e the first derivative of 5/8*a**4 + 4 + 10/3*a**3 + 0*a - 1/2*a**2 - 1/12*a**5. Let i(u) be the second derivative of f(u). Factor i(q).
-5*(q - 4)*(q + 1)
Suppose -155*t = -175*t + 60. Factor -5997 - 5*h**t + 222*h**2 + 3*h**3 - 3876*h - 5537 - h**3 + 2870.
-3*(h - 38)**2*(h + 2)
Let h(p) be the second derivative of 149769*p**5/50 + 10191*p**4/2 + 3112*p**3/15 + 16*p**2/5 + 523*p + 2. Factor h(o).
2*(o + 1)*(387*o + 4)**2/5
Let p(w) be the third derivative of 0 + 0*w + 26*w**2 - 1/60*w**6 - 1/4*w**4 + 1/945*w**7 + 10/27*w**3 + 5/54*w**5. Factor p(n).
2*(n - 5)*(n - 2)*(n - 1)**2/9
Let b(r) = 9*r**2 - 2935*r + 2726. Let s(p) = 35*p**2 - 11690*p + 10905. Let u(d) = 15*b(d) - 4*s(d). Factor u(o).
-5*(o - 546)*(o - 1)
Suppose 3/2*g**2 + 113/2*g + 37 = 0. What is g?
-37, -2/3
Let s(b) be the first derivative of b**4/18 - 194*b**3/27 + 94*b**2/9 + 128*b/3 - 3644. Solve s(a) = 0.
-1, 2, 96
Let u be -16 - 646/(-34) - (-34)/(-12). Suppose -1/3*m**3 - 1/6*m**4 - 1/6 + 1/3*m**2 + 1/6*m + u*m**5 = 0. Calculate m.
-1, 1
Let f(k) be the first derivative of -2*k**5/25 - 253*k**4/10 - 502*k**3/15 + 253*k**2/5 + 504*k/5 + 1203. Solve f(b) = 0.
-252, -1, 1
Let b(x) be the second derivative of -x**5/140 - 11*x**4/14 + 67*x**3/42 + 616*x. Factor b(v).
-v*(v - 1)*(v + 67)/7
Let s(t) be the second derivative of -t**6/24 + t**5/4 + 5*t**4/6 - 10*t**3 - 149*t**2 - 42*t + 2. Let p(f) be the first derivative of s(f). Factor p(z).
-5*(z - 3)*(z - 2)*(z + 2)
Let t(z) be the second derivative of 1/9*z**3 + 1/6*z**2 + 1/36*z**4 - 3 - 12*z. Factor t(g).
(g + 1)**2/3
Solve 0 + 0*j - 2/3*j**4 - 260*j**2 - 394/3*j**3 = 0.
-195, -2, 0
Let r(s) be the second derivative of -2519*s**4/48 - s**3/24 - 19*s + 84. Factor r(p).
-p*(2519*p + 1)/4
Let g(d) be the first derivative of d**4 - 320*d**3/3 + 2250*d**2 + 81000*d - 4295. Factor g(s).
4*(s - 45)**2*(s + 10)
Let j be 2*1 + (-122)/(-5 + 3). Let h = j - 47. Factor -17 + b**2 + h + 0*b**2.
(b - 1)*(b + 1)
Let v(l) be the second derivative of l**7/2940 - 23*l**6/315 + 529*l**5/105 - 8*l**3/3 - l**2/2 - 214*l. Let w(r) be the second derivative of v(r). Factor w(h).
2*h*(h - 46)**2/7
Suppose 5*b - 18 + 8 = 0. Let 0*f**4 + 12*f - 15*f**4 - 24 + 18*f**4 - 15*f**3 + 18*f**b = 0. What is f?
-1, 2
Let r(y) = y**2 - 23*y + 2. Let t be r(0). Factor -103*z**t + 249*z**2 - 435*z - 141*z**2 - 440.
5*(z - 88)*(z + 1)
Solve 197/7*s**3 + 0 + 0*s - 9/7*s**5 - 291/7*s**4 - 33/7*s**2 = 0.
-33, 0, 1/3
Solve -216*f**2 - 124/5*f**3 + 8704/5 - 1664/5*f - 4/5*f**4 = 0 for f.
-17, -8, 2
Let v(k) be the second derivative of k**4/3 - 76*k**3/3 - 160*k**2 + 22*k + 33. Find s such that v(s) = 0.
-2, 40
Let v be ((-40)/14)/((-17020)/23828). Determine x so that 4/3*x**3 + 3/2*x + 0 + 3*x**2 - 1/6*x**5 - 1/3*x**v = 0.
