 Factor -2059 + 25*j**3 - i*j**2 - 40*j + 2059.
5*j*(j - 4)*(5*j + 2)
Let i(s) = s**2 - 1. Let w be i(2). Let g = 20700 + -20698. Find d, given that -6/5*d**2 + 2*d**w - g*d + 8/5 - 2/5*d**4 = 0.
-1, 1, 4
Let q(u) be the first derivative of -2*u**4/3 - 2294*u**3/3 - 246820*u**2 - 369800*u/3 + 1893. What is r in q(r) = 0?
-430, -1/4
Find o such that 32/5*o + 97/10*o**3 + 1/10*o**5 - 9/5*o**4 + 0 - 72/5*o**2 = 0.
0, 1, 8
Let n(f) = -14*f + 72. Let g be n(4). Let u be (((-416)/91)/g)/(2/(-12)). Factor -u*o + 0 + 2/7*o**3 - 2/7*o**2.
2*o*(o - 3)*(o + 2)/7
Suppose -3*g - 4*n + 21 = -7*n, -g - 2*n - 5 = 0. Suppose 18*i**2 - 14*i**4 - 7*i**4 + 3*i**4 + 127*i**g + i**5 - 47*i**3 - 81*i = 0. What is i?
-1, 0, 1, 9
Let h = 109 + 513. Factor -520*i**3 + 900*i - 1020*i**2 - h*i**3 - 4*i**4 + 1266*i**3.
-4*i*(i - 15)**2*(i - 1)
Let k(a) = a + 5. Let p(q) = 2*q**2 + 1152*q + 1134. Let v(f) = 4*k(f) + p(f). Factor v(t).
2*(t + 1)*(t + 577)
Suppose 16*s**3 + 0 + 2/3*s**5 - 44/3*s**2 - 20/3*s**4 + 14/3*s = 0. Calculate s.
0, 1, 7
Solve 7828*c + 4901*c - 11810778 + 7596106 - 2*c**2 - 12224706 - 1261*c = 0.
2867
Factor 0 + 114*s**2 + 6498*s + 1/2*s**3.
s*(s + 114)**2/2
Let z = -42163 + 42167. Let y(u) be the second derivative of 1/4*u**z + 0*u**2 - 3/20*u**5 + 0 + 24*u + 0*u**3. Let y(g) = 0. Calculate g.
0, 1
Suppose -4*h = 42*h - 207*h + 322. Solve -92/9*s + 0 + 2/9*s**h = 0.
0, 46
Let t(w) be the second derivative of -w**10/70560 + w**8/7840 - w**6/1680 + 7*w**4/6 + 5*w. Let z(c) be the third derivative of t(c). Let z(n) = 0. What is n?
-1, 0, 1
Suppose -4*h = -0*h - 2*y - 10, -2*y + 25 = 3*h. Suppose 0 = 9*j - 8*j + l, 8 = -j - h*l. Suppose 0 + 2*r + 2/3*r**j = 0. Calculate r.
-3, 0
Let u(v) = -3*v**5 + v**4 - v**2 - v. Let j(z) = -9*z**5 - 49*z**4 - 140*z**3 - 8*z**2 + 76*z. Let p(d) = -5*j(d) + 20*u(d). Let p(q) = 0. What is q?
-2, -1, 0, 2/3, 20
Let y(i) be the third derivative of -2*i**7/105 + 7*i**6/30 - 6*i**5/5 + 10*i**4/3 - 16*i**3/3 + 9*i**2 - 13*i + 3. Solve y(n) = 0 for n.
1, 2
Let g(z) be the first derivative of -z**5/90 - 2*z**4/9 - 7*z**3/9 + z**2 + 96*z - 244. Let u(q) be the second derivative of g(q). Factor u(p).
-2*(p + 1)*(p + 7)/3
Suppose y - 5*d = 43 + 36, 0 = d + 5. Let h be (y/(-36))/(147/(-30) - -4). Factor 5/3*c**2 + 0*c - h.
5*(c - 1)*(c + 1)/3
Let p(d) be the second derivative of d**4 - 436*d**3/3 + 288*d**2 + 1726*d - 1. Factor p(r).
4*(r - 72)*(3*r - 2)
Let y = -572 + 492. Let c be 29*(-2)/y + (-9)/72. Factor 0 - c*v**3 + 3/5*v + 3/5*v**4 - 3/5*v**2.
3*v*(v - 1)**2*(v + 1)/5
Let g(w) be the third derivative of -5/24*w**6 + 0*w + 166*w**2 + 0 + 0*w**3 + 1/2*w**5 - 1/42*w**7 + 0*w**4. Solve g(o) = 0.
