e the third derivative of -k**6/60 - 4*k**5/3 + 127*k**4/12 - 86*k**3/3 + 1011*k**2. Determine n, given that l(n) = 0.
-43, 1, 2
Let z be (-40 - (-31 + 21 + -12)) + 20. Find j, given that -1/7*j**z + 30/7 + 29/7*j = 0.
-1, 30
Let a(t) be the third derivative of 5*t + 0 + 110/21*t**4 + 605/21*t**5 + 8/21*t**3 + 5*t**2. Solve a(v) = 0.
-2/55
Let u(t) be the first derivative of -1/12*t**3 + 35 - 5/8*t**2 - 3/2*t. Solve u(o) = 0.
-3, -2
Let i(h) be the first derivative of 0*h - 1 + 1/7*h**3 - 3/35*h**5 - 3/7*h**2 + 3/14*h**4. Factor i(d).
-3*d*(d - 2)*(d - 1)*(d + 1)/7
Suppose -a + 180 = 180. Suppose 2*m = -5*h + 2, a = h - 4*m + 8*m + 14. Determine t so that -1/3*t**h + 4/3 - t = 0.
-4, 1
Suppose 0 = -2*o + 2*c + 14 + 10, 0 = 2*c + 4. Let d be -8 + 20/5 - -86. Factor 53*v**2 - 18*v**2 + o - d*v + 37*v.
5*(v - 1)*(7*v - 2)
Let n(d) be the second derivative of 26*d**6/35 - 388*d**5/35 + 604*d**4/21 + 64*d**3/21 + 5377*d. Solve n(t) = 0.
-2/39, 0, 2, 8
Let f(w) be the second derivative of w**8/12600 - w**7/3780 + w**6/5400 - 19*w**4/6 - 38*w. Let h(a) be the third derivative of f(a). Let h(l) = 0. What is l?
0, 1/4, 1
Let t = -165289/60 + 2755. Let m(k) be the first derivative of 0*k + t*k**5 - 7 + 3/16*k**4 + 0*k**2 - 1/18*k**3. Factor m(u).
u**2*(u + 1)*(11*u - 2)/12
Let v = 10602 + -95416/9. Let c(b) be the second derivative of 0*b**2 + v*b**3 - b**4 + 0 + 13*b + 8/5*b**5 - 32/45*b**6. Suppose c(z) = 0. Calculate z.
0, 1/4, 1
Solve 47 - 213/2*h**3 + 95*h - 133/4*h**2 - 9/4*h**4 = 0.
-47, -2/3, 1
Factor 4*t**2 + 2178 + 2148 + 524*t - 4854.
4*(t - 1)*(t + 132)
Let h(v) be the first derivative of 2*v**5/5 + 299*v**4/2 + 15196*v**3 + 66304*v**2 + 87616*v + 12530. Let h(k) = 0. What is k?
-148, -2, -1
Let g(s) be the third derivative of -s**5/20 + 306*s**4/5 + 98*s**3 + 9*s**2 - 293. Factor g(y).
-3*(y - 490)*(5*y + 2)/5
Let f(y) be the third derivative of -y**5/20 + 2*y**4 + 105*y**3/2 + 446*y**2 - 1. Solve f(p) = 0 for p.
-5, 21
Let i(a) be the third derivative of 1/420*a**6 + 0*a**4 - 30*a**2 + 1/70*a**5 + 0*a + 0 - 4/21*a**3. Factor i(c).
2*(c - 1)*(c + 2)**2/7
Let p(i) be the third derivative of -i**5/135 + 56*i**4/27 - 74*i**3/9 + 2*i**2 - 398. Determine z, given that p(z) = 0.
1, 111
Suppose -1364*s = 1367*s - 2722*s. Factor 0 - 1/5*r**3 + s*r + 2/5*r**2 - 1/5*r**4.
-r**2*(r - 1)*(r + 2)/5
Let d(j) be the second derivative of 4*j**2 + 0 + 1/12*j**4 + 81*j + j**3. What is c in d(c) = 0?
-4, -2
Let g(y) = -2*y**2 + 5*y - 3. Let x = -16 + 13. Let w = -69 - -74. Let t(p) = -4*p**2 + 9*p - 5. Let r(j) = w*g(j) + x*t(j). Solve r(o) = 0 for o.
0, 1
Let w(q) = -q**3 + 11*q**2 - 8. Let d be w(10). Let 52*k + 104 - 4*k**2 + d - 244 = 0. Calculate k.
1, 12
Let s(j) = j**3 + 2*j**2 - 4*j + 2. Let w be s(-3). Suppose 0 = 5*g + 5*q - w, -5*g - 83*q + 3 = -80*q. Factor 6/7*d**2 + 2/7*d**4 + 2/7*d + g + 6/7*d**3.
