
Let a be ((-16)/(-64) - 69/(-12)) + -27. Let l(v) = -2*v**2 - 38*v + 87. Let b be l(a). Let 0*n + 0*n**4 + 1/2*n**b + 0*n**2 + 0 - 1/2*n**5 = 0. What is n?
-1, 0, 1
Let d(w) = 5*w**3 - 118*w**2 - 338*w - 227. Let r(p) = 16*p**3 - 358*p**2 - 1016*p - 682. Let m(n) = -10*d(n) + 3*r(n). Factor m(j).
-2*(j - 56)*(j + 1)*(j + 2)
Let b(y) be the third derivative of y**8/1008 - y**7/42 - 11*y**6/72 + y**5/12 + 3*y**4/4 + 389*y**2 + 5. Suppose b(o) = 0. Calculate o.
-3, -1, 0, 1, 18
Let f = -5 + 14. Determine g so that -f*g**5 + 5*g**5 - 2069*g**3 + 728*g**3 - 8280*g**2 - 172*g**4 - 1773*g**3 + 770*g**3 + 24300*g - 13500 = 0.
-15, 1
Let y(n) = -871*n - 55741. Let o be y(-64). Factor 49/3*c**o - 2527/3*c**2 + 1432/3*c - 68.
(c - 51)*(7*c - 2)**2/3
Let u(s) be the second derivative of s**6/70 + 3*s**5/10 - 2*s**4/7 - 240*s**3/7 - 1728*s**2/7 + 6050*s. Find c, given that u(c) = 0.
-12, -4, 6
Let d be 8 - ((-188)/24 + 8)*(27 - -3). Suppose 0*i - 24/7*i**2 + 4/7*i**5 - 32/7*i**4 + 52/7*i**d + 0 = 0. Calculate i.
0, 1, 6
Let k(f) = -6*f**2 - 632*f + 6. Let i(h) = -13*h**2 - 1260*h + 15. Let q(z) = -2*i(z) + 5*k(z). Let q(s) = 0. What is s?
-160, 0
Factor -312/17*j**2 - 106/17 + 2/17*j**4 - 100/17*j**3 - 316/17*j.
2*(j - 53)*(j + 1)**3/17
Determine q, given that -4/3*q**4 + 20*q**3 - 64*q + 0 - 128/3*q**2 = 0.
-1, 0, 4, 12
Let c = -33392/5 + 31668/5. Let g = c - -345. Suppose 2/5*i**3 - 1/5*i + 0 + g*i**2 = 0. What is i?
-1, 0, 1/2
Let m = -146242/9 - -16266. Let n = m - 50/3. Let 2/9*p**4 - n*p**3 + 0 + 2/9*p - 2/9*p**2 = 0. What is p?
-1, 0, 1
Let j(z) be the second derivative of 1/4*z**4 - 13/10*z**3 + 21/10*z**2 + 3/100*z**5 - 2*z + 119. What is r in j(r) = 0?
-7, 1
Let u = -39 - -47. Let l be (-3)/(-15) + u/10. Let n(r) = r. Let m(s) = -3*s**2 - 25*s - 48. Let p(o) = l*m(o) + n(o). Suppose p(k) = 0. Calculate k.
-4
Let a = 815199 - 815187. Solve -11/3*d**2 - 20*d**3 + 20*d + a - 25/3*d**4 = 0 for d.
-6/5, -1, 1
Let v(c) = 2*c**2 + 49*c + 209. Let l be v(-30). Suppose -537*s**3 + 150*s**2 - 98*s**3 - 326*s**3 + 5000*s**4 - l*s**3 - 5*s = 0. Calculate s.
0, 1/10
Let k = -5169/5 - -1034. Let u = 60 + -57. Suppose -1/10*g**4 + 0 + k*g - 1/2*g**2 + 2/5*g**u = 0. What is g?
0, 1, 2
Factor 128/7*n - 128/7 + 2/7*n**2 - 2/7*n**3.
-2*(n - 8)*(n - 1)*(n + 8)/7
Let b(x) = 2*x**2 - 23491*x - 93974. Let v be b(-4). Determine q, given that v*q**4 + 40*q**5 + 32/5*q + 32/5 - 448/5*q**2 - 808/5*q**3 = 0.
-2, -2/5, 1/4, 2
Let t(u) = 3*u - 14. Let j be t(-6). Let c be j/6*7/(84/(-27)). Let 1 + 2 - 12*z**2 - 7 - 4*z**3 - c*z = 0. Calculate z.
-1
Let y(a) = a**3 - 44*a**2 + 43*a + 20. Let q be y(43). Suppose 5*j + q = 0, 3*j + 9 = 12*o - 13*o. Factor 0*b**2 + 0*b + o*b**3 - 3/2*b**4 + 0.
