3 + 3/20*m**5 - 12*m. Let c(z) be the first derivative of j(z). Factor c(d).
3*d*(d - 1)*(d + 1)
Let w(s) be the first derivative of -1/8*s**4 + 0*s**3 + 0*s + 1/8*s**2 + 1/24*s**6 - 56 + 0*s**5. Factor w(b).
b*(b - 1)**2*(b + 1)**2/4
Let f = -9688977/23 + 421335. Factor -80/23*c**3 + 864/23*c - 288/23*c**2 + f + 28/23*c**4 - 2/23*c**5.
-2*(c - 6)**3*(c + 2)**2/23
Let g(t) = -t**3 + 12*t**2 + 30*t - 26. Let z = -979 + 993. Let d be g(z). Find o, given that 1/3*o**d + 0 - 1/3*o**3 - 1/3*o**4 + 1/3*o = 0.
-1, 0, 1
Let w(h) be the first derivative of h**3/9 + 96*h**2 + 5677. Suppose w(d) = 0. What is d?
-576, 0
Let d(r) = -21*r**3 - 26*r**2 - 19*r - 21. Let t(x) be the first derivative of -x**4/2 - x**3/3 + x**2/2 - x + 48. Let b(y) = -2*d(y) + 18*t(y). Factor b(c).
2*(c + 2)*(c + 3)*(3*c + 2)
Let y(v) be the third derivative of -v**6/72 - 31*v**5/12 - 4805*v**4/24 - 37*v**3/3 + 6*v**2 + 3*v. Let h(i) be the first derivative of y(i). Factor h(a).
-5*(a + 31)**2
Let b be (-3 + -1)/((-1470)/210). Factor -4/7*a + 8/7*a**3 + b - 8/7*a**2 + 4/7*a**4 - 4/7*a**5.
-4*(a - 1)**3*(a + 1)**2/7
Suppose 0 = 5*h + 25, 4*k - 8*k - 3*h - 7 = 0. Suppose 2*o - b - 22 = -3*o, k*b - 11 = -o. Solve 0*v**3 - 4/9*v - 8/9*v**2 + 0 + 4/9*v**o + 8/9*v**4 = 0 for v.
-1, 0, 1
Let u(w) = -w**3 + 1514*w**2 + 1489*w + 52. Let z(a) = 504*a**2 + 496*a + 16. Let p(f) = 4*u(f) - 13*z(f). Let p(l) = 0. Calculate l.
-123, -1, 0
Let o(a) be the first derivative of -9/28*a**4 + 9/14*a**2 + 83 + 2/7*a + 2/21*a**3 - 4/35*a**5. Let o(d) = 0. Calculate d.
-2, -1, -1/4, 1
Let 169*i + 1008 - 411*i**4 + 4528*i**2 - 1276*i**3 - 2222*i - 9*i**5 - 1955*i - 953*i + 1121*i = 0. Calculate i.
-42, -6, 2/3, 1
Suppose -5*r - 6*z = -2*z - 355, 0 = z + 5. Suppose 21*g - 180 + r = 0. Factor -i**4 + 0 + 0*i + 0*i**2 + 1/4*i**g + 3/4*i**3.
i**3*(i - 3)*(i - 1)/4
Factor -126/5*f + 36 + 28/5*f**2 - 2/5*f**3.
-2*(f - 6)*(f - 5)*(f - 3)/5
Let b(x) = 7*x**2 - 313*x + 5776. Let c(w) = -4*w**2 - 2*w - w + 7*w**2 - 2*w**2 + 0*w. Let m(t) = -b(t) + 3*c(t). Factor m(u).
-4*(u - 38)**2
Suppose 0 = x - 4*r + 6, -3*x - 6 = 3*r - 18. Factor -11*a + 6*a - 99*a**2 + 11*a + 122*a**x + 15*a**3.
a*(3*a + 1)*(5*a + 6)
Let m be (-14)/(-2) + -3 + -1. Suppose -71 = -m*k + 241. Factor -798*o**4 - 528*o + k*o**5 - 91 - 240*o**2 - 5 + 22*o**5 + 1272*o**3 + 21*o**5.
3*(o - 2)**3*(7*o + 2)**2
Let r(u) = 7*u**2 - 14. Let q be r(0). Let n be ((-48)/q)/((-7)/(-49)). Factor 12*x + n + 3/2*x**2.
3*(x + 4)**2/2
Let n(v) be the third derivative of -v**5/180 + v**4/4 + 595*v**3/18 + 450*v**2 + 2*v + 1. Factor n(r).
-(r - 35)*(r + 17)/3
Factor 0*h**2 + 16/3*h**4 + 0*h + 0 - 2/3*h**5 - 14/3*h**3.