-3, -1, 0, 3
Suppose -3*j - 4*q + 9 = -17, -2*j + 2*q + 22 = 0. Factor j - 14/3*t**2 - 2/3*t**3 - 14/3*t.
-2*(t - 1)*(t + 3)*(t + 5)/3
Let w(f) be the second derivative of -f**7/420 - 3*f**6/100 - 7*f**5/100 + 17*f**4/60 + f**3/4 - 5*f**2/4 - 3854*f. Find z, given that w(z) = 0.
-5, -1, 1
Let j = 4485/7 - 640. Let f = 8/7 - j. Solve -f*r**3 - 3/7*r**2 + 6/7*r + 0 = 0 for r.
-2, 0, 1
Factor 5/2*n + 3/2*n**2 + 1/2*n**4 - 2 - 5/2*n**3.
(n - 4)*(n - 1)**2*(n + 1)/2
Solve 2/3*q**3 - 380/3*q**2 + 0 - 382/3*q = 0 for q.
-1, 0, 191
Let n(v) be the first derivative of -3*v**4/2 + 25*v**2 - 62*v + 28. Let l(x) = -13*x**3 + 101*x - 123. Let k(h) = -2*l(h) + 5*n(h). Solve k(u) = 0.
-4, 2
Suppose -128*r - 1186/7*r**2 + 298/7 + 8/7*r**3 = 0. Calculate r.
-1, 1/4, 149
Suppose -30*j**4 - 22 - 55173*j**2 + 0 - 72*j**3 - 2*j**5 + 55033*j**2 - 28*j**3 - 90*j = 0. Calculate j.
-11, -1
Let i be ((-7)/(-15))/(574/1968). Factor 8/5*t + 0 + 2/5*t**3 - i*t**2.
2*t*(t - 2)**2/5
Let p(c) be the third derivative of 0*c + 4/15*c**3 + 1/75*c**6 - 4/15*c**4 - 7 - 1/150*c**5 + 2*c**2. Find s, given that p(s) = 0.
-2, 1/4, 2
Suppose -i - 4*a = 2*i - 4, 5*i + 12 = -2*a. Let h = i - -8. Determine n so that 2*n**4 - 4*n**h - n**4 - 2*n**2 + 5*n**2 = 0.
-1, 0, 1
Let q be 5*(-50)/(-20)*4/(-2). Let r = q + 61. Solve r*k**2 - 147/2*k**4 + 0 - 63/2*k**3 - 6*k = 0.
-1, 0, 2/7
Let h(u) be the first derivative of u**3/3 - 2*u**2 + 7*u + 3. Let w(n) = 74 - 38 - n - 35. Let d(r) = 3*h(r) + 6*w(r). Let d(y) = 0. What is y?
3
Let a = 1264726 - 13911914/11. Let -70/11*h - a + 2/11*h**2 = 0. Calculate h.
-1, 36
Suppose 0 = -5*n - 4*i + 41, 10 = -5*n + 5*i + 15. Let v(u) be the first derivative of 11 + 0*u**n + 1/4*u**4 - 1/6*u**6 + 0*u**3 + 0*u**2 + 0*u. Factor v(j).
-j**3*(j - 1)*(j + 1)
Let t(i) = i**2 - 8*i - 18. Let z be t(-14). Let f = z - 288. Let 0*d + 0*d**f + 4/9*d**4 + 4/9*d**3 + 0 = 0. What is d?
-1, 0
Let g(p) be the first derivative of -p**4/4 - 122*p**3/3 + 125*p**2/2 + 246*p + 7559. Factor g(u).
-(u - 2)*(u + 1)*(u + 123)
Let w be -6 - -41 - (-3296)/(-96). Solve 2/3*j**4 + 2/3*j**5 - 2/3*j**2 + 0 - w*j**3 + 0*j = 0 for j.
-1, 0, 1
Let w(t) = -6547*t + 2. Let n be w(0). Let 2/3*d**3 + 0*d**n - 2/3*d + 0 = 0. What is d?
-1, 0, 1
Suppose 6*i - 45 - 57 = 0. Find d such that -i + 3*d**4 - 2*d**3 - 5*d**4 - 15 - 8*d + 10*d**3 + 36*d**2 - 2*d**4 = 0.
-2, -1, 1, 4
Let o(l) be the second derivative of 1/120*l**6 - 2*l - 17/12*l**3 + 3/20*l**5 + 27 - 1/16*l**4 + 3*l**2. Factor o(b).
(b - 1)**2*(b + 2)*(b + 12)/4
Let k be (15 - 1012/66)*48/(-72). Factor -98*x**3 + 82/9*x + k + 266/3*x**2.
-2*(x - 1)*(21*x + 1)**2/9
Let h = 617 - 617. Suppose h = -332*i + 338*i. Determine r so that -4/5*r**4 + i*r + 0 - 16/5*r**3 - 16/5*r**2 = 0.
