k**2 + 6*k + 1. Let f(x) = x**3 + 37*x**2 + 54*x + 9. Let o(w) = 2*f(w) - 18*g(w). Determine v, given that o(v) = 0.
-46, 0
Let y = -9222 - -9227. Let b(o) be the third derivative of 0*o**3 + 0*o + 0 + 23*o**2 - 1/72*o**4 - 1/180*o**y. Determine v so that b(v) = 0.
-1, 0
Let k(a) be the first derivative of -4/3*a**3 - 60*a**2 - 116*a - 121. Determine b, given that k(b) = 0.
-29, -1
Let x(v) be the first derivative of -v**6/48 + 11*v**5/20 + 51*v**4/32 - 17*v**3/6 - 25*v**2/4 + 12*v - 961. Let x(y) = 0. What is y?
-2, 1, 24
Let o(p) be the third derivative of -1/50*p**5 - 41*p**2 + 0*p**3 + 0*p - 1/150*p**6 - 1/1680*p**8 + 0 + 1/175*p**7 + 1/24*p**4. What is h in o(h) = 0?
-1, 0, 1, 5
Let g(v) = v**3 - v**2 + 2*v + 2. Let t(p) = -8*p**3 - 2482*p**2 - 310006*p - 307526. Let s(f) = 3*g(f) + t(f). Let s(l) = 0. What is l?
-248, -1
Let b(u) be the second derivative of u**5/5 - 47*u**4/3 - 206*u**3 - 954*u**2 - 210*u - 1. Solve b(s) = 0.
-3, 53
Let s(k) be the second derivative of -3*k**5/160 - 93*k**4/16 - 183*k**3/16 + 555*k**2/8 - 1883*k. Factor s(w).
-3*(w - 1)*(w + 2)*(w + 185)/8
Let y(d) be the first derivative of d**3/7 - 75*d**2/2 + 1038*d/7 - 4753. Factor y(n).
3*(n - 173)*(n - 2)/7
Let g(u) = 8 + 5*u - u + 8*u**2 - 5*u**3 + u - 16. Suppose 4*f - 10*f - 12 = 0. Let c(k) = k**3 - k**2 - k + 1. Let p(v) = f*c(v) - g(v). Factor p(z).
3*(z - 2)*(z - 1)*(z + 1)
Let u = 1152066 - 1152064. Factor 2/5*m**3 - 178/5*m**u + 4048/5*m - 3872/5.
2*(m - 44)**2*(m - 1)/5
Let l(f) be the third derivative of 5*f**8/2352 + 61*f**7/490 - 2789*f**6/840 + 11861*f**5/420 - 690*f**4/7 + 350*f**3/3 - 9594*f**2. Let l(h) = 0. What is h?
-49, 2/5, 2, 5
Let k(q) be the third derivative of q**7/455 + 19*q**6/780 + 7*q**5/130 + 5*q**4/156 - q**2 + 398*q. Solve k(x) = 0 for x.
-5, -1, -1/3, 0
Let w = 56 + -45. Let u = w + -9. Let -13*j**2 - 4*j**3 - 9*j**2 + 26*j**u + 8*j = 0. Calculate j.
-1, 0, 2
Let q(b) be the third derivative of -b**5/72 + 2285*b**4/24 - 1044245*b**3/4 + 8*b**2 + 55*b - 2. Let q(z) = 0. Calculate z.
1371
Let c(f) be the second derivative of f**5/45 - 7*f**4/9 + 16*f**3/3 - 37*f**2 - 23*f - 5. Let h(q) be the first derivative of c(q). Factor h(t).
4*(t - 12)*(t - 2)/3
Let m be (1400/600)/((2*-1)/978). Let p = m - -1143. Solve -4*w + 2 - 5/2*w**p = 0 for w.
-2, 2/5
Solve -3/5*j + 9/5 - 18/5*j**2 + 9/5*j**4 - 3/5*j**5 + 6/5*j**3 = 0 for j.
-1, 1, 3
Let z be (8/44)/(7/(76 - -1)). Let d(n) be the first derivative of -1/10*n**4 - 8/5*n - z + 4/5*n**2 + 2/15*n**3. Factor d(j).
-2*(j - 2)*(j - 1)*(j + 2)/5
Let v(h) be the first derivative of -3*h**5/20 - 33*h**4/8 - 15*h**3 - 87*h**2/4 - 57*h/4 + 226. Factor v(d).
-3*(d + 1)**3*(d + 19)/4
Let n be (-720)/(-300) + 6/(-90)*26. Determine z so that -n*z - 1/3*z**2 + 0 = 0.
