he second derivative of x**6/2160 - x**5/144 + x**4/36 - 11*x**3/6 - 4*x. Let d(j) be the second derivative of q(j). Let d(y) = 0. What is y?
1, 4
Let p(d) be the third derivative of 1/210*d**6 - 1/210*d**5 + 0*d + 0 + 1/21*d**3 - 14*d**2 - 1/42*d**4. Find g, given that p(g) = 0.
-1, 1/2, 1
Let n(p) be the third derivative of p**8/30240 + p**7/3780 - p**6/360 + 4*p**5/15 + 23*p**2. Let s(m) be the third derivative of n(m). Factor s(o).
2*(o - 1)*(o + 3)/3
Suppose -3*s = -73 + 55. Let j = -24/5 + s. Suppose -2/5 - 2/5*n**3 - j*n**2 - 6/5*n = 0. Calculate n.
-1
Factor 20/3*z + 4/3*z**3 + 2/3*z**4 - 26/3*z**2 + 0.
2*z*(z - 2)*(z - 1)*(z + 5)/3
Suppose 4*d - 5*w = 27, 7 = -2*d - 3*w + 4. Factor -4*z**2 - 12*z - d*z**4 - 4*z**4 - 4*z**3 + 11*z**4 + 16*z**3.
4*z*(z - 1)*(z + 1)*(z + 3)
Let f(l) be the third derivative of -2/3*l**3 - 25*l**2 - 1/60*l**6 + 0 + 0*l + 1/12*l**4 - 1/105*l**7 + 1/10*l**5. Find k such that f(k) = 0.
-2, -1, 1
Let i(b) = -10*b + 15. Let x be i(4). Let n be 4 - (-205)/x - -5. Find j, given that -2/5 + n*j + 28/5*j**3 + 2*j**4 + 24/5*j**2 = 0.
-1, 1/5
Let q(g) be the third derivative of -2/245*g**7 + 1/784*g**8 + 0*g + 34*g**2 + 2/35*g**5 + 1/56*g**4 - 1/140*g**6 + 0 - 2/7*g**3. What is x in q(x) = 0?
-1, 1, 4
Let m = -1163/100 - -347/25. Factor 15/4*b**4 - 21/4*b**3 - 3/4*b**5 + 0*b + 0 + m*b**2.
-3*b**2*(b - 3)*(b - 1)**2/4
Factor 2/13*w**3 - 2/13*w**2 + 24/13 - 16/13*w.
2*(w - 2)**2*(w + 3)/13
Suppose 0 = -3*k + 52*m - 48*m + 12, -2*k = -2*m - 8. Suppose -32/3*y - 28/9*y**2 - k = 0. Calculate y.
-3, -3/7
Let l(f) be the first derivative of -5*f**4 + 10 + f**5 + 0*f + 15*f**2 + 5/3*f**3. Factor l(z).
5*z*(z - 3)*(z - 2)*(z + 1)
Determine c so that 324/13 - 42/13*c - 2/13*c**2 = 0.
-27, 6
Suppose 3*t + 21 = 30. Let -3*h**t - 6 - 9*h**2 - 12*h - 3/8*h**4 = 0. Calculate h.
-2
Suppose 3*j - 1 = -c + 4*j, 5*c - 3*j - 7 = 0. Suppose 4*l = c*l + 4. Let 3*k**4 + l - 4*k**2 - 4*k**4 + 3*k**4 = 0. What is k?
-1, 1
Let h(d) be the second derivative of -3/5*d**2 + 0 - 3/10*d**3 - 1/20*d**4 + 12*d. Determine o, given that h(o) = 0.
-2, -1
Let c(p) be the second derivative of -2*p**7/21 - p**6/3 + 2*p**5/5 + p**4/2 + 43*p. Let c(w) = 0. What is w?
-3, -1/2, 0, 1
Let x = 3 + 2. Suppose -x*q + 21 + 4 = 0, n = 2*q - 8. Factor 1 - 11*g**4 + 9*g**4 + g**n + 3*g**2 - 3.
-2*(g - 1)**2*(g + 1)**2
Let m = -46 - 14. Let l be 5 - ((-472)/m - 3). Determine j, given that l*j**2 + 0 + 0*j = 0.
0
Let a(f) be the third derivative of -11*f**2 + 0*f**3 + 1/80*f**5 + 0 + 0*f + 3/32*f**4. Determine t so that a(t) = 0.
-3, 0
Let y(j) = 14*j**3 + 14*j**2 - 6*j + 6. Let b(d) = 2*d**3 - d + 1. Let l(r) = -6*b(r) + y(r). Find m such that l(m) = 0.
-7, 0
Let s(k) be the first derivative of -k**7/63 + 2*k**6/45 - k**5/30 + 17*k - 43. Let u(j) be the first derivative of s(j). Factor u(l).
