be the third derivative of v**6/420 - 3*v**5/14 + 131*v**4/21 - 160*v**3/7 - 8*v**2 - 53*v + 5. Factor k(w).
2*(w - 24)*(w - 20)*(w - 1)/7
Let w(i) = i**2 + 30*i + 83. Let v be w(-27). Let s be (-21)/2*((-232)/112 + v). Let -3/4*y**5 - s*y**2 + 0 + 3/4*y**3 + 3/4*y**4 + 0*y = 0. Calculate y.
-1, 0, 1
Let q be 1/((-3)/4 + 1). Let n = -1403 - -1405. Factor 2*g + g**2 + q - 1 + 0*g - n.
(g + 1)**2
What is c in 229441/6 + 1/6*c**2 + 479/3*c = 0?
-479
Let v = 771882 + -771880. Factor 36/5*a - 32/5 - 4/5*a**v.
-4*(a - 8)*(a - 1)/5
Let z(x) be the first derivative of 0*x**2 + 0*x - 2/25*x**5 + 2/15*x**3 - 39 + 1/20*x**4 - 1/30*x**6. Let z(n) = 0. Calculate n.
-2, -1, 0, 1
Factor -28/5*d - 88/5*d**2 - 12/5*d**3 + 0.
-4*d*(d + 7)*(3*d + 1)/5
Let h(w) be the first derivative of -2*w**3/9 + 77*w**2/3 - 970. Find g such that h(g) = 0.
0, 77
Suppose 125*i = 135*i - 30. Let c(v) be the first derivative of -27 + 92/11*v**i + 6/55*v**5 + 180/11*v**2 + 18/11*v**4 + 150/11*v. Factor c(p).
6*(p + 1)**2*(p + 5)**2/11
Let h(a) be the first derivative of 2/9*a**3 - 48 + 2/15*a**5 + 0*a - 1/36*a**6 - 1/12*a**2 - 1/4*a**4. Suppose h(m) = 0. Calculate m.
0, 1
Let j = -142 + 77. Let x = 67 + j. Determine f so that -11*f + 3*f**2 + 5 + f + 2*f**x = 0.
1
Let d be -2 + (-37580)/176 - 9. Let r = d - -909/4. Factor 0 + 14/11*j**3 + 18/11*j - 2/11*j**4 - r*j**2.
-2*j*(j - 3)**2*(j - 1)/11
Let h(z) be the first derivative of -z**4/20 + z**3/5 + 27*z**2/5 - 278. Factor h(c).
-c*(c - 9)*(c + 6)/5
Let n(y) be the first derivative of y**4/12 - 38*y**3/3 + 522*y**2 + 6728*y/3 + 535. Factor n(f).
(f - 58)**2*(f + 2)/3
Let i(y) = 3*y**2 + 98*y + 182. Let z(k) = -183 + 18*k**2 + 17*k**2 - 56*k**2 - 97*k + 19*k**2. Let l(h) = -3*i(h) - 2*z(h). Suppose l(t) = 0. What is t?
-18, -2
Let r(m) be the third derivative of 7*m**6/600 + 2*m**5/15 - 61*m**4/120 + 7*m**3/15 + 768*m**2. Factor r(j).
(j - 1)*(j + 7)*(7*j - 2)/5
Let q be (-3 + 13 + -5)*(4/(-2))/(-2). Let o(i) be the first derivative of -8/63*i**3 + 1/21*i**2 + 0*i - 8/105*i**q + 3 + 1/63*i**6 + 1/7*i**4. Factor o(v).
2*v*(v - 1)**4/21
Let h = -59264/3 - -118543/6. Find y, given that h + 1/6*y**2 - 4/3*y = 0.
3, 5
Let i = 1270 + -1266. Let y(c) be the second derivative of 7*c + 5*c**3 + 5/2*c**2 + 0 + 15/4*c**i. Let y(q) = 0. What is q?
-1/3
Suppose z - 5*z + 362 = -w, -5*w = 10. Let n = -85 + z. Determine j, given that -j**2 - 21 + 2*j**2 - 24*j + j**2 - n*j**2 = 0.
-7, -1
Determine m, given that -17*m**3 + 371*m + 214*m - 24*m**3 + 35*m**4 - 44*m**3 - 180 - 4002*m**2 + 3647*m**2 = 0.
-3, 3/7, 1, 4
Let t(i) be the third derivative of -1/120*i**6 + 0 + 1/30*i**5 + 0*i - 1/105*i**7 + 1/336*i**8 + 0*i**3 + 47*i**2 + 0*i**4. Let t(z) = 0. What is z?
