Let f(y) = 9*y + 60. Let z be f(-8). Let a(m) = -m**3. Let t(b) = z*a(b) + k(b). Factor t(p).
2*p*(p + 1)**2*(p + 3)
Let c be ((-18088)/(-252))/(-17) + (0 - -1 - -5). Suppose -28/9*u + 2/9*u**2 + 2/9*u**5 + 26/9*u**3 - c + 14/9*u**4 = 0. Calculate u.
-4, -2, -1, 1
Suppose 19*c = 18*c + 5*m + 1, -5*c + 3*m + 5 = 0. Let l(v) be the first derivative of 1/20*v**2 - c + 1/15*v**3 + 1/40*v**4 + 0*v. Factor l(r).
r*(r + 1)**2/10
Let c(m) be the second derivative of m**5/220 - 23*m**4/132 + 7*m**3/11 + 3*m + 342. Suppose c(u) = 0. What is u?
0, 2, 21
Factor 39*z - 35*z + 69*z - 5*z**3 - 4*z**2 - 6*z**2 + 47*z.
-5*z*(z - 4)*(z + 6)
Let r = -23 - -46. Suppose -4*p + 3 + r = -2*q, 0 = 2*p - 4*q - 4. Determine a, given that 2*a**5 + 12*a**3 - 8*a**2 + a - 8*a**4 - 7*a + p*a = 0.
0, 1
Suppose 39486*f - t - 136 = 39484*f, -2*f = -4*t - 166. Suppose 48*b + 15/2*b**5 + 180*b**2 + 0 + f*b**4 + 174*b**3 = 0. What is b?
-4, -2, -2/5, 0
Let x(r) = 2*r**3 + 7*r**2 - 4*r + 3. Let n be x(-4). Suppose 26*z**n - 46*z**3 + 5*z**4 - 30*z**2 - 5*z**3 = 0. What is z?
-1, 0, 6
Let a(q) = 50*q**3 - 123*q**2 - q - 5. Let j(y) = -y**3 - 2*y**2 - y + 1. Let u(b) = -a(b) - 5*j(b). Factor u(f).
-f*(f - 3)*(45*f + 2)
Let l(u) be the third derivative of 0*u + 0 + 0*u**3 + 5/12*u**4 - 5/42*u**7 - 7/12*u**5 - 64*u**2 + 5/336*u**8 + 3/8*u**6. Factor l(s).
5*s*(s - 2)*(s - 1)**3
Let u = -202 + 2343. Let q = 2141 - u. Let -4/7*w**4 + 0*w - 3/7*w**3 - 1/7*w**5 + 0 + q*w**2 = 0. What is w?
-3, -1, 0
Let i(s) be the third derivative of s**5/20 + 2*s**4 + 15*s**3/2 - 1047*s**2. Determine z, given that i(z) = 0.
-15, -1
Let z(m) = -m**3 + m + 1. Let y be (10/50)/(7/35). Let h(f) = -2*f**3 - 3*f**2 - f + 1. Let n be (-2)/(0/1 - -2). Let i(b) = n*z(b) + y*h(b). Factor i(l).
-l*(l + 1)*(l + 2)
Suppose 2*z + 3*z + 4*v + 134 = 0, z + v + 26 = 0. Let p = -25 - z. Factor -2*i**3 - 16*i**2 - 198*i**p + 50*i**3 - 84*i**4 + 48*i**3 + 2*i**5.
-4*i**2*(i + 1)*(7*i - 2)**2
Let i(q) be the first derivative of -3/2*q**2 - 2/3*q**3 - 1/12*q**4 + 0*q - 132. Factor i(c).
-c*(c + 3)**2/3
Suppose x + 2*v = -33 + 47, -2*x = 2*v - 38. Factor -x*f**4 - 48*f**2 + 14*f - 3 + 4*f**5 - 10 + 2*f + 13 + 52*f**3.
4*f*(f - 2)**2*(f - 1)**2
Let s(q) be the first derivative of q**6/6 + 141*q**5/5 + 5559*q**4/4 + 41159*q**3/3 + 31020*q**2 - 108900*q - 2745. Let s(w) = 0. Calculate w.
-66, -5, 1
Suppose -256*q + 746 + 22 = 0. Factor -3/8*n + 9/4 - 1/2*n**2 + 1/8*n**q.
