467. Let -1/5*f**5 - 23/5*f**3 - 12/5*f + 0 - 28/5*f**2 - j*f**4 = 0. What is f?
-3, -2, -1, 0
Let g(s) = -s**2 + 2*s. Let k(y) = -17*y**2 - 58*y - 8. Suppose 4*t - 4*r - 23 = 13, -5 = -5*t - 5*r. Let h(j) = t*g(j) + k(j). Factor h(z).
-2*(z + 2)*(11*z + 2)
Let -88*a + 216*a**3 + 20/3*a**4 - 404/3*a**2 + 0 = 0. Calculate a.
-33, -2/5, 0, 1
Let v(f) be the third derivative of 0*f**3 + 3*f**2 + 13/252*f**4 + 0*f - 1/630*f**5 + 9. Factor v(x).
-2*x*(x - 13)/21
Factor 10/7*n + 0 - 2/7*n**3 + 8/7*n**2.
-2*n*(n - 5)*(n + 1)/7
Suppose -5*d = -0*d. Suppose 0 = -v - d*v - b + 8, v - 13 = -2*b. Determine y, given that v*y + 15*y**2 + 0*y + 5*y - 5*y**3 - 15 - 3*y = 0.
-1, 1, 3
Let u be 426/15*(-825)/(-30). Factor -2*d**4 - d**3 + 4*d**3 - u*d**5 + 780*d**5.
-d**3*(d - 1)*(d + 3)
Let t(s) be the second derivative of s**7/280 - 47*s**6/240 + 3*s**5/4 + 41*s**4/4 - 67*s. Let d(g) be the third derivative of t(g). Factor d(f).
3*(f - 15)*(3*f - 2)
Let d be (12/(-28))/(111/(-54) - 8/(-4)). Factor -d*p**2 + 0 - 6*p**3 - 12/7*p.
-6*p*(p + 1)*(7*p + 2)/7
Suppose 2*r = -2*r + 20, 9 = 2*h + r. Let i = 9 - h. Let z(x) = 5*x**2 - 18*x. Let o(w) = -10*w**2 + 37*w. Let v(p) = i*z(p) + 3*o(p). Factor v(u).
5*u*(u - 3)
Let c be (4 - 3)/1 + -2. Let q be c/4 + 2*(-168)/(-832). Let 0*v**2 + 0 + 0*v - 2/13*v**3 + q*v**4 = 0. What is v?
0, 1
Factor 172/7*t + 2/7*t**2 + 0.
2*t*(t + 86)/7
Let x(a) be the second derivative of 115/6*a**3 - 2*a**5 + 12 + 5/42*a**7 - 25*a**2 - 25/6*a**4 + 3*a + 2/3*a**6. Solve x(l) = 0 for l.
-5, -2, 1
Let s(m) = 5*m**2 - 45*m. Let g(c) be the second derivative of 5*c**4/12 - 15*c**3/2 - 20*c. Let u(z) = -5*g(z) + 4*s(z). Suppose u(j) = 0. Calculate j.
0, 9
Let l(t) be the second derivative of 0*t**2 - 1/60*t**3 + 1/40*t**4 + 45*t + 0. Factor l(v).
v*(3*v - 1)/10
Let d(g) be the second derivative of 0*g**3 - 2/21*g**4 + 14 + 0*g**2 - 1/70*g**5 + 2*g. Factor d(f).
-2*f**2*(f + 4)/7
Let a = 2711 - 2708. Let v(k) be the third derivative of 1/12*k**5 - 1/42*k**7 + 0*k + 5/12*k**4 + 8*k**2 + 0*k**a + 0 - 1/12*k**6. Factor v(w).
-5*w*(w - 1)*(w + 1)*(w + 2)
Let w = 4915167/3932140 + 2/983035. Let x be (-2)/(-1 + 0 + 0). Factor -l + 1/4*l**x - w.
(l - 5)*(l + 1)/4
Let p(q) be the third derivative of -q**6/900 - q**5/450 + q**4/90 + 242*q**2. Determine a so that p(a) = 0.
-2, 0, 1
Let j(w) be the second derivative of -w**7/15120 - w**6/180 - w**5/5 - 5*w**4/6 + w**2/2 - w - 48. Let o(c) be the third derivative of j(c). Factor o(s).
-(s + 12)**2/6
Let f(i) be the third derivative of i**7/70 + 9*i**6/40 - 63*i**5/20 - 149*i**4/8 - 39*i**3 + 43*i**2 + 2*i. Factor f(g).
3*(g - 6)*(g + 1)**2*(g + 13)
Let n be (1850/333)/((-375)/(-900)). Factor 4/3*f**2 + 100/3 - n*f.
