 9 + 0*f + 4/15*f**3 + 0*f**2. Find k, given that c(k) = 0.
0, 1, 2
Let f = -93 - -101. Let j be (-6)/8 - 3*f/(-32). Suppose 2/11*z**3 + 0*z + 2/11*z**2 + j = 0. What is z?
-1, 0
Let f(d) = 3*d**2 + 7*d + 11. Let h be f(-3). Let b = h + -67/4. Factor 1/4*m**3 + 0*m + b*m**2 + 0.
m**2*(m + 1)/4
Let x(d) be the first derivative of -d**4/2 - 50*d**3/3 + 26*d**2 + 212. Find q, given that x(q) = 0.
-26, 0, 1
Let s(n) be the second derivative of -3*n**4/4 + 17*n**3/2 + 9*n**2 + 75*n + 2. Determine i, given that s(i) = 0.
-1/3, 6
Factor -10/11 - 78/11*n + 32/11*n**3 - 144/11*n**2.
2*(n - 5)*(4*n + 1)**2/11
Let g(v) be the first derivative of -3/25*v**5 + 0*v + 13 - 1/2*v**4 + 3/5*v**2 - 1/15*v**3. Factor g(p).
-p*(p + 1)*(p + 3)*(3*p - 2)/5
Let v(n) be the third derivative of 0*n - n**2 - 45*n**3 + 135/8*n**4 - 1/42*n**7 - 15/4*n**5 + 11/24*n**6 + 0. Factor v(x).
-5*(x - 3)**3*(x - 2)
Let q(h) be the second derivative of 0 - 5/12*h**4 - 5/12*h**3 - 1/8*h**5 - 15*h + 0*h**2. Factor q(x).
-5*x*(x + 1)**2/2
Let p(u) = -u**2 - 4*u + 17. Let v be p(-6). Suppose -2*j - 10 = -v*k, -3*k + j = 2*k - 5. Factor -1/7*f**3 + k + 0*f**2 + 1/7*f.
-f*(f - 1)*(f + 1)/7
What is z in 1/2*z**5 + 531/4*z**2 + 54*z**3 + 81*z - 81 + 35/4*z**4 = 0?
-6, -3, 1/2
What is d in -21*d - 45/2*d**2 + 0 - 3/2*d**3 = 0?
-14, -1, 0
Find v such that -2/11*v + 2/11*v**3 - 1/11 + 1/11*v**4 + 0*v**2 = 0.
-1, 1
Suppose 255/4*x**4 + 87/4*x**5 + 0 - 135*x**3 + 12*x - 165*x**2 = 0. What is x?
-4, -1, 0, 2/29, 2
Let n(d) = 2*d**3 + 3*d**2 + 3*d + 2. Let b be n(-2). Let k be 1*21*(1 - b/(-10)). What is l in -3/5 + 48/5*l**5 - 69/5*l**2 + 72/5*l**4 - 27/5*l - k*l**3 = 0?
-1, -1/4, 1
Suppose -5*w = w - 36. Factor w*k**3 - 5*k**4 + 21*k - 21*k + 2*k**4 - 3*k**2.
-3*k**2*(k - 1)**2
Let j(x) be the third derivative of x**10/52920 - x**8/11760 - x**4/8 - 18*x**2. Let g(y) be the second derivative of j(y). Factor g(v).
4*v**3*(v - 1)*(v + 1)/7
Let c = -32 - -35. Determine a, given that -10*a**3 + 5*a - 5*a**c - 5*a**4 + 15*a = 0.
-2, 0, 1
Let v(f) be the first derivative of f**6/150 + 2*f**5/25 - 64*f**3/15 + 3*f**2/2 - 9. Let k(c) be the second derivative of v(c). Suppose k(l) = 0. What is l?
-4, 2
Find g, given that 27/2*g - 243/2 + 1/2*g**3 + 15/2*g**2 = 0.
-9, 3
Let i(y) = y**2 - 12*y - 43. Let x be i(15). What is b in 12*b + x*b**2 + b**2 - b**2 = 0?
-6, 0
Let v(k) be the first derivative of -k**7/252 - k**6/60 + k**4/18 - 29*k - 7. Let t(p) be the first derivative of v(p). Factor t(c).
-c**2*(c - 1)*(c + 2)**2/6
Let i(s) be the third derivative of -1/252*s**7 - 1/1008*s**8 - 1/180*s**6 - 14*s**2 + 0*s**4 - 1/360*s**5 + 0 + 0*s**3 + 0*s. Factor i(r).
