6 - -5/48. What is k in -2*k - 4/3*k**2 + 4/3*k**3 - 2/3 + i*k**b + 2*k**4 = 0?
-1, 1
Let b(c) be the first derivative of -4*c**3/3 + 48*c**2 - 176*c + 174. Factor b(v).
-4*(v - 22)*(v - 2)
Let h(k) be the first derivative of 14 - 1/2*k**2 + 1/3*k**3 - 2*k. Find n, given that h(n) = 0.
-1, 2
Factor 0 + 3/2*g**4 - 3*g + 15/2*g**2 - 6*g**3.
3*g*(g - 2)*(g - 1)**2/2
Let j = -11 - -10. Let v be 2 + (4 - 3 - j). Determine z so that 1/5*z**2 - 1/5*z**3 + 0 + 0*z - 1/5*z**v + 1/5*z**5 = 0.
-1, 0, 1
Let o = -82 + 138. Factor 8*t**3 + 51*t + 12 + 3*t**4 + 10*t**3 - 15*t - 17*t**2 + o*t**2.
3*(t + 1)**2*(t + 2)**2
Let a = -45 + 36. Let r(t) = -t - 5. Let w be r(a). Determine z, given that 10/7*z**5 + 26/7*z + 4/7 + 76/7*z**3 + 64/7*z**2 + 44/7*z**w = 0.
-1, -2/5
Let z be ((8/42)/((-6)/(-9)))/((-60)/(-294)). Determine m so that m**2 + 3/5 - 1/5*m**3 - z*m = 0.
1, 3
Let 0*v + 2/3*v**3 + 0 + 0*v**2 - 2/3*v**4 = 0. Calculate v.
0, 1
Let h(d) be the second derivative of -d**6/2340 + d**5/780 + d**3/2 - 2*d. Let a(v) be the second derivative of h(v). Suppose a(i) = 0. What is i?
0, 1
Suppose -1/5*u**2 - 2 - 7/5*u = 0. What is u?
-5, -2
Let x(l) be the third derivative of l**8/1680 - l**7/210 + l**6/600 + 17*l**5/300 - 11*l**4/60 + 4*l**3/15 + 148*l**2 + 3*l. Let x(r) = 0. Calculate r.
-2, 1, 4
Let v(w) be the third derivative of w**8/1512 - 2*w**7/315 + 13*w**6/540 - 2*w**5/45 + w**4/27 - 19*w**2 + 2. Find i, given that v(i) = 0.
0, 1, 2
Let s be 4/15 + (-52)/(-780). Let f(q) be the first derivative of -s*q**3 + 0*q - 6 - 1/2*q**2. Factor f(w).
-w*(w + 1)
Let v(l) be the second derivative of 3*l**5/10 - l**4/6 - 8*l**3/3 - 4*l**2 - 71*l - 2. Let v(q) = 0. Calculate q.
-1, -2/3, 2
Let c be (50/175 - 33/(-7)) + -3. Suppose o = -c*o - 0*o. Determine f, given that -4/7*f**2 + 0 + o*f + 4/7*f**4 + 0*f**3 = 0.
-1, 0, 1
Suppose 96 = 2*s - 122. Let 15*i + 5*i**3 - s*i**2 + 66*i**2 + 5 + 58*i**2 = 0. What is i?
-1
Suppose 0 = 40*c - 6*c - 17*c - 51. Suppose -1/4*k**c - 3/4 + 1/4*k + 3/4*k**2 = 0. Calculate k.
-1, 1, 3
Suppose -66 = -5*x - 4*l, -3*x - 3*l + 53 = x. Let d be (-4)/x - ((-69)/21 - -3). Factor 3/5*j + 3/5*j**3 + 6/5*j**2 + d.
3*j*(j + 1)**2/5
Let r(z) be the third derivative of 1/360*z**6 + 0*z + 0 - 1/90*z**5 + 1/630*z**7 + 0*z**4 + 6*z**2 + 0*z**3. Determine q, given that r(q) = 0.
-2, 0, 1
Let w(c) be the first derivative of -c**4/6 - 4*c**3/9 + c**2/3 + 4*c/3 + 81. Find z such that w(z) = 0.
-2, -1, 1
Let w(h) be the third derivative of 0*h**7 + 0*h**3 + 1/36*h**4 + 0*h - 1/90*h**6 + 1/504*h**8 + 0 - 18*h**2 + 0*h**5. Suppose w(n) = 0. Calculate n.
-1, 0, 1
Suppose -4*j + 4 + 60 = 0. Suppose -2*f - j = -0*f - 4*t, 3*t = 15. Factor 4*i**2 + 10*i**2 - 15*i - 18*i**3 - f*i**2 + 6 + 15*i**3.
