a) be the second derivative of a**4/15 - 244*a**3/5 + 66978*a**2/5 - 3*a - 11. Factor t(b).
4*(b - 183)**2/5
Let u(x) be the third derivative of x**2 + 1/75*x**5 - 1/30*x**4 + 0 + 0*x + 0*x**3 - 1/600*x**6. Find o such that u(o) = 0.
0, 2
Factor 0 + 1/5*k**2 + 19/10*k**3 + 0*k.
k**2*(19*k + 2)/10
Let g(b) be the second derivative of 0 + 2/35*b**5 + 2/7*b**2 + 1/21*b**4 + 1/147*b**7 - 4/105*b**6 + 29*b - 5/21*b**3. What is j in g(j) = 0?
-1, 1, 2
Let q be 20/(-6)*350/(-875). Factor 2/3*l**2 - q*l + 2/3*l**3 + 0.
2*l*(l - 1)*(l + 2)/3
Let x(a) be the first derivative of -a**4/7 - 16*a**3/21 + 50*a**2/7 + 16*a + 744. Determine g, given that x(g) = 0.
-7, -1, 4
Let x = 14564 + -101947/7. Solve x*p**2 - 1/7*p**5 + 0 + 1/7*p**3 - 1/7*p**4 + 0*p = 0 for p.
-1, 0, 1
Factor 74*y - 507*y**2 + 189*y**2 + 15*y**3 + 133*y**2 - 55 + 151*y.
5*(y - 11)*(y - 1)*(3*y - 1)
Let n(r) be the first derivative of r**4/2 + 296*r**3/9 + 193*r**2/3 + 32*r + 353. Factor n(l).
2*(l + 1)*(l + 48)*(3*l + 1)/3
Solve -1/4*j**5 + 0*j + 0 + 0*j**2 - 1/4*j**4 + 0*j**3 = 0 for j.
-1, 0
Let i(u) = u**3 - u**2 - u - 1. Suppose z - 2 = -0*z. Let v(o) = -6*o - 3*o**3 + 30 - 2*o**3 - 5*o**z - o**3 - 7*o**2. Let k(q) = -3*i(q) - v(q). Factor k(p).
3*(p - 1)*(p + 3)**2
Let c = -14222 - -14224. Factor 6/7*o**3 + 3/7*o**c + 0 + 0*o + 3/7*o**4.
3*o**2*(o + 1)**2/7
Let p(j) = 3*j**2 - 3*j - 4. Let l(m) = 4. Let y(g) = 1. Let z(n) = l(n) - 3*y(n). Let t = 42 + -46. Let k(f) = t*z(f) - p(f). Factor k(a).
-3*a*(a - 1)
Find c, given that 35/2 - 160*c**3 + 200*c**2 + 130*c = 0.
-1/4, 7/4
Let z(a) be the second derivative of -a**6/6 + 27*a**5/2 - 1215*a**4/4 - 2*a + 15. Factor z(p).
-5*p**2*(p - 27)**2
Let q(n) = n**4 - n**2 - n. Let p(c) = -6*c**4 + 11*c**2 - 3*c + 21. Let s(t) = p(t) + 5*q(t). Let d(m) be the first derivative of s(m). Factor d(a).
-4*(a - 1)**2*(a + 2)
Let a(g) be the first derivative of -g**4/10 + 22*g**3/5 - 32*g**2/5 + 65. Factor a(t).
-2*t*(t - 32)*(t - 1)/5
Let d = 2/1369 + 8180/23273. Let d*q + 4/17 + 2/17*q**2 = 0. What is q?
-2, -1
Suppose 2*h - 26 = -20. Find l such that 51*l**2 + 16*l**h + 4*l + l - 31*l**2 - l = 0.
-1, -1/4, 0
Suppose -4*k = -2*w - 18, -w + 3 = -2*w. Suppose -3*r = 3*o, k*r - r = 4*o. Factor -24/5*i**2 + 12*i**4 + 10*i**5 + r + 8/5*i - 22/5*i**3.
2*i*(i + 1)**2*(5*i - 2)**2/5
Factor -142/3 - 2/3*l**2 - 48*l.
-2*(l + 1)*(l + 71)/3
Let n(f) be the first derivative of -f**2/2 + 6*f - 40. Let o be n(4). What is c in 2/3 - 6*c**3 + 10*c**o - 14/3*c = 0?
1/3, 1
Let d(z) = z**4 + 7*z**2 - 6. Let u(s) = -s**2 + 1. Let k(n) = -d(n) - 4*u(n). Let g(m) = 3*m**4 + 6*m**2 + m - 5. Let c(x) = 2*g(x) + 5*k(x). Factor c(l).
l*(l - 1)**2*(l + 2)
Let p(j) = -11*j**2 + 69*j + 180. Let c(i) = -5*i**2 + 33*i + 90. Let k(b) = -7*c(b) + 3*p(b). Factor k(d).