2*d*(d + 1)**3/7
Let i = 649/1977 + 10/1977. Let s(w) be the first derivative of -16/9*w**3 + 30 - i*w**4 - 8/3*w - 10/3*w**2. Solve s(j) = 0 for j.
-2, -1
Let v(u) be the second derivative of -1/78*u**4 + 1 + 42/13*u**3 + 42*u - 3969/13*u**2. Solve v(q) = 0.
63
Solve 816/5*d - 3/5*d**2 - 324 = 0 for d.
2, 270
Factor 158*b - 58*b - 310*b + 225 + 50*b**3 - 80*b**2 + 15*b**4.
5*(b - 1)*(b + 3)**2*(3*b - 5)
Let o(d) = -377 + 376 + d**2 + 3*d + d**5 - 2*d**3 - 4*d. Let y(b) = 3*b**3 - 3*b**2 - 3*b - 3. Let s(v) = 3*o(v) - y(v). Determine l, given that s(l) = 0.
-2, 0, 1
Let x(h) = 2*h**3 - 38*h**2 + 99*h - 29. Let z be x(16). Let w(i) be the second derivative of 0 + 1/20*i**4 - 6/5*i**2 + 3/10*i**3 - z*i. Factor w(o).
3*(o - 1)*(o + 4)/5
Let r be -5 - -8 - (-1 + 2)*1. Factor -3*g - g**2 + g + 7 + 6*g**r - 4*g**2 - 6*g.
(g - 7)*(g - 1)
Let k(p) be the first derivative of 2*p**4/7 - 10*p**3/21 - 2*p**2/7 + 6*p/7 - 1087. Factor k(t).
2*(t - 1)**2*(4*t + 3)/7
Let y(d) = -2*d**3 + 127*d**2 + 1235*d - 1356. Let s(p) = -p**3 + p + 4. Let r(n) = 2*s(n) - 2*y(n). Factor r(i).
2*(i - 136)*(i - 1)*(i + 10)
Let n(i) be the first derivative of -87 + i - 1/12*i**3 - 3/8*i**2. Factor n(v).
-(v - 1)*(v + 4)/4
Suppose -51*w = 71*w. Let h(m) be the third derivative of -1/180*m**6 + 0 + 0*m - 27*m**2 + w*m**3 - 2/45*m**5 + 0*m**4. Factor h(i).
-2*i**2*(i + 4)/3
Let i(l) be the first derivative of l**6/540 - l**5/90 + l**4/54 + 18*l**2 + 67. Let k(n) be the second derivative of i(n). Factor k(y).
2*y*(y - 2)*(y - 1)/9
Let a(r) be the third derivative of 1/588*r**8 + 0*r**3 + 0*r**6 - 8/735*r**7 - 8/21*r**4 + 16/105*r**5 + 64*r**2 + 0*r - 2. Let a(h) = 0. What is h?
-2, 0, 2
Suppose -179/4*r**2 + 9/4 + 66*r + 15/2*r**3 = 0. What is r?
-1/30, 3
Let w = -6932 + 6937. Let c(x) be the first derivative of -1/33*x**6 + 3/22*x**4 + 0*x - 2/11*x**2 + 2/55*x**w - 10 - 2/33*x**3. Let c(a) = 0. What is a?
-1, 0, 1, 2
Let u(q) be the third derivative of -11*q**6/15 - 19*q**5/15 + 47*q**4/6 - 4*q**3 + 4279*q**2. Factor u(x).
-4*(x - 1)*(x + 2)*(22*x - 3)
Let w = -588 + 591. Let d be (-12)/60 - (-21)/5. Factor -2*g**4 + 6*g**3 - 6*g**d + 6*g**w - 3*g**5 + 5*g**5 + 2*g - 8*g**2.
2*g*(g - 1)**4
Determine z so that -90*z - 69*z - 315*z**3 - 168*z - 4 - 2 - 636*z**2 = 0.
-1, -2/105
Factor -475*w + 197*w + 188*w + 429*w**2 - 3*w**3 + 522*w.
-3*w*(w - 144)*(w + 1)
Let z = -20 - -73. Let k = -48 + z. Determine h, given that -6*h**3 + 4*h - 6*h**2 + k*h - 69 - 3*h**5 + 9*h**4 + 66 = 0.
-1, 1
Let m = -980851 + 3923405/4. Suppose -m*k**2 + 0 + 2*k = 0. Calculate k.
0, 8
Suppose 2*b = 8 - 4. Let o(g) = -g**2 + 1. Let y(c) = 2 - 4*c - 28*c**2 + c**2 + 13*c**2 - 4*c**2. Let q(u) = b*o(u) - y(u). Factor q(r).