-3*(i - 2)*(i - 1)**2
Let h be (-706)/1680 + (-21)/(-49). Let t(u) be the third derivative of 1/10*u**5 + 0*u + 0 + 1/2*u**4 + 4/3*u**3 + 4*u**2 + h*u**6. Factor t(g).
(g + 2)**3
Let y be 2*(3 - 13/(-2)). Let f = y - 16. Suppose 6*h**4 + 4*h - 5*h**2 - 5*h**3 - 2*h**2 - 2*h**5 + f*h**3 + h**2 = 0. Calculate h.
-1, 0, 1, 2
Let o(g) be the third derivative of g**7/280 - g**6/20 + 3*g**5/40 + g**4/4 - 7*g**3/8 - 2*g**2 - 156*g. Factor o(j).
3*(j - 7)*(j - 1)**2*(j + 1)/4
Let n(o) be the first derivative of -o**3 + 3/5*o**5 + 0*o - 3/4*o**4 + 6 + 3/2*o**2. Factor n(y).
3*y*(y - 1)**2*(y + 1)
Let b = -3718 + 3720. What is j in -4/7*j - 4/7 - 1/7*j**b = 0?
-2
Let a = -21 + 26. Suppose -a*f + q + 14 = -2, 3*q = 3*f. Factor 1/4*r**f - 3/4*r**3 + 0 + 1/2*r**2 + 0*r.
r**2*(r - 2)*(r - 1)/4
Let m(d) = -4*d**3 + 6*d**2 - 5*d - 5. Let j(y) = -6*y**3 + 5*y**3 + 4*y + 4 - 5*y**2 + 4*y**3. Let z(b) = 5*j(b) + 4*m(b). Factor z(s).
-s**2*(s + 1)
Let y(a) = a**4 + 10*a**3 - 6*a**2 - 7*a + 14. Let l(j) = 4*j**4 + 30*j**3 - 18*j**2 - 20*j + 44. Let v(o) = -3*l(o) + 10*y(o). Factor v(r).
-2*(r - 4)*(r - 1)**2*(r + 1)
Let -1/3*f**5 + 0 + f - 2/3*f**3 - 4/3*f**2 + 4/3*f**4 = 0. What is f?
-1, 0, 1, 3
Let z(c) be the second derivative of -c**4/8 - 3*c**3/4 - 2*c + 10. Factor z(g).
-3*g*(g + 3)/2
Let c(o) be the second derivative of 4*o**5/85 + 5*o**4/102 - o**3 + 18*o**2/17 + 67*o. Factor c(u).
2*(u - 2)*(u + 3)*(8*u - 3)/17
Let s(c) be the first derivative of -1/3*c - 1/6*c**2 + 2/9*c**3 + 1/6*c**4 - 1/15*c**5 + 5 - 1/18*c**6. Let s(q) = 0. What is q?
-1, 1
Let w = 82 + -78. Let o(k) be the first derivative of -4 + k**3 - 3/5*k**5 + 0*k + 3/2*k**2 - 3/4*k**w. Determine a so that o(a) = 0.
-1, 0, 1
Let l(x) be the first derivative of x**4/30 + 2*x**3/15 + x**2/5 + 8*x + 11. Let d(h) be the first derivative of l(h). Factor d(p).
2*(p + 1)**2/5
Suppose 5*j = 15, -4*j + j = -4*w + 3. Suppose w*q = 5*u - 19, -2*q + 12*u = 10*u + 6. Factor -17/2*l**2 + q + 9/4*l**3 + 7*l.
(l - 2)**2*(9*l + 2)/4
Let m(x) be the second derivative of x**4/6 - 2*x**3 + 8*x**2 - 8*x - 1. Factor m(b).
2*(b - 4)*(b - 2)
Let v(j) be the first derivative of -5*j**4/4 + 10*j**3/3 + 60*j**2 + 372. Factor v(f).
-5*f*(f - 6)*(f + 4)
Let l(u) be the first derivative of 4*u**3/3 + u**2 + 7*u - 13. Let d(j) = j**2 - j + 1. Let c(i) = -15*d(i) + 5*l(i). Find v such that c(v) = 0.
-4, -1
Let s(j) be the second derivative of -j**7/840 + j**6/120 + j**5/120 - j**4/8 + 4*j**3/3 - 7*j. Let u(f) be the second derivative of s(f). Factor u(k).
-(k - 3)*(k - 1)*(k + 1)
Suppose -2/21*a**4 + 2/21*a**5 + 4/3*a**2 + 2/7 - 22/21*a - 4/7*a**3 = 0. Calculate a.
-3, 1
Let z(r) be the third derivative of -10/3*r**3 - 5*r**2 + 20/3*r**4 + 25/8*r**6 + 0*r - 85/12*r**5 + 0. Determine u so that z(u) = 0.