-r**2*(r + 1)**2*(2*r + 1)/6
Let r(h) = -3*h**4 + 36*h**3 - 30*h**2 - 36*h + 30. Let t(x) = 3*x**4 - 37*x**3 + 31*x**2 + 37*x - 30. Let f(m) = 4*r(m) + 3*t(m). Factor f(o).
-3*(o - 10)*(o - 1)**2*(o + 1)
Let b(c) be the third derivative of -c**8/3360 + c**6/360 - c**4/4 - 13*c**2. Let g(j) be the second derivative of b(j). Factor g(u).
-2*u*(u - 1)*(u + 1)
Let v(u) = -3*u**5 - u**4 + u**3 - 21*u**2 - 24*u + 1. Let l(n) = -4*n**5 - 2*n**4 + 2*n**3 - 22*n**2 - 26*n + 2. Let q(d) = 5*l(d) - 6*v(d). Factor q(h).
-2*(h - 2)*(h + 1)**4
Suppose 22*q - 25*q + 4*p = -5, 3*p = -5*q + 18. Factor 4/7*a**2 - 2/7*a**q + 0 - 2/7*a.
-2*a*(a - 1)**2/7
Suppose k + 15*k + 7*k + 5*k**2 + 10 - 8*k = 0. What is k?
-2, -1
Let u(w) be the first derivative of -5/4*w**4 + 0*w + 0*w**2 + 5/6*w**6 + 0*w**5 + 0*w**3 - 1. Factor u(k).
5*k**3*(k - 1)*(k + 1)
What is d in 0 + 0*d + 2/7*d**2 - 1/7*d**3 - 1/7*d**4 = 0?
-2, 0, 1
Let i(z) be the second derivative of z**6/15 + 4*z**5/5 + 13*z**4/6 + 2*z**3 - 206*z. Solve i(g) = 0 for g.
-6, -1, 0
Let w(s) be the second derivative of 1/50*s**5 - 4/15*s**3 - 1/15*s**4 + 8/5*s**2 + 2*s + 0. Factor w(a).
2*(a - 2)**2*(a + 2)/5
Let c(w) be the first derivative of -w**4/6 - 2*w**3/3 - 15*w - 18. Let z(j) be the first derivative of c(j). Factor z(g).
-2*g*(g + 2)
Let h(j) = -j - 13. Let d be h(-16). Let q(o) be the third derivative of 0 + 0*o - 1/60*o**5 - 1/8*o**4 - 1/3*o**d + 6*o**2. Find t such that q(t) = 0.
-2, -1
Let l = -56756/9 + 261472/45. Let u = l + 496. Determine z, given that 0 + 2/15*z**3 - 2/5*z + u*z**2 = 0.
-3, 0, 1
Let a(m) be the first derivative of m**7/231 - m**6/55 + 3*m**5/110 - m**4/66 - 11*m - 6. Let i(g) be the first derivative of a(g). Suppose i(b) = 0. What is b?
0, 1
Find u, given that 3/4*u**5 - 45/4*u**3 - 3/4*u**4 - 15/2*u - 69/4*u**2 + 0 = 0.
-2, -1, 0, 5
Let g(v) be the second derivative of v**7/23940 + v**6/684 + 5*v**5/228 + v**4/3 - 14*v. Let r(l) be the third derivative of g(l). Factor r(u).
2*(u + 5)**2/19
Let x(v) be the first derivative of v**6/225 - v**5/150 - v**4/30 + v**3/9 - 2*v**2/15 - 10*v - 7. Let h(s) be the first derivative of x(s). Factor h(t).
2*(t - 1)**3*(t + 2)/15
Let f(o) be the third derivative of -13*o**5/30 + 25*o**4/6 + 8*o**3/3 - 35*o**2 + 6. Factor f(r).
-2*(r - 4)*(13*r + 2)
Factor -165/2*a**2 - 9075/2*a - 1/2*a**3 - 166375/2.
-(a + 55)**3/2
Factor 96 - 16*b + 11*b + 2*b**3 + 22*b**2 + 38*b + 17*b + 30*b.
2*(b + 3)*(b + 4)**2
Let l(i) = i**2 + 6*i + 10. Let m be l(-4). Suppose -4*b + 7 = 3*h - 2*b, m*b + 11 = 3*h. Factor 3/4*a**h + a**2 + 0 + 1/4*a.
a*(a + 1)*(3*a + 1)/4
Let d(q) be the first derivative of -5*q**4/4 - 13*q**3 + 4*q**2 - 157. Factor d(m).
-m*(m + 8)*(5*m - 1)
Let g(x) be the second derivative of x**8/6720 + x**7/504 + 7*x**6/720 + x**5/40 + 5*x**4/3 + 9*x. Let u(f) be the third derivative of g(f). Factor u(k).