-3*b**3*(b - 2)/2
Let k(f) = f**3 + 3*f**2 - 60. Let o be k(0). Let s be (-34)/o - 16/240. Determine b, given that -7/4*b**4 + s*b - 2*b**2 + 23/8*b**3 + 0 + 3/8*b**5 = 0.
0, 2/3, 1, 2
Suppose 2*m = -4*z + 6 + 32, 2*z - 4*m = 14. Let w be (-7)/((-105)/(-5)) + 6/z. Factor 2/3*i + w*i**4 + 0*i**3 + 0 - i**2.
i*(i - 1)**2*(i + 2)/3
Let d = 497 - 322. Factor 106 + 3*p**4 - d*p**3 - 731*p + 106*p**3 - 486*p**2 - 802 - 486*p + 197*p.
3*(p - 29)*(p + 2)**3
Let m = 14683/4 - 3670. Let h(q) be the second derivative of -1/20*q**6 - m*q**3 + 3/2*q**2 + 0 + 9/40*q**5 - 1/8*q**4 - 2*q. What is z in h(z) = 0?
-1, 1, 2
Let b be (9 - 4 - 5) + -5 + 3. Let u be (-275)/(-44) + -6 + b/(-4). Factor 5/4*x**2 - u*x - 1/2.
(x - 1)*(5*x + 2)/4
Let s(d) = d**3 - 17*d**2 + 18*d + 5. Let c be s(16). Suppose 0 = 2*u - 2*q - 6, 0 = -2*u + 4*q + 2 + 4. Factor 61*g**5 - 29*g**5 - c*g**5 + 5*g**u.
-5*g**3*(g - 1)*(g + 1)
Let j be -2*(7 - 32/4). Factor -10*g**2 + 22*g**2 - 7*g**2 - 11 - 4*g**j - 10*g.
(g - 11)*(g + 1)
Solve -3888/5 - 1212/5*u**2 + 3708/5*u + 148/5*u**3 - 4/5*u**4 = 0.
3, 4, 27
Let y(i) be the second derivative of i**4/3 - 1883*i**3/6 - 471*i**2/2 - i + 602. Factor y(h).
(h - 471)*(4*h + 1)
Let q(k) be the third derivative of 7*k**6/360 - k**5/30 - 7*k**4/72 + k**3/3 - k**2 + 498. Solve q(b) = 0 for b.
-1, 6/7, 1
Let z(t) be the first derivative of 29*t**4/4 + t**3/3 - t**2/2 + 8. Let q be z(1). Let 16*v**2 - 20*v + q*v**2 + 10*v = 0. What is v?
0, 2/9
Suppose -13*l - 4*l = -102. Let z be l/51 + (-1524)/(-340) - 3. Factor -24/5*t**4 + 0 + 1/5*t - z*t**2 + 22/5*t**3 + 9/5*t**5.
t*(t - 1)**2*(3*t - 1)**2/5
Let b(m) = m**3 + 8*m**2 + 2*m + 19. Let u be b(-8). Suppose -d + 0*d = -u. Solve 4*l**3 - 12*l**2 - 2*l**3 + l**d = 0 for l.
0, 4
Factor 6*r - 599*r**3 + 0*r**2 + 617*r**3 + 10*r**4 - 34*r**2.
2*r*(r - 1)*(r + 3)*(5*r - 1)
Let l(g) be the second derivative of 1 - 3/2*g**3 + 0*g**2 + g + 1/12*g**4. Solve l(i) = 0 for i.
0, 9
Let p(v) be the first derivative of -3*v**4/8 - 3*v**3/2 + 6*v - 1331. Factor p(j).
-3*(j - 1)*(j + 2)**2/2
Let x = 79 + -77. Suppose 5*u - x*u = -3*l - 6, -2*u = -l - 11. Solve 0*f**2 - 65 - u*f**2 + 3*f + 65 = 0.
0, 1
Let h be (3/19)/((-1440)/(-41040))*-8*1/(-18). What is f in -477/5*f - 24 + 12/5*f**h = 0?
-1/4, 40
Let b = -527 - -112777/214. Let u = 435/1498 + b. What is v in u*v**3 + 0*v + 0 - 4/7*v**2 = 0?
0, 2
Let z(v) be the second derivative of v**4/72 - 5*v**3/9 - 87*v**2/4 - v + 160. Suppose z(g) = 0. What is g?
-9, 29
Let l(y) = -y + 4. Let f be l(2). Suppose 7*p = f*p + 10. Factor -3*h**2 + 5*h**2 + 11*h + 5 - 15 - 3*h**p.
-(h - 10)*(h - 1)
Suppose -4*x = -3*f + 66, 0 = 5*f - 10*f + 3*x + 99. Suppose -f*k = -10*k - 16. Find z, given that -z**3 + 0 - 1/2*z + 5/4*z**k + 1/4*z**4 = 0.
