k**3 = 0.
-3, -1
Suppose 14*s + 62 + 12 = 61*s - 67. Factor 0*j - 2/13*j**5 + 50/13*j**4 + 0 + 288/13*j**2 - 336/13*j**s.
-2*j**2*(j - 12)**2*(j - 1)/13
Let l(t) be the second derivative of 2*t**7/105 - 3722*t**6/75 + 231012*t**5/5 - 47896240*t**4/3 + 95331200*t**3/3 + 2512*t. Factor l(b).
4*b*(b - 620)**3*(b - 1)/5
Suppose 3*j - 9*j = 4986. Let s = j - -831. Determine m, given that 16/5*m**3 + 2*m**4 + 8/5*m**2 + s*m + 2/5*m**5 + 0 = 0.
-2, -1, 0
Let o be 4/(-7)*5/((-20)/14). Suppose -i + 4*q = -16, -o*i - 5*q = 1 + 6. What is y in -15*y**3 - 8*y**2 + 8*y - 8*y**2 + i*y**4 + 7*y**3 + 12 = 0?
-1, 1, 3
Solve 92/3*w - 12 - 77/3*w**2 + 22/3*w**3 - 1/3*w**4 = 0 for w.
1, 2, 18
Let g(s) be the first derivative of s**4/6 + 152*s**3 + 51984*s**2 + 7901568*s + 258. Determine w, given that g(w) = 0.
-228
Let s(a) be the first derivative of a**6/54 - a**5/10 - 11*a**4/36 - 5*a**3/27 - 17*a + 6. Let z(d) be the first derivative of s(d). Factor z(f).
f*(f - 5)*(f + 1)*(5*f + 2)/9
Let t be 3/135*((-648)/(-48) + -12). Let z(h) be the third derivative of 0 + 0*h - 1/6*h**4 - 38*h**2 - 4*h**3 + 4/15*h**5 - t*h**6. Find s such that z(s) = 0.
-1, 2, 3
Let w be (30 - -9 - -10)*-19. Let y = w + 933. Suppose 4/7*n**3 - 4/7*n - 1/7*n**4 + 3/7 - 2/7*n**y = 0. What is n?
-1, 1, 3
Factor 209*l**3 - 46*l**3 - 54*l**3 + 148*l**2 - 4800 - 52*l**3 - 1120*l - 61*l**3.
-4*(l - 20)**2*(l + 3)
Find o, given that 4693/3 + 1/6*o**3 + 32/3*o**2 + 1349/6*o = 0.
-26, -19
Let m(p) = -p**2 + 18*p + 33. Let u be m(12). Factor -s**3 - 21*s**2 - 213*s + u*s + 108*s.
-s**2*(s + 21)
Let q(k) = 25*k**2 + 81*k + 414. Let w(g) = -8*g**2 - 2*g. Let x(v) = -4*q(v) - 12*w(v). Suppose x(d) = 0. Calculate d.
-69, -6
Let o(z) = -5*z**3 + 2*z**2 + 8. Let j be (-6)/(-12)*-2 - 3. Let y(a) = 11*a**3 - 4*a**2 - 18. Let p(k) = j*y(k) - 9*o(k). Let p(q) = 0. Calculate q.
0, 2
Factor 837/7 + 3/7*n**3 - 531/7*n + 75/7*n**2.
3*(n - 3)**2*(n + 31)/7
Let n(c) be the first derivative of 2*c**3/27 - 206*c**2/9 - 418*c/3 - 1832. Factor n(k).
2*(k - 209)*(k + 3)/9
Solve 50/17*n**3 + 2/17*n**5 - 30/17*n**4 + 0 + 30/17*n**2 - 52/17*n = 0 for n.
-1, 0, 1, 2, 13
Let r(v) be the third derivative of v**7/3780 - v**5/20 + 71*v**4/24 - 68*v**2. Let k(h) be the second derivative of r(h). Factor k(i).
2*(i - 3)*(i + 3)/3
Let g = -184 + 187. Factor -10*u**3 + 6 - 100*u**4 + 198*u**4 - 101*u**4 + 9*u - 3*u**2 + u**g.
-3*(u - 1)*(u + 1)**2*(u + 2)
Find a such that 0*a**2 - 1226740*a + 4*a**2 + 1226604*a - 780 = 0.
-5, 39
Let f be (-7 - 665/(-60)) + -4. Let n(v) be the second derivative of 10*v + 0*v**4 - 1/120*v**5 + 1/6*v**2 + f*v**3 + 0. Factor n(i).
-(i - 2)*(i + 1)**2/6
Let s(d) be the first derivative of 77 + 2/3*d**2 - 2/15*d**5 + 0*d - 1/9*d**6 + 1/2*d**4 + 10/9*d**3. Solve s(z) = 0 for z.
