/2*k**2 + 1/2*k**3 + 1/2*k**4 + 0*k.
-k**2*(k - 1)**2*(k + 1)/2
Suppose 637*j - 192 = 573*j. Let o(p) be the third derivative of 1/1080*p**6 + 13*p**2 - 1/18*p**j + 0 + 1/180*p**5 + 0*p - 1/216*p**4. Factor o(x).
(x - 1)*(x + 1)*(x + 3)/9
Let w be (4*1 + -23 + 69)/1. Let c = w - 48. Factor -4/5 + 2/5*k + 16/5*k**c + 2*k**3.
2*(k + 1)**2*(5*k - 2)/5
Let r = 1354/579 + -968/579. Determine k, given that 40/9 + r*k**4 - 70/9*k**2 - 8/9*k - 16/9*k**3 = 0.
-2, -1, 2/3, 5
Let d be (-37 + 15 + 22)/((-8)/1). Factor -3/2*r**2 + 51/2*r + d.
-3*r*(r - 17)/2
Suppose 126 - 21 = 3*h. Let t = -22 + h. Solve 2 + 2 + t*j**4 - 8*j**2 - 9*j**4 = 0 for j.
-1, 1
Let x(t) be the second derivative of 0*t**4 + 1/72*t**6 + 1/24*t**5 + 0 - 7/3*t**3 + 0*t**2 + 9*t. Let j(p) be the second derivative of x(p). Factor j(s).
5*s*(s + 1)
Determine t so that 8181*t - 117*t**2 - 16483*t + 7*t**3 + 0*t**3 + 8242*t - t**3 = 0.
-1/2, 0, 20
Let r(b) = 10*b + 522. Let a be r(-52). Let z(x) be the second derivative of 0 - 1/21*x**4 + 0*x**3 - 1/70*x**5 - 23*x + 0*x**a. Solve z(u) = 0.
-2, 0
Factor -345*c**2 - 13687875 + 119025*c + 1/3*c**3.
(c - 345)**3/3
Let b = -1209 + 2841. Let u = -4888/3 + b. Factor u + 8/3*n + 2/3*n**2.
2*(n + 2)**2/3
Let h(d) = d**2 - 10*d - 84. Let z be h(-6). Let -z - 216*m**3 + 478*m**3 + 54*m**2 - 242*m**3 + 9*m**2 + 31*m = 0. What is m?
-12/5, -1, 1/4
Factor -48*p**2 - 16*p + 13*p + 100 - 23*p - 9*p - 19*p + 2*p**3.
2*(p - 25)*(p - 1)*(p + 2)
Let h be (-20)/((-1600)/(-260))*(-10)/65. Suppose -h*y**4 - 1 + 17/6*y**2 - 5/6*y**3 + 13/6*y = 0. What is y?
-3, -1, 1/3, 2
Let f(w) be the second derivative of 1/180*w**6 + 123*w + 1/12*w**4 - 1/9*w**3 + 1/24*w**5 - 2/3*w**2 + 0. Let f(s) = 0. Calculate s.
-2, 1
Let t = 65495 + -65462. Factor 7*f**2 + t*f + 1/3*f**3 - 121/3.
(f - 1)*(f + 11)**2/3
Let i(a) be the first derivative of a**6/3 + 26*a**5/5 + 5*a**4 - 236*a**3/3 + 149*a**2 - 110*a - 1883. Suppose i(m) = 0. What is m?
-11, -5, 1
Let -262/11*m**3 - 400/11 + 292/11*m**2 + 216/11*m - 2/11*m**5 + 60/11*m**4 = 0. Calculate m.
-1, 2, 25
Let a be (-329)/231 + -1 + 3 - 45948/(-42119). What is n in -4/3*n**4 + a*n**3 + 0*n + 1/3*n**5 + 0 - 2/3*n**2 = 0?
0, 1, 2
Factor -177/4*s**2 - 3/4*s**3 + 363/4*s - 183/4.
-3*(s - 1)**2*(s + 61)/4
Let g(p) be the third derivative of 5*p**3 + 0*p - 112*p**2 + 1 + 1/80*p**5 - 13/32*p**4. Factor g(k).
3*(k - 8)*(k - 5)/4
Let i(b) be the third derivative of 0*b - 1/24*b**4 + 1/80*b**6 - 1/120*b**5 - 91*b**2 + 0*b**3 + 0. Factor i(w).
w*(w - 1)*(3*w + 2)/2
Let f(b) be the third derivative of -b**6/12 + 13*b**5/4 - 145*b**4/8 + 85*b**3/3 - 1176*b**2. Factor f(r).
-5*(r - 17)*(r - 2)*(2*r - 1)
Let o(u) be the third derivative of -2*u**7/315 - 23*u**6/30 - 143*u**5/5 - 363*u**4/2 - 1938*u**2. Factor o(i).
