r**2 = 0.
-1, -1/2
Let x(n) be the first derivative of -n**4/10 - 42*n**3/5 + 129*n**2/5 - 26*n - 258. Find h such that x(h) = 0.
-65, 1
Let k = -1205 - -1205. Let f(v) be the third derivative of -5*v**2 + 4/3*v**3 + 3/2*v**4 + 0*v + k + 1/5*v**5 - 2/15*v**6. Factor f(g).
-4*(g - 2)*(g + 1)*(4*g + 1)
Let k = 12 - 8. Factor 4*g + 2*g**3 + 2*g**2 - k*g.
2*g**2*(g + 1)
Let b(g) = g**2 + 57*g + 216. Let r be b(-53). Let c(v) be the second derivative of -4*v - 1/6*v**r + 0*v**2 - 1/6*v**3 + 0 - 1/20*v**5. Solve c(q) = 0.
-1, 0
Factor -337*n**3 + 4*n**4 - 3*n**4 + 343*n**3 + 11*n**2 + 6*n.
n*(n + 1)*(n + 2)*(n + 3)
Factor 24/5 + 62/5*l + 53/5*l**2 + 16/5*l**3 + 1/5*l**4.
(l + 1)**2*(l + 2)*(l + 12)/5
Let h(z) be the third derivative of 1/200*z**6 + 1/40*z**4 + 0*z + 5*z**2 + 1/50*z**5 + 0*z**3 + 0. Factor h(f).
3*f*(f + 1)**2/5
Let p(c) = c**3 - 10*c**2 - 9*c - 18. Let d be p(11). Suppose -27 = -5*h - d*h. Determine r, given that 1/4*r**2 + 3/4 + 5/4*r - 1/4*r**h = 0.
-1, 3
Let q(b) be the first derivative of 3/11*b**2 + 2/11*b + 3 + 2/11*b**3 + 1/22*b**4. Factor q(k).
2*(k + 1)**3/11
Suppose -331*p + 327*p = 4*o - 12, 0 = 4*o - p - 7. Let m be ((-8)/10)/((-7)/5). Factor -m*b + 16/7*b**o + 0.
4*b*(4*b - 1)/7
Let f(z) be the third derivative of -z**5/90 + 10*z**4/9 - 400*z**3/9 + 54*z**2 + z. Determine d so that f(d) = 0.
20
Let q(w) be the first derivative of -w**5/15 - w**4/3 - 3*w**2/2 - 15. Let f(b) be the second derivative of q(b). Let f(k) = 0. Calculate k.
-2, 0
Let q = 18 - -26. Let s be -12*4/(-264) - (-14)/q. Factor 1/2*n + s*n**2 + 0.
n*(n + 1)/2
Let f(j) be the third derivative of -1/80*j**6 + 1/280*j**7 + 0*j + 0*j**3 + 1/80*j**5 + 16*j**2 + 0 + 0*j**4. Suppose f(c) = 0. What is c?
0, 1
Let i = -579 + 582. Let n(b) be the second derivative of 1/12*b**4 + 1/2*b**i + 4*b + 0*b**2 + 0. Let n(h) = 0. Calculate h.
-3, 0
Let d be (-3 - (-46 + 3)) + -4. Let f = d + -22. Suppose -16*m**2 - 6*m - 252*m**3 + 248*m**3 - 8 - f*m = 0. Calculate m.
-2, -1
Let a be ((-1)/26)/(-5 + 705/144). Let r = 2/65 + a. Solve -4/5*x - r*x**2 - 2/5 = 0 for x.
-1
Let o(g) be the second derivative of 5*g**7/21 - 7*g**6/6 - 3*g**5/2 + 55*g**4/3 - 100*g**3/3 + 55*g. Suppose o(w) = 0. What is w?
-5/2, 0, 2
Let p = -126 + 166. Let -2*b**2 + 2*b**2 + 200 + 2*b**2 + p*b = 0. Calculate b.
-10
Let f(l) = -2*l**3 + 8*l**2 + 10*l + 6. Let w(g) = -5*g**3 + 26*g**2 + 31*g + 17. Let h(s) = 17*f(s) - 6*w(s). Determine u so that h(u) = 0.
-4, -1, 0
Let f(q) be the third derivative of -q**6/75 + 17*q**5/75 - 16*q**4/15 + 8*q**3/5 + 114*q**2. Find h, given that f(h) = 0.
1/2, 2, 6
Let o be (4 + 1)*(1035/700 + (-10)/8). Factor -6/7*c - 2/7*c**3 + 0 - o*c**2.
-2*c*(c + 1)*(c + 3)/7
Factor 0 + 8/3*o**2 + 8/9*o**3 - 2/9*o**4 + 0*o.
