/14 - 2*l**6/5 - 9*l**5/20 + 11*l + 20. Factor u(m).
-3*m**3*(m + 1)*(m + 3)
Suppose 446*v - 5*h + 5 = 445*v, 0 = 2*v - 2*h + 2. Factor -4/3 + t**2 - 1/3*t**3 + v*t.
-(t - 2)**2*(t + 1)/3
Let g(t) be the first derivative of 3*t**4/4 + 6*t**3 + 27*t**2/2 - 371. Factor g(f).
3*f*(f + 3)**2
Suppose 0 - 56/13*v - 2/13*v**2 = 0. Calculate v.
-28, 0
Let g(y) = -1. Let z(x) = 0*x**2 + 11 - x - x**2 - 2 + 1. Let o(k) = 24*g(k) + 3*z(k). Factor o(l).
-3*(l - 1)*(l + 2)
Let u(o) be the first derivative of 3/2*o**2 + o**3 - 3/5*o**5 + 0*o + 4 - 3/4*o**4. Suppose u(i) = 0. What is i?
-1, 0, 1
Suppose 2*g = 4 + 2. Let o be 4/g*3/2. Solve -3*a**o + 4*a**3 + a**2 - 5*a**3 - a + 0*a**3 = 0.
-1, 0
Let w be 1*20/8 - 1/2. Find f, given that -413*f**3 + 0*f**2 + 417*f**3 + 12*f**w = 0.
-3, 0
Determine y so that -19 + 9 + 69*y**2 - 40 - 74*y**2 - 12*y + 47*y = 0.
2, 5
Let w(x) be the third derivative of -x**5/150 + x**4/60 + 4*x**3/3 - 27*x**2. Find n such that w(n) = 0.
-4, 5
Let q(v) be the second derivative of -v**6/20 + 3*v**5/20 - v**3/2 + 11*v**2/2 - 10*v. Let x(m) be the first derivative of q(m). Solve x(t) = 0 for t.
-1/2, 1
Let d(i) be the third derivative of -i**9/7560 - i**8/3360 + i**7/630 + 11*i**4/12 + 9*i**2. Let b(m) be the second derivative of d(m). Factor b(f).
-2*f**2*(f - 1)*(f + 2)
Let z = 92683/6 + -264407/18. Let s = z - 757. Factor 20/9*f**2 - 16/9 - s*f**4 - 2/9*f**3 + 8/9*f - 2/9*f**5.
-2*(f - 1)**2*(f + 2)**3/9
Let j(a) be the second derivative of -1/7*a**4 - 3/7*a**2 + 3/140*a**5 + 11*a + 0 + 5/14*a**3. Determine h so that j(h) = 0.
1, 2
Let h(y) be the third derivative of y**7/35 - y**6/30 - 2*y**5/15 + y**4/6 + y**3/3 + 94*y**2. Factor h(t).
2*(t - 1)**2*(t + 1)*(3*t + 1)
Let g(a) be the third derivative of 5*a**8/672 - 5*a**7/84 + 7*a**6/48 - a**5/8 + 3*a**2 - 3. Solve g(o) = 0.
0, 1, 3
Let f(x) be the first derivative of 0*x**4 + 6 - 2/3*x**3 + 2/5*x**5 + 0*x**2 + 0*x. Solve f(h) = 0 for h.
-1, 0, 1
Factor 0 - 3*k - 1/4*k**2.
-k*(k + 12)/4
Let x = 55 + -46. Find h, given that 4*h**3 - x*h**3 - 14*h**2 + 25*h - 6*h**2 + 10*h**3 - 10 = 0.
1, 2
Let i be (-6724)/(-40) - 1/10. Let k be (-3)/(-24) + 21/i. Factor -1/4 - k*n**3 + 1/4*n**2 + 1/4*n.
-(n - 1)**2*(n + 1)/4
Let r(i) be the first derivative of -2/3*i - i**3 - 1/15*i**5 - 7/6*i**2 - 5/12*i**4 + 14. Factor r(q).