2*(d - 15)*(d + 3)
Let x(v) be the second derivative of -2*v**7/105 + 2*v**5/5 - 4*v**4/3 + 2*v**3 - 8*v**2/5 + 15*v + 1. Find z, given that x(z) = 0.
-4, 1
Let f = -1173 - -5869/5. Let r(p) be the first derivative of 0*p - 4/3*p**3 - p**4 + f*p**5 + 2*p**2 + 6. Factor r(g).
4*g*(g - 1)**2*(g + 1)
Let o(d) be the third derivative of d**6/20 - 23*d**5/30 + 37*d**4/12 - 17*d**3/3 - 4*d**2 + 72*d. Suppose o(s) = 0. Calculate s.
1, 17/3
Let g(v) be the first derivative of 1/3*v**3 + 7/2*v**2 + 0*v + 17. What is y in g(y) = 0?
-7, 0
Let 0*m + 1/3*m**4 - 4*m**2 + 0 - 4/3*m**3 = 0. Calculate m.
-2, 0, 6
Let r(x) be the third derivative of 27/8*x**4 + 0*x + 0 - 27/2*x**3 + 1/40*x**6 - 9/20*x**5 - 10*x**2. Factor r(m).
3*(m - 3)**3
Factor 14*i**3 - 4*i**2 + i**4 + 10*i**2 + 9*i**5 + 9*i**4 - 7*i**5.
2*i**2*(i + 1)**2*(i + 3)
Let t(f) = 112*f + 4260. Let y be t(-38). Suppose -4/5*p**y + 4/5*p**2 - 2/5*p**5 + 0*p**3 + 2/5*p + 0 = 0. What is p?
-1, 0, 1
Let n(t) be the first derivative of -t**4/10 + 4*t**3/15 - 216. Suppose n(f) = 0. Calculate f.
0, 2
Let p be (((-126)/(-5))/(-21))/(99/(-60)). Factor -p - 10/11*y - 2/11*y**2.
-2*(y + 1)*(y + 4)/11
Let p be 87/12 - ((-15)/20)/1. Factor -24*b - 3*b**2 - p*b**2 - 20 + 2*b**2 - b**3.
-(b + 2)**2*(b + 5)
Suppose -101/5*a**3 - 4*a - a**5 + 42/5*a**4 + 0 + 84/5*a**2 = 0. What is a?
0, 2/5, 1, 2, 5
Suppose -5*x + 77 = 47. Factor 4*c**2 + 846*c**4 - 846*c**4 - x*c**3 + 2*c**5.
2*c**2*(c - 1)**2*(c + 2)
Let l(f) be the second derivative of 4*f**5/35 + f**4/14 - 8*f**3/21 - 3*f**2/7 - f - 19. Factor l(s).
2*(s - 1)*(s + 1)*(8*s + 3)/7
Let g = 78 - 73. Suppose s**2 - 7*s + 7*s**2 - 4*s**g - 3*s**4 + 5*s**5 + 2 - 2*s**3 + s**4 = 0. Calculate s.
-2, 1
Let w = -39/85 - -18/17. Let h(k) be the first derivative of 0*k**2 - 3/2*k**4 - 5 + w*k**5 + 0*k + k**3. Solve h(n) = 0.
0, 1
Suppose 15*d - 10 = 10*d, 3*d = 5*x + 6. Let v(c) be the first derivative of 1/4*c**4 + x*c**3 + 1/10*c**5 + 0*c + 0*c**2 + 4. Factor v(r).
r**3*(r + 2)/2
Let p(g) be the first derivative of 4*g**5/5 - 25*g**4/2 + 54*g**3 - 216*g + 590. Factor p(m).
2*(m - 6)**2*(m + 1)*(2*m - 3)
Let c be ((-4)/(-355))/(14*(-1)/(-5155)). Let b = c + 30/71. Find z, given that 16/7*z - 2/7*z**2 - b = 0.
4
Let y = 8427/22 + -383. Let w(i) be the first derivative of -y*i**4 + 6 + 0*i**2 + 0*i + 4/33*i**3 - 2/55*i**5. Factor w(c).
-2*c**2*(c - 1)*(c + 2)/11
Let v(x) = 10*x**4 + 14*x**3 - 8*x + 20. Let l(c) = -12*c**4 - 15*c**3 - c**2 + 8*c - 22. Let o(g) = 6*l(g) + 7*v(g). Factor o(z).
-2*(z - 2)**2*(z - 1)*(z + 1)
Let c(n) be the first derivative of -n**3/12 + 29*n**2/8 - 27*n/2 - 55. Let c(r) = 0. Calculate r.