-2*o**2*(o - 6)*(o + 2)/9
Let h(s) be the third derivative of 5*s**9/3024 + s**8/56 + 3*s**7/56 - 5*s**3 - 34*s**2. Let a(r) be the first derivative of h(r). Factor a(p).
5*p**3*(p + 3)**2
Let m(y) be the second derivative of 1/21*y**4 - 9*y + 2 + 20/21*y**3 + 18/7*y**2. Let m(d) = 0. What is d?
-9, -1
Let z(d) be the second derivative of -d**5/100 - 13*d**4/60 - 7*d**3/6 + 49*d**2/10 - 141*d. Determine b so that z(b) = 0.
-7, 1
Let i(y) be the first derivative of -35*y**4/12 + 85*y**3/3 - 35*y**2/3 - 200. Factor i(o).
-5*o*(o - 7)*(7*o - 2)/3
Suppose -26*g = 4*p - 25*g - 9, 0 = -2*p - g + 3. Factor 0 + 74/3*k**p - 40/3*k**2 + 6*k**5 + 8/3*k - 20*k**4.
2*k*(k - 1)**2*(3*k - 2)**2/3
Let o(u) be the third derivative of -u**5/30 + 467*u**4/84 + 134*u**3/21 - 13*u**2 - 6*u. Factor o(z).
-2*(z - 67)*(7*z + 2)/7
Let x = -695 - -10433/15. Factor 2/15 + x*w**2 + 8/15*w.
2*(2*w + 1)**2/15
Find o such that 423/5*o**4 + 681/5*o**3 + 84/5*o**5 - 24/5 + 66*o**2 - 36/5*o = 0.
-2, -1, -2/7, 1/4
Let w(s) = -s**2 + 62*s - 515. Let l be w(10). What is q in 3/5*q**l + 0 - 3/5*q**3 + 0*q - 3/5*q**4 + 3/5*q**2 = 0?
-1, 0, 1
Solve 40/3*j - 1/3*j**5 - 7/3*j**4 - 2*j**3 + 0 + 28/3*j**2 = 0.
-5, -2, 0, 2
Let s(l) = -3*l**2 - 57*l + 84. Let d(v) = -v**2 - 2*v + 1. Let p(u) = -6*d(u) + s(u). Factor p(r).
3*(r - 13)*(r - 2)
Let c = -1946/3 + 3901/6. Let o = -9/2 - -6. Solve 0 + 3/2*r**5 - c*r**3 + 0*r + 3/2*r**4 - o*r**2 = 0.
-1, 0, 1
Let v be 3/(-6)*(-1 - -1). Let r(x) be the second derivative of -4*x + 0 + 1/2*x**3 + v*x**2 - 1/5*x**6 - 1/14*x**7 + 0*x**5 + 1/2*x**4. Factor r(c).
-3*c*(c - 1)*(c + 1)**3
Factor -16*y + 1/2*y**5 + 30*y**2 - 23/2*y**3 + 0 - 3*y**4.
y*(y - 8)*(y - 1)**2*(y + 4)/2
Let n be (-6)/(-4) - ((-85)/(-25) - 2). Let s(b) be the second derivative of b + 0 - 1/3*b**4 + 0*b**2 - 1/3*b**3 - n*b**5. Factor s(l).
-2*l*(l + 1)**2
Suppose 16 = 5*m + 151. Let i be (12/(-9))/(6/m). Solve 3*r**4 - 1 + i*r + r**3 + 2 - 4 - 7*r**3 = 0.
-1, 1
Let t(d) be the second derivative of d**4/24 - d**3/4 - 5*d**2/2 - 71*d. Determine r so that t(r) = 0.
-2, 5
Let s(a) = -5*a**3 + 354*a**2 + 43206*a + 1727988. Let y(v) = 6*v**3 - 353*v**2 - 43207*v - 1727986. Let p(c) = -7*s(c) - 6*y(c). Factor p(l).
-(l + 120)**3
Let l(w) be the second derivative of -1/18*w**3 - 1/180*w**6 + 1/60*w**5 + 1/12*w**2 + 0*w**4 + 0 - 5*w. Factor l(a).
-(a - 1)**3*(a + 1)/6
Let j = 27412 - 109623/4. Factor -115/4*r - j*r**3 - 55/2*r**2 - 15/2.
-5*(r + 1)*(r + 3)*(5*r + 2)/4
Suppose -14 = 10*q - 34. Let u(h) be the second derivative of -5/2*h**q + 0*h**3 + 0*h**5 + 0 - 9*h - 1/6*h**6 + 5/6*h**4. Suppose u(y) = 0. What is y?
-1, 1
Let h(j) = -2*j**2 - 50*j - 27. Let u be h(-25). Let x = 27 + u. Factor 0 - 1/4*q - 1/4*q**5 + 1/2*q**3 + x*q**4 + 0*q**2.