-1, 0, 2
Let a(i) = -7*i**2 - 2206*i + 241976. Let y(v) = -12*v**2 - 4411*v + 483956. Let o(p) = -11*a(p) + 6*y(p). Factor o(h).
5*(h - 220)**2
Let r(c) be the third derivative of 1/700*c**7 - 1/50*c**5 + 0*c + 1/3360*c**8 + 0*c**3 + 1 + 2*c**2 - 1/30*c**4 - 1/600*c**6. Find p such that r(p) = 0.
-2, -1, 0, 2
Factor 72 + 86/13*t - 2/13*t**2.
-2*(t - 52)*(t + 9)/13
Let z = -5625 + 5627. Let j(h) be the second derivative of -3/40*h**5 + 1/8*h**4 + 0*h**z + 0*h**3 + 0 - 27*h. What is d in j(d) = 0?
0, 1
Let l be (-66)/231*(-7)/60. Let h(o) be the third derivative of l*o**6 - 2/3*o**4 + 0*o - 1/15*o**5 - 35*o**2 + 8/3*o**3 + 0. Factor h(t).
4*(t - 2)*(t - 1)*(t + 2)
Let k(x) = -3*x**2 + 77*x - 29. Let p be k(15). Let g = -449 + p. Let 13/2*n**2 + 1/2*n**4 + g + 6*n + 3*n**3 = 0. What is n?
-2, -1
Let a(w) = 6*w**4 - 4*w**3 + 15*w**2 + 25*w - 5. Let l(f) = -3 - f**3 + f**4 + 2 + 2*f**3. Let i(y) = a(y) - 5*l(y). Factor i(j).
j*(j - 5)**2*(j + 1)
Let r(t) be the first derivative of t**6/6 + 81*t**5/5 + 951*t**4/2 + 10702*t**3/3 + 21201*t**2/2 + 12321*t + 2950. Find k, given that r(k) = 0.
-37, -3, -1
Let a = -2917 - -4204. Let 50*v**3 + 21*v - 1237*v**2 + 4*v + 5*v**5 + 25*v**4 + 5 + a*v**2 = 0. What is v?
-1
Let z = 43 + -30. Suppose -2*n - 2*x - 21 = 3*x, n + 3*x + z = 0. Factor 2*d**3 + 4 - 2*d**2 - 4*d + 2*d**3 - n*d - 2*d**4 + 2*d**3.
-2*(d - 2)*(d - 1)**2*(d + 1)
Let b(f) = -17*f**3 + 567*f**2 - 3280*f. Let v(c) = 8*c**3 - 278*c**2 + 1640*c. Let j(o) = -3*b(o) - 7*v(o). Find n, given that j(n) = 0.
0, 8, 41
Factor -135 - 3/2*j + 3/2*j**2.
3*(j - 10)*(j + 9)/2
Let j(i) be the first derivative of i**5/35 - 121*i**4/28 - 82*i**3/7 + 2269. Factor j(v).
v**2*(v - 123)*(v + 2)/7
Let a(p) be the second derivative of 13*p**4/12 - 11*p**3/6 - p**2 - p + 247. Find q, given that a(q) = 0.
-2/13, 1
Let w be ((-8)/(-6))/(30/1125*-5). Let o be w/8*(-32)/80. Suppose 8*f - 7/2*f**2 + o*f**3 - 6 = 0. Calculate f.
2, 3
Let w(o) be the second derivative of 1/10*o**5 - 3*o - 1/2*o**4 + 0*o**2 + 0*o**3 - 4. Factor w(y).
2*y**2*(y - 3)
Suppose 9335088/5 + 10584/5*q + 3/5*q**2 = 0. What is q?
-1764
Let z(u) = -6*u**3 + u - 1. Let x be z(1). Let y = 8 + x. Solve -81*h**5 + 18*h**3 - 9*h + 17*h**y - 65*h**2 + 9*h**3 - 3*h + 162*h**4 = 0 for h.
-1/3, 0, 2/3, 2
Suppose 0 = -4*f + i - 2, -66*f + 63*f + 3*i = 24. Let 0 - 2/13*n**4 + 2/13*n + 2/13*n**f - 2/13*n**3 = 0. Calculate n.
-1, 0, 1
Let g = -228 - -231. Factor 676*a**g - 1305 + 2096*a + 647 + 498 - 6968*a**2.
4*(a - 10)*(13*a - 2)**2
Let b(c) be the third derivative of -c**5/12 - 11*c**4/6 + 49*c**3/6 + 149*c**2. Solve b(o) = 0.