-2, 0
Factor 343/3*n**5 + 308*n**3 + 931/3*n**4 + 0 + 400/3*n**2 + 64/3*n.
n*(n + 1)*(7*n + 4)**3/3
Let j(k) be the first derivative of 3/2*k**2 - 311 + 9/4*k + 1/4*k**3. Factor j(u).
3*(u + 1)*(u + 3)/4
Suppose -63*q - 185 - 183*q + 75*q**2 - 67 - 653*q - 133*q = 0. Calculate q.
-6/25, 14
Let a(w) be the first derivative of -9*w**4/13 + 2*w**3/13 + 4*w**2/13 - 2*w/13 - 629. Suppose a(s) = 0. Calculate s.
-1/2, 1/3
Let u(h) be the first derivative of -6*h**3 - 3*h**4 - 225 - 2/5*h**5 - 4*h**2 + 0*h. Factor u(z).
-2*z*(z + 1)**2*(z + 4)
Find h, given that 0 - 14*h**2 - 4*h**4 - 23/2*h**3 - 1/2*h**5 - 6*h = 0.
-3, -2, -1, 0
Let z be ((-16)/(-4) + -3)*120/10. Let q be (-6 + 309/54)*z/(-15). Factor -8/9 + q*a**2 - 2/3*a.
2*(a - 4)*(a + 1)/9
Let z = -2445 - -2437. Let y be 2/(-8) - z*(-221)/(-544). Factor -2/3*j**4 - 4/3 - 14/3*j - 6*j**2 - 10/3*j**y.
-2*(j + 1)**3*(j + 2)/3
Let l(o) be the third derivative of o**6/80 - 9*o**5/5 - 75*o**4/4 - 76*o**3 + 1225*o**2. Let l(k) = 0. Calculate k.
-2, 76
Suppose 8/11*h**3 - 2040/11*h**2 + 0 + 2/11*h**4 + 0*h = 0. What is h?
-34, 0, 30
Let v = 536352 - 536352. Let 0*x + 4/7*x**4 - 8/7*x**2 + v - 4/7*x**3 = 0. Calculate x.
-1, 0, 2
Factor -3/2*u**2 + 249/2 - 123*u.
-3*(u - 1)*(u + 83)/2
Let -20*s**5 + 12*s**4 - 12*s**2 + 8*s**5 + 8*s**5 - 326 + 326 - 4*s**3 + 8*s = 0. Calculate s.
-1, 0, 1, 2
Let 4992*j - 1314*j**3 - 123*j**4 - 1122*j**5 + 3350*j**2 + 1119*j**5 - 6902*j**2 = 0. What is j?
-26, -8, 0, 1
Factor 40/7*i**2 - 20/7 + 46/7*i + 6/7*i**3.
2*(i + 2)*(i + 5)*(3*i - 1)/7
Factor -496 + 2216/3*b - 271*b**2 - 3*b**3.
-(b + 93)*(3*b - 4)**2/3
Let m be (6/10)/((-3)/(-15)). Let z be ((-6)/(-42) - (-6072)/(-462)) + 13. Factor z + 2/3*v**4 - 2*v**2 + 4/3*v + 0*v**m.
2*v*(v - 1)**2*(v + 2)/3
Let p(x) be the third derivative of 13/60*x**5 + 2*x - 1/210*x**7 - 1/336*x**8 + 0 - 57*x**2 + 7/120*x**6 + 0*x**3 + 1/4*x**4. Factor p(q).
-q*(q - 3)*(q + 1)**2*(q + 2)
Let a(i) be the first derivative of -i**3/6 + 735*i**2/2 - 540225*i/2 + 2007. Factor a(j).
-(j - 735)**2/2
Let w(h) be the second derivative of 0 + 0*h**2 + 8/3*h**3 + h**4 - 23/10*h**5 + 3/5*h**6 + 114*h. Factor w(z).
2*z*(z - 2)*(z - 1)*(9*z + 4)
Let f(w) be the third derivative of 2*w + 1/3*w**5 + 5/6*w**4 - 1/6*w**6 + 2/105*w**7 + 0 - 4*w**3 - 32*w**2. Determine p, given that f(p) = 0.
-1, 1, 2, 3
Let p(z) be the first derivative of z**5/140 - 3*z**4/56 - 9*z**3/7 + 41*z**2/2 + 50. Let n(u) be the second derivative of p(u). Suppose n(g) = 0. What is g?
-3, 6
Let w(j) be the third derivative of -j**5/420 - 127*j**4/42 - 32258*j**3/21 + 687*j**2. Factor w(k).
-(k + 254)**2/7
What is z in -386978*z + 56*z**4 + 772983*z + 800*z**3 - 4*z**5 + 680*z**2 - 736 - 386801*z = 0?
