t a(x) be the third derivative of -x**5/510 - 61*x**4/204 - 58*x**3/17 + 1339*x**2. Find l, given that a(l) = 0.
-58, -3
Let c(i) be the third derivative of 8*i - 1/150*i**5 + 0 - 2*i**2 + 1/5*i**4 - 12/5*i**3. Determine t, given that c(t) = 0.
6
Let w(o) = o**2 + 26*o + 101. Let f be w(-5). Let t be f*-4*(-4)/(-14). Find b, given that -6/7*b**2 + 0*b + t + 1/7*b**3 = 0.
-2, 4
Determine n so that 0 + 104/3*n + 44/3*n**4 + 256/3*n**2 - 2/3*n**5 + 66*n**3 = 0.
-2, -1, 0, 26
Let o(k) = 90*k**2 + 405*k + 395. Let g(m) = -109*m**2 - 406*m - 393. Let c(q) = -5*g(q) - 6*o(q). Factor c(l).
5*(l - 81)*(l + 1)
Suppose z = -q - 3*z, -4*q - 3*z = 0. Let t be (q + -2 + 3)*3. Factor -2*s**4 + 8/3*s**t + 0 + 0*s - 2/3*s**2.
-2*s**2*(s - 1)*(3*s - 1)/3
Factor -67/6*s - 155/3 - 1/6*s**2.
-(s + 5)*(s + 62)/6
Suppose -81*s + i + 20 = 31*s, 0 = 2*s + 5*i + 100. Suppose s*y - 1/2*y**5 - 1/2*y**3 + y**4 + 0*y**2 + 0 = 0. Calculate y.
0, 1
Let p(m) = m**3 + 4*m**2 - 6*m - 25. Let l be -1*(-26)/(-8) + 12/48. Let x be p(l). Let 2/5*o**4 - 4/5 + 2/5*o**3 - 2*o - 6/5*o**x = 0. What is o?
-1, 2
Let j(f) be the first derivative of -f**3/9 + 25*f**2/6 + 28*f + 1894. Suppose j(w) = 0. Calculate w.
-3, 28
Factor -8/3*n**2 + 0*n + 0 - 4/3*n**4 - 2/3*n**5 + 14/3*n**3.
-2*n**2*(n - 1)**2*(n + 4)/3
Suppose 3*b = 17 - 32, -3*i = -13*b - 74. Factor 10/17*t**2 - 2/17*t**i + 6/17 - 14/17*t.
-2*(t - 3)*(t - 1)**2/17
Let v(i) = -112*i**2 + 204*i. Let n(c) = -126*c**2 + 203*c - 1. Let r(q) = -5*n(q) + 6*v(q). Factor r(a).
-(a - 5)*(42*a + 1)
Suppose -38*q + 298 - 66 = 80. Suppose 0 + 2/3*s**q + 46/3*s**2 - 26/3*s**3 - 22/3*s = 0. What is s?
0, 1, 11
Let r(w) = -84*w + 12351. Let c be r(147). Let -4/3*s**4 + 0 - 4/3*s**c + 0*s - 1/3*s**5 + 0*s**2 = 0. What is s?
-2, 0
Let s(p) = 5*p**2 - p - 13. Let v(y) = 8*y**2 - 31*y**2 + 14 + 2*y + 19*y**2. Let l(a) = 4*s(a) + 6*v(a). Let l(x) = 0. Calculate x.
-2, 4
Solve 13/4*f**3 - 3 + 1/4*f**4 + 11/4*f**2 - 13/4*f = 0.
-12, -1, 1
Let g be -9 - (374/(-23) + 22 + (-195)/13). Factor -g - 8/23*r - 2/23*r**2.
-2*(r + 1)*(r + 3)/23
Let d(s) be the second derivative of -s**7/168 + s**6/24 + 3*s**5/40 - 11*s**4/24 - 37*s**3/24 - 15*s**2/8 + 2875*s. Factor d(z).
-(z - 5)*(z - 3)*(z + 1)**3/4
Let x be ((8 + -6)/(-8))/(1/(-236)). Suppose -2*h - 3*l + 60 = x, 5*h = l + 11. Find d, given that 0 - 6/7*d**h + 3*d**3 + 0*d = 0.
0, 2/7
Let q(z) = 4*z**2 - 110*z + 746. Let w be q(12). Let n be ((-87)/(-60) - 1)*4. Factor -6/5 - 3/5*g**w + n*g.
-3*(g - 2)*(g - 1)/5
Let v(q) be the second derivative of 8/9*q**3 - 23/9*q**2 - 1/54*q**4 - 70*q + 0. Factor v(t).
-2*(t - 23)*(t - 1)/9
Factor -2/9*u**2 - 1556/3*u + 0.