-49/5, 1
Let s(o) be the third derivative of o**5/20 + 149*o**4/4 + 22201*o**3/2 - 79*o**2 + 5*o. Determine t, given that s(t) = 0.
-149
Suppose 19*h = 12*h + 21. Let i be (-4)/12*7 + h/1. Factor -2/3*v**2 + 0*v + 0 - i*v**3.
-2*v**2*(v + 1)/3
Let l(o) be the first derivative of -2*o**5/45 + 29*o**4/18 - 518*o**3/27 + 245*o**2/3 - 1323. Factor l(k).
-2*k*(k - 15)*(k - 7)**2/9
Let u = 5197 - 5192. Let l(q) be the third derivative of 0 - 1/100*q**u + 0*q**3 + 0*q + 13*q**2 + 1/40*q**4. Factor l(y).
-3*y*(y - 1)/5
Let p be ((-30)/8)/((-15)/(-420)). Let f be (-7)/(-10) + (7 - p/(-14)). Suppose -2/5*a + f*a**2 + 0 = 0. What is a?
0, 2
Let m be (-351)/78 + (-1111)/(-217). Let f = m - 3/62. Determine x so that f*x - 8/7*x**2 + 4/7 = 0.
-1/2, 1
Let j(n) be the third derivative of -n**7/315 - n**6/30 + 43*n**5/90 + 25*n**4/3 + 28*n**3 - 9*n**2 - 6*n - 3. What is d in j(d) = 0?
-6, -1, 7
Find p, given that 65*p**3 + 35/3*p**4 + 0 + 70/3*p**2 - 2/3*p**5 - 88/3*p = 0.
-4, -1, 0, 1/2, 22
Factor -1/6*c**2 + 4*c - 22/3.
-(c - 22)*(c - 2)/6
Let g(s) be the second derivative of -5*s**4/12 + 2420*s**3/3 + 4845*s**2/2 + 5167*s. Factor g(u).
-5*(u - 969)*(u + 1)
Let p = -76 + 76. Let g be p - 0 - 4 - 7/(-1). What is u in -15*u**2 + 15 - g - 2*u**4 + 3*u**4 + 2*u**4 = 0?
-2, -1, 1, 2
Let i(c) be the third derivative of -2*c**7/245 - 89*c**6/280 - 45*c**5/14 + 59*c**4/8 + 65*c**3/7 + 2638*c**2. Suppose i(t) = 0. Calculate t.
-13, -10, -1/4, 1
Let d be 4/22*165/150. Let f(x) be the first derivative of -10 - 1/6*x**6 + 0*x + d*x**5 + 0*x**3 + 0*x**4 + 0*x**2. Solve f(g) = 0 for g.
0, 1
Let a(r) be the first derivative of r**4/26 + 5*r**3/39 + 2*r**2/13 + 205*r + 128. Let t(j) be the first derivative of a(j). Factor t(z).
2*(z + 1)*(3*z + 2)/13
Suppose -9/5*x**3 - 12/5*x**4 + 0 + 12/5*x**2 + 12/5*x - 3/5*x**5 = 0. What is x?
-2, -1, 0, 1
Let 1/4*l**4 + 957/4*l**2 + 119 + 121/2*l**3 + 298*l = 0. Calculate l.
-238, -2, -1
Let h(c) be the second derivative of 18*c - 9/2*c**2 + 0*c**3 + 0 + 1/200*c**6 + 1/10*c**4 - 1/25*c**5. Let t(r) be the first derivative of h(r). Factor t(y).
3*y*(y - 2)**2/5
Let s(d) be the third derivative of -d**9/40320 + d**7/3360 + 13*d**5/30 - 14*d**2. Let o(g) be the third derivative of s(g). Find q such that o(q) = 0.
-1, 0, 1
Let f(g) be the third derivative of g**7/6720 + g**6/2880 - g**5/120 - g**4/16 - 14*g**3/3 + 5*g**2 - 9. Let o(q) be the first derivative of f(q). Factor o(r).
(r - 3)*(r + 2)**2/8
Let o = -4342 + 30396/7. Suppose 3*u - 3*l + 22 - 7 = 0, -5*l + 25 = 2*u. Factor -o*p**3 + 0 + 2/7*p + u*p**2.
-2*p*(p - 1)*(p + 1)/7
Let n(q) be the first derivative of q**6/1140 + q**5/570 - 5*q**4/114 + 8*q**3/57 + 27*q**2/2 - 24. Let m(a) be the second derivative of n(a). Factor m(o).
2*(o - 2)*(o - 1)*(o + 4)/19
Let a(o) be the second derivative of -o**4/28 + 417*o**3/7