Let p(c) be the third derivative of -5*c**8/84 - 16*c**7/35 + c**6/3 + 8*c**5/5 - 5*c**4/6 + 9*c**2 - 14*c. Determine n, given that p(n) = 0.
-5, -1, 0, 1/5, 1
Let p = -57335 - -57337. Factor 0 + 0*h + 6/11*h**3 - 8/11*h**4 + 0*h**p + 2/11*h**5.
2*h**3*(h - 3)*(h - 1)/11
Let i(p) = 5*p**3 - 471*p**2 + 930*p - 452. Let o(q) = 7*q**3 - 473*q**2 + 929*q - 447. Let a(h) = 4*i(h) - 3*o(h). Factor a(m).
-(m - 1)**2*(m + 467)
Let k be (344/(-301) - 6/7) + 2*3. Let w(m) be the third derivative of 0*m**3 + 0*m**k + 4/105*m**5 - 38*m**2 - 1/210*m**6 + 0 + 0*m. Solve w(r) = 0 for r.
0, 4
Let d = -67676 - -67678. Let 1/4*y**d - y + 1 = 0. What is y?
2
Suppose 3*g + 5 = 3*q + 2*g, -2*g + 6 = 2*q. Let 4*y - 20*y**3 + 17*y + 18*y**q + 3*y + 10*y**2 = 0. Calculate y.
-3/5, 0, 2
Suppose -n - 2 = 2*y - 8, 0 = -2*y + 4. Let i(r) be the second derivative of 15*r + 0*r**n - 21/170*r**5 + 8/51*r**4 + 0 + 3/85*r**6 - 4/51*r**3. Factor i(k).
2*k*(k - 1)*(3*k - 2)**2/17
Let v be (74/(-222) - 7/(-15))*(-4)/(-4)*10. Factor 0 - 4/9*m**4 + 4/3*m**3 - v*m**2 + 4/9*m.
-4*m*(m - 1)**3/9
Let s(h) be the second derivative of h**4/12 - 977*h**3/6 + 488*h**2 + 255*h + 8. Let s(x) = 0. What is x?
1, 976
Suppose -252 = -5*q + 17*q. Let y be (-51)/q + 9/(-21). Factor 0 + 2*p**5 + p**3 - 7/2*p**4 + 1/2*p**y + 0*p.
p**2*(p - 1)**2*(4*p + 1)/2
Suppose 7*s + 8*s - 330 = 0. Let u(o) = 4*o**3 - 10*o**2 - 3. Let b(n) = 15*n**3 - 37*n**2 - 11. Let m(k) = s*u(k) - 6*b(k). Let m(c) = 0. What is c?
0, 1
Let o(y) = y**3 - 23*y**2 + 25*y - 64. Let l(p) = -8*p - 210. Let k be l(-29). Let j be o(k). Solve -8/7 + 16/7*z + 6*z**j + 4/7*z**3 - 2*z**4 = 0 for z.
-1, 2/7, 2
Suppose -1115*z - 596 = 998*z - 2262*z. Let -2*g + 3/2*g**3 + 0*g**2 + 0 + 1/2*g**z = 0. Calculate g.
-2, 0, 1
Let r be (-70)/(-5) + -2 + -5 + 860. Let s = r + -867. Find a, given that 0*a + s + 2/15*a**3 - 2/3*a**2 = 0.
0, 5
Suppose -4032*n - 15*n**2 - 183*n**2 - 34080*n**3 + 34077*n**3 - 23520 = 0. Calculate n.
-28, -10
Let r(x) = -6*x**2 - 2043*x + 5742. Let s(i) = -3*i**2 - 1025*i + 2871. Let q(c) = 11*r(c) - 21*s(c). Let q(n) = 0. Calculate n.
-319, 3
Let f(g) be the second derivative of g**5/120 + g**4/8 - 4*g**3/3 - 71*g**2/2 - 104*g. Let t(y) be the first derivative of f(y). Find q, given that t(q) = 0.
-8, 2
Let w be (-28)/(-98) - (-133)/49. Let m(g) be the second derivative of -8/15*g**2 + 1/45*g**4 + 0 + 18*g - 1/150*g**5 + 4/45*g**w. Factor m(z).
-2*(z - 2)**2*(z + 2)/15
Let u = 159 + -153. Let n be 3/u*(-20)/(-40). Factor 0 + r - n*r**3 - 3/4*r**2.
-r*(r - 1)*(r + 4)/4
Let 13/7*x**4 + 40/7 - 1/7*x**5 + 127/7*x**2 - 61/7*x**3 - 118/7*x = 0. What is x?
1, 2, 4, 5
Let g be 153/3078 - (61 - 62)/(20 + -2). Suppose 4*v + 4 = 20. Solve -g*x**v + 0*x + 0 + 0*x**2 + 4/19*x**3 = 0 for x.