-q*(q - 1)**2*(q + 1)**2/4
Let y be ((-2)/8 + 0)*(-5)/5. Factor -y*i - 1/8 - 1/8*i**2.
-(i + 1)**2/8
Let g(p) be the second derivative of p**4/21 + 6*p**3/7 + 16*p**2/7 + 48*p. Factor g(u).
4*(u + 1)*(u + 8)/7
Suppose 9*v - 32*v = -14*v. Let m(r) be the second derivative of -1/2*r**2 + 1/12*r**4 + 0 + v*r**3 + 4*r. Factor m(z).
(z - 1)*(z + 1)
Let p(v) be the first derivative of 3*v**7/7 + 11*v**6/5 + 23*v**5/5 + 5*v**4 + 3*v**3 + v**2 + 9*v + 1. Let f(l) be the first derivative of p(l). Factor f(b).
2*(b + 1)**3*(3*b + 1)**2
Let o be ((-165)/132)/(2/(-8)). Let g(j) be the first derivative of -2/5*j**o - 2*j**2 + 0*j - 3/2*j**4 + 1/3*j**6 - 2 + 10/3*j**3. Solve g(b) = 0.
-2, 0, 1
Let h(p) = -3*p**3 + 40*p**2 - 64*p + 27. Let t be (-3 - 1) + (-56)/14. Let k(u) = 4*u**3 - 60*u**2 + 96*u - 40. Let f(i) = t*h(i) - 5*k(i). Factor f(g).
4*(g - 2)**2*(g - 1)
Let r = -1549 + 10849/7. Determine p so that 8/7*p + 0 + 2/7*p**4 - r*p**3 + 0*p**2 = 0.
-1, 0, 2
Let x(v) = -v**3 - 4*v**2 - 4*v + 4. Let a be x(-6). Find y, given that a - 6*y + 3*y**3 - 94 - 9*y + 9*y**2 - 3*y**4 = 0.
-2, 1
Let r = 110 - 102. Let w be (r/(-4))/(3/(-1)). Suppose 0 + 2/3*m**3 - w*m - 2/3*m**2 + 2/3*m**4 = 0. Calculate m.
-1, 0, 1
Factor 8/3*n - 8/3*n**3 + 4/3*n**2 - 4/3*n**4 + 0.
-4*n*(n - 1)*(n + 1)*(n + 2)/3
Suppose 113*r = 89*r. Factor -1/6*x**2 - 1/6*x + r.
-x*(x + 1)/6
Let g = 1429/42 + -34. Let n(b) be the second derivative of 0 + g*b**4 + 1/35*b**5 - 1/7*b**2 + 2*b - 2/21*b**3. Factor n(q).
2*(q - 1)*(q + 1)*(2*q + 1)/7
Let y be 2*7/20 + -10 + 494/52. Suppose -8/5*a + 16/5 + y*a**2 = 0. What is a?
4
Let q(b) be the first derivative of 6 - 10*b + 5/2*b**2 + 5/3*b**3. Factor q(t).
5*(t - 1)*(t + 2)
Let f(s) be the first derivative of -5*s**3/6 - 10*s**2 - 75*s/2 + 160. Solve f(y) = 0.
-5, -3
Factor 0*w + 3/5*w**3 - 3/5*w**4 + 12*w**2 + 0.
-3*w**2*(w - 5)*(w + 4)/5
Solve 45/4*b + 15/4*b**2 + 25/4 - 5/4*b**3 = 0 for b.
-1, 5
Let i = -41 - -38. Let f(o) = 3*o**3 + 2*o**2 - 13*o + 12. Let q(a) = 2*a**3 + 3*a**2 - 12*a + 13. Let z(h) = i*f(h) + 2*q(h). Factor z(w).
-5*(w - 1)**2*(w + 2)
Let y(m) be the third derivative of -25/56*m**4 + 0 + 0*m + 31*m**2 - 1/840*m**6 - 125/42*m**3 - 1/28*m**5. Solve y(s) = 0.
-5
Let 32/7*n - 384/7 + 8*n**2 - 2/7*n**4 - 2/7*n**3 = 0. What is n?
-4, 3, 4
Find w such that 0 - 7/3*w**3 - 1/3*w**4 + 1/3*w**2 + 7/3*w = 0.
-7, -1, 0, 1
Let c(p) be the second derivative of -p**9/3024 + p**8/672 - p**7/504 - 17*p**4/6 + 11*p. Let q(i) be the third derivative of c(i). Factor q(k).
-5*k**2*(k - 1)**2
Solve 19/5*p + 1 - 4/5*p**2 = 0 for p.
-1/4, 5
Suppose -2688 + 1068 = 9*g. Let l be 2/8 + 201/g + 1. Factor -2/5 + 2/5*w**2 + l*w - 2/15*w**3.
-2*(w - 3)*(w - 1)*(w + 1)/15
Let l(