5870. Find h, given that z(h) = 0.
0, 954
Let l = -132 + 218. Factor -21*b**2 - l + 159 + 48*b + 3*b**3 - 109.
3*(b - 3)*(b - 2)**2
Let h(w) = 2*w - 23. Let z be h(0). Let j = -15 - z. Let -5*l**5 + 20*l**2 + j*l - 15*l**4 - 8*l = 0. Calculate l.
-2, 0, 1
Factor -292/3 - 361/3*w - 68/3*w**2 + 1/3*w**3.
(w - 73)*(w + 1)*(w + 4)/3
Let o be (-1)/(-7)*(-777 + 777)/(1/1). Factor o*w**3 + 0 - 4/3*w**4 - 8/3*w + 4*w**2.
-4*w*(w - 1)**2*(w + 2)/3
Let i(a) be the first derivative of -2*a**5/45 + 56*a**4/9 - 872*a**3/27 + 48*a**2 - 2393. Factor i(c).
-2*c*(c - 108)*(c - 2)**2/9
Let g(l) be the third derivative of 0*l**3 - 5/18*l**4 - 1/360*l**6 + 1/15*l**5 - 79*l**2 + 0 + 0*l. Factor g(w).
-w*(w - 10)*(w - 2)/3
Let s(p) = p**3 + 4*p**2 + 153*p + 455. Let w be s(-3). Let y(c) be the second derivative of 0 - 7/6*c**4 - 9*c**2 - 1/10*c**5 - w*c**3 - 35*c. Factor y(v).
-2*(v + 1)*(v + 3)**2
Let c(p) = -28*p**2 - 158*p - 309. Let y(g) = 23*g**2 + 157*g + 306. Let w(v) = 4*c(v) + 5*y(v). Suppose w(a) = 0. What is a?
-49, -2
Suppose 0 = -360*t + 350*t + 400. Find w such that -t*w**4 - 42*w - 58*w + 128*w**3 - 28*w**3 - 20 - 105*w**2 + 165*w**4 = 0.
-1, -2/5, 1
Let k(a) = -a**2 - 3*a + 20. Let m be k(3). What is u in -6*u**5 + 176*u**2 - 25*u**4 - 200*u + 80 + 25*u**3 - 51*u**m - 8*u**5 + 9*u**5 = 0?
-4, 1
Let r(s) be the first derivative of -s**4/22 + 62*s**3/33 - 84*s**2/11 - 1151. Factor r(l).
-2*l*(l - 28)*(l - 3)/11
Let v(c) = -c + 12. Let m be v(10). Let a = -787/21 - -793/21. Find i, given that 2/7*i**3 + 6/7*i**m + a + 6/7*i = 0.
-1
Let y(c) be the second derivative of -2*c**6/135 - 26*c**5/45 + 775*c**4/27 - 7400*c**3/27 - 1000*c**2 + 1765*c. Solve y(m) = 0 for m.
-45, -1, 10
Let c(r) = -78*r**2 - 6*r - 7. Let j(f) = -40*f**2 - 4*f - 4. Let a = 481 + -488. Let i(h) = a*j(h) + 4*c(h). Factor i(b).
-4*b*(8*b - 1)
Factor 658*l - 1317/2 + 1/2*l**2.
(l - 1)*(l + 1317)/2
Let n = 92610105/8 + -86220017081/7448. Let r = -2/931 - n. Let -1/4*y**2 - r - 3/2*y = 0. Calculate y.
-5, -1
Let z be (0 - (-5)/(-2))/(28/6832). Let o = -606 - z. Suppose -1/2*k + k**3 - 1/2*k**5 - 1/6*k**o - 1/6 + 1/3*k**2 = 0. What is k?
-1, -1/3, 1
Let y be (0 + 140/(-12))/(((-136)/(-51))/(-4)). Factor 13/2*r**2 - y*r - 49/2 - 1/2*r**3.
-(r - 7)**2*(r + 1)/2
Let n(l) = l. Let o(r) = 3*r**3 + 52*r**2 + 111*r + 60. Let c(t) = -10*n(t) + 5*o(t). Factor c(s).
5*(s + 1)*(s + 15)*(3*s + 4)
Suppose 2/9*k**3 + 28/3 - 28/3*k**2 - 2/9*k = 0. What is k?
-1, 1, 42
Let d = -3307 + 3309. Let x(h) be the third derivative of 18*h**d + 0*h + 0*h**3 + 1/20*h**5 + 0 - 3/8*h**4. Factor x(i).
3*i*(i - 3)
Let x = 42 + -122/3. Let q(y) = y + 4. Let h be q(-1). Solve x*o**h + 4/3*o**5 + 4*o**2 - 8/3*o - 4*o**4 + 0 = 0 for o.
