 36. Determine v, given that -6*v**2 + 3/2*v**u + y*v**3 - 12*v + 0 = 0.
-2, 0, 2
Let t(s) = -s**2 + 5*s + 63. Let u be t(0). Factor 124*o**3 + 76*o + 86*o - 59*o**3 - u*o**3 + 36*o**2.
2*o*(o + 9)**2
Let c(w) = 5*w**3 - 213*w**2 + 634*w - 432. Let k(b) = -20*b**3 + 854*b**2 - 2537*b + 1726. Let u(q) = -23*c(q) - 6*k(q). Suppose u(x) = 0. What is x?
1, 2, 42
Let r = 2652479/44121 - 11834/191. Let b = -23/33 - r. Factor 0*m - 2/7*m**5 + 4/7*m**2 + 0 + b*m**4 - 10/7*m**3.
-2*m**2*(m - 2)*(m - 1)**2/7
Let t = -3/43621 - -71058624/218105. Let q = 327 - t. Factor 2/5*a**2 - q + 4/5*a.
2*(a - 1)*(a + 3)/5
Let b(z) be the second derivative of -z**9/6048 + z**8/3360 + z**7/840 - z**3/2 - 10*z**2 + 179*z. Let g(l) be the second derivative of b(l). Solve g(k) = 0.
-1, 0, 2
Let k(g) be the first derivative of g**5/12 - 5*g**4/12 - 5*g**3/2 - 125*g**2/2 + 81. Let a(w) be the second derivative of k(w). Factor a(p).
5*(p - 3)*(p + 1)
Let c(x) be the second derivative of -10*x**3 + 135*x + 90*x**2 + 0 + 5/12*x**4. Factor c(n).
5*(n - 6)**2
Let k(j) be the second derivative of -1/12*j**4 - 2/15*j**5 + 29*j - 2 + 1/30*j**6 + 2/3*j**3 + 2/3*j**2. Factor k(s).
(s - 2)**2*(s + 1)*(3*s + 1)/3
Let s(u) be the third derivative of -u**7/210 - 17*u**6/120 + 29*u**5/30 - 5*u**4/3 + 6*u**2 - 2*u - 4. Find r, given that s(r) = 0.
-20, 0, 1, 2
Let n = -7823 - -7825. Factor 15/4*j**n - 5/4*j**3 + 0*j - 5.
-5*(j - 2)**2*(j + 1)/4
Suppose 4*i - 8 = -2*r, -925*r = i - 929*r - 20. Suppose 1/5*b**5 + 18/5*b**i - 56/5*b**2 + 78/5*b**3 - 162/5 - 279/5*b = 0. Calculate b.
-9, -1, 2
Let t = -182549/15 + 12170. Let l(z) be the third derivative of 0*z - 24*z**2 + 5/6*z**4 + 0 + 8/3*z**3 + t*z**5. Let l(w) = 0. Calculate w.
-4, -1
Let l = -71/810 - 609373/810. Let d = l - -754. Factor -d - 156/5*s - 1014/5*s**2 - 2197/5*s**3.
-(13*s + 2)**3/5
Let l(j) be the second derivative of -62/3*j**3 + 32*j**2 + 14/3*j**4 - 6 + 2*j + 1/5*j**5. Factor l(p).
4*(p - 1)**2*(p + 16)
Let r(w) be the second derivative of -14/5*w**5 + 0 + 16/3*w**3 - 4*w**4 + 0*w**2 - 95*w + 2*w**6 + 6/7*w**7. Let r(n) = 0. What is n?
-2, -1, 0, 2/3
Factor 1/2*l**4 + 116*l - 62*l**2 - 29*l**3 + 240.
(l - 60)*(l - 2)*(l + 2)**2/2
Let v = -592806/7 - -84687. Let 0 - v*q**3 + 3/7*q + 3/7*q**4 - 3/7*q**2 = 0. What is q?
-1, 0, 1
Let k = -2/249 - -512/1743. Let a(o) be the first derivative of -5 - k*o**2 + 2/21*o**3 + 2/7*o. What is g in a(g) = 0?
1
Factor 4*d - 112 + 40/7*d**2 - 4/7*d**3.
-4*(d - 7)**2*(d + 4)/7
Let y(c) = 10*c - 145. Let n be y(18). What is p in 50*p**2 - 120 + n*p**2 - 15*p**3 + 294*p - 89*p**2 + 25*p**2 = 0?
-4, 2/5, 5
Let -84 - 165/2*u**4 - 3*u**5 + 39*u + 507/2*u**2 + 51*u**3 = 0. What is u?
