. Let d(s) be the second derivative of w(s). Factor d(a).
-(a - 10)*(a - 2)
Suppose b = -9, -35 = -13*p - 1392*b + 1393*b. What is j in -2/7*j**3 - 12/7 + 2/7*j + 12/7*j**p = 0?
-1, 1, 6
What is j in 201/7*j**2 + 1/7*j**3 + 200/7*j + 0 = 0?
-200, -1, 0
Let l(h) = 20*h**3 + 25*h**2 - 40. Let q(k) be the first derivative of -9*k**4/4 - 13*k**3/3 + 20*k - 69. Let o(u) = 2*l(u) + 5*q(u). Factor o(m).
-5*(m - 1)*(m + 2)**2
Let y(u) be the second derivative of -u**6/40 + u**5/10 - 7*u**4/48 + u**3/12 + 7556*u. Factor y(m).
-m*(m - 1)**2*(3*m - 2)/4
Let v(p) be the third derivative of -3*p**6/440 - 131*p**5/132 + 73*p**4/132 - 88*p**2 + 33. Let v(c) = 0. Calculate c.
-73, 0, 2/9
Suppose -53*k = -52*k + 6*m - 9, 2*k + 4*m - 10 = 0. Factor 20/3*p - 4*p**2 + 100/9 + 4/9*p**k.
4*(p - 5)**2*(p + 1)/9
Let g(v) be the third derivative of 2*v**7/315 + 91*v**6/360 + 337*v**5/180 - 5*v**4/4 - v**2 + 1162. Suppose g(j) = 0. Calculate j.
-18, -5, 0, 1/4
Let c(s) = 10*s**2 + 343*s + 1026. Let i be c(-31). Let -4/13*y**i - 2/13*y**4 + 0*y + 6/13*y**2 + 0 = 0. What is y?
-3, 0, 1
Let x = 6059932/5 + -1211986. Factor x*s + 12/5 - 2/15*s**2.
-2*(s - 6)*(s + 3)/15
Let a(c) be the second derivative of c**4/6 - 497*c**3/3 - 4290*c. Determine w so that a(w) = 0.
0, 497
Let p = 61576 - 61571. Factor 3*s**4 - 3*s**3 - 21/2*s - 3 + 3/2*s**p - 12*s**2.
3*(s - 2)*(s + 1)**4/2
Let t = 239 - 233. Let f(u) be the second derivative of 10/3*u**3 + 1/6*u**t + 5/2*u**4 - 16*u + u**5 + 5/2*u**2 + 0. Factor f(q).
5*(q + 1)**4
Suppose 4*l - 15 = -3*n + 5*l, -5*n + 5*l = -35. Suppose 0 = k - p - 1, -2 = -n*k + 3*p + 6. Factor 41 + 20*g - k*g**2 - 41.
-5*g*(g - 4)
Let k(w) be the second derivative of -w**6/6 + 3*w**5/2 + 165*w**4/4 + 440*w**3/3 + 210*w**2 - 2*w + 368. Suppose k(o) = 0. Calculate o.
-6, -1, 14
Solve 632/13*k**3 + 372/13*k**2 + 18/13*k**5 - 228/13*k**4 + 80/13 - 426/13*k = 0.
-1, 1/3, 5, 8
Find u, given that 708/5 - 702/5*u**2 + 366/5*u - 366/5*u**3 - 6/5*u**4 = 0.
-59, -2, -1, 1
Let x = 69020 - 1035208/15. Find j such that -8/15 - x*j**3 - 8/15*j**5 + 46/15*j**4 - 8/15*j + 14/3*j**2 = 0.
-1/4, 1, 2
Let i(l) be the second derivative of -185/8*l**3 - 2 + 1/16*l**5 + 76*l - 35/24*l**4 - 225/2*l**2. Let i(w) = 0. What is w?
-3, 20
Suppose 3*d - 4 + 16 = 0. Let z(q) = 7*q**4 - 99*q**3 + 971*q**2 - 2205*q + 1350. Let i(n) = -n**4 - 5*n**2. Let k(b) = d*i(b) - z(b). Factor k(j).
-3*(j - 15)**2*(j - 2)*(j - 1)
Let h be (-15)/(-6) - 1*(-5)/(-10). Factor 27*s + 2*s**h - 9*s - 15 - 3*s**2 - 66.
-(s - 9)**2
Suppose 54*r - 53*r + 1 - 4 = 0. Let p(x) be the second derivative of 1/10*x**r - 1/10*x**4 + 0*x**2 - 15*x + 0 + 3/100*x**5. Factor p(u).
3*u*(u - 1)**2/5
Let m(k) be the second derivative of k**8/1680 + k**7/315 - k**6/60 + 17*k**4/6 - 69*k. Let p(n) be the third derivative of m(n). Suppose p(h) = 0. Calculate h.