-1, 0, 1, 2
Let g(y) be the third derivative of 7/60*y**6 + 1/35*y**5 + 104/735*y**7 + 0*y**3 + 2/147*y**8 + 0*y - 2*y**2 + 0*y**4 + 0. Find d, given that g(d) = 0.
-6, -1/4, 0
Let v be (-52)/8*14/((-2184)/36). Solve 9*u + 27/2 + v*u**2 = 0 for u.
-3
Suppose -420*i + 1041 = 447*i - 308*i - 1195. Find d, given that 2*d + 15*d**2 + 7/2*d**3 - 20 - 1/2*d**i = 0.
-2, 1, 10
Determine o so that 1/4*o**2 - 395/4*o + 0 = 0.
0, 395
Let o(s) be the second derivative of 0 - 4/5*s**2 + 21*s + 0*s**3 + 1/10*s**4 - 1/50*s**5. Factor o(b).
-2*(b - 2)**2*(b + 1)/5
Let o be 2943/(-327) - 28/(-3). Let b = 4/19 - -26/57. Suppose o*x**3 + 0 + x**2 + b*x = 0. Calculate x.
-2, -1, 0
Let r(q) = 3*q**2 + 251*q + 5172. Let h be r(-47). Factor 10/7 + 12/7*t + 2/7*t**h.
2*(t + 1)*(t + 5)/7
Suppose 13*p = 2088 + 4412. Solve 14*m**2 - 63*m - 47*m**2 + 469 - m**3 - p = 0 for m.
-31, -1
Suppose -117 = 4*x + 9*x. Let s be 0/(3 + x)*1. Find v, given that -3*v**2 - 15/2*v**3 + 0*v + s - 6*v**4 - 3/2*v**5 = 0.
-2, -1, 0
Suppose 3*i - 4*q = 9, -4*i - 13 = -3*q - 25. Determine d so that 7*d + 3*d**3 + d**3 - 2*d**4 + 8*d**2 - 4*d**3 + 4*d**i - 23*d = 0.
-2, 0, 2
Let z be 140/(-12)*(-5 - -2). Suppose -z + 10 = -5*r. What is h in -r*h - 2*h**2 + 3*h - h**3 + h = 0?
-1, 0
Let q be 3*290/75 + (-4 - 36/6). Let -q*w**3 + 0 - 52/5*w**2 - 8*w + 4/5*w**4 = 0. What is w?
-2, -1, 0, 5
Let c(j) = j**3 - 13*j**2 + 14*j + 17. Suppose -4*z + 3*n + 26 = -31, -5*n + 33 = 4*z. Let b be c(z). Factor 2*l**2 + 269 - 52*l + 28 + b.
2*(l - 13)**2
Let r(v) = 5*v**2 - 344*v + 1044. Let a(s) = 15*s**2 - 1034*s + 3119. Let t(k) = -3*a(k) + 8*r(k). Factor t(y).
-5*(y - 67)*(y - 3)
Factor -267/8*f - 3/8*f**2 + 135/4.
-3*(f - 1)*(f + 90)/8
Let r(k) be the third derivative of -k**8/2352 - k**7/490 + k**6/70 + k**5/21 - 2*k**4/7 + 9*k**2 + 95*k. Find d such that r(d) = 0.
-4, -3, 0, 2
Let q(x) be the third derivative of 0 + 7/60*x**5 - 1/12*x**4 + 8*x + 2*x**2 + 3/40*x**6 + 0*x**3. Factor q(r).
r*(r + 1)*(9*r - 2)
Let u(p) be the third derivative of -p**5/100 - 163*p**4/5 - 212552*p**3/5 - 1956*p**2. Find a such that u(a) = 0.
-652
Let k(v) be the second derivative of -v**7/483 + 16*v**6/345 - 4*v**5/23 - 41*v**4/23 + 99*v**3/23 + 486*v**2/23 + 1252*v - 2. Find q, given that k(q) = 0.
-3, -1, 2, 9
Solve -36300 - 617*i**2 + 2*i**3 + 695*i**2 + i**3 + 26728*i + 8912*i + 579*i**2 = 0.
-110, 1
Let v(p) be the first derivative of -p**4/7 + 104*p**3/21 + 170*p**2/7 + 232*p/7 + 4208. Factor v(f).
-4*(f - 29)*(f + 1)*(f + 2)/7
Let b(a) be the first derivative of 4*a**5/5 - 636*a**4 + 202248*a**3 - 32157432*a**2 + 2556515844*a - 714. Factor b(h).