-(q + 1)**3*(q + 2)/3
Suppose -2*l + 7*l - 15 = 0. Suppose 1 = 3*g - 5. Factor -4 - n - n**g - l*n + 0.
-(n + 2)**2
Let x(t) be the first derivative of 4*t**5/25 + t**4/5 - 4*t**3/15 - 2*t**2/5 - 201. Solve x(h) = 0 for h.
-1, 0, 1
Let k(z) = 3*z + 57. Let w be k(-19). Suppose w = 8*a + 4 - 4. Factor 4/5 - 4/5*c**2 + a*c.
-4*(c - 1)*(c + 1)/5
Suppose 17/2*i + 1/2*i**2 + 15 = 0. What is i?
-15, -2
Let y = -1830 + 1833. Let n(i) be the second derivative of -3*i**2 + 1/5*i**5 - 4/3*i**y - 7*i + 1/6*i**4 + 0. Find s such that n(s) = 0.
-1, 3/2
Suppose 4*g - 8*x - 24 = -4*x, 6 = 3*g - x. Solve 8/17*c**3 - 10/17*c**2 + 4/17*c - 2/17*c**4 + g = 0 for c.
0, 1, 2
Let v(f) = f**3 - 7*f**2 - 7*f - 9. Let z(j) = -4*j**2 - 4*j - 4. Let y = -83 - -88. Let x(a) = y*z(a) - 2*v(a). Factor x(q).
-2*(q + 1)**3
What is t in t**3 + 0*t**3 + 2*t**3 + 3*t**2 - 9*t**2 = 0?
0, 2
Factor 374/7*g - 34969/7 - 1/7*g**2.
-(g - 187)**2/7
Suppose 0 = -3*l - 5*g + 341, 0*l + 114 = l + 2*g. Let i = -110 + l. Factor 1/3*j**i - 2/3*j - 1.
(j - 3)*(j + 1)/3
Suppose 1/4*l**3 - 1 + 2*l - 5/4*l**2 = 0. Calculate l.
1, 2
Suppose -3*q - 120 + 132 = 0. Let o(j) be the second derivative of -1/20*j**5 - 1/3*j**q - j**2 - 9*j + 0 - 5/6*j**3. Factor o(b).
-(b + 1)**2*(b + 2)
Let b(c) be the first derivative of -2*c**3/45 + 44*c**2/15 + 6*c + 86. Let b(x) = 0. What is x?
-1, 45
Factor -89*d**3 + 84*d**3 - 1725*d - 5848 + 1348 - 170*d**2.
-5*(d + 4)*(d + 15)**2
Let w = -75 + 78. Factor 25*y**3 - 10*y**3 + y**5 - w*y**4 + 3 - 6*y**2 + y - 17*y**3 + 6*y**4.
(y - 1)**2*(y + 1)**2*(y + 3)
Let m be (-213)/12 + (-3)/12. Let n be (-3)/m + 11/6. Factor 0*b**2 - 5*b**2 - 6*b - 3*b**3 - 5*b**n + b**2.
-3*b*(b + 1)*(b + 2)
Suppose 426 + 102 = -12*o. Let r = 44 + o. Factor -1/3*p**2 + r + 0*p - 1/3*p**3.
-p**2*(p + 1)/3
Let x(h) = h**3 - 23*h**2 + 2*h - 10. Let m be x(23). Factor -2*d - 54*d - m + 24*d + 4*d**2.
4*(d - 9)*(d + 1)
Find m, given that 40*m**2 + 0*m + 0 - 38/5*m**4 + 32*m**3 + 2/5*m**5 = 0.
-1, 0, 10
Find h such that 81/2*h**4 - 21/4*h**5 - 165/2*h**3 + 567/4*h - 27*h**2 + 81/2 = 0.
-1, -2/7, 3
Suppose -2*f - 5*u - 22 + 6 = 0, -5*f + 18 = -2*u. Factor -3 - 140*j**f + 149*j**2 - 3*j**3 + 6 - 9*j.
