. What is k?
-1, 0
Let w(f) be the third derivative of -121*f**10/6048 + 11*f**9/756 - f**8/336 + f**4/6 + 12*f**2. Let c(y) be the second derivative of w(y). Factor c(p).
-5*p**3*(11*p - 2)**2
Let p(g) = 420*g**2 - 85*g - 11. Let w(i) = -2940*i**2 + 595*i + 75. Let t(q) = 20*p(q) + 3*w(q). Factor t(m).
-5*(4*m - 1)*(21*m + 1)
Let o(w) be the first derivative of 1/12*w**2 - 11 + 1/18*w**3 - 1/3*w. Solve o(m) = 0.
-2, 1
Let a(q) be the third derivative of -q**7/70 + 14*q**6/5 - 331*q**2. Solve a(k) = 0 for k.
0, 112
Let b(g) be the first derivative of 0*g + 2/27*g**3 + 2 + 4/9*g**2. Find t, given that b(t) = 0.
-4, 0
Suppose 18*q**3 - 21*q + 3*q**2 + 33*q**4 - 36*q**4 + 3*q = 0. What is q?
-1, 0, 1, 6
Let a(y) be the second derivative of -2*y**6/15 - 2*y**5/5 - y**4/3 + 57*y. Find b such that a(b) = 0.
-1, 0
Let z(f) = 6*f**3 + 497*f**2 + 14112*f + 131712. Let q(l) = 3*l**3 + 248*l**2 + 7056*l + 65856. Let u(x) = -7*q(x) + 4*z(x). What is y in u(y) = 0?
-28
Factor -8/11*k - 12/11 - 1/11*k**2.
-(k + 2)*(k + 6)/11
Find t such that -3/2 - 3*t**3 - 5*t - 6*t**2 - 1/2*t**4 = 0.
-3, -1
Let t(o) be the third derivative of 0 - 3/44*o**4 + 0*o + 42*o**2 - 1/330*o**5 + 10/33*o**3. Suppose t(i) = 0. What is i?
-10, 1
Let n(u) = u**3 + 9*u**2 + u + 12. Let s be n(-9). Suppose -l - s*l = -8. Find z such that 3/2 + 21/2*z**l - 15/2*z - 9/2*z**3 = 0.
1/3, 1
Suppose 2*k - 6*s + 5*s - 3 = 0, k + 2*s - 9 = 0. Let r(o) be the first derivative of 1/9*o**k + 10 + 4/3*o**2 + 16/3*o. Factor r(n).
(n + 4)**2/3
Determine x so that -2/9*x**3 - 20000/3*x + 200/3*x**2 + 2000000/9 = 0.
100
Let o(y) be the third derivative of y**8/2856 - y**6/1020 - 2*y**2 + 19*y. Factor o(a).
2*a**3*(a - 1)*(a + 1)/17
Let c(r) = -9*r + 141. Let j be c(15). Let h(d) be the first derivative of 1/20*d**4 + 1/30*d**6 + 0*d**3 - j + 0*d**2 + 0*d + 2/25*d**5. Factor h(q).
q**3*(q + 1)**2/5
Let c = 203 + -196. Let x(w) be the second derivative of 1/2*w**6 + 0 + 4*w**3 - 21/20*w**5 + 4*w - 6*w**2 - 1/14*w**c - 1/4*w**4. Solve x(f) = 0 for f.
-1, 1, 2
Let b(a) be the third derivative of 0*a**3 - 7/30*a**6 - 11*a**2 + 0*a + 1/3*a**5 + 2/35*a**7 - 1/6*a**4 + 0. Suppose b(i) = 0. What is i?
0, 1/3, 1
Let u(l) = -l**3 + 8*l**2 + 7*l + 11. Let x be u(9). Let b be (7/5)/(x/(-35)). Determine z, given that -8*z + 2*z**2 + b*z**2 - 8*z**2 + 3*z**2 = 0.
0, 2
Let x = 160 - 2392/15. Solve -2/15*w**2 - 8/15 + x*w = 0.
2
Let h = -165 - -174. Factor 15*b**2 - 21*b**4 + 44*b**4 - h*b - 22*b**4 - 7*b**3.
b*(b - 3)**2*(b - 1)
Factor 1/3*v + 0 + 4*v**2 + 12*v**3.
v*(6*v + 1)**2/3
Let z(l) be the third derivative of l**7/35 - l**6/30 - 3*l**5/10 + 4*l**3/3 + 78*l**2 + l. Factor z(j).
2*(j - 2)*(j + 1)**2*(3*j - 2)
Let d(m) be the second derivative of 2*m**7/63 + 4*m**6/45 - 2*m**5/5 - 8*m**4/9 + 10*m**3/9 + 4*m**2 + 72*m. Find v such that d(v) = 0.