4*(f - 5)**2/3
Determine r, given that -16*r**4 + 5231603*r**5 + 2 + 16*r**3 - 2 - 5231599*r**5 = 0.
0, 2
Suppose 60 = -m + 5*g, -60 = -14166*g + 14162*g. Solve 225/2 + m*x + 1/2*x**2 = 0.
-15
Let b = 15546 + -15544. Let z(h) be the first derivative of 24 - 1/18*h**4 - 10/9*h - 14/27*h**3 - 11/9*h**b. Determine f so that z(f) = 0.
-5, -1
Let j be 736/36 - (-8)/(-18). Suppose 21*c - 19*c + 5*d + j = 0, -5*c - d = 4. Factor 1/5*r**3 + 0*r + 1/5*r**2 - r**4 + c + 3/5*r**5.
r**2*(r - 1)**2*(3*r + 1)/5
Let q be (-10920)/(-1170) - 112/12. Suppose 0*s + 8/19*s**2 + 2/19*s**3 + q = 0. What is s?
-4, 0
Let j be (-1 + -3 - 0/6) + 7. Find d, given that 10*d**2 - 13*d**2 - 13*d**2 + 39*d - 8*d**2 + 3*d**j - 18 = 0.
1, 6
Let f(w) be the third derivative of w**8/336 - w**6/24 + w**5/12 - 26*w**3/3 + 2*w**2 - 3. Let y(d) be the first derivative of f(d). Find v such that y(v) = 0.
-2, 0, 1
Let f(c) be the second derivative of 1/40*c**5 + 10 - 13/12*c**3 - 3*c - 7/4*c**2 - 5/24*c**4. Factor f(h).
(h - 7)*(h + 1)**2/2
Let u = 232 - 228. Let 4*h**3 - 12*h**2 + 6*h**2 + 3*h**5 - 7*h + 0*h**3 + 8*h**4 - u + 2 = 0. What is h?
-1, -2/3, 1
Determine c, given that -5*c**4 - 1 + c**4 + 441 - 44 + 152*c**2 + 128*c**3 - 672*c = 0.
-3, 1, 33
Find x, given that -3*x**2 - 18*x + 627 + 677 + 0*x**2 - 563 = 0.
-19, 13
Let -1136/3*j - 4/3*j**2 - 1132/3 = 0. What is j?
-283, -1
Let g(v) be the first derivative of 2*v**2 - 6*v + 148 - 1/6*v**3. Factor g(m).
-(m - 6)*(m - 2)/2
Determine b, given that 42*b**2 + 2176*b + 2999 + 4*b**3 - 1006 + 105*b**2 + 149*b**2 + 2231 = 0.
-66, -4
Factor -2/9*d**3 - 124*d - 562/9*d**2 + 0.
-2*d*(d + 2)*(d + 279)/9
Let d(c) be the third derivative of -c**7/105 - c**6/3 + 2*c**5/5 + 64*c**4/3 + 320*c**3/3 - 1645*c**2. Factor d(y).
-2*(y - 4)*(y + 2)**2*(y + 20)
Let i = -78/10171 - -10327/20342. Solve i*m**3 + 0*m - 3/2*m**4 + 0 + m**2 = 0 for m.
-2/3, 0, 1
Let x be -75 - -65 - (-129)/12. Let f(y) be the second derivative of 18*y - 1/8*y**3 + x*y**2 - 1/16*y**4 + 0. Find w, given that f(w) = 0.
-2, 1
Let g(p) = -3*p**3 - 6*p**2 - p + 2. Let s be g(-2). Factor 1032 - 6*o**s + 4*o + 2*o**2 - 8*o**3 - 1032.
-2*o*(o + 1)**2*(3*o - 2)
Let p(q) be the second derivative of q**5/50 - 3*q**4/4 + 157*q**3/30 + 9*q**2 + 18*q + 28. Factor p(h).
(h - 18)*(h - 5)*(2*h + 1)/5
Let l(f) = -20*f**3 - 65*f**2 + 188*f + 47. Let m(j) = j - 1. Let q(k) = l(k) - 3*m(k). Let q(v) = 0. Calculate v.
-5, -1/4, 2
Let b = -396/7 + 1195/21. Factor b*x + 1/3*x**2 + 0.
x*(x + 1)/3
Let q(x) be the third derivative of -x**6/960 + 1067*x**5/160 - 1138489*x**4/64 + 1214767763*x**3/48 - 3*x**2 - 180*x. Factor q(i).
-(i - 1067)**3/8
Let a(p) be the second derivative of -p**5/110 + 5*p**4/66 - 2*p**3/33 - 8*p**2/11 + 2417*p. Find n such that a(n) = 0.