0, 2
Suppose 12*r**3 - 280908*r - 3403*r**2 - 3*r**3 - 28652616 - 10*r**3 + 2485*r**2 = 0. Calculate r.
-306
Let x = -325529 + 325545. Find g such that 3*g**2 - x + 1/2*g**3 + 0*g = 0.
-4, 2
Suppose 0 = 3*l - 5*g - 20, -l - l = -5*g - 20. Suppose 81*r - 5866 + 2538 = -751*r. Factor 9/5*t**2 - 6/5*t**3 + 1/5*t**r + 0*t + l.
t**2*(t - 3)**2/5
Let h(n) be the second derivative of -2*n + 20 + 0*n**2 - 128*n**6 - 120*n**5 + 0*n**3 - 125/3*n**4 - 1024/21*n**7. Factor h(m).
-4*m**2*(8*m + 5)**3
Let x(c) = 7*c**2 + 284*c + 78. Let n(m) = -28*m**2 - 1132*m - 310. Let o(w) = -3*n(w) - 13*x(w). What is z in o(z) = 0?
-42, -2/7
Let h(d) be the third derivative of d**6/120 + 47*d**5/60 + 41*d**4/3 + 104*d**3 - 5*d**2 - 176. Suppose h(a) = 0. What is a?
-39, -4
Let v be 65/10 - 2/12*3. Factor 389 + v*a**3 + 3*a**4 - 3*a**5 - 389.
-3*a**3*(a - 2)*(a + 1)
Suppose 195*q - 1520 = -109*q. Factor q*m + 0 - 1/4*m**2.
-m*(m - 20)/4
Let o(r) be the first derivative of r**4/3 + 7*r**3/3 - 54*r**2 + 2364. Find f such that o(f) = 0.
-12, 0, 27/4
Let x(j) = j**3 + j**2 - 2*j. Let c(a) = 4*a**3 - 114*a**2 + 106*a + 228. Let k(p) = c(p) - 2*x(p). Factor k(q).
2*(q - 57)*(q - 2)*(q + 1)
Let c be ((-16)/(-6))/(140/30). Suppose -7 = -2*s + j - 16, 4*s + j - 9 = 0. Factor -24/7*q + c*q**4 + 16/7*q**3 + s + 4/7*q**2.
4*q*(q - 1)*(q + 2)*(q + 3)/7
Let b(d) be the third derivative of -1/420*d**6 - 1/1470*d**7 - 5 + 3*d**2 + 1/84*d**4 + 0*d + 1/105*d**5 - 1/14*d**3. Determine l, given that b(l) = 0.
-3, -1, 1
Let m(u) = u**3 + 3*u**2 + 2*u + 2. Let a be ((-40)/(-180))/((-1)/9). Let f be m(a). Factor 10/7*l**f + 4/7*l + 0.
2*l*(5*l + 2)/7
Suppose 0 = 6*d - 3*s - 171, -8*d - 5*s = -6*d - 15. Let h(y) be the first derivative of -y - d + 7/12*y**3 + y**2 - 5/16*y**4. Let h(v) = 0. What is v?
-1, 2/5, 2
Let k(o) be the first derivative of -5*o**4/4 + 735*o**2/2 - 3430*o - 2292. Factor k(b).
-5*(b - 7)**2*(b + 14)
Let z(w) be the second derivative of 0*w**3 - 1/294*w**7 + 3/28*w**4 - 3/28*w**5 + 1/30*w**6 + 0 + 58*w + 0*w**2. Factor z(m).
-m**2*(m - 3)**2*(m - 1)/7
Let f be (13 - -2)*(-3 + 0 + 4). Let 6*b**4 - 30 + f*b**3 - 10*b**2 - 51*b + b**2 - 3*b**4 + 0*b**3 = 0. Calculate b.
-5, -1, 2
Let b(t) be the second derivative of -3*t**5/20 - t**4/3 + 74*t**3/3 - 48*t**2 + 1050*t. Find d, given that b(d) = 0.
-8, 2/3, 6
Factor -131/2*i - 1/4*i**2 + 0.
-i*(i + 262)/4
Let p = -161/654 - -1071/218. Factor 2/3*s**4 + 2*s + 10/3*s**3 + 0 + p*s**2.
2*s*(s + 1)**2*(s + 3)/3
Let w be (-136)/(-6)*12/(-8). Let y = w + 37. Determine c so that 12*c - 12 + 39*c**2 + 16*c**y + 11*c**3 - 12*c**3 = 0.
-2, -1, 2/5
Let w(p) be the third derivative of -p**5/40 + 3*p**4/4 + 133*p**3/4 + 2990*p**2. Suppose w(s) = 0. Calculate s.