-3, 0, 1
Let p(v) be the first derivative of 3*v**5/5 - 42*v**4 + 2549. Factor p(q).
3*q**3*(q - 56)
Suppose 5*z = 12*z - 14. Determine h, given that -764*h + 8 + 2*h**2 + 0*h**z + 756*h = 0.
2
Let w(i) be the first derivative of -i**6/12 - 83*i**5/30 - 23*i**4 + 212*i**3/9 + 140*i**2 + 392*i/3 - 2399. Suppose w(c) = 0. Calculate c.
-14, -1, -2/3, 2
Let q(u) = 3*u**4 + 12*u**3 + 9*u**2 - 12. Let c(w) = -9*w**4 - 36*w**3 - 28*w**2 - 4*w + 37. Let j(s) = -3*c(s) - 10*q(s). Factor j(d).
-3*(d - 1)*(d + 1)**2*(d + 3)
Let d(z) be the third derivative of 0*z + 0*z**3 + 128*z**2 + 0 + 1/60*z**5 + 1/40*z**4. Factor d(j).
j*(5*j + 3)/5
Let l be 1 + -2 - (-54)/18. Suppose 120 = l*s + 6*s. Determine u, given that -22*u**2 - 20 - 14*u**2 + 60*u + s*u**4 - 24*u**2 + 15*u**2 - 10*u**3 = 0.
-2, 2/3, 1
Let v(b) be the second derivative of b**5/60 - 41*b**4/36 + 20*b**3/9 - 9*b + 10. Find o, given that v(o) = 0.
0, 1, 40
Factor -8 - 11 + 5 - 5*z**2 - 13*z - 17*z - 11.
-5*(z + 1)*(z + 5)
Let w(k) be the first derivative of -k**8/2352 + 3*k**6/280 + k**5/105 - k**4/14 - k**2 - 11*k + 64. Let d(b) be the second derivative of w(b). Solve d(t) = 0.
-2, 0, 1, 3
Let q(r) be the second derivative of -7*r**6/20 - 51*r**5/10 - 169*r**4/8 - 18*r**3 + 27*r**2 + 156*r - 2. Find x, given that q(x) = 0.
-6, -3, -1, 2/7
Let a(k) = -k**3 - 52*k**2 + 199*k + 1870. Let f be a(-55). Factor 2/7*z**3 + f*z**2 - 8/7*z + 0.
2*z*(z - 2)*(z + 2)/7
Let j be (3/4)/((-3)/(-8)). Suppose -3*n + 1 = -4*y, -j*n + 0*y = -5*y + 4. Factor -5*t**3 - 22*t + 17 - n*t - 20*t**2 - 27.
-5*(t + 1)**2*(t + 2)
Let w be (-12)/(-69) + 12672/3312. Determine y, given that 4/19*y - 12/19*y**w + 2/19*y**2 - 14/19*y**3 + 0 = 0.
-1, -2/3, 0, 1/2
Let l(m) be the second derivative of 1/36*m**4 + 1/2*m**3 - 2*m - 7 + 10/3*m**2. Find u, given that l(u) = 0.
-5, -4
Let 6*j**3 + 120/7 - 46/7*j**4 - 302/7*j - 4/7*j**5 + 190/7*j**2 = 0. Calculate j.
-12, -5/2, 1
Let f(d) be the third derivative of 0*d**3 - 2/15*d**5 + 89*d**2 + 1/105*d**7 + 0*d - 1/15*d**6 + 1/168*d**8 + 0*d**4 + 0. Factor f(x).
2*x**2*(x - 2)*(x + 1)*(x + 2)
Factor -932*f + 273*f - 1380*f**2 + 1282*f**2 - 1800 - 181*f.
-2*(7*f + 30)**2
Let b(u) be the first derivative of -u**5/25 + u**4/10 + 23*u**3/15 - 12*u**2/5 - 144*u/5 - 41. Suppose b(i) = 0. What is i?
-3, 4
Suppose -d + 5 = a, 5*d + a = 2*a + 13. Factor 27*g**4 - 26*g**d + 2*g - 18*g**3 + 36*g**3 - 16*g**3 - 5*g**2.
g*(g - 1)*(3*g + 1)*(9*g - 2)
Let l(y) = -3*y**2 + 679*y + 4902. Let w be l(-7). Factor -3/8*m**3 - 21/8*m + 9/8 + 15/8*m**w.
-3*(m - 3)*(m - 1)**2/8
Let d(l) be the first derivative of l**4/16 + 377*l**3/12 - 153. Factor d(m).
m**2*(m + 377)/4
Suppose -55*o = 28*o - 498. Let c(p) be the third derivative of 0*p - 1/168*p**4 + 0 + 0*p**3 - 1/210*p**5 + 3*p**2 - 1/840*p**o. Factor c(l).