-1, 2, 4
Let c = -145699 + 145701. Determine i so that 4/3 - 17/3*i**c + 28/3*i - 5*i**3 = 0.
-2, -2/15, 1
Solve 1170/7*a**2 - 386/7*a**3 + 56 - 1174/7*a - 2/7*a**4 = 0.
-196, 1
Let r be 3 + -10 + 7 + -7. Let p be (r - (-215)/30)/(3/135). Solve 55/6*o**2 - 5/3 - p*o = 0.
-2/11, 1
Let z = -8/2481 - -12437/9924. Find t such that -5/2*t - 5/4*t**2 - z = 0.
-1
Let k(m) be the second derivative of m**4/36 - 463*m**3/9 - 309*m**2/2 - 1854*m - 1. Solve k(c) = 0 for c.
-1, 927
Let r(y) = 37*y - 256. Let s be r(7). Suppose n + 4*w + 4 = 0, 2*w - 1 = 4*n + 3*w. Factor n + 0*h**2 - 1/6*h**5 + 1/3*h**4 - 1/6*h**s + 0*h.
-h**3*(h - 1)**2/6
Suppose 4*m = 9*m - 50. Let r be (-2)/(-1 - m/(-14)). Factor -4*y - r*y**3 - y + 5*y**2 + 12*y**3 - 5*y**4.
-5*y*(y - 1)**2*(y + 1)
Let v(a) be the first derivative of -33/4*a - 1/2*a**3 - 69/8*a**2 + 53. What is o in v(o) = 0?
-11, -1/2
Let q(t) be the third derivative of t**6/840 + t**5/15 + 121*t**4/168 + 23*t**3/7 + 1195*t**2. Solve q(o) = 0.
-23, -3, -2
Let k = -21676 - -21705. Let p(j) be the first derivative of -39/8*j**2 - 21/16*j**4 - 3/20*j**5 - 3*j - 15/4*j**3 - k. Find b such that p(b) = 0.
-4, -1
Let l(a) = 3526*a + 126939. Let y be l(-36). Let -2/11*b + 2/11*b**y + 2/11 - 2/11*b**2 = 0. Calculate b.
-1, 1
Let f(h) be the third derivative of -h**8/336 + 3*h**7/70 - h**6/20 - 4*h**5/15 - 2210*h**2. Factor f(u).
-u**2*(u - 8)*(u - 2)*(u + 1)
Let m(j) be the third derivative of j**5/20 - 37*j**4/8 - 532*j**3 - j**2 - 2*j - 15. Factor m(c).
3*(c - 56)*(c + 19)
Let m = -735/29 - -4081/145. Find v such that 2/5*v**5 + 18/5*v**2 + 0*v + m*v**4 + 0 + 6*v**3 = 0.
-3, -1, 0
Suppose -3*m = 2*s - 5 + 4, -5*s - 3*m = -7. Find y such that 17*y + 4*y**s - 3*y**2 - 30*y = 0.
0, 13
Let m be (8 + 6046/(-756))*10748/22. Let d = m - 2/297. Factor 6/7*x + 1/7*x**2 + d.
(x + 3)**2/7
Solve 4/9*b**2 + 643204/9 - 3208/9*b = 0.
401
Determine u, given that -3*u**3 - 3330 + 1625 + 1417 - 9*u**2 + 300*u = 0.
-12, 1, 8
Let w be (-1 + 1)/(-3)*(1054 - 1053). Factor 0*y + w - 4*y**2 - 44/3*y**3 - 32/3*y**4.
-4*y**2*(y + 1)*(8*y + 3)/3
Suppose 0 = -4*d + d - 9. Let r(n) = -6*n**2 - 3*n + 15. Let a(k) = -7*k**2 - 3*k + 14. Let j(p) = d*a(p) + 4*r(p). Solve j(h) = 0.
-3, 2
Suppose -11*g = 17*g - 112. Suppose -4*f = -0*x + 5*x - 12, f - 3 = -g*x. Let 0 + 10*n**f + 6*n**2 + 4/3*n + 2*n**5 + 22/3*n**4 = 0. Calculate n.
-1, -2/3, 0
Let n = 25951/19488 + 11/6496. Let b(d) = d**3 - 5*d**2 - 5*d - 3. Let u be b(6). Solve -11/3*o + n*o**2 + 2 + 1/3*o**u = 0.
-6, 1
Suppose 0 = -35*b - 4*b + 1638. Solve 15*a - b + 29*a + 0 + a**2 - 3*a**2 = 0.
1, 21
What is o in -352/9*o**2 - 46/9*o**3 - 2/9*o**4 - 896/9*o + 0 = 0?
-8, -7, 0
Let d be (-3100)/465*9/(-12). Determine o, given that 0 - 4/3*o**3 + 4/3*o*