-2*u*(u + 2334)/9
Suppose 5 = 5*r + m, 3*r + 2*m = -r - 2. Suppose 2*x + 2*w + r = 3*x, x + 2*w - 14 = 0. Solve -38*f**3 - 50*f**2 - 14*f**4 - x*f + 5*f - 2*f**5 - 29*f - 8 = 0.
-2, -1
Suppose -3*a - 107*a = 0. Let d(w) be the first derivative of a*w**2 + 0*w - 11 + 1/10*w**4 + 2/5*w**3. Factor d(t).
2*t**2*(t + 3)/5
Suppose 2*p + f = 3*p - 194, -5*p = 4*f - 952. Suppose 0 = 35*n - 39*n + p. Factor n*i**4 - 2*i**5 + 43*i**4 + 54*i - 107*i**4 - 36*i**3.
-2*i*(i - 1)*(i + 3)**3
Let p be (-9)/(117/(-52))*1. Let z(a) be the first derivative of -1/10*a**p + 3/5*a**3 + 3/5*a - a**2 + 23. Factor z(s).
-(s - 3)*(s - 1)*(2*s - 1)/5
Suppose -12*a + 8*a + 27 = 5*h, -5*a - 5*h = -30. Let k(p) be the first derivative of -10/3*p**a + 8*p**2 + 8*p - 21. Factor k(z).
-2*(z - 2)*(5*z + 2)
Determine i so that 1681/2*i**3 - 2501/2*i**2 + 460*i - 50 = 0.
10/41, 1
Let l(u) = -u**3 + 85*u**2 + 175*u - 87. Let x be l(87). Factor -1/7*s**4 + x - 2/7*s**3 + 2/7*s + 1/7*s**2.
-s*(s - 1)*(s + 1)*(s + 2)/7
Let t(n) = -11*n**2 + 14*n - 2. Let v(q) be the third derivative of q**5/12 - q**4/4 + q**3/6 - 55*q**2. Let p(r) = 4*t(r) + 9*v(r). Factor p(x).
(x + 1)**2
Let b(o) be the third derivative of 1/120*o**6 - 1/2688*o**8 + 1/40*o**5 + 0*o**4 + 0*o**3 + 0*o - 1/1680*o**7 - 69*o**2 + 0. Let b(g) = 0. What is g?
-2, 0, 3
Let s(p) be the first derivative of -4/5*p**5 + 128*p - 15 - 88/3*p**3 + 9*p**4 + 0*p**2. Determine n, given that s(n) = 0.
-1, 2, 4
Let j(k) be the third derivative of -5/18*k**3 + 1/90*k**6 + 1/30*k**5 + 0*k - 1/630*k**7 + 51*k**2 - 1/18*k**4 - 4. Factor j(v).
-(v - 5)*(v - 1)*(v + 1)**2/3
Let x(r) be the first derivative of -r**6/33 - 16*r**5/55 - 12*r**4/11 - 64*r**3/33 - 16*r**2/11 - 2066. Factor x(u).
-2*u*(u + 2)**4/11
Factor -18225 - 5*v**3 - 6*v**3 + 2*v**3 - v**3 + 5*v**3 - 295*v**2 - 4995*v.
-5*(v + 5)*(v + 27)**2
Let x(r) be the second derivative of -r**6/60 - 9*r**5/40 + 25*r**4/24 + 11*r**3/4 + 9489*r. What is w in x(w) = 0?
-11, -1, 0, 3
Suppose 48*n - 26 = 50 + 20. Let t(u) be the first derivative of 4/5*u**5 + 32*u + 24*u**3 - 38 + 40*u**n + 7*u**4. Factor t(g).
4*(g + 1)*(g + 2)**3
Let y = 14541 - 14537. Let -8/9 + 14/9*x**3 - 10/3*x**2 + 26/9*x - 2/9*x**y = 0. What is x?
1, 4
Suppose -217308*s = -217279*s. Suppose 4/9*f**2 + s*f - 4/9*f**3 + 0 = 0. What is f?
0, 1
Let l(i) = -3*i**2 - 43*i + 296. Let m be l(5). Let d(n) be the first derivative of m*n + 3/4*n**4 - 3/2*n**2 - 2*n**3 + 5. Factor d(c).
3*(c - 2)*(c - 1)*(c + 1)
Factor 1974 - 16*o**2 - 1977*o + 21*o**2 - 5*o**2 + 4*o**2 - o**2.
3*(o - 658)*(o - 1)
Let w(h) = -h - 9. Let s be w(-11). Let c be -3*(-10)/(-25)*10/(-14). Solve 0 + 0*r + 0*r**s - c*r**5 + 2/7*r**4 + 4/7*r**3 = 0 for r.
-2/3, 0, 1
Let i(l) = 1017*l - 99664. Let c be i(98). Factor 169/7 + 143/7*w - 25/7*w**c + 1/7*w**3.