-28, -1, 1/2, 2
Let n be ((-200)/(-45) + -4)*9. Let p(s) be the first derivative of 7 + 16*s**n - 32/3*s**3 + 64*s - 28/5*s**5 - 32*s**2 + 2/3*s**6. Let p(y) = 0. What is y?
-1, 2
Suppose -2*g + 20 = 3*g. Suppose -g*p + 2*f + 111 + 93 = 0, 4*f = 5*p - 252. Let -p*j**2 - 6*j**4 + 9*j**4 + 3 + 46*j**2 = 0. Calculate j.
-1, 1
Let p be 0 + (8 - 1) + 148/37. Let f be p - (-110)/(-40)*4. Factor -9/5*u**2 + 9/5*u**4 + 0 - 1/5*u**3 + 1/5*u**5 + f*u.
u**2*(u - 1)*(u + 1)*(u + 9)/5
Let o(t) be the second derivative of -t**7/378 + 29*t**5/90 + 14*t**4/27 - 19*t**3/18 - 28*t**2/9 + 2310*t. Find y, given that o(y) = 0.
-7, -1, 1, 8
Solve 15*d**5 - 585*d + 7298/5*d**3 - 284*d**4 - 5008/5*d**2 - 324/5 = 0 for d.
-1/5, 4/3, 9
Let s(v) be the third derivative of -1/4*v**5 + 0*v + 0*v**4 + 0*v**3 + 5/24*v**6 - 215*v**2 + 0 + 1/21*v**7. Let s(f) = 0. What is f?
-3, 0, 1/2
Let i(j) be the third derivative of -4*j**7/105 + 41*j**6/120 - j**5 + 9*j**4/8 + 1231*j**2 + 5. Factor i(d).
-d*(d - 3)*(d - 1)*(8*d - 9)
Factor 278/3 - 137/3*o - 1/3*o**2.
-(o - 2)*(o + 139)/3
Factor -872/9 - 226/9*k - 2/9*k**2.
-2*(k + 4)*(k + 109)/9
Factor 66/7 - 843/7*s - 195/7*s**2.
-3*(5*s + 22)*(13*s - 1)/7
Let -7697*f**2 - 43*f - 11*f**3 + 7653*f**2 + 10*f**3 = 0. What is f?
-43, -1, 0
Let c(m) be the first derivative of -m**4/26 - 228*m**3/13 - 2301*m**2 - 17576*m + 1540. Factor c(q).
-2*(q + 4)*(q + 169)**2/13
Let f(h) = 2*h**2 + 29*h + 21. Let c be f(-15). Suppose 3*r + 6*r = c. Let -6/7*i + 6/7*i**2 - 4/7 + 2*i**3 + 6/7*i**r = 0. Calculate i.
-1, 2/3
Let d = 1467202 + -16139206/11. Factor -2/11*u**3 + 10/11*u**2 - 4/11*u - d.
-2*(u - 4)*(u - 2)*(u + 1)/11
Find q, given that 28/9 - 4/9*q - 8/3*q**2 = 0.
-7/6, 1
Suppose -r + 12 = -0*r - 2*y, -5*y - 85 = -5*r. Factor 5*h**3 + r*h**2 - 47*h**2 + 5*h**3 + 10*h.
5*h*(h - 2)*(2*h - 1)
Let b(n) be the second derivative of -n**6/90 - 4*n**5/15 - 5*n**4/2 + 17*n**3/6 - n + 19. Let z(c) be the second derivative of b(c). Factor z(y).
-4*(y + 3)*(y + 5)
Let o be -66 + (-4940)/(-76) + -2 + (-28)/(-4). Factor -o*l + 4/7*l**2 + 1/7*l**3 + 32/7.
(l - 2)**2*(l + 8)/7
Let m be (18343/52)/(((-6)/(-4))/3). Let j = 707 - m. Factor 0*i + 3*i**2 + 0 - j*i**3.
-3*i**2*(i - 2)/2
Let q(r) be the third derivative of 2*r**3 + 0 + 0*r + 27/40*r**6 - 27/112*r**8 + 27/70*r**7 + 15*r**2 - 31/20*r**5 + 0*r**4. Let q(v) = 0. Calculate v.
-1, -1/3, 2/3, 1
Let x(m) = -260*m**3 - 270*m**2 + 907*m + 1227. Let a(z) = -87*z**3 - 90*z**2 + 302*z + 410. Let h(v) = -17*a(v) + 6*x(v). Factor h(d).
-(d - 2)*(9*d + 14)**2
Let z(a) be the first derivative of 20/3*a**2 + 112/3*a - 1/9*a**3 - 1/12*a**4 + 43. Factor z(q).
-(q - 7)*(q + 4)**2/3
Let y be (4/(-32))/(285/(-1824))*10/4. Suppose -1/4*z**y + 4*z - 16 = 0. Calculate z.