-7, 19
Let a be (0 + -8)/(2184/(54 + -96)). Factor 80/13*h + 36/13*h**3 + a*h**4 + 0 - 2/13*h**5 - 8*h**2.
-2*h*(h - 2)**3*(h + 5)/13
Suppose -31*c + 8*c + 92 = 0. What is q in -8 - 11 + 8*q**3 + 29 - 6*q**2 - 3 - q**c - 4*q - 4*q = 0?
-1, 1, 7
Let i = -17 - -22. Factor -5*c**5 + 4*c**i - c**2 + c**3 + 51*c**4 - 97*c**4 + 47*c**4.
-c**2*(c - 1)**2*(c + 1)
Let m(f) be the third derivative of f**5/210 + 571*f**4/84 + 568*f**3/7 + 5*f**2 + 656. Factor m(o).
2*(o + 3)*(o + 568)/7
Let i(p) be the first derivative of 5*p**3 - 6275*p**2 + 8360*p - 5503. Factor i(x).
5*(x - 836)*(3*x - 2)
Let i(r) be the first derivative of -4*r**3/3 - 6780*r**2 - 11492100*r - 4816. Factor i(d).
-4*(d + 1695)**2
Let d(s) be the third derivative of s**6/660 - 2*s**5/165 - s**4/44 + 6*s**3/11 + 6*s**2 - 318*s. Find j, given that d(j) = 0.
-2, 3
Let u(o) = o**4 - o**3 + o + 2. Suppose 2 = f - 0. Let s(b) = 8*b**3 - 18*b**2 + 16*b. Let i(h) = f*u(h) - s(h). Solve i(z) = 0 for z.
1, 2
Determine u so that 202*u**2 + 9*u**2 - 145*u**2 - 3*u**3 = 0.
0, 22
Suppose 14*a - 145 = -2*k + 9*a, -2*k - 4*a + 140 = 0. Suppose -k + 12 = -12*n. Factor -1/6*v**2 + 1/6*v**n + 1/6*v**3 - 1/6*v + 0.
v*(v - 1)*(v + 1)**2/6
Let v be (8 + (-222)/21 + 3)*((-1190)/180)/(-17). Factor -30*a - 1350 - v*a**2.
-(a + 90)**2/6
Suppose -3*p - 155 = -b, -89 - 51 = 3*p + 2*b. Let k = 109 - p. Factor -195*n + 90 - 59*n**2 + 14*n**3 - 29*n**3 + k*n**2.
-5*(n - 3)**2*(3*n - 2)
Let h(q) be the second derivative of q**6/40 - 183*q**5/80 + 57*q**4/8 + 61*q**3/2 - 177*q**2 + 3*q + 132. Let h(s) = 0. Calculate s.
-2, 2, 59
Suppose 0 = 13*h + 5306 + 12816. Let g = h - -1398. Suppose -8/3 + 4/3*c - 4/3*c**g + 4*c**2 - 4/3*c**3 = 0. Calculate c.
-2, -1, 1
Let q = -12 + 6. Let o(d) = -4*d**3 - d**2 - 5*d - 5. Let l(y) = 15*y - 5*y**3 - 6 - 2*y**2 - 9*y - 7*y - 5*y + 0*y**3. Let f(n) = q*o(n) + 5*l(n). Factor f(h).
-h**2*(h + 4)
Let v(f) be the third derivative of -f**6/360 + 4*f**5/45 - 43*f**4/72 - 10*f**3/3 + 11*f**2 + 39. Let v(r) = 0. Calculate r.
-1, 5, 12
Let u(l) be the first derivative of -3*l**5/40 + 15*l**4/32 + l**3 - 9*l**2 - 3844. Solve u(m) = 0.
-3, 0, 4
Let z = 584311 + -4090108/7. Factor 96/7*k**2 - z*k + 6/7*k**4 + 3/7*k**5 + 18/7 - 54/7*k**3.
3*(k - 1)**4*(k + 6)/7
Let u(g) = 4*g**2 + 15. Let v be u(0). Determine k so that -v*k**3 + 8*k**2 - 34*k**2 + 10*k**3 - 24*k**2 - 45*k = 0.
-9, -1, 0
Let n(j) be the second derivative of -j**7/630 + j**6/90 - j**5/60 + 69*j**2/2 + 8*j + 3. Let p(w) be the first derivative of n(w). Factor p(v).
-v**2*(v - 3)*(v - 1)/3
Let z be 217/(-31) - -1*1. Let h be ((-3)/z)/(((-5)/(-4))/5). Suppose -4/9 - 2/9*u**3 + 0*u**h + 2/3*u = 0. What is u?
-2, 1
Factor 2*y**4 - 2761*y**2 - 4*y**3 + 2753*y**2 - 2*y + 18*y