 465. Find x such that -30/7*x**5 - 8/7 + 0*x + 30/7*x**s - 38/7*x**4 + 46/7*x**2 = 0.
-1, -2/3, 2/5, 1
Let a(o) be the first derivative of o**5/120 - o**4/48 + 15*o**2 + 8. Let x(d) be the second derivative of a(d). Determine y, given that x(y) = 0.
0, 1
Suppose -3*g - 5*n = -0*g - 35, -2*g - 5*n + 30 = 0. Find k such that 1/2*k**g + 0*k + k**4 + 0*k**2 + 1/2*k**3 + 0 = 0.
-1, 0
Let m(u) = -2*u**3 - 32*u**2 - 99*u - 34. Let l be m(-12). Factor -2/9*o**2 + 2/9*o**3 + 2 - l*o.
2*(o - 3)*(o - 1)*(o + 3)/9
Let i be (-24)/16*64/(-60). Factor -8/5*x - 2/5*x**2 - i.
-2*(x + 2)**2/5
Let w(d) = 188*d - 3570. Let f be w(19). Suppose 8/3*n + 2/3*n**4 - 2*n**3 + 0*n**f + 0 = 0. Calculate n.
-1, 0, 2
Let x be (5 + -9 + 15)*4/22. Determine b so that 6/13*b**x - 6/13*b**4 - 16/13*b**3 - 8/13 + 24/13*b = 0.
-2, 1/3, 1
Let m(n) = 21*n + 4. Let d be m(2). Suppose -51*f + 5 = -d*f. Solve f - 2/3*v**2 - 1/3*v = 0 for v.
-3/2, 1
Let o(m) be the second derivative of -m**6/70 - 3*m**5/14 - 17*m**4/28 - 4*m**3/7 + 2*m. Solve o(z) = 0 for z.
-8, -1, 0
Let q(s) be the first derivative of -2*s**5/95 - 2*s**4/19 - 10*s**3/57 - 2*s**2/19 - 41. Determine b, given that q(b) = 0.
-2, -1, 0
Let w(j) = j**5 + j**4 + j**3 - j**2 + j + 1. Let y(d) = -40*d**5 + 40*d**4 - 15*d**3 + 5*d**2 - 5*d - 5. Let m(b) = 5*w(b) + y(b). Factor m(x).
-5*x**3*(x - 1)*(7*x - 2)
Let q(c) be the first derivative of -c**4/20 - 22*c**3/15 + c**2/10 + 22*c/5 - 780. Determine v, given that q(v) = 0.
-22, -1, 1
Let j be -4*(-5)/(-12) - -2. Let p(m) be the second derivative of 0*m**2 - 4*m + 0 - j*m**3 - 1/12*m**4. Find a such that p(a) = 0.
-2, 0
Let z(k) be the first derivative of k**6/50 - k**4/20 + k - 22. Let o(u) be the first derivative of z(u). What is l in o(l) = 0?
-1, 0, 1
Let y be (-40)/(-70) + 17/7. Factor 2*p**2 - 6*p**y + 15*p**3 - 6*p**3 + p**2.
3*p**2*(p + 1)
Let d(n) be the first derivative of n**5/5 + n**4 - 8*n**2 - 16*n - 57. Factor d(w).
(w - 2)*(w + 2)**3
Suppose -22 + 22 = g. Let b(j) be the third derivative of 1/20*j**5 + 0*j**3 + 8*j**2 + 1/12*j**4 + 0*j**6 + 0*j + g - 1/210*j**7. What is a in b(a) = 0?
-1, 0, 2
Let t(l) = -l**3 + 41*l**2 - 111*l - 11. Let n(o) = -o**3 + 21*o**2 - 56*o - 6. Let p(s) = -11*n(s) + 6*t(s). Factor p(h).
5*h*(h - 2)*(h + 5)
Let f(i) be the third derivative of -i**8/336 - i**7/35 - i**6/60 + i**5/3 + 9*i**4/8 + 5*i**3/3 + 312*i**2. What is p in f(p) = 0?
-5, -1, 2
Let i(p) = -14*p**2 - 11*p - 17. Let o(z) = 16*z**2 + 10*z + 18. Let y(q) = -6*i(q) - 5*o(q). Factor y(v).
4*(v + 1)*(v + 3)
Factor 120/7 + 23/7*h + 1/7*h**2.
(h + 8)*(h + 15)/7
Let b(i) be the first derivative of i**3 + 21*i**2/2 + 30*i - 87. Find d, given that b(d) = 0.
-5, -2
Let h(q) be the first derivative of 6/5*q**2 + 0*q - 2 - 8/5*q**3 - 3/25*q**5 + 3/4*q**4. Factor h(y).