-4*i*(i + 3)*(i + 33)**2/3
Let h = 167 + -167. Factor -8*p**3 - 42*p**2 - 8*p**3 + h*p**3 - 2*p**4 - 36*p.
-2*p*(p + 2)*(p + 3)**2
Suppose 3*u + 0*u = 5*f + 2, 4*f = 4*u - 8. Find r, given that 0*r**2 + r**2 - 6*r**f - 15 - 10 + 30*r = 0.
1, 5
Let l be -9 - -16 - (6 + (-2)/1). Factor -3*a**2 + 2*a - 4*a + l*a + 4*a**2.
a*(a + 1)
Let m(s) be the first derivative of 8*s**4/7 - 16*s**3/3 - 31*s**2/7 - 8*s/7 - 13028. Solve m(d) = 0.
-1/4, 4
Suppose 5*w - 13 - 7 = 0. What is h in -7 + 7*h + w - 10*h - h**2 + 1 = 0?
-2, -1
Let p(a) = a**2 - 31*a + 186. Let k be p(12). Let l = k + 42. Factor l - 1/2*m - m**2 - 1/2*m**3.
-m*(m + 1)**2/2
Factor -80/17*q**2 + 278/17*q + 2/17*q**3 + 360/17.
2*(q - 36)*(q - 5)*(q + 1)/17
Suppose 0 = -1064*f + 1068*f - 1896. Find y such that 485*y**3 + 24*y**2 - 947*y**3 - 4*y**4 + f*y**3 - 32*y = 0.
-2, 0, 1, 4
Let k(q) = 11 - 10 - q + 6*q**2 - 7*q**2. Let p(r) = 2*r**2 + 42*r - 47. Let g(n) = 3*k(n) - p(n). Factor g(c).
-5*(c - 1)*(c + 10)
Let u = -2/570117 - -13682822/3990819. Suppose 0 - u*w - 50/7*w**2 - 4*w**3 - 2/7*w**4 = 0. What is w?
-12, -1, 0
Let f(n) be the second derivative of -1/45*n**6 - 4/9*n**3 - 5 + 1/6*n**4 - n - 4/3*n**2 + 1/15*n**5. Factor f(g).
-2*(g - 2)**2*(g + 1)**2/3
Let x(o) be the first derivative of -170*o + 234 - 5/3*o**3 + 95/2*o**2. Factor x(r).
-5*(r - 17)*(r - 2)
Let q(p) = 20*p**2 - 5*p - 8. Let o be q(-3). Factor -o*v - 2420 - 14*v**2 + 9*v**2 + 149*v - 182*v.
-5*(v + 22)**2
Let g be -80 + 90 - 1348/2. Let c = -5311/8 - g. Solve -1/8*l**4 + 0*l**2 - 1/4*l**3 + c + 1/4*l = 0 for l.
-1, 1
Factor -10374 - 20976*k - 108413 - 42*k**3 - 23*k**3 - 283*k**2 - 14521 + 64*k**3.
-(k + 7)*(k + 138)**2
Let t(g) be the second derivative of 2/5*g**3 - 3/100*g**5 + 0*g**2 + 1/5*g**4 + 0 - 1/50*g**6 - 75*g. Factor t(u).
-3*u*(u - 2)*(u + 1)*(u + 2)/5
Let s(l) be the first derivative of 2*l**5/25 - 103*l**4/10 + 134*l**3/5 + 103*l**2/5 - 404*l/5 + 234. Solve s(i) = 0.
-1, 1, 2, 101
Let h(w) be the first derivative of 1/2*w**3 + 0*w - 5/16*w**6 + 3/4*w**4 + 0*w**2 - 21/40*w**5 - 46. Determine c so that h(c) = 0.
-2, -2/5, 0, 1
Let p(j) be the first derivative of j**6/6 - 5*j**5/2 - 115*j**4/12 - 10*j**3 - 44*j - 63. Let h(n) be the first derivative of p(n). Factor h(t).
5*t*(t - 12)*(t + 1)**2
Let o be 4/(-9)*(-54)/(-180)*-15. Let l be (-770)/(-1225) + 6*o/(-28). Factor 4/5*g + l*g**2 + 0.
g*(g + 4)/5
Suppose 2*l + 9 = 3*l + 4*s, -4*l = -5*s + 27. Let y be 4 + -3 - 2 - l. Factor -10*q**y - 7 - 26*q + 20*q + 11*q**2.
(q - 7)*(q + 1)
Let w be -6*(-6 - (-92)/12). Let c be (-260)/208*6/w. Suppose c - 3/4*a**2 - 3/4*a**3 + 3/4*a = 0. What is a?