-3*(j - 1)**3
Let q(h) be the third derivative of -3/10*h**5 + 0 - 1/40*h**6 - 3/2*h**4 + 21*h**2 - 4*h**3 + 0*h. Factor q(j).
-3*(j + 2)**3
Let b(o) be the third derivative of o**6/720 - o**5/60 + 8*o**3/9 + 8*o**2 - 23. What is a in b(a) = 0?
-2, 4
Let a(x) be the first derivative of -15 + 1/2*x**4 + 10/9*x**3 + 1/3*x**2 - 4/9*x**6 - 2/3*x**5 + 0*x. What is i in a(i) = 0?
-1, -1/4, 0, 1
Let y(u) = 118*u + 19 + 28*u**2 + 157 - 6*u. Suppose 61*m - 5 = 60*m. Let d(p) = 9*p**2 + 37*p + 59. Let h(a) = m*y(a) - 16*d(a). Factor h(b).
-4*(b + 4)**2
Let s(j) be the second derivative of -j**4/84 + 3*j**3/7 + 20*j**2/7 + 380*j. Factor s(b).
-(b - 20)*(b + 2)/7
Let l(g) be the second derivative of g**5/100 + 7*g**4/60 + 8*g**3/15 + 6*g**2/5 - 430*g. Factor l(w).
(w + 2)**2*(w + 3)/5
Find u, given that -48/5*u**2 + 6/5*u**4 - 6 + 1/5*u**5 - 2/5*u**3 - 71/5*u = 0.
-5, -2, -1, 3
Let z(y) be the first derivative of y**4/8 + y**3/6 - 10*y**2 - 56*y + 162. Factor z(b).
(b - 7)*(b + 4)**2/2
Let y(g) be the first derivative of 9/16*g**4 + 6 - g + 1/10*g**5 + 0*g**2 + 11/12*g**3. Solve y(a) = 0 for a.
-2, -1, 1/2
Suppose -12 = -5*q - 4*z, 5*q - 4*q - 5*z = 14. Suppose -2*y + 5*v = -6*y + 3, 5*y - 14 = q*v. Factor o - 3*o**3 - 16*o**2 + 16*o**y + 2*o**3.
-o*(o - 1)*(o + 1)
Let -2/17*a**4 + 0*a + 0 + 12/17*a**3 - 16/17*a**2 = 0. Calculate a.
0, 2, 4
Let g(l) be the third derivative of l**5/360 - l**4/24 - 4*l**3/9 - 78*l**2. Factor g(f).
(f - 8)*(f + 2)/6
Let b = 38 - 31. Factor 7*n - n**2 - 11*n + n - 3 + b*n.
-(n - 3)*(n - 1)
Suppose g**3 + 20*g + g**3 - 25*g - 26*g**2 - 23*g = 0. Calculate g.
-1, 0, 14
Let h(u) = u - 29. Let a be h(29). Let s(r) be the second derivative of 2/9*r**3 - 6*r - 1/3*r**2 + a - 1/18*r**4. Let s(i) = 0. What is i?
1
What is n in 8/11*n**2 + 0 - 2/11*n**4 - 2/11*n**5 + 12/11*n**3 - 16/11*n = 0?
-2, 0, 1, 2
Let v(y) = -y - 9. Let n be v(-13). Let b(m) be the second derivative of 1/6*m**n + 0*m**2 + 0 + 0*m**3 + m. Factor b(w).
2*w**2
Suppose -391 + 365 = -13*a. Factor 0 + 4*j**3 + 8/3*j**2 + 0*j + a*j**4 + 1/3*j**5.
j**2*(j + 2)**3/3
Let 2/7*m**2 - 108/7 - 50/7*m = 0. Calculate m.
-2, 27
Let f be (-8)/3*(-159)/530. Factor 0 + f*j - 2/5*j**2.
-2*j*(j - 2)/5
Let k(c) = -c**3 - 4*c**2 + 10*c - 9. Let d be k(-6). Let p = 215/154 - 17/14. Factor p*w*