8
Factor -187*y**2 - 440 + 61*y**2 + 131*y**2 - 210*y.
5*(y - 44)*(y + 2)
Let k(j) be the first derivative of j**6/180 + j**5/4 - 4*j**4/3 + j**3 - 5*j**2/2 + 37. Let d(g) be the third derivative of k(g). Find y such that d(y) = 0.
-16, 1
Factor 95*i - 1/3*i**3 - 143/3 - 47*i**2.
-(i - 1)**2*(i + 143)/3
Let j = 174 + -171. Suppose j = 258*r - 257*r. Determine t, given that 0 + 1/7*t**5 - 1/7*t**4 - 3/7*t**r - 2/7*t + 5/7*t**2 = 0.
-2, 0, 1
Suppose 16504*q = 16498*q + 30. Let a(c) be the third derivative of 1/180*c**6 - 2/9*c**3 + 5*c**2 - 1/12*c**4 + 0*c**q + 0*c + 0. Factor a(d).
2*(d - 2)*(d + 1)**2/3
Let n = 8443/123 + -2746/41. Find y such that -1400/3*y - n*y**5 - 85/3*y**4 - 215/3*y**3 + 1205/3*y**2 + 500/3 = 0.
-10, 1
Let t = 540 + -537. Solve 197*g**3 - 315*g**3 + 21*g**5 + 893*g**2 + 450*g + 1012*g**2 + 279*g**4 + 1351*g**t = 0.
-5, -3, -2/7, 0
Let c be (-846)/(-936) - (-2)/(-13). Suppose 39/8*u + c*u**2 + 15/4 - 3/8*u**3 = 0. Calculate u.
-2, -1, 5
Suppose 2*r - 3*o = 21, -5*r + 4*o + 69 = 2*o. Let w be 18/27*r + -5. Find n such that 0 + 0*n + 3/7*n**4 + 2/7*n**w - 1/7*n**2 + 0*n**3 = 0.
-1, 0, 1/2
Let a be ((-1)/(-2))/(((-119)/42)/(-17)). Factor -5*j**3 + 127*j**2 - 121*j**2 + 4*j**a + 7*j.
-j*(j - 7)*(j + 1)
Let w(r) be the first derivative of -r**4/6 - 142*r**3/9 - 139*r**2/3 - 46*r + 2938. Factor w(t).
-2*(t + 1)**2*(t + 69)/3
Let f(t) be the third derivative of t**6/90 - 6*t**5/5 + 54*t**4 + 31*t**3/3 - 56*t**2. Let l(r) be the first derivative of f(r). Factor l(q).
4*(q - 18)**2
Suppose 0 = 5*m - 2*o - 7, -2*o + 6 = m - 5. Suppose -3/7*l**2 + 2/7*l + 0 + 0*l**m + 1/7*l**4 = 0. Calculate l.
-2, 0, 1
Let c(m) be the second derivative of m**6/120 + m**5/5 + 15*m**4/8 + 5*m**3/6 + 7*m**2/2 + 36*m. Let y(z) be the second derivative of c(z). Factor y(h).
3*(h + 3)*(h + 5)
Factor -1/4 + 167/4*w + 42*w**2.
(w + 1)*(168*w - 1)/4
Factor 1254/5*n**2 + 262086/5*n + 2/5*n**3 + 18258658/5.
2*(n + 209)**3/5
Let n(r) be the second derivative of -3*r**4/14 - 1529*r**3/21 + 170*r**2/7 + 11597*r. Factor n(j).
-2*(j + 170)*(9*j - 1)/7
Let h be (-6 + (-40)/(-5))*9. Let l(y) = -y**2 + 19*y - 14. Let r be l(h). Suppose -9/4*d**2 - 1/4*d**r - 5/4*d**3 - 7/4*d - 1/2 = 0. What is d?
-2, -1
Let o(m) = -73*m + 952. Let s be o(13). Let p(l) be the second derivative of 1/12*l**4 - 5*l - 2*l**2 + 1/2*l**s + 0. Find i, given that p(i) = 0.
-4, 1
Let p(j) be the second derivative of j**6/30 + 251*j**5/30 - 14*j**4 - 79*j**3/3 + 50*j - 3. Let x(w) be the second derivative of p(w). Factor x(g).
4*(g + 84)*(3*g - 1)
Let r(d) = -14*d**2 - 993*d - 1996. Let z(c) = 11*c**2 + 997*c + 1994. Let i(v) = -2*r(v) - 3*z(v). Find u, given that i(u) = 0.
-199, -2
Let o(a) be the second derivative of -a**5/20 - a**4 + 9*a**3/2 + 12*a**2 - 96*a + 2. Let t(k)