d derivative of 5/12*x**4 + 5*x**2 - 10 - 5/2*x**3 + x. Factor v(m).
5*(m - 2)*(m - 1)
Let u = -78219 - -78223. Find o, given that 0 - 3/5*o**3 + 1/5*o**5 + 4/5*o**2 + 4/5*o - 2/5*o**u = 0.
-1, 0, 2
Let x = -125/114 - -115/76. Let o(z) be the second derivative of 0 + 5/6*z**3 - 5*z + 15*z**2 - x*z**4. Factor o(v).
-5*(v - 3)*(v + 2)
Let d(l) be the third derivative of l**6/480 - l**5/60 - 55*l**4/96 - 25*l**3/12 + 18*l**2 - 16*l. Factor d(q).
(q - 10)*(q + 1)*(q + 5)/4
Let -3 - 1/2*a + 1/2*a**3 - 1/6*a**4 + 19/6*a**2 = 0. Calculate a.
-3, -1, 1, 6
Let t(r) be the second derivative of r**6/5 - 5*r**5/2 - 5*r**4 + 100*r**3/3 + 72*r**2 - 530*r + 1. Find f such that t(f) = 0.
-2, -2/3, 2, 9
Let w(z) = -z**2 + 14*z + 56. Let g be w(17). Determine k, given that 12*k**2 + 40*k**2 - g + 24*k + 5 = 0.
-6/13, 0
Let l(v) be the third derivative of -v**2 - 15 + 0*v - 10*v**3 - 1/12*v**5 + 35/24*v**4. Factor l(u).
-5*(u - 4)*(u - 3)
Let c(d) be the second derivative of -22*d - 3 - 1/80*d**5 + 0*d**2 - 1/4*d**3 + 5/48*d**4. Factor c(z).
-z*(z - 3)*(z - 2)/4
Let l(k) = -k**3 + 6*k**2 - 27*k + 80. Let j be l(4). Let m(d) be the first derivative of -8*d**2 + 0*d**3 + 13 - 4/5*d**5 + 3*d**j + 0*d. Factor m(y).
-4*y*(y - 2)**2*(y + 1)
Suppose -18*l = -3*l - 30. Solve -61 + 0*v**2 + 117 - 91 + 30*v + 5*v**l = 0.
-7, 1
Let i(u) be the second derivative of 2*u**6/75 + 134*u**5/5 + 49952*u**4/5 + 22477508*u**3/15 + 22179134*u**2/5 + 785*u. Find o, given that i(o) = 0.
-223, -1
Let w(r) be the first derivative of 46 + 1/12*r**3 + 1/2*r**2 + r. Factor w(p).
(p + 2)**2/4
Let d(c) be the second derivative of c**7/12600 - c**6/360 + 17*c**4/12 + 164*c + 1. Let y(o) be the third derivative of d(o). Factor y(b).
b*(b - 10)/5
Suppose 69 + 55 = 16*g + 44. Let d(u) be the third derivative of -1/6*u**4 + 1/30*u**5 + 1/3*u**3 + 0*u + g*u**2 + 0. Determine b, given that d(b) = 0.
1
Let k(n) = 4*n**2 + 20*n - 55. Let r be k(-9). Let g be (r + -95)/(27/(-4)). Factor 0*q + 0*q**3 + 4/9*q**4 + 4/9 - g*q**2.
4*(q - 1)**2*(q + 1)**2/9
Let g(n) be the second derivative of n**5/4 - 455*n**4/12 - 5*n**3/6 + 455*n**2/2 - 12*n + 178. Factor g(w).
5*(w - 91)*(w - 1)*(w + 1)
Suppose 4*t = -2*z + 38, 2*z + 18*t = 19*t + 13. Let h(l) be the first derivative of 0*l + 6*l**3 - 21/8*l**4 - z + 3*l**2. Solve h(n) = 0 for n.
-2/7, 0, 2
Let t(k) be the second derivative of -1/6*k**3 - 9*k**5 - 2 + 0*k**2 + 17/8*k**4 + 36/5*k**6 + 21*k. Factor t(y).
y*(3*y - 2)*(12*y - 1)**2/2
Let r(d) = 1248*d - 178462. Let w be r(143). Factor 1/2 + 0*b - 1/2*b**w.
-(b - 1)*(b + 1)/2
Let b(l) be the second derivative of l**6/24 + 69*l**5/2 + 21385*l**4/2 + 4140500*l**3/3 + 22607130*l**2 + 14922*l. Factor b(v).
5*(v + 6)*(v + 182)**3/4
Factor -512/17 - 48/17*k + 2/17*k**2.