-l*(l + 1)**2/7
Let n = -34987/3 - -384947/33. Factor -n*h + 14/11*h**2 + 18/11 - 2/11*h**3.
-2*(h - 3)**2*(h - 1)/11
Let l be (1 + 6 - 1)/(57/114). Let k = 6 - 4. Let -61*m**k + 17*m + 33*m + 69*m**2 + l = 0. Calculate m.
-6, -1/4
Let q(r) be the third derivative of 0*r**4 - 2*r - 2*r**2 - 1/3864*r**8 - 8/345*r**6 + 0*r**3 + 0 - 16/345*r**5 - 2/483*r**7. Factor q(l).
-2*l**2*(l + 2)*(l + 4)**2/23
Let j(r) be the third derivative of -r**6/80 - 429*r**5/40 + 27*r**4 + 215*r**3 + 38*r**2 + 3*r - 1. Factor j(g).
-3*(g - 2)*(g + 1)*(g + 430)/2
Let h(r) be the second derivative of -7/80*r**5 + 0 - 141*r + 1/3*r**4 - 3/4*r**2 + 17/24*r**3. Suppose h(l) = 0. Calculate l.
-1, 2/7, 3
Let k(f) be the third derivative of -f**8/840 - f**7/175 + 13*f**6/300 + 47*f**5/150 + 4*f**4/5 + 16*f**3/15 - 2817*f**2. What is r in k(r) = 0?
-4, -1, 4
Let m be 5520/1200*(-2 - -17). Determine v, given that -m*v + 1587/2 + 3/2*v**2 = 0.
23
Suppose -3*l + 328 = 403. Let t(w) = -w**3 - 25*w**2 + 8*w + 200. Let h be t(l). Find m, given that 1/7*m**3 + 0*m + h + 3/7*m**2 = 0.
-3, 0
Let n(p) = -2*p**2 + 3 + 7*p + 15*p + 20*p - 6*p. Let a be n(18). Factor -9/2*k + 9/8*k**3 - a + 3/8*k**4 - 3/4*k**2.
3*(k - 2)*(k + 1)*(k + 2)**2/8
Let i = 2 + 2. Suppose 71*d - 69*d - 8 = 0. Factor 7*r**4 - i*r**d - 4*r**4 + 4*r**3 - 8*r**2 + 5*r**4.
4*r**2*(r - 1)*(r + 2)
Suppose -4*b**5 + 968*b - 17823 - 10025 - 9591*b**3 - 4321*b**3 + 598*b**4 - 126*b**4 + 41748*b - 1424*b**2 = 0. Calculate b.
-2, 1, 59
Factor 191*x - 552 + 124*x - 28*x - 54*x + 49*x - 3*x**2.
-3*(x - 92)*(x - 2)
Let g(f) be the third derivative of 0 - 2/165*f**5 + 90*f**2 + 0*f + 0*f**3 + 0*f**4 - 1/1155*f**7 - 1/165*f**6. Determine z so that g(z) = 0.
-2, 0
Solve 2*k**2 + 30*k + 35*k**2 - 11*k**3 + 6*k - 9*k**2 - 4*k**2 + k**4 = 0.
-1, 0, 6
Let x = -89269/10 - -8927. Let p(b) be the second derivative of -1/3*b**4 - x*b**5 + 0*b**2 + 1/3*b**3 + 10*b + 2/15*b**6 + 0. Find i, given that p(i) = 0.
-1, 0, 1/2, 1
Let o be 5942/(-364) - 70/(-1820) - -18. Factor 32/7*y + 4*y**2 + 8/7*y**3 + o.
4*(y + 1)**2*(2*y + 3)/7
Factor 3/5*u**2 - 21/5*u**3 + 3/5*u**4 + 54/5 + 81/5*u.
3*(u - 6)*(u - 3)*(u + 1)**2/5
Let t(w) = -w**2 + 17*w - 24. Let j be t(15). Let q be 5 + (-58)/j + 5. Factor q*k**3 + 2/3*k**2 + 0*k + 0.
k**2*(k + 2)/3
Let u(q) be the third derivative of q**6/60 - 89*q**5/15 - 30*q**4 - 2*q**2 + 585*q + 3. Factor u(a).
2*a*(a - 180)*(a + 2)
Let u be -3*((-12)/(-16) + -1) + 0. Let i(k) = 35*k**2 + 313*k - 16. Let j be i(-9). Suppose -u - 3/4*r**j - 5/2*r = 0. Calculate r.
-3, -1/3
Let v(z) be the third deriv