-2*l**3*(l - 1)**2/3
Let p be (21/(-7))/(1*-3). Let r = p - -3. Factor -5*t**2 - 2*t - 5 - 4*t - r*t.
-5*(t + 1)**2
Let r be 2/(-4)*8*(-2)/4. Factor -5*l**2 + 7*l**2 + 4*l**4 + 4 - 8*l**2 - 2*l**r.
4*(l - 1)**2*(l + 1)**2
Let i(m) be the first derivative of m**6/2 + 2*m**5 - 9*m**4/4 - 4*m**3/3 - 680. Determine q so that i(q) = 0.
-4, -1/3, 0, 1
Suppose -15*q - q = -48. Let j(k) be the third derivative of -1/300*k**6 + 0 + 1/15*k**q - 3*k**2 + 0*k - 1/150*k**5 + 1/60*k**4. Factor j(z).
-2*(z - 1)*(z + 1)**2/5
Let p(m) = -5*m**4 + 53*m**3 - 14*m. Let n(x) = -5*x**4 + 54*x**3 - 12*x. Let w(h) = 7*n(h) - 6*p(h). Factor w(d).
-5*d**3*(d - 12)
Suppose -11*n + 29 + 15 = 0. Suppose m - 3 = -n*d - 9, -4*m + 5*d = -18. Suppose -a**5 - 11/2*a - 23/2*a**3 - 11/2*a**4 - 23/2*a**m - 1 = 0. What is a?
-2, -1, -1/2
Let h(d) be the third derivative of -d**8/90720 + d**7/11340 - d**5/60 + 21*d**2. Let c(t) be the third derivative of h(t). Factor c(f).
-2*f*(f - 2)/9
Let r be ((1 + -17)/(-4))/((-12)/(-15)). Suppose 7*q = -10 + 38. Factor 4/15*a**2 + 0*a**q + 0*a + 2/15*a**r + 0 - 2/5*a**3.
2*a**2*(a - 1)**2*(a + 2)/15
Suppose -7*s - 3 = -17. Let w be (-26)/(-24) + s/3 + -1. Suppose 1/4*b + 1/4*b**4 + 0 + w*b**2 + 3/4*b**3 = 0. What is b?
-1, 0
Let f = -10 - -9. Let z(x) = x**2 - x. Let j(m) = 12*m**2 - 8*m + 12. Let k(v) = f*j(v) + 16*z(v). Let k(c) = 0. Calculate c.
-1, 3
Let n = -30503/24 - -1271. Let v(o) be the second derivative of -11*o + 0 - o**2 + 0*o**3 + n*o**4. Let v(k) = 0. What is k?
-2, 2
Let k(y) = -15*y**3 - 45*y + 42*y**2 - 192*y**2 + 36*y**3 + 24*y**3. Let m(j) = -22*j**3 + 75*j**2 + 22*j. Let s(i) = 2*k(i) + 5*m(i). Factor s(c).
-5*c*(c - 4)*(4*c + 1)
Let q(t) be the first derivative of -1/30*t**4 + 1/15*t**2 + 22 + 0*t**3 + 0*t. Find y, given that q(y) = 0.
-1, 0, 1
Factor -3*a + 18/5 + 3/5*a**2.
3*(a - 3)*(a - 2)/5
Let c(q) = q**5 + q**4 + 2*q**3 + q**2 - q. Let t(a) = 3*a**5 + 8*a**4 + 13*a**3 + 6*a**2 - 2*a. Let z(j) = 6*c(j) - 3*t(j). Factor z(h).
-3*h**2*(h + 1)**2*(h + 4)
Let b(x) = x**3 + 2*x**2 - x. Let h(y) = 3*y**3 - y**2 - 6*y + 20. Let a(g) = 2*b(g) - h(g). Factor a(t).
-(t - 5)*(t - 2)*(t + 2)
Suppose -1 = 4*u - 5*c + 11, 2*c - 12 = -2*u. Factor 3*b**3 - 7*b**2 + 10*b**u - 4*b**3 - 2*b**3.
-3*b**2*(b - 1)
Suppose 11*l - 31 = 2. Find m such that -m - m + 4 - 4*m**2 + 2*m**3 - l*m + 3*m = 0.
-1, 1, 2
Let w(t) = 5*t**3 - t**2 - t + 1. Let n be w(1). Determine z so that -z**n + 2*z**5 - z**5 + 3*z**2 - 2*z + z**3 - 2*z**4 + 0*z**5 = 0.
-1, 0, 1, 2
Let c(i) be the second derivative of i**5/15 + i**4/3 + 2*i**3/3 - 4*i**2 + 21*i. Let t(k) be the first derivative of c(k). Factor t(m).
4*(m + 1)**2
Factor 4/5*h**2 + 4/5*h - 4/5 - 4/5*h**3.