4*r*(4*r + 1)
Suppose 25*h - 77 = 148. Let p be (-6)/(-4)*((4 - h) + 7). Find n such that 2/7*n**2 + 0*n + 0 - 4/7*n**p + 2/7*n**4 = 0.
0, 1
Let w(c) = -c**3 - 3*c**2 + 4*c + 4. Suppose i + 0*i + 4 = 0. Let j be w(i). Factor -3*u**4 + 5*u**j - 4*u**3 + 3*u**5 + 3*u**3.
u**3*(u + 1)*(3*u - 1)
Let n(d) be the second derivative of 2*d**7/21 + 58*d**6/5 + 387*d**5 + 1849*d**4/3 + 130*d. Factor n(m).
4*m**2*(m + 1)*(m + 43)**2
Let v(b) = 10*b - 10. Let z = 191 + -190. Let q be v(z). Factor q*f + 3/4*f**4 + 0*f**2 + 0 - 1/4*f**3.
f**3*(3*f - 1)/4
Suppose 33*l + 4382 - 4382 = 0. Suppose 0 - 10/3*c**2 + l*c + 2/3*c**3 = 0. What is c?
0, 5
Let u(k) be the third derivative of -k**8/2856 - k**7/595 - k**6/340 - k**5/510 - k**2 - 2*k + 206. Suppose u(a) = 0. Calculate a.
-1, 0
Suppose a = -4*k + 65, 5*a - 160 = 2*a - 5*k. Suppose -52*f + 28 = -a*f. Factor -f*z**2 + 0 + 16/3*z**3 - 4/3*z.
4*z*(z - 1)*(4*z + 1)/3
Let k(s) be the third derivative of -s**8/6720 - s**7/840 + s**6/16 + s**5/30 + 11*s**4/24 - 6*s**2 + 2. Let b(g) be the third derivative of k(g). Factor b(h).
-3*(h - 3)*(h + 5)
Let d(x) be the first derivative of -1/14*x**2 + 8/7*x - 277 - 8/21*x**3 + 1/28*x**4. Factor d(q).
(q - 8)*(q - 1)*(q + 1)/7
Let n be -4 + (-444)/(-54) - (-4)/(-18). Factor -n*j - 5*j**2 - 3*j - 3*j.
-5*j*(j + 2)
Let d = 5254 + -5249. Let c(v) be the first derivative of 2/25*v**d + 0*v + 5 + 0*v**2 - 2/5*v**4 + 2/5*v**3. Let c(i) = 0. What is i?
0, 1, 3
Let x(y) = -4*y**4 - 37*y**3 + 372*y**2 - 652*y + 265. Let j(r) = -2*r**4 - 19*r**3 + 186*r**2 - 322*r + 133. Let a(s) = 14*j(s) - 6*x(s). Factor a(z).
-4*(z - 4)*(z - 1)**2*(z + 17)
Let w(a) be the second derivative of a**7/7 + 83*a**6/45 + 57*a**5/10 - 47*a**4/18 - 20*a**3 - 12*a**2 - 1889*a. Determine g so that w(g) = 0.
-6, -3, -1, -2/9, 1
Suppose 4 = -10*p - 16. Let i(g) = 3*g**2 + 109*g - 1352. Let f(t) = -t**2 - 54*t + 676. Let u(l) = p*i(l) - 5*f(l). Factor u(o).
-(o - 26)**2
Suppose -o + 5*v - 3525 = -3482, -5*v = 4*o - 128. Factor 58/5*x**3 + o*x + 106/5*x**2 + 13/5*x**4 + 1/5*x**5 + 5.
(x + 1)**3*(x + 5)**2/5
Let -247/2*s - 1/2*s**2 + 124 = 0. Calculate s.
-248, 1
Let o(h) be the first derivative of 6*h + h**3 - 81/10*h**2 - 90. Find a, given that o(a) = 0.
2/5, 5
Let f be (-55)/(-22) + (-148)/8 - 112/(-6). What is i in 38*i**2 + f - 232/3*i = 0?
2/57, 2
Suppose 833*p - 836*p = -2*u + 15, -5*p - 4*u = -63. Suppose 170*z - 578/3 + 2/3*z**p + 22*z**2 = 0. What is z?
-17, 1
Suppose 2*n + 1 = w, 27*n - 29*n + 5*w = 21. Factor 0 + 0*z**n + 0*z + 2/9*z**4 + 2*z**3.
2*z**3*(z + 9)/9
Let j(y) be the first derivative of 5*y**3 - 1445*y**2/2 - 970*y + 340. Find h, given th