1/3, 2/5
Let c(r) = r**3 + 6*r**2 - 7*r + 5. Let n be 2 - (27/3)/1. Let i be c(n). Factor 2/3*y**3 - 1/3*y + 0*y**4 - 1/3*y**i + 0*y**2 + 0.
-y*(y - 1)**2*(y + 1)**2/3
Suppose -678 = -3*t + 2*y - 178, -y = t - 160. Suppose t*q = 159*q + 20. Let -8/3*n + 20/3*n**q + 28/3*n**2 - 12*n**3 - 4/3*n**5 + 0 = 0. What is n?
0, 1, 2
Let f(z) be the first derivative of -5*z**8/336 + z**6/24 + 5*z**2/2 + 6. Let b(h) be the second derivative of f(h). Find o such that b(o) = 0.
-1, 0, 1
Let x(d) be the first derivative of -d**4/8 + 7*d**3/18 - 2*d/3 + 197. Factor x(a).
-(a - 2)*(a - 1)*(3*a + 2)/6
Suppose 4*a + 4 = -0*o + 5*o, 4 = a. Factor 5*t**2 + 26*t**2 - 6*t**2 - 15*t**3 + 3*t**o + 2*t**2 + 6 - 21*t.
3*(t - 2)*(t - 1)**3
Let d = 131 - 47. Let k be 8/28*d/9. Suppose k*b + 1/3*b**2 + 16/3 = 0. What is b?
-4
Let u = -30836 + 30839. Find y, given that 0*y + 2/7*y**2 + 0 + 2/7*y**u = 0.
-1, 0
Let n(h) be the third derivative of h**5/60 + 2*h**4/3 + 32*h**3/3 + 2*h**2 - 52. Solve n(z) = 0.
-8
Let x(r) be the first derivative of r**6/16 - 3*r**5/8 - 9*r**4/32 + 13*r**3/8 + 15*r**2/8 - 371. Solve x(m) = 0.
-1, 0, 2, 5
Let k(q) = -2*q**4 - 2*q**3 - 45*q**2 + 64*q - 25. Let n(v) = 3*v**4 + 3*v**3 + 45*v**2 - 63*v + 24. Let b(m) = 6*k(m) + 5*n(m). Factor b(a).
3*(a - 2)*(a - 1)**2*(a + 5)
Factor -50*f**2 - 5 - 9*f**3 + 16*f**4 - 17*f - 13*f**2 + 3 + f**3 + 24*f**2.
(f - 2)*(f + 1)*(4*f + 1)**2
Let w(h) be the second derivative of h**7/126 - h**6/72 - h**5/12 + 5*h**4/72 + 5*h**3/9 - 9*h**2 - h. Let l(f) be the first derivative of w(f). Factor l(j).
5*(j - 2)*(j - 1)*(j + 1)**2/3
Let y = -33 - -26. Let k be ((-224)/12)/y - 2. Solve 0 + 4/3*v + k*v**2 - 2/3*v**3 = 0.
-1, 0, 2
Let q(h) = h. Let i be q(1). Let o be i*3 - (5 - 5). Factor 2*f**3 - 5*f**3 + 12*f**2 + 12*f + 6*f**o.
3*f*(f + 2)**2
Let g(j) be the first derivative of j**5/20 + j**4/4 - 13*j**3/6 - 15*j**2/2 + 225*j/4 - 547. Factor g(r).
(r - 3)**2*(r + 5)**2/4
Let d = 23479/15654 - -1/7827. Factor -1029/2 - 441/2*n - 63/2*n**2 - d*n**3.
-3*(n + 7)**3/2
Let u(t) be the first derivative of t**8/280 - 2*t**7/105 + t**6/30 - t**4/12 + 5*t**3 - 1. Let n(w) be the third derivative of u(w). Let n(p) = 0. What is p?
-1/3, 1
Let 15/2*l + 4 + 11/4*l**2 = 0. Calculate l.
-2, -8/11
Let w be (-15 + 6)/(-3) + 1 + -2. Suppose w*p + 8*p = p. Factor -2/7 + p*f + 2/7*f**2.
2*(f - 1)*(f + 1)/7
Factor 0 + 40/3*l + 4/3*l**2.
4*l*(l + 10)/3
Let g(w) = w**3 + 49*w**2 + 51*w + 157. Let d be g(-48). Let h(q) be the first derivative of d - 2/21*q**3 - 5/14*q**4 + 0*q**2 + 0*q. Factor h(n).
-2*n**2*(5*n + 1)/7
Suppose 92*k - 5*k**3 + 11*k**2 + 24*k**2 - 2*k = 0. What is k?
-2, 0, 9
Let p(w) be the first derivative of -w**3/4 + 9*w**2/2 