-3*y*(y - 2)**2*(y - 1)/5
Let -23*x**4 + 5*x**4 + 28*x**2 - 80*x**3 + 8*x**5 - 18*x**4 + 20*x**2 = 0. What is x?
-2, 0, 1/2, 6
Suppose -33*q + x + 3 = -30*q, 2*q = x + 3. Solve 0 + q*r + 1/3*r**3 - 2/3*r**2 = 0.
0, 2
Suppose -8*r + 4*p - 20 = -4*r, 0 = 4*r + 4*p + 12. Let v be (-3 + -1)*(r/26)/2. Find n, given that 4/13*n**2 + 0*n**4 + 6/13*n - 8/13*n**3 - v + 2/13*n**5 = 0.
-2, -1, 1
Suppose -81*g + 44*g = -40*g + 6. Let -2/3*s**g - 2/3*s + 0 = 0. What is s?
-1, 0
Let k(t) = 3*t**3 - 15*t**2 + 30*t - 12. Let x(d) = d - 6*d**2 - 2*d**2 + 9*d**2. Let l(y) = k(y) - 3*x(y). Find g such that l(g) = 0.
1, 4
Suppose -167*s = -168*s. Determine i, given that 0*i**2 - 1/3*i + 1/3*i**3 + s = 0.
-1, 0, 1
Suppose -8 - 2 = -5*f. Suppose -5*i - 8 = 3*t, f*t + i = 5*i + 24. Factor 3 + y + t*y + 0*y**2 - 2*y**2 - y**3 + 3*y**2.
-(y - 3)*(y + 1)**2
Let s(w) be the second derivative of -w**4/18 - 8*w**3/9 - 4*w**2 - 8*w - 1. Factor s(x).
-2*(x + 2)*(x + 6)/3
Let f(c) be the second derivative of -c**5/15 - 19*c**4/9 - 160*c**3/9 + 200*c**2/3 + 142*c. Suppose f(s) = 0. Calculate s.
-10, 1
Let w(s) = -s**2 + 14*s - 48. Let q(v) = -2*v**2 + 35*v - 96. Let a(r) = 4*q(r) - 9*w(r). Determine k, given that a(k) = 0.
-8, -6
Determine o so that 0*o + 12*o**2 - 2/5*o**4 + 58/5*o**3 + 0 = 0.
-1, 0, 30
Let y(q) be the third derivative of q**6/180 - q**5/90 + 5*q**2 + 7*q. Determine a, given that y(a) = 0.
0, 1
Factor -3691*j - 9*j**3 + 5*j**3 - 44*j**2 + 3691*j.
-4*j**2*(j + 11)
Let l(o) be the third derivative of o**7/350 - 7*o**6/300 + 7*o**5/300 + o**4/30 + 7*o**2 - 5*o. Find c such that l(c) = 0.
-1/3, 0, 1, 4
Let g(f) = -44*f**2 + 4704*f - 460976. Let o(k) = -14*k**2 + 1568*k - 153659. Let s(w) = 5*g(w) - 16*o(w). Factor s(h).
4*(h - 196)**2
Let m = -124 - -129. Let g(y) be the second derivative of 0 - 5*y + 11/24*y**4 + 3/40*y**m + y**2 + y**3. Determine u so that g(u) = 0.
-2, -1, -2/3
Suppose -2*x = 6 - 12. Find o, given that -8 + x + 3*o**2 - 4 + 6 = 0.
-1, 1
What is q in -3*q + 40*q**4 + 24*q**4 + 3*q + q**3 + 6*q**2 - 65*q**4 = 0?
-2, 0, 3
Let p be 8/(-20) + 162/30. Let a(y) be the second derivative of 0 + 0*y**3 + p*y - 1/5*y**2 + 1/30*y**4. Factor a(j).
2*(j - 1)*(j + 1)/5
Let w be 1/((3/2)/3). Let i = -1105 - -4421/4. Factor i*q - 1/2 + 1/4*q**w.
(q - 1)*(q + 2)/4
Let d = 11/191 + 889/1146. Let t(m) be the first derivative of 5/4*m**4 + 0*m**2 + d*m**6 + 2*m**5 + 0*m**3 + 0*m + 4. Suppose t(r) = 0. Calculate r.
-1, 0
Suppose -3*o = i - 4, -2 = -o + 1. Let l(a) = -11*a**3 + 24*a**2 + 61*a + 41. Let m(j) = 6*j**3 - 12*j**2 - 30*j - 21. Let p(z) = i*m(z) - 3*l(z). Factor p(s).
3*(s - 6)*(s + 1)**2
Suppose -5*p - 51 = -2*l, -2*l + 2*p + 44 = -10. What is x in -13*x**5 - 20*x**3 + 4*x**4 - 3*x**5 + 4*x**2 + l*x**4 = 0?