(w - 13)**2*(w + 1)/7
Suppose 0 = -5*g + 2*z + 27, -2*g + 4*z = -5*g - 15. Let q(w) be the second derivative of 0 - 1/12*w**g - 1/48*w**4 - 1/8*w**2 - 3*w. Factor q(c).
-(c + 1)**2/4
Let m(z) = 3*z + 16*z - 17 + 7*z. Let b be m(6). Find t such that -3 + 11*t**2 - 136*t + 13*t**2 - 9*t**2 + 9*t**3 + b*t = 0.
-1, 1/3
Let z be 1*(-11 + 7) + 82/20. Let w(l) be the second derivative of z*l**5 - 1/3*l**3 + 1/6*l**4 - 4*l + 0 - l**2. Determine f, given that w(f) = 0.
-1, 1
Let l = -133 + 129. Let n(s) = 13*s**4 + 9*s**3 - 24*s**2 - 23*s - 3. Let g(m) = 3*m**4 + 2*m**3 - 6*m**2 - 6*m - 1. Let c(r) = l*n(r) + 18*g(r). Factor c(z).
2*(z - 3)*(z + 1)**3
Let w = 3817827/11 - 347321. Let l = 246 + w. Factor -8/11*n + l*n**2 + 8/11.
2*(n - 2)**2/11
Let t(j) be the first derivative of -j**6/10 - j**5 - 9*j**4/4 - 5*j**3/3 + 25*j + 21. Let s(m) be the first derivative of t(m). Find w such that s(w) = 0.
-5, -1, -2/3, 0
Let p(f) be the first derivative of -f**4/4 - 16*f**3/3 + 119*f**2/2 + 294*f + 3701. Factor p(o).
-(o - 7)*(o + 2)*(o + 21)
Let x(f) be the third derivative of 4*f**7/315 + 139*f**6/180 + 293*f**5/18 + 1375*f**4/12 - 125*f**3 - 3136*f**2. Determine t so that x(t) = 0.
-15, -5, 1/4
Let z(j) be the third derivative of 2/19*j**3 - 16*j**2 + 4 + 43/228*j**4 + 7/570*j**5 + 0*j. Let z(t) = 0. What is t?
-6, -1/7
Let j(b) be the first derivative of 36*b**2 - 8/3*b - 162*b**3 - 132. What is l in j(l) = 0?
2/27
Let w(x) be the second derivative of x**4/12 + 13*x**3/2 - 40*x**2 - 173*x. Let v be w(-41). Solve -9/2 - 3*y + 3/2*y**v = 0 for y.
-1, 3
Let p(q) = -q**2. Let g(v) = 15*v**2 - 65*v + 1690. Let h(d) = g(d) + 20*p(d). Factor h(i).
-5*(i - 13)*(i + 26)
Let n = 29601 - 29599. Factor 22/5*u**3 - 24/5*u**n + 4/5*u**4 - 2/5*u**5 - 72/5*u + 0.
-2*u*(u - 3)**2*(u + 2)**2/5
Suppose 3073 = 5*m - 1322. Solve 12*v**3 + 3*v**4 + 15*v**2 + m - 879 + 6*v = 0 for v.
-2, -1, 0
Factor 108/5 + 0*b**2 - 2/5*b**3 + 54/5*b.
-2*(b - 6)*(b + 3)**2/5
Factor -57624/5 - 2/15*c**4 - 16874/15*c**2 + 7448*c - 76/3*c**3.
-2*(c - 3)**2*(c + 98)**2/15
Let w = -40025892/125 + 94901864382/296375. Let l = w + -2/2371. Factor 8*r + 5 + 1/5*r**4 - l*r**3 + 6/5*r**2.
(r - 5)**2*(r + 1)**2/5
Let s = 54328396/21127715 + 2/3018245. Factor -s*k**2 + 48/7 + 2/7*k**3 + 4*k.
2*(k - 6)*(k - 4)*(k + 1)/7
Let p(z) = -3*z**2 + 2*z + 20. Let u be p(0). Suppose r - u = -3*r. Factor 49 - r*c**5 - 49 + 5*c**3.
-5*c**3*(c - 1)*(c + 1)
Let b = -5028 - -5031. Let i(y) be the second derivative of 1/4*y**4 - 3/20*y**5 + 0*y**2 + 0 + 1/2*y**b - 1/10*y**6 - 26*y. Suppose i(f) = 0. What is f?
-1, 0, 1
Let k(a) = -7*a**2 - 6*a - 2. Let q(m) = 16*m**2 + 12*m + 3. Let o be 21*(-1 + 12/18). Let u(t) = o*k(t) - 3*q(t). Factor u(x).
(x + 1)*(x + 5)
Let y(r) be the third derivative