-2*h**3*(h - 7)*(h - 1)/3
Let r(m) be the second derivative of 3*m**5/20 + 7*m**4 + 25*m**3/2 - 81*m**2 + 4480*m. Factor r(s).
3*(s - 1)*(s + 2)*(s + 27)
Factor 57/2 + 28*r**3 - 28*r + 1/2*r**4 - 29*r**2.
(r - 1)**2*(r + 1)*(r + 57)/2
Let v(k) be the second derivative of 8/5*k**2 - 32/15*k**3 - 57*k + 11/25*k**5 + 0 - 1/30*k**7 - 1/30*k**6 + 4/15*k**4. Suppose v(n) = 0. What is n?
-2, 2/7, 1, 2
Let g(v) be the third derivative of v**6/420 + v**5/42 - 22*v**4/21 + 208*v**3/21 - 281*v**2. Factor g(b).
2*(b - 4)**2*(b + 13)/7
Let w(m) be the second derivative of -7/5*m**5 + 16*m**2 + 10*m + 2/15*m**6 - 4 - 40/3*m**3 + 6*m**4. Factor w(d).
4*(d - 2)**3*(d - 1)
Let q(m) be the third derivative of -m**5/510 - 49*m**4/51 - 9604*m**3/51 - 932*m**2. Factor q(x).
-2*(x + 98)**2/17
Factor 47/2*u**2 + 525 - 1/4*u**3 - 865/4*u.
-(u - 84)*(u - 5)**2/4
Let x(d) be the first derivative of -3*d**5/5 + 3*d**4/2 + 75*d**3 + 372*d**2 + 528*d + 8221. Factor x(n).
-3*(n - 11)*(n + 1)*(n + 4)**2
Let c(q) be the third derivative of q**5/15 + 746*q**4/3 + 1113032*q**3/3 - 1914*q**2. Factor c(z).
4*(z + 746)**2
Let h(t) be the third derivative of 0*t - 24*t**2 + 1/8*t**4 + 2/35*t**7 + 0*t**3 - 7/40*t**6 + 2 + 1/10*t**5. Factor h(w).
3*w*(w - 1)**2*(4*w + 1)
Suppose -1873 + 1881 = 2*s + 2*a, 2*a - 14 = -5*s. Factor t**3 + 7/4 - 27/4*t + 6*t**s.
(t + 7)*(2*t - 1)**2/4
Let f(o) = 55*o + 387. Let v be f(-7). Let x(b) be the second derivative of 3*b**v + 0 - 1/6*b**4 - 2/3*b**3 - 17*b. Factor x(z).
-2*(z - 1)*(z + 3)
Suppose 9*j + j = 140. Let z(y) be the first derivative of -7*y + j*y**3 - 5*y - 14 - 13*y**3 - 1. Suppose z(m) = 0. Calculate m.
-2, 2
Find j, given that -313*j**4 + 32*j**2 - j**5 + 21*j**3 + 315*j**4 - 14*j**2 = 0.
-3, -1, 0, 6
Let s = 108 + -51. Solve -128*n**2 - 16*n**2 - 180*n - 24 - s*n**2 + 39*n**2 - 39*n**3 = 0 for n.
-2, -2/13
Let w(k) = 76*k**2 + 70*k + 4. Let s(h) = -h**3 + 229*h**2 + 209*h + 14. Let r(u) = -2*s(u) + 7*w(u). Factor r(a).
2*a*(a + 1)*(a + 36)
Let z(l) be the second derivative of 0 + 6*l**2 + 22*l**3 + 153/4*l**4 + 243/10*l**5 - 148*l. Let z(u) = 0. Calculate u.
-1/2, -2/9
Suppose -3*t + 5*y + 49 = 0, -t = -4*y - 13 - 15. Factor -4*x**5 + 2*x**5 + 7*x**2 - t*x**4 + 115*x + 400 + 10*x**3 + 69*x**2 + 36*x**3 - 555*x.
-2*(x - 2)**3*(x + 5)**2
Let q(c) = -c**2 - 11*c + 15. Let a = 766 + -778. Let l be q(a). Factor -2/11*o + 0 - 3/11*o**2 - 1/11*o**l.
-o*(o + 1)*(o + 2)/11
Let g = -8/112379 + 337169/449516. Factor 33/8*h - g*h**2 + 15.
-3*(h - 8)*(2*h + 5)/8
Suppose 5*p - 4*s = -2*s + 1938, 0 = -p + 5*s + 406. Suppose 390*n = p*n. Factor 1/9*a**5 - 2/9*a**2 - 1/9*a + 2/9*a**4 + n + 0*a**3.
a*(a - 1)*(a + 1)**3/9
Let l(p) be the first derivative of 37/42*p**4 + 0*p - 40/63*p**3 - 12 + 4/21*p**2 - 4/7*p**5 + 1/7*p**6. Factor l(k).