-1, 1
Let b(z) be the second derivative of z**4/36 + 47*z**3/18 - 49*z**2/3 - z - 2. Solve b(c) = 0 for c.
-49, 2
Let m(x) be the third derivative of 0*x + 0*x**3 + 0*x**4 - 1/20*x**5 - x**2 - 29 + 1/120*x**6. Factor m(s).
s**2*(s - 3)
Let 1/2*r**3 - 132*r + 7/2*r**2 - 1224 = 0. What is r?
-12, 17
Let n(r) be the third derivative of -280/3*r**3 - 13/5*r**5 + 44*r**2 + 1/30*r**6 + 4*r + 24*r**4 + 0. Let n(a) = 0. Calculate a.
2, 35
Let s(j) = -18*j**2 - 542*j + 70. Let f(m) = -17*m**2 - 543*m + 65. Let a(q) = -14*f(q) + 13*s(q). Factor a(r).
4*r*(r + 139)
Let k(c) = -c**4 + 103*c**3 + 52*c**2 - 32*c - 4. Let i(y) = -4*y**4 + y**3 + y**2 + y - 1. Let h(l) = -4*i(l) + k(l). Determine f, given that h(f) = 0.
-6, -1, 0, 2/5
Let k(q) = q**2 - 2*q + 1. Let x(z) be the first derivative of -4*z**3/3 + 4*z**2 - 2*z - 62. Let f(n) = -2*k(n) - x(n). Factor f(b).
2*b*(b - 2)
Let s(c) be the second derivative of -c**6/40 - c**5/5 - c**4/8 + 3*c**3 + 99*c**2/2 + 141*c. Let z(a) be the first derivative of s(a). Solve z(l) = 0.
-3, -2, 1
Factor -4*t + 12/7*t**3 - 18/7*t**2 + 0 + 2/7*t**4.
2*t*(t - 2)*(t + 1)*(t + 7)/7
Solve 20*g**3 - 12771*g**2 + 12691*g**2 - 4*g**4 - 36*g**3 - 32*g**3 + 0*g**4 = 0.
-10, -2, 0
Let t(f) be the third derivative of -f**8/1848 - 2*f**7/1155 + f**5/165 + f**4/132 - 302*f**2. Factor t(l).
-2*l*(l - 1)*(l + 1)**3/11
Let q(k) be the third derivative of 2/105*k**5 + 1/42*k**4 + 1/210*k**6 + 28*k + 0*k**3 + k**2 + 0. Factor q(i).
4*i*(i + 1)**2/7
Let u(r) be the first derivative of -r**4/6 + 10*r**3/9 + 8*r**2 - 5518. Determine h, given that u(h) = 0.
-3, 0, 8
Let v(q) be the first derivative of 0*q**3 + 0*q + 40 - 31/10*q**5 + 1/12*q**6 + 0*q**4 + 0*q**2. Determine g so that v(g) = 0.
0, 31
Let u(g) be the third derivative of g**6/360 - 101*g**5/45 + 40397*g**4/72 + 41209*g**3/9 + g**2 - 143*g. Solve u(w) = 0 for w.
-2, 203
Let o(q) be the third derivative of q**2 + 0*q - 14 + 0*q**3 - 15/8*q**4 + 1/20*q**5. Suppose o(v) = 0. What is v?
0, 15
Suppose 94*f - 81*f = -39. Let i(z) = -z**4 + z**3 - z**2. Let g(m) = -m**4 + 33*m**3 - 113*m**2 + 156*m - 72. Let o(r) = f*i(r) - g(r). Factor o(u).
4*(u - 3)**2*(u - 2)*(u - 1)
Let r(a) = 6*a + 11. Let w be r(9). Let y = -56 + w. Factor 5*v + 5*v - 2*v**3 + v**3 - y*v.
-v*(v - 1)*(v + 1)
Let v = 210 - 207. Factor 4*o - 28*o**v - 7*o**3 - 14*o - 72*o**2 + 147*o**2.
-5*o*(o - 2)*(7*o - 1)
Let y(z) = 6*z + 5. Let i be y(0). Solve 379*k**2 + 29*k**4 + 200*k + 41*k**2 + 46*k**4 + i*k**5 + 46*k**3 + 244*k**3 = 0.
-10, -2, -1, 0
Let a(v) be the first derivative of 2/15*v**3 + 88/5*v + 24/5*v**2 - 166. Factor a(u).
2*(u + 2)*(u + 22)/5
Let y(v) = 56*v**3 - 115*v**2 + 69*v - 5. Let w(r) = -364*r**3 + 748*r**2 + 9 + 152*r + 23 - 600*r. Let p(d) = 5*w(d) + 32*y(d). Factor p(h).
-4*h*(h - 1)*(7*h - 8)
Let a(l) be the third