0, 1, 2
Let q(w) be the first derivative of -w**4/42 + 62*w**3 - 60543*w**2 + 26275662*w - 6427. What is y in q(y) = 0?
651
Factor 840*b**2 + 275 + 5*b**4 + 54*b + 555*b + 290*b**3 + 221*b.
5*(b + 1)**3*(b + 55)
Let p(b) be the second derivative of -1/70*b**5 - 10*b + 2/21*b**4 - 1 - 18/7*b**2 + 5/7*b**3. Find r such that p(r) = 0.
-3, 1, 6
Factor -6993800/7 - 2/7*o**2 - 7480/7*o.
-2*(o + 1870)**2/7
Suppose 26*t - 6*t + 5*t**5 - 54 + 36*t**4 - 150*t**2 - 6*t**4 + 0*t**5 - 25*t**3 + 174 = 0. What is t?
-6, -2, -1, 1, 2
Determine j, given that -2/9*j**4 + 0 + 32/9*j**2 - 112/9*j**3 + 7/9*j**5 + 0*j = 0.
-4, 0, 2/7, 4
Let z(v) = -v**3 + 170*v**2 - 2180*v - 621. Let r be z(156). Suppose 1/2*x**r - 15/2*x - 18 + x**2 = 0. Calculate x.
-3, 4
Let v = 44/2633 - -2545/5266. Let 8*x**4 + 3*x + v*x**2 - 12*x**3 + 1/2 = 0. Calculate x.
-1/4, 1
Let q(l) be the first derivative of 9 + 0*l**3 + 0*l + 0*l**2 - 7/20*l**4 - 1/25*l**5. Find y such that q(y) = 0.
-7, 0
Suppose 5*l = -2*f + 24, -3*l = -6*l + 12. Factor 16*z**f - 2 + 681*z - 718*z + 17*z**2 + 6*z**2.
(z - 1)*(39*z + 2)
Let k be 5 + (938/182 - 10). Factor -2/13*u**3 + 0 + 0*u - k*u**4 + 2/13*u**2 + 2/13*u**5.
2*u**2*(u - 1)**2*(u + 1)/13
What is n in 2/7*n**3 + 122/7*n**2 - 384/7*n + 0 = 0?
-64, 0, 3
Let y(o) be the second derivative of -11 - 1/10*o**6 + 3/20*o**5 - 1/12*o**4 + o + 0*o**3 + 0*o**2 + 1/42*o**7. Suppose y(c) = 0. What is c?
0, 1
Let a(r) = 4*r**4 - 56*r**3 - 132*r**2 + 1088*r - 1204. Let p(q) = 2*q**2 - 12*q + 1. Let n(x) = -a(x) - 4*p(x). Solve n(u) = 0.
-5, 2, 15
Let n(r) be the first derivative of 49*r**6/24 + 287*r**5/20 + 191*r**4/16 - 863*r**3/12 - 30*r**2 + 144*r - 8859. What is q in n(q) = 0?
-24/7, -1, 1
Suppose 2*c - 4*s + 19 - 39 = 0, 2*c = 3*s + 17. Suppose -a - 3*o - 12 = 0, 6*a - 4*a = -2*o - c. Determine j, given that -1/4*j**a + 0*j + 0 - 1/4*j**2 = 0.
-1, 0
Determine n, given that 9/2*n**2 - 78 - 1/2*n**3 + 32*n = 0.
-6, 2, 13
Find x such that -1630*x + 6130*x**3 - 550 + 185*x**2 + 1975 - 6110*x**3 = 0.
-15, 1, 19/4
Let f be (81/(-2124))/(15/(-216)). Let g = f + 3/59. Factor 6*k - g*k**2 - 15.
-3*(k - 5)**2/5
Let z(c) be the third derivative of c**8/84 - 32*c**7/105 + 27*c**6/10 - 182*c**5/15 + 94*c**4/3 - 48*c**3 - 4609*c**2. Solve z(o) = 0 for o.
1, 2, 9
Let o(u) be the third derivative of u**6/24 - 161*u**5/12 - 2065*u**4/12 - 1660*u**3/3 + 7126*u**2. Factor o(s).
5*(s - 166)*(s + 1)*(s + 4)
Let z(r) be the third derivative of -r**8/60480 + r**7/5040 - r**6/1080 - r**5/15 + 3*r**2 - 6*r. Let a(l) be the third derivative of z(l). Factor a(s).
-(s - 2)*(s - 1)/3
Let d = -83 + 74. Let f be d*(-6 - 200/(-36)). Factor -5/2*y**2 - f + 11*y.
-(y - 4)*(5*y - 2)/2
Let t(a) = 2*a**2 - 40*a + 41. Let v be t(19). Let u be 14