-4*(h - 1)**2*(h + 1)/5
Let w(p) = -p**3 - 14*p**2 - 12*p + 17. Let v be 147/(-12) + 12/(-16). Let l be w(v). What is y in 3*y**5 - 9*y**3 - 3*y**l + 2*y**2 + y**2 - 4*y + 10*y = 0?
-1, 0, 1, 2
Let u(d) = d**2 - d - 4. Let o be u(-2). Solve h + 3*h**o + 7*h + 0*h + 16*h + 48 = 0.
-4
Let t(a) be the first derivative of a**3/6 + a**2/4 - 50. Solve t(v) = 0.
-1, 0
Let u(v) be the first derivative of -15 - 9/4*v**2 - 3/4*v**4 - 3/20*v**5 + 11/4*v**3 + 0*v. Solve u(a) = 0 for a.
-6, 0, 1
Let o(s) be the first derivative of 3*s**5/20 + 9*s**4/8 + 9*s**3/4 + 3*s**2/2 + 92. Factor o(y).
3*y*(y + 1)**2*(y + 4)/4
Let u(x) be the second derivative of 3*x**5/40 + 7*x**4/8 + 2*x**3 - 12*x**2 - 151*x. Factor u(z).
3*(z - 1)*(z + 4)**2/2
Solve -18*r**2 + 12 - 5*r - 3*r**3 + 6*r**2 + 8*r + 0 = 0.
-4, -1, 1
Let f = 526/1855 + 4/1855. Factor 6/7 - 8/7*r**2 - f*r.
-2*(r + 1)*(4*r - 3)/7
Let f(h) = -5*h**5 + 20*h**4 - 2*h**3 - 2*h**2 - 2. Let w(z) = 35*z**5 - 140*z**4 + 15*z**3 + 15*z**2 + 15. Let m(s) = 15*f(s) + 2*w(s). Solve m(n) = 0 for n.
0, 4
Let 28/9*y + 26/9 + 2/9*y**2 = 0. Calculate y.
-13, -1
Let y = -10 + 5. Let n be 3 + y + (-6)/3. Let r(v) = 5*v**3 + 2*v**2 + v. Let u(j) = 6*j**3 + 3*j**2 + j. Let s(q) = n*u(q) + 5*r(q). Factor s(o).
o*(o - 1)**2
Let o = 1 - -2. Suppose -u + 3*m = -5, -6 = -4*u + m + 3. Let -o*t + 4*t + 3*t + 0*t - 2 - u*t**2 = 0. What is t?
1
Let o(d) be the third derivative of 0*d + 1/8*d**4 + 1/6*d**3 + 0 + 1/20*d**5 - 22*d**2 + 1/120*d**6. Solve o(j) = 0 for j.
-1
Let m be (-50)/15 - (-4)/12. Let u be (-2720)/(-520) - 8/(-6)*m. Factor -u*x - 32/13 - 2/13*x**2.
-2*(x + 4)**2/13
Let z(s) = 7*s**4 - 20*s**3 + 22*s**2 - 12*s + 3. Let y(v) = -v**5 + 2*v**3 - v. Let r(m) = y(m) + z(m). Let r(f) = 0. Calculate f.
1, 3
Let m(j) = -46*j**2 - 54*j - 9. Let n(f) = -22*f**2 - 29*f - 4. Let v(b) = -4*m(b) + 10*n(b). Factor v(d).
-2*(d + 2)*(18*d + 1)
Let w(j) = -j**3 + 21*j**2 - 35*j - 43. Let l be w(19). Factor -8*r**3 - 14 + 7*r**3 - 15*r + 9*r**2 - l + 3.
-(r - 5)**2*(r + 1)
Let d(s) = s - 9. Let g be d(11). Let i be (6/g)/((-39)/(-26)). Determine n, given that 1/2 + i*n**2 - 2*n = 0.
1/2
Let w(h) be the second derivative of -h**7/14 + h**6 - 9*h**5/2 + 10*h**4 - 25*h**3/2 + 9*h**2 - 8*h - 4. Find l such that w(l) = 0.
1, 6
Let p be (54 - 53)/((-25)/3*(-2)/30). Determine r, given that -3/5*r**5 - 24/5*r**2 + p*r**3 + 6/5*r**4 + 12/5*r + 0 = 0.
-2, 0, 1, 2
Let u(k) be the second derivative of k**6/40 + 3*k**5/20 + 5*k**4/16 + k**3/4 + 123*k. Let u(l) = 0. Calculate l.
-2, -1, 0
Let l(w) = 3*w**2 - 8*w + 14. Let o(z) = -2*z**2 + z + 1. Let m(a) = l(a) + 2*o(a). Suppose m(c) = 0. Calculate c.
-8, 2
Let o be -6*1/2 + 318/42. Let u be 