2*k*(k - 1)**2*(3*k - 2)**2/21
Let z(s) be the first derivative of 2/9*s**4 + 0*s**5 + 0*s - 1/27*s**6 - 168 + 0*s**3 + 0*s**2. Factor z(t).
-2*t**3*(t - 2)*(t + 2)/9
Let k be 2/8 + (-81)/4. Let t be (-48)/k - (-4)/(-10). Factor -271 + l**2 + t*l + 271.
l*(l + 2)
Find j, given that 200*j + 0 + 5/11*j**4 + 1022/11*j**3 - 3/11*j**5 + 6940/11*j**2 = 0.
-10, -1/3, 0, 22
Let g(m) = 4*m**3 - 27*m**2 - 52*m - 21. Let u(j) = 52*j + 10*j**2 - 697 - 4*j**3 + 16*j**2 + 719. Let v(p) = 6*g(p) + 7*u(p). Find i such that v(i) = 0.
-1, 7
Let d = -810 - -814. Suppose -1082*o + d = -1081*o. Factor 0 + 0*y + 8/3*y**3 + 4/3*y**5 + 0*y**2 + 4*y**o.
4*y**3*(y + 1)*(y + 2)/3
Let a(v) be the third derivative of v**7/210 + 17*v**6/30 + 11*v**5/5 - 5*v**2 - 191*v. Determine w, given that a(w) = 0.
-66, -2, 0
Let o(a) be the third derivative of 49*a**6/60 + 14*a**5/15 + a**4/3 + 1112*a**2. Factor o(s).
2*s*(7*s + 2)**2
Let y be -1 - (28/(-13) - (-8)/52). Let g be -7*y - 2240/(-315). Find t, given that 1/3*t**2 + 1/3*t + 1/9 + g*t**3 = 0.
-1
Let t(i) be the first derivative of 7*i**6/30 - 36*i**5/5 - 437*i**4/20 - 102*i**3/5 - 28*i**2/5 + 2157. Suppose t(q) = 0. Calculate q.
-1, -2/7, 0, 28
Let l(i) be the third derivative of -i**7/3780 + i**6/180 + 55*i**4/24 - 65*i**2. Let d(o) be the second derivative of l(o). Factor d(m).
-2*m*(m - 6)/3
Let g(m) = 17*m**2 - 403*m + 362. Let y(c) = -11*c**2 + 268*c - 242. Let v(b) = 5*g(b) + 8*y(b). Factor v(d).
-3*(d - 42)*(d - 1)
Determine s so that -2662 - 2/11*s**2 - 44*s = 0.
-121
Let y(i) be the first derivative of i**4/2 - 314*i**3/3 + 154*i**2 + 624*i + 9381. What is p in y(p) = 0?
-1, 2, 156
Let j(t) be the second derivative of -t + 5/2*t**3 + 3/20*t**5 + 75*t**2 + 0 - 2*t**4. Factor j(l).
3*(l - 5)**2*(l + 2)
Let q(j) be the second derivative of -j**6/20 - 357*j**5/40 - 369*j**4 + 8960*j**3 - 24576*j**2 + 2869*j. Solve q(b) = 0.
-64, 1, 8
Let c(v) be the third derivative of v**5/15 - 29*v**4/2 - 356*v**3/3 - 6184*v**2. Factor c(w).
4*(w - 89)*(w + 2)
Let h(d) = 11*d**3 - 15*d**2 + 51*d. Let k(v) = 13*v**3 - 15*v**2 + 50*v. Let o(g) = -6*h(g) + 5*k(g). Factor o(b).
-b*(b - 8)*(b - 7)
Let n = 33310/13503 - -6/643. Let f(z) be the second derivative of 8*z - 67/70*z**5 + 0 + 2/15*z**6 - n*z**3 + 17/7*z**4 + 8/7*z**2. Solve f(l) = 0.
2/7, 1/2, 2
Let u(i) be the second derivative of i**5/20 - 35*i**4/2 + 244*i. Factor u(c).
c**2*(c - 210)
Let c(p) = -p**2 + 7*p + 101. Let s be c(14). Let 2*u**4 - 4*u**3 - 4*u**5 - 6*u**4 - 4*u**s + 8*u**5 = 0. Calculate u.
-1, 0, 2
Factor -13*i**3 + 151 - 52*i - 17*i**3 + 34*i**3 - 199.
4*(i - 4)*(i + 1)*(i + 3)
Let t(j) be the second derivative of -j**6/105 + 17*j**5/70 - 17*j**4/7 + 12*j**3 - 216*j**2/7 - 3340*j. Suppose t(z) = 0. Calculate z.
2, 3, 6
Suppose 4*i = 4*