2, 27
Let o(r) = r**2 - 16*r - 13. Let c be o(16). Let n = -11 - c. Factor -n - 3*y**2 - 2*y**2 - 20*y - 12 - 1.
-5*(y + 1)*(y + 3)
Let q(a) be the third derivative of -a**7/504 - a**6/144 - 11*a**4/24 - 24*a**2. Let t(f) be the second derivative of q(f). Solve t(l) = 0.
-1, 0
Let i(s) be the second derivative of -s**5/4 - 45*s**4/4 - 405*s**3/2 - 3645*s**2/2 - 7*s - 1. Solve i(r) = 0.
-9
Determine h so that -26/5*h + 14/5 - 46/5*h**2 - 6/5*h**3 = 0.
-7, -1, 1/3
Factor -174*t + 84 - 106*t - t**2 - 268 + 7*t**2 + 8*t.
2*(t - 46)*(3*t + 2)
Suppose -3*o + 21 = 3*r, -4*r + 5 + 2 = -3*o. Suppose -4*p + 4*y - 5 = -1, y - 1 = -r*p. Factor p*w**2 + w + 2*w**3 - 2*w**2 - w**3.
w*(w - 1)**2
Suppose 63 + 126 = 63*u - 0. Factor 0*c**2 + 2/7*c**u - 2/7*c + 0.
2*c*(c - 1)*(c + 1)/7
Factor -88/3 - 2/3*i**2 - 16*i.
-2*(i + 2)*(i + 22)/3
Factor 0*w + 0 + 27*w**2 - 3/4*w**3.
-3*w**2*(w - 36)/4
Let i(y) be the first derivative of 5*y**4/4 - 10*y**3/3 + 68. Factor i(j).
5*j**2*(j - 2)
Let l(m) be the first derivative of 3*m**4/28 + 2*m**3 - 324. Find k, given that l(k) = 0.
-14, 0
Let j = 1130/861 + -46/41. Let l(z) be the second derivative of -5*z - 1/42*z**4 - 4/7*z**2 + 0 + j*z**3. Factor l(s).
-2*(s - 2)**2/7
Let u = -6411/2 + 12823/4. Factor -1/4*d**2 + u*d + 0.
-d*(d - 1)/4
Let x(k) be the first derivative of -k**6/3 + 84*k**5/25 - k**4/10 - 272*k**3/15 + 132*k**2/5 - 64*k/5 - 305. Let x(h) = 0. What is h?
-2, 2/5, 1, 8
Suppose -2*p + 583 = w, -6*w + p = -5*w - 577. Let l = 6387/11 - w. Factor l*d + 4/11 + 8/11*d**2.
2*(d + 2)*(4*d + 1)/11
Let q = -9 + 5. Let l = 8 + q. Solve 0*f - 2*f**l + 0*f + 3*f**2 - f**4 = 0 for f.
-1, 0, 1
Suppose 11*o - 60 = -60. Let j(b) be the second derivative of -1/48*b**4 - 1/2*b**2 + 1/6*b**3 + o + 10*b. Determine n so that j(n) = 0.
2
Let x(j) = -j**3 + 8*j**2 + 11*j - 13. Let c be x(9). Suppose -c*w = 1 - 11. Factor -w*d**2 + 1 + 6*d**2 + 12*d - 8 - 9.
4*(d - 1)*(d + 4)
Let p(f) be the second derivative of f**7/420 + f**6/72 - f**5/30 - f**4/8 + f**3 + 8*f. Let a(x) be the second derivative of p(x). Factor a(n).
(n - 1)*(n + 3)*(2*n + 1)
Factor 0 + 17/4*c - 1/8*c**2.
-c*(c - 34)/8
Let h(z) be the first derivative of 1/28*z**4 + 1/42*z**6 - 2/35*z**5 + 6 + 0*z**2 + 0*z**3 + 0*z. Factor h(g).
g**3*(g - 1)**2/7
Let h(w) = w**2 + 10*w + 11. Let a be h(-9). Factor 3/2 + 5/4*u**a + 17/4*u.
(u + 3)*(5*u + 2)/4
Let t(g) be the second derivative of -g**7/3360 - g**6/240 - g**5/40 + 5*g**4/6 - g. Let l(z) be the third derivative of t(z). Factor l(r).
-3*(r + 2)**2/4
Let m be (8 + (1 - -3))*2. Let r be (-3)/(-18) - (-140)/m. Factor 5 - r + 2 + w**2 - 2*w + 0.
(w - 1)**2
Let q = -63 + 87. Let x be (-2 + 93/q)*8/20. Solve -x*k**5 + 0 - 6*k**3 + 0*k - 15/4*k**4 - 3*k**2 = 0 for k.
-2, -1, 0
Let f = -32 + 35. Suppose -4*t**2 - t