-1, 0, 1, 2
Let h = -79416 - -555914/7. Factor h*i**2 + 54/7 + 24/7*i.
2*(i + 3)*(i + 9)/7
Suppose 2119*o - 8 = 2115*o. Let f be 28/(-210) + o/15. Let 2/23*m**2 + f - 6/23*m = 0. What is m?
0, 3
Solve -10*g - 1/2*g**3 - 6 - 9/2*g**2 = 0 for g.
-6, -2, -1
Let a = -78026/3 + 26011. Factor -3*d**2 + 1/3*d**3 + 5*d - a.
(d - 7)*(d - 1)**2/3
Let q be (4/14)/((-51)/(-16065)*240). Factor q*x**2 - 3/8 + 0*x.
3*(x - 1)*(x + 1)/8
Let d = -271 - -284. Let m(w) be the first derivative of 1/24*w**6 + 3/16*w**4 + 0*w + 0*w**2 - d + 1/12*w**3 + 3/20*w**5. What is c in m(c) = 0?
-1, 0
Let r(n) be the third derivative of n**6/120 - 9*n**5/5 - 225*n**4/8 - 171*n**3 - 165*n**2 - 17. Factor r(d).
(d - 114)*(d + 3)**2
Suppose 0 = 5*z + 2*d - 14, -78*z + 15 = -75*z - d. Let c(o) be the first derivative of -24 - o**2 - 1/16*o**z + 4*o - 7/12*o**3. What is w in c(w) = 0?
-4, 1
Let y(j) = 4*j**3 - j**2 - 27*j - 43. Let u(s) = 15*s + 100. Let h be u(-7). Let q(z) = 2*z**3 - 14*z - 22. Let w(x) = h*q(x) + 2*y(x). What is n in w(n) = 0?
-2, 3
Suppose -611*f = -612*f - 5*u - 12, -3*f + 2*u + 15 = 0. Factor -2/3*y**2 - 4/9*y**f - 8/9 + 2/9*y**4 + 16/9*y.
2*(y - 2)*(y - 1)**2*(y + 2)/9
Suppose -a + 7 = 4*p, 3*p + 10*a = 5*a - 16. Suppose -18*j**3 + 37799*j**2 - 30*j - 37763*j**2 + 8 + p*j**4 + 1 = 0. What is j?
1, 3
Suppose -1216/3*h - 2/3*h**4 + 322*h**2 - 236/3*h**3 + 488/3 = 0. What is h?
-122, 1, 2
Suppose 0 = 5*j - 3*j - 4. Suppose -3*m - 15 = 0, -5*m + 47 = n + j*n. Solve 21*u + 5*u**3 - u**3 + 11*u**3 - 6*u**3 - 6 - n*u**2 = 0 for u.
2/3, 1
Factor 386*d**4 - 194*d**4 - 339*d**3 - 189*d**4 - 342*d**2.
3*d**2*(d - 114)*(d + 1)
Solve 336 - 120*c**2 + c**3 + 9*c**3 + 273 - 90*c + 5*c**4 + 66 = 0 for c.
-5, -3, 3
Factor -425*g**2 + 3748 - 96*g - 628 + 422*g**2.
-3*(g - 20)*(g + 52)
Let w(v) be the first derivative of -2*v**3/57 + 426*v**2/19 - 90738*v/19 + 525. Solve w(a) = 0 for a.
213
Let y(o) = -o**4 - 46*o**3 + 225*o**2 + 304*o - 974. Let n(a) = -3*a**4 - 88*a**3 + 450*a**2 + 612*a - 1947. Let f(v) = -6*n(v) + 13*y(v). Factor f(s).
5*(s - 7)**2*(s - 2)*(s + 2)
Let q(n) be the second derivative of -n**4/84 + 152*n**3/21 - 11552*n**2/7 - 507*n + 3. Factor q(x).
-(x - 152)**2/7
Let w(h) be the first derivative of 0*h**2 - 6/5*h**5 - 3*h**4 - 1/6*h**6 - 8/3*h**3 + 0*h + 81. Determine m, given that w(m) = 0.
-2, 0
Let b(o) be the second derivative of o + 81/20*o**5 + 0*o**2 - 83 - 3*o**3 - 17/4*o**4 - 2/5*o**6. Suppose b(p) = 0. What is p?
-1/4, 0, 1, 6
Let m be 2/(-3) + 1 + 175/15. Let u be 9/(-12) + 153/m. Determine a, given that -10*a**3 - 27*a**2 + 15*a**4 - u*a + 2*a - 8*a**2 = 0.
-1, -1/3, 0, 2
Let n(t) be the second derivative of 0*t**2 - 16/3*t**3 - 3/56*t**7 - 11/12*t**6 - 14*t**4 - 11*t - 57/10*t**5 + 0. Factor n(m).