2*(k - 32)*(k + 8)/17
Let y(o) = 17*o**3 + 754*o**2 + 987*o + 250. Let s(u) = -19*u**3 - 754*u**2 - 985*u - 250. Let m(z) = -7*s(z) - 8*y(z). Solve m(n) = 0.
-250, -1, -1/3
Solve 13499*t**2 + 1298 - 4492*t**2 - 4502*t**2 - 260*t - 4500*t**2 - 123 = 0 for t.
5, 47
Factor 9/2 - 37/2*b**2 + 45/4*b + 11/4*b**3.
(b - 6)*(b - 1)*(11*b + 3)/4
Let h(w) be the second derivative of -w**7/21 + 16*w**6/15 + 39*w**5/10 - 25*w**4/3 - 76*w**3/3 + 72*w**2 + w + 190. Let h(a) = 0. What is a?
-2, 1, 18
Factor 27*n + 1/2*n**2 - 55/2.
(n - 1)*(n + 55)/2
Let j(h) be the second derivative of 5*h**4/21 + 272*h**3/7 - 328*h**2/7 + 397*h - 2. Suppose j(m) = 0. What is m?
-82, 2/5
Suppose -22 = 5*m + 8, -3*a - 3 = 5*m. Factor -4 + 1/2*r**4 + 0*r**3 - a*r - 11/2*r**2.
(r - 4)*(r + 1)**2*(r + 2)/2
Let v(h) be the third derivative of -h**6/24 - 17*h**5/12 + 2105*h**4/24 - 2015*h**3/6 - 10*h**2 - 3*h. Determine p, given that v(p) = 0.
-31, 1, 13
Let a = -350 - -352. Suppose 2*n = -7*x + 6*x + 8, 15 = 3*n + 3*x. Let 1/5*p + 1/5*p**n + 0 - 2/5*p**a = 0. What is p?
0, 1
Let p = -956555/7 - -136651. Factor p + 1/7*f**2 + 3/7*f.
(f + 1)*(f + 2)/7
Suppose -16 + 276/7*r + 10/7*r**2 = 0. What is r?
-28, 2/5
Let d(x) = 4*x + 30. Suppose 28*o - 21 = 31*o. Let t be d(o). Solve 66*g + 61*g - 133*g + 3*g**t = 0.
0, 2
Suppose -2*f - 2 = -u, 2 = f + 4*u + 3. Let y(z) = 4*z**2 - 10*z - 11. Let c(x) = x**2 - x - 1. Let j(k) = f*y(k) + 5*c(k). Let j(i) = 0. Calculate i.
-3, -2
Let v(i) be the third derivative of -i**7/840 - 59*i**6/480 - 1003*i**5/240 - 1287*i**4/32 - 243*i**3/2 + 3*i**2 - 146*i. Factor v(z).
-(z + 1)*(z + 4)*(z + 27)**2/4
Let v(t) be the first derivative of 16/25*t**5 - 7/10*t**4 + 0*t**2 - 65 + 0*t + 4/15*t**3 - 1/5*t**6. Solve v(h) = 0.
0, 2/3, 1
Factor -22 + 25 - 57 - 45*g - 22*g**3 + 7*g**3 + 66*g**2.
-3*(g - 3)*(g - 2)*(5*g + 3)
Let u(q) = -31*q**3 + 814*q**2 - 13*q + 78. Let h(g) = -14*g**3 + 408*g**2 - 6*g + 36. Let b(s) = 13*h(s) - 6*u(s). Factor b(m).
4*m**2*(m + 105)
Let c(l) = 11*l**4 - 4*l**3 - 7*l**2. Let a(t) = t**4 - t**2. Let v(o) = -20*o - 18*o + 17 + 45*o. Let p be v(-5). Let x(n) = p*a(n) + 2*c(n). Factor x(g).
4*g**2*(g - 1)**2
Let v be (-8)/(-22)*2/4 - 91542/(-79497). Solve -4/3*y**5 + 4*y**3 + 0 - v*y**2 + 4/3*y**4 - 8/3*y = 0.
-1, 0, 1, 2
What is m in 3/5*m**5 + 0*m + 132/5*m**2 - 52*m**3 + 91/5*m**4 + 0 = 0?
-33, 0, 2/3, 2
Factor -309*i + 3*i**3 - 15*i**2 + 63 - 244*i + 502*i.
3*(i - 7)*(i - 1)*(i + 3)
Let m(y) be the third derivative of y**7/210 + 83*y**6/24 - 1263*y**5/20 + 3807*y**4/8 - 1908*y**3 + 179*y**2 - y. Factor m(w).
(w - 3)**3*(w + 424)
Let g = -21 - -15. Let z(d) = 6 + 0 + d**3 - 7 - d. Let l(h) = -5*h**3 - 2*h**2 + 7*h + 6. Let c(i) = g*z(i) - l(i). Find k, given that c(k) = 0.