4*(h - 159)**4
Suppose 10*x - 735 = -205. Let f(q) = -3*q - 3. Let y be f(-2). What is z in 51*z**4 - 7*z + 2*z**3 + 4 - x*z**4 - y*z + 6*z**2 = 0?
-2, 1
Let k(p) be the first derivative of 3*p**5/5 + 57*p**4/4 - 42*p**3 + 51. Factor k(f).
3*f**2*(f - 2)*(f + 21)
Let x(n) be the first derivative of 3*n**5/20 + 4*n**4 - 164*n + 147. Let v(f) be the first derivative of x(f). Find h such that v(h) = 0.
-16, 0
Let i(t) be the second derivative of -3*t**5/140 - 12*t**4/7 + 50*t**3/7 - 3937*t. Factor i(h).
-3*h*(h - 2)*(h + 50)/7
Let c(j) = 6*j + 5. Let a be c(0). Let p(m) = -m + 8. Let s be p(a). Suppose 2*r**s + 0*r - 2*r + 12*r + 225*r**2 - 213*r**2 = 0. Calculate r.
-5, -1, 0
Let q(c) be the third derivative of -c**6/288 - 17*c**5/48 - 1445*c**4/96 - 13*c**3/3 + 60*c**2. Let i(d) be the first derivative of q(d). Factor i(o).
-5*(o + 17)**2/4
Let t(a) = -10*a**2 + 16*a - 22. Let i be t(2). Let l be (-110)/275 - 112/i. Factor 16/3*j**2 + l*j**3 + 2/3*j - 4/3.
2*(j + 1)**2*(5*j - 2)/3
Let r = 1/29946 - -33719191/149730. Let p = -225 + r. Determine t so that 3/5*t - p - 3/5*t**2 + 1/5*t**3 = 0.
1
Let n(a) be the second derivative of -a**4/16 - 9*a**3/4 + 345*a**2/8 - 3*a - 213. Factor n(d).
-3*(d - 5)*(d + 23)/4
Let m(a) be the first derivative of -a**6/810 + a**5/135 + a**4/18 - 17*a**3 + 67. Let g(u) be the third derivative of m(u). Let g(i) = 0. What is i?
-1, 3
Let o(z) be the first derivative of 86 - 42/5*z**2 + 3/20*z**4 + 7/5*z**3 + 12*z. Suppose o(d) = 0. Calculate d.
-10, 1, 2
Let t(v) be the third derivative of -v**7/70 - v**6/20 + 21*v**5/20 - 9*v**4/4 + 96*v**2 - 2*v. Solve t(o) = 0.
-6, 0, 1, 3
Factor 235*a**5 + 73*a**4 - 123*a**4 - 240*a**5 + 70*a**2 + 60*a**3 + 60*a**4 + 25*a.
-5*a*(a - 5)*(a + 1)**3
Let d(o) be the first derivative of o**4/2 + 88*o**3/3 + 81*o**2 - 252*o - 211. Solve d(a) = 0.
-42, -3, 1
Let u(c) be the third derivative of c**6/540 - c**5/18 - 4*c**4/3 - 220*c**3/27 + 889*c**2. Factor u(w).
2*(w - 22)*(w + 2)*(w + 5)/9
Solve 5*m**5 - 1095746 + 35*m**4 - 60*m + 55*m**3 + 1095746 - 35*m**2 = 0 for m.
-4, -3, -1, 0, 1
Let x be 319/(-29) + 4 + -1 + 11. Let n(s) be the first derivative of -9*s**4 + x*s**2 + 0*s - 3*s**3 - 21/5*s**5 + 34. Factor n(w).
-3*w*(w + 1)**2*(7*w - 2)
Suppose 81*b + 5938 + 56 = 0. Let u be (-2)/4 - 37/b. Let -1/4*r**2 - 1/4*r + u = 0. Calculate r.
-1, 0
Let q(n) be the first derivative of -n**4/10 - 184*n**3/5 - 549*n**2/5 - 548*n/5 + 222. Factor q(a).
-2*(a + 1)**2*(a + 274)/5
Let n(l) be the second derivative of -l**7/7 - 21*l**6/10 - 3*l**5/5 + 59*l**4/4 - 6*l**3 - 30*l**2 + 653*l. Let n(z) = 0. Calculate z.
-10, -2, -1/2, 1
Suppose 0 + 1/3*s**5 + 16/3*s**4 - 64/3*s**2 + 8*s**3 - 112/3*s = 0. Calculate s.
-14, -2, 0, 2
Let t(a) be the first derivative of a**6/1080 - a**5/60 + a**4/8 - 109*a**3/3 + 56. Let x(g) be the third derivative of t(g). Let x(d) = 0. Calculate d.
3