-6, 0, 1
Let -9268*n**4 + 184*n + 207*n**2 + 8 + 7492*n**4 - 1163*n**2 + 576*n**5 - 20 + 1984*n**3 = 0. What is n?
1/6, 3/4, 1
Let 1/5*i**5 - 4/5*i**3 + 0*i + 28/5*i**2 + 0 - 7/5*i**4 = 0. Calculate i.
-2, 0, 2, 7
Factor -150/13*r**2 + 306/13*r - 154/13 - 2/13*r**3.
-2*(r - 1)**2*(r + 77)/13
Suppose -8*q = -3 - 21. Factor -6*n + 2*n**3 - 16*n**2 + 0*n**3 + 2*n**q + 6*n.
4*n**2*(n - 4)
Suppose 0 = 21*f - 17*f - 5*r - 2, -5*r + 10 = 0. Factor 0 + b**f + 1/3*b - 1/3*b**4 - b**2.
-b*(b - 1)**3/3
Let j(z) = 75*z**2 + 1540*z + 1505. Let n(q) = 51*q**2 + 1026*q + 1003. Let w(t) = 7*j(t) - 10*n(t). Factor w(h).
5*(h + 1)*(3*h + 101)
Let c(k) be the first derivative of -15/2*k**2 + 57 + 75*k + 1/4*k**3. What is j in c(j) = 0?
10
Let v = -59 - -64. Let -2 - 76*z - 4*z**3 + 36*z - 2*z**2 + 4*z**4 + 45*z - z**v = 0. Calculate z.
-1, 1, 2
Let p = 3629/105 - 512/15. Factor 36/7 + 48/7*s + p*s**3 + 3*s**2.
3*(s + 2)**2*(s + 3)/7
Let l(k) = -10*k**2 - 119*k + 10. Let q(w) = -2*w**2 - 24*w + 2. Let d(m) = -2*l(m) + 11*q(m). Let c be d(-13). Factor y - 2*y**2 + c*y - 2 + 3*y - 2.
-2*(y - 2)*(y - 1)
Suppose -4*f - 6 = -2*f + 4*b, -3*f + 3 = 2*b. Suppose 0 = 4*s, -2*j - 5*s - 4 = -4*j. Determine d so that -25*d**2 + 25*d**j + f*d - 6*d**3 + 3*d**5 = 0.
-1, 0, 1
Let x be 8 - ((-4212)/(-90))/6. Let s(v) be the second derivative of -28*v - x*v**5 + 1/6*v**4 + 2*v**3 + 0 - 9/2*v**2 - 1/30*v**6. Solve s(m) = 0.
-3, 1
Let r(d) be the second derivative of d**7/14 + d**6/5 - 3*d**5/20 - d**4/2 + 5*d - 375. Find o such that r(o) = 0.
-2, -1, 0, 1
Let g(k) be the second derivative of 8*k**5/5 - 5*k**4/42 + 13*k - 39. Find b, given that g(b) = 0.
0, 5/112
Let r(b) be the first derivative of b**4 + 2228*b**3 + 1861494*b**2 + 691234772*b - 1598. Factor r(z).
4*(z + 557)**3
Let d(l) be the first derivative of -2*l**3/3 + 15*l**2 + 252*l - 9127. Factor d(z).
-2*(z - 21)*(z + 6)
Suppose 38 = -287*u + 306*u. Solve 0 + 9/8*m + 3/8*m**u - 9/8*m**3 - 3/8*m**4 = 0 for m.
-3, -1, 0, 1
Let m(q) be the third derivative of q**5/140 + 5*q**4/7 - 192*q**3/7 - 314*q**2 - 2*q - 1. Find t such that m(t) = 0.
-48, 8
Let x(q) be the second derivative of -q**7/42 + 23*q**6/45 - 8*q**5/5 - 47*q**4/6 - 77*q**3/18 + 10*q**2 - 973*q + 2. Find s, given that x(s) = 0.
-1, 1/3, 5, 12
Let r = 30 - -106. Let v = r - -35. Find a such that 3*a**2 - 29*a + v - 63 + 0*a - 7*a = 0.
6
Let q(x) = x**5 + 9*x**4 + 12*x**3 + x**2 - 8*x - 10. Let k(w) = 4*w**4 + 6*w**3 - 4*w - 4. Let p(d) = -5*k(d) + 2*q(d). Factor p(h).
2*h*(h - 2)*(h - 1)*(h + 1)**2
Let c(x) be the second derivative of 21*x + 0 + 5/2*x**3 + 0*x**2 - 3/2*x**4. Determine m, given that c(m) = 0.
0, 5/6
Let l(s) be the first derivative of 3/2*s**2 - 1/5*s**5 + 0*s + 1/2*s**4 + 1/30*s**6 - 2/3*s**3 + 1. Let c(d) be the second derivative of l(d). Factor c(v).