(k + 1)**2*(k + 3)
Let v(r) be the first derivative of -r**4/4 + 3*r**2/2 - 8*r + 28. Let o(m) be the first derivative of v(m). Factor o(z).
-3*(z - 1)*(z + 1)
Let u(o) be the first derivative of -6*o**5/5 + 19*o**4/2 - 2*o**3 - 19*o**2 + 12*o + 554. Determine y, given that u(y) = 0.
-1, 1/3, 1, 6
Let u be 22/42 - -5*(-1)/(-35). Let s(d) be the first derivative of -3/2*d**2 - 2 + 1/2*d**4 - u*d**3 + 1/6*d**6 + 3/5*d**5 - d. Factor s(i).
(i - 1)*(i + 1)**4
Suppose -3*u = -4*h - 145, 5*h - 2*u + 155 = -7*u. Let x = h + 36. Factor -1/2*d**4 - 1/2*d**3 + 0 + 1/2*d**x + 1/2*d.
-d*(d - 1)*(d + 1)**2/2
Let m(r) be the third derivative of -r**8/1848 - r**7/385 + r**6/220 + 7*r**5/330 - r**4/22 + 639*r**2. Let m(d) = 0. What is d?
-3, -2, 0, 1
Let t = 113 + -15. What is m in -25*m**3 - 40 + 63*m - t*m + 0*m**2 - 115*m - 135*m**2 = 0?
-4, -1, -2/5
Let t = 1076/45 + -352/15. Factor 2/9*x**4 - t*x**3 + 0 + 0*x**2 + 0*x.
2*x**3*(x - 2)/9
Let r(k) = 20*k**3 + 28*k**2 + 40*k. Let z(p) = -44*p**3 - 56*p**2 - 80*p. Let v(i) = 9*r(i) + 4*z(i). Find y such that v(y) = 0.
-5, -2, 0
Let s(x) = x**2 - 1. Let t(k) = 4*k**2 - 16*k - 17. Let m(o) = -3*s(o) + t(o). Let y be m(17). Suppose 3/4*i**2 + 1/2*i + 0 - 5/4*i**y = 0. Calculate i.
-2/5, 0, 1
Let w(t) be the first derivative of t**3 + 33*t**2 + 63*t - 205. Factor w(q).
3*(q + 1)*(q + 21)
Let l(x) = x**2 - 11*x - 10. Suppose 2*m = 4*m - 2*c - 20, -c + 2 = 0. Let j be l(m). Factor 0 + 3 + 3*d**j + 0*d**2 + 0 - 6*d.
3*(d - 1)**2
Factor -140/3*v + 1225/3 + 4/3*v**2.
(2*v - 35)**2/3
Suppose y + 5*n = -21, 0 = y + y - 2*n - 18. Solve -y*x + 324 - 56*x**2 + 60*x**2 + 76*x = 0.
-9
Let l be 8/28 - (-36)/21. Suppose -4*j = -k + j + 12, 3*k + 4*j = -2. Factor -k*i**3 - i**l + 5*i**3 - i**2 - 2*i**3.
i**2*(i - 2)
Let r(c) = -8*c**2 - 15*c + 117. Let z(t) = -4*t**2 - 8*t + 60. Let s(f) = -4*r(f) + 7*z(f). Factor s(a).
4*(a - 3)*(a + 4)
Find b such that 0*b - 1/3*b**3 + 4/3 - b**2 = 0.
-2, 1
Let l(c) be the third derivative of -c**8/5040 - c**7/2520 + c**6/1080 + c**5/360 - 5*c**3/6 + c**2. Let b(r) be the first derivative of l(r). Factor b(s).
-s*(s - 1)*(s + 1)**2/3
Suppose 0 - 4 = -4*d. Suppose d = -2*z + 9. Let -p**2 + 2*p**2 + 3*p**3 - z*p**2 = 0. Calculate p.
0, 1
Let f(h) = 3*h**2 - 11*h - 9. Let y(n) = -464*n**2 - 470*n**2 + 929*n**2 + 14 + 17*n. Suppose s - 2*s = -8. Let r(p) = s*f(p) + 5*y(p). Factor r(k).
-(k + 1)*(k + 2)
Let n(b) be the third derivative of b**7/4620 + b**6/495 + b**5/165 - 19*b**3/6 - 3*b**2. Let d(o) be the first derivative of n(o). Factor d(x).
2*x*(x + 2)**2/11
Let q(g) be the third derivative of g**7/315 - 7*g**6/60 - g**5/30 + 65*g**4/36 - 14*g**3/3 + 7*g**2 + 46*g. What is w in q(w) = 0?
-2, 1, 21
Deter