0, 1/2, 1
Let q(i) be the second derivative of 0*i**2 - 2/45*i**6 - 1/9*i**3 - 20*i + 1/9*i**4 + 0*i**5 + 1/63*i**7 + 0. Factor q(r).
2*r*(r - 1)**3*(r + 1)/3
Let o(i) = -13*i - 1. Let m be o(-1). Let v = -9 + m. Factor -p**2 + 4*p**v - 3*p**2 + 4*p + 2*p**2 - 6*p**2.
4*p*(p - 1)**2
Let s = -340 - -3062/9. Let l(c) be the first derivative of s*c**2 - 6 - 1/6*c**4 + 0*c - 10/27*c**3. Factor l(o).
-2*o*(o + 2)*(3*o - 1)/9
Let u(t) be the first derivative of -9 + 3*t + 15/8*t**2 + 1/4*t**3. Factor u(h).
3*(h + 1)*(h + 4)/4
Let c(u) be the second derivative of -3*u**5/40 - 3*u**4/8 + 9*u**3/4 - 15*u**2/4 - 57*u. Factor c(w).
-3*(w - 1)**2*(w + 5)/2
Let c(w) = -9*w + 12. Let t(j) = 18*j - 23. Let d(o) = -13*c(o) - 6*t(o). Let i be d(2). Factor -8*r**3 - 16/3*r**4 + i - 16/3*r**2 - 4/3*r - 4/3*r**5.
-4*r*(r + 1)**4/3
Let r(u) be the first derivative of -u**6/12 + 29*u**5/20 - 3*u**4/4 - 29*u**3/12 + 7*u**2/4 - 51. Determine t so that r(t) = 0.
-1, 0, 1/2, 1, 14
Let h be ((-5)/(-15))/(2/36). Let r be 0 - 4*(-3)/h. Determine a so that -2/3*a + 0 - 2/3*a**r = 0.
-1, 0
Factor 5 - 1 - 11*t**2 + 9*t**2 + 2*t.
-2*(t - 2)*(t + 1)
Factor -2/3*n + 1/9*n**3 + 5/9*n**2 + 0.
n*(n - 1)*(n + 6)/9
Factor 6 + 62/5*h + 34/5*h**2 + 2/5*h**3.
2*(h + 1)**2*(h + 15)/5
Let k(y) be the second derivative of -y**4/78 + 5*y**3/39 + 6*y**2/13 - 318*y + 1. Factor k(p).
-2*(p - 6)*(p + 1)/13
Let b = -12 + 28. Let d = -12 + b. Suppose -12*l**2 - 8*l - 6*l**d + 10*l**3 + l**4 + 16 + 3*l**4 = 0. What is l?
-1, 2
Factor 0 + 4/7*g**2 + 2/7*g**3 + 0*g.
2*g**2*(g + 2)/7
Suppose -64*z**3 + 668*z**2 - 2694*z + 0*z**4 + 198*z + 2*z**4 + 3042 = 0. Calculate z.
3, 13
Suppose 2*h - 3*h - 3*r - 9 = 0, -h = 5*r + 19. Determine f, given that -f**2 + 0*f - h*f**4 + 7*f**4 + 5*f + f**3 - 6*f = 0.
-1, 0, 1
Let u(r) be the third derivative of -r**5/120 - r**4/16 + 4*r**2 + 3*r. Find f, given that u(f) = 0.
-3, 0
Suppose 0 = 2*s + 210 - 220. Let g(c) be the third derivative of -5/24*c**4 - 2*c**2 - 1/20*c**s + 1/3*c**3 + 0 + 0*c. Suppose g(q) = 0. What is q?
-2, 1/3
Factor 49*q - 216 - 59*q**2 + 11*q + 55*q**2.
-4*(q - 9)*(q - 6)
Let h be 123/246 + (-1)/6. Factor -2*g**2 + 4/3*g**3 - 1/3*g**4 + 4/3*g - h.
-(g - 1)**4/3
Let c(a) = -a**2 - 24*a + 81. Let d be c(-22). Suppose -d*r = -117*r. Solve 6/13*f + r - 4/13*f**3 - 10/13*f**2 = 0 for f.
-3, 0, 1/2
Let n be (-5 + 6)/((-2)/(-10)). Suppose -c + 65 = 3*w - w, -n*c = -3*w + 130. Factor -35*o**3 + 2*o**4 - 2*o**2 + w*o**3.
2*o**2*(o - 1)*(o + 1)
Let d be ((-12)/42)/(2/(-14)). Let 0*p + p - 3*p**3 + 2*p - 18*p**d + 3*p**4 + 15*p**2 = 0. Calculate p.
-1, 0, 1
Suppose 20 = -a + 3*a. Suppose -30 + a = -2*g. Factor 0*j - 2*j + g*j