-3, -1, 1, 2
Factor -72/23 - 2/23*h**2 - 30/23*h.
-2*(h + 3)*(h + 12)/23
Suppose -4*l - 20 = 2*t - 7*t, 5*t - 20 = 3*l. Let q(v) be the first derivative of l*v**3 - 6/5*v**5 + 0*v**2 + 0*v - 3/4*v**4 - 5. Solve q(k) = 0.
-1/2, 0
Factor -3*a + 29*a - 15*a**2 + 4374*a**3 - 4373*a**3.
a*(a - 13)*(a - 2)
Suppose -2*d - d = 2*x - 4, 28 = 3*d - 4*x. Suppose 4 = v - 2*y, -d*v - 2*y - 1 - 3 = 0. Factor v - 1/4*q**4 + 1/4*q**5 - 3/4*q**3 + 1/4*q**2 + 1/2*q.
q*(q - 2)*(q - 1)*(q + 1)**2/4
Let i(l) = l**2 - 10*l + 2. Let u(f) = 2*f**3 + 12*f**2 - 4*f - 14. Let r be u(-6). Let o be i(r). Suppose 0 + 1/3*p - 1/3*p**o = 0. What is p?
0, 1
Let u = 34 + -31. Factor 6 + 2*f**u + f**4 + f**2 - 6.
f**2*(f + 1)**2
Let o(u) be the second derivative of -u**4/24 - u**3/2 - 9*u**2/4 - 61*u. Let o(h) = 0. Calculate h.
-3
Let s(v) be the first derivative of -v**5 - 15*v**4/2 - 25*v**3/3 - 67. Find x, given that s(x) = 0.
-5, -1, 0
Factor 1/8*s**3 - 7/8*s**2 + 3/2*s + 0.
s*(s - 4)*(s - 3)/8
Let f(i) = -5*i**3 - 35*i**2 + 105*i - 50. Let c(u) = 5*u**3 + 33*u**2 - 105*u + 49. Let j(p) = -5*c(p) - 6*f(p). Let j(g) = 0. Calculate g.
-11, 1
Let o(i) = -i**3 - 5*i**2 + 6*i. Let d(u) = u**2 - u. Let b = -20 - -22. Suppose 24 = -3*j + b*j. Let l(v) = j*d(v) - 3*o(v). Factor l(m).
3*m*(m - 2)*(m - 1)
Determine s, given that -1/9*s**3 - 7/9*s + 5/3 - 7/9*s**2 = 0.
-5, -3, 1
Let k(z) be the third derivative of -z**6/120 + z**4/6 + 99*z**2 + 2. Factor k(i).
-i*(i - 2)*(i + 2)
Let x = 92 - 23. Let 24*p**3 - 5*p**2 - x*p + 61*p + p**2 = 0. Calculate p.
-1/2, 0, 2/3
Factor -616/5*s - 11858/5*s**2 - 8/5.
-2*(77*s + 2)**2/5
Solve 4*n - 2*n**3 + 0*n**3 - 86*n**2 + 21*n**4 - 3 + n**3 + 6 + 5 = 0 for n.
-2, -2/7, 1/3, 2
Let p(o) be the first derivative of o**5/5 - 3*o**4 + 10*o**3/3 + 6*o**2 - 11*o - 207. What is z in p(z) = 0?
-1, 1, 11
Let u = 251/1230 + -1/246. Let v(h) be the third derivative of 0 - 8/3*h**3 + 0*h + 1/30*h**6 + u*h**5 - 7*h**2 + 0*h**4. Factor v(w).
4*(w - 1)*(w + 2)**2
Let s(v) be the first derivative of -v**6/540 + v**4/36 - 8*v**3/3 - 13. Let n(m) be the third derivative of s(m). Factor n(i).
-2*(i - 1)*(i + 1)/3
Let c(x) be the third derivative of x**9/8064 + 5*x**8/8064 - x**7/1008 + 11*x**5/20 - 50*x**2. Let m(j) be the third derivative of c(j). Factor m(s).
5*s*(s + 2)*(3*s - 1)/2
Let i be (-6)/(0 + -2) - 2. Factor 46*k**3 + 12*k**4 + 4*k**5 - 1 + i - 34*k**3 + 4*k**2.
4*k**2*(k + 1)**3
Suppose -138*i - 34 = -155*i. Let a(q) be the second derivative of -1/8*q**4 - 4*q + 3/4*q**3 + 0 - 3/2*q**i. Factor a(x).
-3*(x - 2)*(x - 1)/2
Let r(d) = d**3 + 11*d**2 + 9*d - 10. Let m be r(-10). Suppose m = -i - 2*i + 15. Factor 3*f**i + 3*f**3 - 7*f**4 + f**4 + 0*f**3.
