1/4*n**2. Find u, given that c(u) = 0.
0, 1/3, 1
Let b(l) be the first derivative of -3*l**4/20 + 176*l**3/5 - 10108. Find x such that b(x) = 0.
0, 176
Let z(t) = -527*t + 7908. Let s be z(15). Find l such that -6 - 9*l + 1/3*l**4 - 7/3*l**2 + l**s = 0.
-3, -2, -1, 3
Let u(c) be the second derivative of -c**6/210 - c**5/21 - 2*c**4/21 - 163*c**2/2 - 52*c + 2. Let x(p) be the first derivative of u(p). What is j in x(j) = 0?
-4, -1, 0
Let x = -1431 - -17173/12. Let d(v) be the first derivative of 1/4*v**2 + 1/4*v - 6 + x*v**3. Factor d(n).
(n + 1)**2/4
Let d be 62805/945*(-5)/187. Let l = 1/1309 - d. Factor -2/9*b**3 + l + 8/9*b - 4/9*b**2.
-2*(b - 2)*(b + 2)**2/9
Let v = 144818 + -144816. Factor q - 1/2*q**v - 1/2.
-(q - 1)**2/2
Let w(d) = -43*d**3 + 353*d**2 + 3646*d + 5788. Let l(c) = 13*c**3 - 118*c**2 - 1216*c - 1928. Let h(n) = -7*l(n) - 2*w(n). Factor h(y).
-5*(y - 32)*(y + 2)*(y + 6)
Suppose -14*t - 116 = -158. Let m be ((-3)/(27/t))/(7/(-42)). What is o in 10/9*o**3 + 1/3*o**4 + 1/9 + 4/3*o**m + 2/3*o = 0?
-1, -1/3
Let l(a) be the first derivative of -21/22*a**4 + 0*a - 3/11*a**2 + 34/33*a**3 - 139 - 18/55*a**5. Factor l(j).
-2*j*(j + 3)*(3*j - 1)**2/11
Let c(j) be the first derivative of 24*j**2 + 4/5*j**5 - 5*j**4 + 145 - 32/3*j**3 + 0*j. Factor c(q).
4*q*(q - 6)*(q - 1)*(q + 2)
Let l(v) = 32*v**3 + 152*v**2 + 172*v - 26. Let k(g) = -31*g**3 - 152*g**2 - 174*g + 27. Let a(q) = -6*k(q) - 5*l(q). Let a(i) = 0. What is i?
-4, -2, 2/13
Let z(x) = -304*x - 126. Let i(b) = b**2 - 153*b - 64. Let n(f) = 20*i(f) - 12*z(f). Let n(s) = 0. Calculate s.
-29, -2/5
Let o = -14543 - -14550. Let n(z) be the second derivative of 0 + 0*z**4 + 3/49*z**o - 3/35*z**5 + 0*z**3 - 9*z + 0*z**2 + 1/35*z**6. Factor n(t).
6*t**3*(t + 1)*(3*t - 2)/7
Let s(z) be the first derivative of -19*z**5/45 - 119*z**4/36 - 86*z**3/9 - 106*z**2/9 - 40*z/9 + 1401. Let s(g) = 0. Calculate g.
-2, -5/19
Suppose 5*o - 120 + 38 = 2*q, 0 = -2*o - 5*q + 56. Suppose 366*i - 372*i = -o. Factor -4 - i*k**2 - 6*k - 1/2*k**3.
-(k + 2)**3/2
Let p = 476 - 455. Solve 6*z**2 - z**2 - 161 + 4*z + p*z + 131 = 0 for z.
-6, 1
Let d(o) = -3*o**2 - 35*o - 4. Let c be d(-11). Find s, given that c + 14*s**4 + 5*s**4 - 12*s - 111*s**3 - 93*s + 177*s**2 + 2*s**4 = 0.
2/7, 1, 3
Let f be (24 + 2)*((-4)/2 - 1). Let r = 81 + f. Determine y, given that -10*y - 5*y**4 + y**3 - 6*y**2 + 12*y**4 - 5*y**4 + y**r - 4 = 0.
-1, 2
Let s(q) be the first derivative of -1/5*q + 103 - 2/5*q**2 + 1/3*q**3. Factor s(w).
(w - 1)*(5*w + 1)/5
Let d(i) be the first derivative of i**6/10 + 3*i**5/4 - 2*i**4 - 6*i**3 - 104*i - 2. Let q(r) be the first derivative of d(r). Factor q(j).
3*j*(j - 2)*(j + 1)*(j + 6)
Factor 2061*a - 1577*a + 804*a - 2*a**2 + 1290.