-m*(m + 4)**3*(9*m + 2)/4
Let q(i) be the second derivative of 40/27*i**3 + 1/54*i**4 + 0 + 13/3*i**2 + 60*i. Solve q(a) = 0.
-39, -1
Let 0 + 951/4*p**2 + 237*p + 3/4*p**3 = 0. What is p?
-316, -1, 0
Let v(f) = -12*f**2 - 3*f. Let k(h) = 70*h**2 + 300*h + 572. Let r(i) = k(i) + 6*v(i). Find x such that r(x) = 0.
-2, 143
Let r be 4/32*((-143)/(-11) + -13). Let b(m) be the first derivative of 2/15*m**3 + 0*m**4 + 0*m**2 + 32 - 2/25*m**5 + r*m. Let b(t) = 0. What is t?
-1, 0, 1
Suppose 0 = -310*r + 1592 - 662. Suppose -4/11*q**2 - 48/11 + 2/11*q**r - 40/11*q = 0. What is q?
-2, 6
Let h(o) be the first derivative of -o**4/2 - 40*o**3/3 - 67*o**2 - 96*o - 5726. Factor h(c).
-2*(c + 1)*(c + 3)*(c + 16)
Let w(z) = z**2 - z + 14. Let g be w(3). Suppose -4*b**3 + 20*b**2 - 6*b**3 - g + 16*b**3 - 5*b - b**3 = 0. What is b?
-4, -1, 1
Let s(c) be the second derivative of -c**7/11340 + 11*c**6/324 - 605*c**5/108 + 77*c**4/6 + 218*c. Let a(b) be the third derivative of s(b). Factor a(v).
-2*(v - 55)**2/9
Let w(d) be the third derivative of 1/42*d**3 + 0 - 1/28*d**4 + 1/84*d**5 - 2*d**2 + 9*d. Factor w(n).
(n - 1)*(5*n - 1)/7
Let q(j) be the first derivative of -2*j**3/3 - 4*j**2 + 10*j - 3675. Factor q(c).
-2*(c - 1)*(c + 5)
Let a(z) = z**4 - z. Let x(y) = -723*y**4 + 4617*y**3 + 3294*y**2 + 742*y + 56. Let f be -2*(2/6)/((-48)/(-72)). Let p(i) = f*x(i) + 6*a(i). Factor p(w).
(w - 7)*(9*w + 2)**3
Let c = 1905 + -614. Let u = c - 1291. Factor u - 4/13*n - 2/13*n**2.
-2*n*(n + 2)/13
Let w be -9*5/(-15)*3. Let m be (8 - w) + (-2 - -5) + 21. Solve -361*n**3 + 3*n + n**4 + 321*n**3 - m*n**2 + 7*n - 8*n**4 = 0.
-5, -1, 0, 2/7
Suppose -2*o - d + 6 = 1, 2*d + 17 = 5*o. Factor -40*t - t**3 + 18*t**o - 9*t**3 - 3*t**3 - 25*t**2 + 60.
5*(t - 6)*(t - 1)*(t + 2)
Suppose -285/4*k**2 - 27/4 - 175/4*k**3 - 153/4*k = 0. Calculate k.
-3/5, -3/7
Let a(u) be the second derivative of -4232/3*u**3 - 3*u - 92/3*u**4 + 0*u**2 - 1/5*u**5 + 52. Suppose a(h) = 0. What is h?
-46, 0
Suppose -3*t + 94 = -131. Let m = -71 + t. Determine w, given that w**2 + m*w + 19 - 19 - 3*w**2 = 0.
0, 2
Let t be -2 + (-40)/(-36) + (-228196)/(-126918). Factor t*z**2 + 0 + 6/11*z**4 + 2/11*z + 14/11*z**3.
2*z*(z + 1)**2*(3*z + 1)/11
Let v(p) = 4*p**2 - 32*p + 16. Let q(l) = -l**2 + 3. Suppose -2*i - 102 = -104. Let j(h) = i*v(h) + 6*q(h). Factor j(r).
-2*(r - 1)*(r + 17)
Let b be 1 + (-6282)/(-270) + -20. Let 26/15*r**3 + 2/15*r**5 - 16/15*r**4 + 52/15*r**2 + b - 128/15*r = 0. Calculate r.
-2, 1, 4
Let c(b) be the second derivative of b**4 - 296*b**3/15 - 8*b**2 - 11203*b. Factor c(l).
4*(l - 10)*(15*l + 2)/5
Let v(p) = 4*p**2 + 51*p + 206. Let w(y) = -4*y**2 - 52*y - 204. Suppose 28*f - 26*f + 8 = 0. Let h(i) = f*v(i) - 5*w(i). Find t, given that h(t