3*f**3*(f - 1)**2
Suppose 49*m + 35 = 115 + 67. Suppose 54/7*h**4 + 6/7 + 69/7*h**m - 18/7*h**2 - 27/7*h = 0. What is h?
-1, 2/9, 1/2
Suppose 2*x + 4*c + c = 29, -x + 5*c = 23. Let j be -3 + (112/20 - 2). Factor -12/5*f + 12/5 + j*f**x.
3*(f - 2)**2/5
Let q(z) be the third derivative of z**6/180 + 19*z**5/90 - z**4/36 - 19*z**3/9 + 55*z**2. Factor q(p).
2*(p - 1)*(p + 1)*(p + 19)/3
Let v = -2164 + 153638/71. Let c = 367/142 + v. Factor 1/2*n**3 - 2*n**2 + c*n - 1.
(n - 2)*(n - 1)**2/2
Let g(k) be the third derivative of -k**6/120 + k**5/6 - 25*k**4/24 - 17*k**2 + 2. Determine s so that g(s) = 0.
0, 5
Let c(q) be the second derivative of q**4/18 + 4*q**3/9 - 5*q**2/3 + 3*q - 4. Factor c(b).
2*(b - 1)*(b + 5)/3
Let d = -463574 - -1403222/3. Factor 5000/3*m**2 - 12500/3*m - 4/3*m**5 + 100/3*m**4 + d - 1000/3*m**3.
-4*(m - 5)**5/3
Suppose 3*y = -3*w + 9, -15 = -39*y + 42*y - 5*w. Factor 4/9*p - 2/3*p**2 + y + 0*p**3 + 2/9*p**4.
2*p*(p - 1)**2*(p + 2)/9
Let j(f) be the first derivative of 1/14*f**4 + 1/7*f**3 - 3/35*f**5 - 1/7*f**2 + 0*f + 2. Factor j(p).
-p*(p - 1)*(p + 1)*(3*p - 2)/7
Let s(n) = 3*n**2 - 20*n - 23. Let c(k) be the first derivative of -k**3/3 + 5*k**2 + 11*k + 29. Let z(i) = 7*c(i) + 4*s(i). Factor z(a).
5*(a - 3)*(a + 1)
Let i(t) be the third derivative of t**7/105 + 13*t**6/60 + 23*t**5/15 + t**4 - 24*t**3 + 76*t**2 + 2*t. Let i(z) = 0. What is z?
-6, -2, 1
Let l(m) be the first derivative of m**4/28 + 12*m**3/7 + 216*m**2/7 + 19*m - 41. Let r(o) be the first derivative of l(o). Find b, given that r(b) = 0.
-12
Let z(o) be the second derivative of -3/100*o**5 + 0 + 0*o**2 + 0*o**3 - 13*o + 0*o**4 - 1/70*o**7 + 1/25*o**6. Factor z(v).
-3*v**3*(v - 1)**2/5
Let t(q) be the first derivative of 3*q**2 - 3/4*q**4 + q**3 + 0*q + 6. Factor t(y).
-3*y*(y - 2)*(y + 1)
Let h(z) be the first derivative of z**4/54 - 2*z**3/27 - 3*z - 11. Let n(l) be the first derivative of h(l). Factor n(r).
2*r*(r - 2)/9
Suppose 136*t**2 + t**3 - 12*t**3 - 44 - 86*t + 5*t**3 = 0. Calculate t.
-1/3, 1, 22
Let t(p) = -2*p**2 + 9*p. Let y be t(4). Suppose 0 = 5*r - 2*s - 0*s - y, -5*r + s = -7. Let 2*i**r + 0 - 1/2*i**3 - 2*i = 0. What is i?
0, 2
Let v be 4/54 - (-1976)/1026. Let c(q) be the first derivative of -2/15*q**3 - 5 + 4/5*q**v - 8/5*q. Factor c(d).
-2*(d - 2)**2/5
Let b(i) be the second derivative of -8*i**6/5 + 366*i**5/5 - 225*i**4/4 - 459*i**3/2 + 405*i**2 - 22*i - 2. Solve b(s) = 0 for s.
-1, 3/4, 30
Let f = -657 - -660. Let d(h) be the first derivative of 2/3*h**f - 3*h**2 + 2/15*h**5 + 0*h + 5/6*h**4 + 6. Factor d(i).
2*i*(i - 1)*(i + 3)**2/3
Let i be 5 - (-4 + 0 + 13) - -6. Factor -3 - 7/3*q**i - 5*q - 1/3*q**3.
-(q + 1)*(q + 3)**2/3
Le