-2*(a - 645)*(a + 1)
Let a(l) be the second derivative of -l**4/12 + 19*l**3/3 - 36*l**2 + 1673*l. Determine t so that a(t) = 0.
2, 36
Let b = 2 - 3. Let c(d) = 4*d - 2. Let y(n) = 11*n**2 - 48*n + 14. Let p be y(4). Let f(g) = -g**2 + 1. Let j(t) = b*c(t) + p*f(t). Suppose j(o) = 0. What is o?
0, 2
Let u = 955819 - 955816. Factor -15*y**2 + 1/3*y**u - 43/3 + 29*y.
(y - 43)*(y - 1)**2/3
Let v(t) be the third derivative of t**5/120 + t**4/12 - 15*t**3/4 + 2*t**2. Suppose v(n) = 0. Calculate n.
-9, 5
Let s(p) be the first derivative of -p**3/3 - 870*p**2 - 756900*p - 3199. Solve s(t) = 0.
-870
Let p be (1112/136 - 7)/(2*1). Suppose 2/17*q**5 - 12/17*q**3 + 8/17*q**4 - 8/17*q**2 + 0 + p*q = 0. What is q?
-5, -1, 0, 1
Solve -105911*r**3 - 3873*r + 134 - 1284*r**2 + 105914*r**3 - 2720 = 0.
-2, -1, 431
Let b(d) = 3*d**2 - 1896*d + 3858. Let c(j) = -39*j. Let r(s) = b(s) + c(s). Factor r(n).
3*(n - 643)*(n - 2)
Let z(k) be the second derivative of -k**4/3 + 142*k**3/3 + 760*k**2 - 5283*k. What is o in z(o) = 0?
-5, 76
Let t(s) = -6*s**2 + 17*s + 16. Let k be t(-1). Let h(f) = -5*f - 33. Let j be h(k). Solve -2/19*x - 2/19*x**j + 4/19 = 0.
-2, 1
Let j(n) be the first derivative of n**3/4 - 213*n**2/8 + 1725*n/2 + 1121. Factor j(g).
3*(g - 46)*(g - 25)/4
Let m = 36/1055 + 4517402/3165. Let q = -1414 + m. Factor -8/3 - 6*i**2 - q*i.
-2*(i + 2)*(9*i + 2)/3
Let h(y) be the first derivative of 301 + 0*y + 63/4*y**4 + 1/2*y**6 - 22*y**3 - 24/5*y**5 + 12*y**2. Determine d so that h(d) = 0.
0, 1, 2, 4
Let s(b) be the third derivative of -b**6/900 - 3*b**5/25 - 27*b**4/5 - 40*b**3/3 - 105*b**2. Let c(y) be the first derivative of s(y). What is u in c(u) = 0?
-18
Let x(b) be the third derivative of b**6/660 + 14*b**5/165 + 53*b**4/132 + 26*b**3/33 - 1238*b**2. Solve x(c) = 0 for c.
-26, -1
Let h(q) = -52*q**2 - 648*q. Let j(u) = -11*u**2 - 129*u. Let b(x) = -3*h(x) + 14*j(x). Factor b(p).
2*p*(p + 69)
Factor b + 1/3*b**3 - 5/3*b**2 + 1/3*b**4 + 0.
b*(b - 1)**2*(b + 3)/3
Let r(a) = a**3 - 59*a**2 + 359*a + 292. Let d be r(52). Let x(m) be the first derivative of -6*m**3 - 5 - d*m - 1/2*m**4 - 24*m**2. Solve x(s) = 0.
-4, -1
Let z be 32/3 + (-80 - -79) - 9. Factor z*n**4 + 8*n + 0 - 16/3*n**2 - 2/3*n**3.
2*n*(n - 2)**2*(n + 3)/3
Let w be (2/(-5))/((-2)/21430). Let -5 - 7 + 4284*b**2 - w*b**2 + 10*b = 0. Calculate b.
2, 3
Factor -43293 - 4*w**2 - 5139 - 1352*w - 65812.
-4*(w + 169)**2
Let t(r) = 2*r. Let f be t(2). Let o be 5 - (5 + (-12)/f). Solve -4*u**2 - 75*u**3 - 78*u**3 - 81*u**o + 220*u**3 = 0.
-2/7, 0
Let g = -120381 - -120383. Find z, given that -14/5*z + 8/5*z**g + 2/5*z**3 - 4 = 0.