4*(v - 1)**3
Let g(q) = -q**2 + 8*q - 13. Let d be g(3). Suppose 4*f - d*f = 6. Factor -2*c - 35 + 5*c**2 - f*c + 30 + 5*c**3.
5*(c - 1)*(c + 1)**2
Let k(x) = -10*x**3 - 5*x**2 + 2*x**4 + 4*x**3 + 2*x**2 - 3*x - 8*x**2 + 6. Let q(t) = -t**4 - t - 2. Let h(y) = k(y) + 3*q(y). Find g such that h(g) = 0.
-3, -2, -1, 0
Let n = -6334 + 6334. Factor 1/3*o**2 + n + 14/3*o.
o*(o + 14)/3
Let w(i) be the second derivative of -9 + 1/220*i**5 - 1/66*i**3 - 1/12*i**4 - 4*i + 1/2*i**2. Factor w(a).
(a - 11)*(a - 1)*(a + 1)/11
Let k(h) be the second derivative of h**6/150 + 21*h**5/100 + 139*h**4/60 + 77*h**3/10 - 196*h**2/5 - 216*h - 3. Determine i so that k(i) = 0.
-8, -7, 1
Let z(d) be the third derivative of 13/840*d**7 + 0*d**3 - 10*d**2 + 0*d - 1/240*d**6 + 0*d**5 + 0*d**4 + 0. Solve z(h) = 0.
0, 2/13
Let a(f) be the second derivative of f**6/120 + 9*f**5/40 + 85*f**4/48 + 3*f**3 - 22*f**2 - 9*f - 12. Factor a(z).
(z - 1)*(z + 4)**2*(z + 11)/4
Let r(g) = g**3 - 10*g**2 - 23*g + 7. Let p(u) = -2*u**2 - 2*u - 1. Let i(x) = 5*p(x) - r(x). Suppose i(o) = 0. What is o?
-4, 1, 3
Let j be (-450)/(-210) - 1/7. Factor 85 - 90*c - 88*c**2 + 48*c**2 + 45*c**j.
5*(c - 17)*(c - 1)
Let i(a) be the second derivative of -7*a**4/6 + 2515*a**3/3 - 718*a**2 + 2615*a. Factor i(h).
-2*(h - 359)*(7*h - 2)
Let f(m) = -2*m**3 + 7*m**2 + 31*m - 42. Let n(w) = 9*w**3 - 37*w**2 - 156*w + 212. Let l(d) = -14*f(d) - 3*n(d). Solve l(t) = 0 for t.
-8, -6, 1
Suppose -10*j = j - 22. Factor -4 + 22*i + j*i**2 + 1 + 3.
2*i*(i + 11)
Let v = -15 - -18. Suppose 4*s + v*a = -a + 156, a = -3*s + 111. Let -27*j**2 - 12 + s*j - 10 + 10 = 0. Calculate j.
2/3
Let j(c) be the first derivative of 10 - 6/5*c**2 - 8/15*c**3 + 21*c - 7/60*c**4 - 1/100*c**5. Let z(m) be the first derivative of j(m). Factor z(p).
-(p + 2)**2*(p + 3)/5
Let h(j) be the first derivative of j**3/6 + 335*j**2/2 + 112225*j/2 + 1057. Solve h(c) = 0 for c.
-335
Suppose -186 = -4*r + 3*i, 0*r = -3*r + 5*i + 134. Suppose -24 = r*m - 60*m. Factor 6/7 - 4/7*q**m - 1/7*q - 1/7*q**3.
-(q - 1)*(q + 2)*(q + 3)/7
Let t = 462 - 383. Let i = -236/3 + t. Factor 0*p + i*p**3 - 1/3*p**4 + 1/9*p**5 - 1/9*p**2 + 0.
p**2*(p - 1)**3/9
Let u(g) be the first derivative of -8*g**3/3 - 927*g**2 + 464*g + 1063. Let u(n) = 0. What is n?
-232, 1/4
Let y = -69405/4 - -624653/36. Let q = 1/471 - -1567/1413. Let -8/9*s - y*s**2 + q = 0. Calculate s.
-5, 1
Let g(a) = a**3 + 22*a**2 + 39*a + 2. Let k be g(-20). Let d be (k/10 + -2)*20/20. Factor 3/5*i - d*i**2 - 2/5.
-(i - 2)*(i - 1)/5
Let a(v) be the third derivative of -7*v**6/900 + 13*v**5/150 + 2*v**4/15 - 25*v**3/2 - 82*v**2. Let p(r) be the first derivative of a(r). Factor p(w).
-2*(w - 4)*(7*w + 2)/5
Let i(b) be the second derivative of b**