-2, 0
Suppose 4*f = -f + 45. Suppose 6*t + f*t = 75. Factor -13*z + 17*z - 5*z**5 + 9*z**t - 8*z**3.
4*z*(z - 1)**2*(z + 1)**2
Let r(w) = w**4 + 2*w**3 + 47*w**2 - w + 1. Let n(c) = 3*c**4 + 30*c**3 + 35*c**2 + 376*c - 304. Let a(v) = -n(v) + 4*r(v). Factor a(s).
(s - 11)*(s - 7)*(s - 2)**2
Suppose 2651 + 2901 = -16*p. Let y = p - -349. Let 0 - 2/5*x**4 + 6/5*x + y*x**2 + 2/5*x**3 = 0. What is x?
-1, 0, 3
Let s be (-37)/222*((-12)/4 - 22). Let z(j) be the third derivative of 5/12*j**4 + 0*j - s*j**3 - 1/60*j**5 - 9*j**2 + 0. Suppose z(c) = 0. Calculate c.
5
Let f(s) be the third derivative of 11*s**5/30 - s**4/12 + 898*s**2. Solve f(u) = 0.
0, 1/11
Let b(n) be the first derivative of -n**4/6 + 30*n**3 - 2025*n**2 + 73*n - 227. Let y(j) be the first derivative of b(j). Factor y(i).
-2*(i - 45)**2
Let i(t) be the first derivative of -t**4 + 52*t**3 - 630*t**2 + 2900*t - 2719. Factor i(q).
-4*(q - 29)*(q - 5)**2
Let h(w) be the second derivative of -w**4/21 + 64*w**3/21 - 384*w**2/7 - 180*w + 4. Factor h(f).
-4*(f - 24)*(f - 8)/7
Let n be ((-3)/(-6))/(1248/1664). Determine h so that -n - 2/3*h**2 + 4/3*h**4 - 3*h + 3*h**3 = 0.
-2, -1, -1/4, 1
Let d(m) be the third derivative of m**5/160 + 47*m**4/64 + 45*m**3/8 - m**2 + 65*m - 2. Suppose d(a) = 0. What is a?
-45, -2
Let 43/2*m**2 + 39/4*m**3 + 14 - 25/4*m**4 - 39*m = 0. Calculate m.
-2, 14/25, 1, 2
Let u(f) be the second derivative of 0 + 4/27*f**3 + 1/54*f**4 + 30*f + 1/3*f**2. Find n, given that u(n) = 0.
-3, -1
Let d(n) be the second derivative of -n**6/30 - 7*n**5/20 + n**4/4 + 23*n**3/6 + 7*n**2 + 403*n. What is h in d(h) = 0?
-7, -1, 2
Let g be (-5)/(-15)*(3 - -2)*(3345/(-225) - -15). Let -g*f**5 - 2/9*f**3 + 0*f**2 + 0 + 0*f + 4/9*f**4 = 0. Calculate f.
0, 1
Let h(p) be the third derivative of -2*p**7/105 - 3*p**6/5 + 136*p**5/15 - 32*p**4 + 1022*p**2 - 3*p + 1. Solve h(j) = 0.
-24, 0, 2, 4
Let m(w) be the second derivative of -7 + 4*w + 40/3*w**3 + 1/4*w**5 + 0*w**2 + 10/3*w**4. Factor m(a).
5*a*(a + 4)**2
Let k(u) = -u**2 - 21*u + 78. Let r be k(-24). Let w be (r + -1)/((-2)/((-32)/104)). Find t, given that w + 2/13*t**3 + 14/13*t**2 + 22/13*t = 0.
-5, -1
Factor 2/3*s**2 + 32/3*s - 38.
2*(s - 3)*(s + 19)/3
Suppose -2*u = 2*c - 108, 6*u - 3*u + 15 = 0. Factor 11*r - 5*r**4 + c*r + 30 - 15*r**3 + 15*r**2 - 15*r + 0*r**4.
-5*(r - 2)*(r + 1)**2*(r + 3)
Let t be 3/((-21)/(-35)) + -1*11. Let j be 123/(-41)*t*4/18. What is a in 0*a**2 - 4/5*a**j + 0*a**3 + 0 + 2/5*a**5 + 0*a = 0?
0, 2
Let l(i) be the second derivative of -i**4/42 + 96*i**3/7 - 1692*i**2/7 + 3477*i. What is x in l(x) = 0?
6, 282
Let b = 497 - 491. Let c be (b/1)/((-30)/135*-12). Suppose c*x + 1/4*x**3 + 3/2*x**2 + 1 = 0. What is x?
-4, -1
Let i be 12/