-5, -1, 2
Let t(z) be the third derivative of 0*z + 1/36*z**4 + 0 + 1/945*z**7 - 1/180*z**6 - 1/54*z**5 + 4/27*z**3 + 45*z**2. Factor t(o).
2*(o - 4)*(o - 1)*(o + 1)**2/9
Let w be (28/105)/(42/(-245)) - 4/(-2). Let v(y) be the third derivative of 4/45*y**5 + w*y**4 + 1/180*y**6 + 0 + 18*y**2 + 0*y**3 + 0*y. Factor v(h).
2*h*(h + 4)**2/3
Let f(z) be the third derivative of 5/21*z**3 + 0*z + 1/28*z**4 + 0 + 22*z**2 - 1/105*z**5. Determine g so that f(g) = 0.
-1, 5/2
Let a(t) be the third derivative of -t**9/30240 + t**7/630 - 2*t**5/5 - 22*t**2 + 4*t. Let r(u) be the third derivative of a(u). Factor r(l).
-2*l*(l - 2)*(l + 2)
Let v(f) be the first derivative of -9*f**2 - 233 - 1/2*f**3 - 30*f. What is k in v(k) = 0?
-10, -2
Let u(g) be the second derivative of g**4/3 - 788*g**3/3 - 790*g**2 - 2*g - 2440. Factor u(o).
4*(o - 395)*(o + 1)
Suppose -1437 = -224*w - 564*w + 139. Factor 2/3 + 2/3*x**w + 4/3*x.
2*(x + 1)**2/3
Let s(k) be the second derivative of -k**5/20 + 5*k**4/6 - 8*k**3/3 + k**2 + 14*k. Let y be s(8). Factor -1075 + 1075 + u**y - 2*u.
u*(u - 2)
Let j be (-23)/46*6*3 + (-144)/(-15). Let s(f) be the first derivative of -1/2*f**2 + 20 - j*f**5 - 5/3*f**3 - 7/4*f**4 + 0*f. Factor s(r).
-r*(r + 1)**2*(3*r + 1)
Let h(k) be the third derivative of k**7/525 - 151*k**6/300 + 77*k**5/2 - 375*k**4/4 + 3997*k**2. Factor h(m).
2*m*(m - 75)**2*(m - 1)/5
Let b = -220 - 472. Let r = b + 695. Factor 0*t + 0*t**r + 0 + t**2 - 1/4*t**4.
-t**2*(t - 2)*(t + 2)/4
Let b be 1 - ((-1575)/147 - -10). Suppose 2/7*a**2 + b*a + 0 = 0. What is a?
-6, 0
Let n(r) be the second derivative of 7*r**4 - 588*r**3 - 1/30*r**5 + 5*r + 24696*r**2 + 0. Let n(o) = 0. What is o?
42
Let v = -65371/74 - 966/37. Let n = v - -911. Determine m, given that -m**5 + 1/2*m - n*m**2 + 3/2*m**4 + 1/2*m**3 + 0 = 0.
-1, 0, 1/2, 1
Let n(a) be the second derivative of -5*a**4/36 + 178*a**3/3 + 214*a**2/3 - 1268*a. Solve n(t) = 0 for t.
-2/5, 214
Let r(d) be the first derivative of -d**4/6 + 2*d**3/3 - d**2 + 57*d - 75. Let n(v) be the first derivative of r(v). Find o, given that n(o) = 0.
1
Let o = -4574 + 4574. Let p(n) be the third derivative of 0*n**3 + o*n**5 + 1/1020*n**6 - 21*n**2 + 0 - 1/204*n**4 + 0*n. Factor p(m).
2*m*(m - 1)*(m + 1)/17
Let p(w) be the second derivative of -2 - 25/4*w**4 + 1/4*w**5 + 45/2*w**3 - 65/2*w**2 - 123*w. Suppose p(k) = 0. Calculate k.
1, 13
Let i(n) be the second derivative of -n**7/84 - n**6/5 + 7*n**5/20 + n**4/2 - 13*n**3/12 - n - 8. Let i(u) = 0. Calculate u.
-13, -1, 0, 1
Let f = 28212/51601 - 6/4691. Let 8/11*n**4 + 0*n - 2/11*n**5 - f*n**3 + 0*n**2 + 0 = 0. What is n?
0, 1, 3
Let v = 708244 + -708242. Factor 1/4*u**v - 1/2*u + 1/4.
(u - 1)**2/4
Let i(v) be the first derivative of -v**4/24 - 1037*v**3/6 - 2073*v**2/4 - 3109*v/6 - 1310. Factor i(w).
-(w + 1)**2*(w + 3109)/6
Let v(f) be the third derivat