-8, -1, 1, 23
Let g = -8860/27 + 811/189. Let n = 324 + g. Determine s so that -n*s - 1/7*s**4 + 0 + 1/7*s**2 + 1/7*s**3 = 0.
-1, 0, 1
Let p(u) be the third derivative of u**6/600 + 19*u**5/60 - 1477*u**4/120 + 5341*u**3/30 - 67*u**2 + 4*u + 2. Factor p(k).
(k - 7)**2*(k + 109)/5
Let z(t) be the second derivative of 1/12*t**4 + 0 - 11/8*t**2 + 33*t + 43/24*t**3. Solve z(l) = 0.
-11, 1/4
Let z(v) be the second derivative of v**4/6 - 101*v**3 - 304*v**2 + 2876*v. Factor z(j).
2*(j - 304)*(j + 1)
Let b(c) be the third derivative of -c**8/4032 - 11*c**7/504 - 3*c**5/4 - 198*c**2. Let o(i) be the third derivative of b(i). Suppose o(w) = 0. Calculate w.
-22, 0
Let k be (-9)/15 - 105/75. Let p be (10 + k)*(12/16)/3. Determine z so that 0 + 0*z**p + 0*z + 1/4*z**4 + 1/4*z**3 = 0.
-1, 0
Let a = -33 + 111. Suppose 42*p - 106*p - 128 + 171*p**3 - 85*p**3 - 2*p**4 - a*p**3 + 24*p**2 = 0. What is p?
-2, 4
Suppose -6525 = 12*k - 1209. Let i = 446 + k. Factor 0 + 0*o**2 - 3/4*o**i + 3/2*o**4 + 0*o - 3/4*o**5.
-3*o**3*(o - 1)**2/4
Let u be ((-60)/(-22) - 3)*(-1 + 103). Let t = 1541/55 + u. Let 0 - t*m**2 + 2/5*m = 0. Calculate m.
0, 2
Factor -864/19 - 2/19*q**2 - 96/19*q.
-2*(q + 12)*(q + 36)/19
Let r(l) = -5*l**4 + 2*l**3 - 14*l**2 + 7*l. Let i(y) = -2*y**4 + y**3 - 6*y**2 + 3*y. Let u = 212 - 219. Let w(p) = u*i(p) + 3*r(p). Factor w(k).
-k**3*(k + 1)
Let m = 2216/47 + -5614/141. Suppose m*c + 2/3*c**2 - 8 = 0. What is c?
-12, 1
Let j(w) be the third derivative of -w**5/120 - 191*w**4/12 - 36481*w**3/3 + 5*w**2 - 224. Suppose j(a) = 0. Calculate a.
-382
Let k(p) = p**2 + 5*p - 20. Let z be k(-5). Let i be (-1*(-15)/z)/(-2 - -1). Factor i*u - 1 + 1/4*u**2.
(u - 1)*(u + 4)/4
Let i be (1/10)/((-2)/(-8)). Let s be (32*20/4000)/((-19)/(-190)). Determine l, given that 0*l - s + i*l**2 = 0.
-2, 2
Solve 48/11*q**4 - 2/11*q**5 + 60/11*q**3 - 256/11*q**2 + 150/11*q + 0 = 0.
-3, 0, 1, 25
Let n be 7084/2277*(-10)/(-35). Factor -2*w**2 - 10/9*w + n.
-2*(w + 1)*(9*w - 4)/9
Let g(c) be the first derivative of c**4/6 - 5*c**3/3 - 6*c**2 - 21*c - 22. Let h(o) be the first derivative of g(o). Suppose h(n) = 0. Calculate n.
-1, 6
Let u = 3034967/19950 - -122/1425. Let d = 305/2 - u. Let 0 + 0*x + d*x**2 = 0. What is x?
0
Factor 7/3 + 17/3*j**2 + j**3 - 9*j.
(j - 1)*(j + 7)*(3*j - 1)/3
Let x(w) = -39*w + 6. Let u be x(2). Let h be 2/7 - u/42. Find q, given that 12 - 132*q - 8 + 32 + 160*q**h - 64*q**3 = 0.
3/4, 1
Suppose 90*h - 1512 = 76*h. Suppose -108 = -54*p + h. Find f, given that -4/3*f**p + 20/9*f**2 - 8/9 + 20/9*f - 20/9*f**3 = 0.
-2, -1, 1/3, 1
Let m(w) be the first derivative of -w**5/5 + 3*w**4/2 + 31*w**3/3 - 18*w**2 + 715. Find y such that m(y) = 0.
-4, 0, 1, 9
Suppose 55*i + 21624 = 38*i. Let o = i - -636