0, 1
Let h(u) = 2*u**2 + 70*u + 72. Let b be h(-34). Factor 25*s + 47*s**3 + 80*s**2 + 5*s**5 - 19*s**b + 59*s**4 + 43*s**3.
5*s*(s + 1)**3*(s + 5)
Let a(b) = b**2 + b - 1. Let n(o) = 42*o + 61*o**2 + o**3 - 45 - 29*o**2 - 33*o**2. Let l(y) = -18*a(y) + 2*n(y). Factor l(x).
2*(x - 4)*(x - 3)**2
Let k be 1 - ((-216)/(-16) + -13). Let t(v) be the first derivative of 14 + 2*v - 2/3*v**3 - k*v**4 + v**2. What is s in t(s) = 0?
-1, 1
Let s = 119173/99315 + 1/19863. Factor 6*r**2 + 24/5 - s*r**3 - 48/5*r.
-6*(r - 2)**2*(r - 1)/5
Let n(j) = j**3 + 6*j**2 + 5*j - 12. Let l be n(-4). Let z be l + 5 + (-7 - -2). Suppose -2/9*v**3 + 0*v**2 + 1/9*v**5 + z*v - 1/9*v**4 + 0 = 0. What is v?
-1, 0, 2
Let t = -208701 - -417483/2. Factor 3/8*l**2 + t*l + 2187/2.
3*(l + 54)**2/8
Let c(p) = -19*p**5 - 30*p**4 - 14*p**3 + 8*p**2 + 3*p - 2. Let r(u) = 21*u**5 + 32*u**4 + 15*u**3 - 7*u**2 - u + 3. Let v(d) = 7*c(d) + 6*r(d). Factor v(x).
-(x - 1)*(x + 1)**3*(7*x + 4)
Let m be (3/10)/(5/20). Suppose -3*l = 5*o - 50, -3*l + 16*o = 13*o + 6. What is g in 0 + 0*g - 2*g**4 + m*g**l + 2/5*g**3 + 2/5*g**2 = 0?
-1/3, 0, 1
Let j(i) be the third derivative of -1/180*i**5 + 0 + 13/36*i**4 - 169/18*i**3 - 39*i**2 + 0*i. Factor j(l).
-(l - 13)**2/3
Let d(k) be the first derivative of -k**6/60 - k**5/6 - 7*k**4/12 - k**3 - 3*k**2 + 28. Let c(h) be the second derivative of d(h). Solve c(z) = 0.
-3, -1
Let r(g) be the second derivative of 3*g**7/7 - 7*g**6/2 - 36*g**5/5 - 7*g**4/4 + 203*g. Suppose r(j) = 0. Calculate j.
-1, -1/6, 0, 7
Let n be 69*(-4 - (-4)/(-6) - -5). Solve -45 - 5*y**2 + 17*y + y - 45*y - n*y = 0 for y.
-9, -1
Let m be 27/60 + (-12)/48. Let x(p) be the first derivative of 3/25*p**5 + 3/10*p**2 - 3/20*p**4 + 0*p - m*p**3 + 5. Suppose x(d) = 0. Calculate d.
-1, 0, 1
Let g = -851339 + 851483. Factor 312/5*o - g - 44/5*o**2 + 2/5*o**3.
2*(o - 10)*(o - 6)**2/5
Let i = 51557/1544910 + -2/51497. Let n(t) be the second derivative of -2*t**2 + 13/6*t**3 - 3*t - i*t**6 + 7/20*t**5 - 5/4*t**4 + 0. What is z in n(z) = 0?
1, 4
Let i(f) = -f + 8. Let j be i(5). Let -12*r**5 - 12594*r**3 + j*r - 58*r**4 + 12516*r**3 - 9*r - 38*r**2 = 0. Calculate r.
-3, -1, -1/2, -1/3, 0
Let b(r) = 6*r**2 - 453*r + 420. Let c(j) = -j**2 + 5*j - 1. Let g(q) = b(q) + 9*c(q). Factor g(w).
-3*(w - 1)*(w + 137)
Let h(v) be the second derivative of -v**8/60480 - v**7/11340 - v**6/6480 + 2*v**4 + 86*v. Let a(z) be the third derivative of h(z). Factor a(o).
-o*(o + 1)**2/9
Let w(d) be the first derivative of -49 + 48*d - 14/3*d**4 + 244/9*d**3 + 4/15*d**5 - 56*d**2. Find x, given that w(x) = 0.
1, 6
Let c = -33 + -25. Let x be 78/63 - c/(-87). Factor 0 + 4/7*l**2 + 2/7*l + 0*l**3 - x*l**4 - 2/7*l**5.
-2*l*(l - 1)*(l + 1)