(n - 3)**2*(n + 2)/8
Let q(k) be the second derivative of k**6/15 + 33*k**5/10 - 117*k**4/2 + 369*k**3 - 1134*k**2 - k - 1697. Find h such that q(h) = 0.
-42, 3
Let o(l) be the third derivative of l**8/60480 - l**7/7560 - l**5/10 - l**2 - 17*l. Let h(c) be the third derivative of o(c). Solve h(j) = 0.
0, 2
Factor 10547*d + 26*d**2 + 27*d**3 - 10547*d + d**4.
d**2*(d + 1)*(d + 26)
Suppose -3984*m + 3978*m = -96. Let y be (7/(84/m))/((-42)/(-72)). Determine s, given that -y + 0*s + 4/7*s**3 + 12/7*s**2 = 0.
-2, 1
Suppose 0 = -r + 3*i - 10, -6*r - 2*i + 3 = -3*r. Let q(k) = 2*k**2 - 1. Let a(j) = -4*j**4 + 72*j**3 - 44*j**2 - 12. Let l(u) = r*a(u) + 12*q(u). Factor l(x).
4*x**2*(x - 17)*(x - 1)
Let k(r) be the first derivative of 14*r**5/5 - 65*r**4/2 - 944*r**3/3 + 140*r**2 - 2403. Factor k(x).
2*x*(x - 14)*(x + 5)*(7*x - 2)
Let q(d) = -7*d - 32. Let p be q(-5). Suppose -p*v = 6*v. Factor v*b**2 + 6*b**3 + 2*b**2 - 7*b**3 - b**4.
-b**2*(b - 1)*(b + 2)
Let c(l) be the second derivative of 9*l**5/10 + 224*l**4/3 + 341*l**3/3 - 98*l**2 - 1023*l. Find x such that c(x) = 0.
-49, -1, 2/9
Let j = 5018 - 5014. Let n(w) be the third derivative of 0*w + 1/15*w**3 - 1/60*w**j - 1/75*w**5 + 0 - w**2. Factor n(t).
-2*(t + 1)*(2*t - 1)/5
Let w be (-7)/14 + 16388/(-952) - -18. Factor -4/7*l - 2/7*l**2 - w.
-2*(l + 1)**2/7
Let u(k) be the first derivative of 4*k**3 - 1/60*k**5 - 1/6*k**4 + 1/180*k**6 + 1 + 0*k**2 + 0*k. Let s(a) be the third derivative of u(a). Factor s(v).
2*(v - 2)*(v + 1)
Let n(g) be the first derivative of -3*g**4/4 - 25*g**3 + 39*g**2 + 1635. Find q such that n(q) = 0.
-26, 0, 1
Let f(t) = -2*t**3 - 268*t**2 + 8954*t - 31740. Let s(a) = -a**3 - 2*a**2 + 2*a + 3. Let j(x) = f(x) - 4*s(x). Factor j(z).
2*(z - 63)**2*(z - 4)
Let d(f) be the first derivative of -1/27*f**3 + 101 - 2/9*f**2 - 1/3*f. Let d(c) = 0. Calculate c.
-3, -1
Factor -270 - 345*h - 5*h**3 - h**3 + 1272865*h**2 + h**3 - 1272945*h**2.
-5*(h + 1)*(h + 6)*(h + 9)
Let j(p) be the first derivative of 23/14*p**4 - 24/7*p**2 + 50 + 32/7*p - 18/35*p**5 + 1/21*p**6 - 2/3*p**3. What is y in j(y) = 0?
-1, 1, 4
Let h(z) = -z - 6. Let x(a) = a**2 - 47*a + 192. Let v(q) = -30*h(q) + 3*x(q). Factor v(w).
3*(w - 28)*(w - 9)
Suppose -481*s = -459*s - 44. Suppose -3*o + k = 6*k + 25, -k - 5 = -5*o. Factor o - 7/3*g + 1/3*g**s.
g*(g - 7)/3
Let i be (-111)/(-30) + 5885/(-2354). Factor -i*f**2 - 9/5 + 3*f.
-3*(f - 1)*(2*f - 3)/5
Let q(s) be the first derivative of -s**4/14 + 10*s**3/3 + 38*s**2/7 - 144*s/7 - 2067. Factor q(o).
-2*(o - 36)*(o - 1)*(o + 2)/7
Suppose -75*d - 1525 = 454*d - 4170. Let y(j) be the first derivative of 3 - 1/15*j**d + 0*j + 2/3*j**4 - 13/9*j**3 + j**2. Factor y(c).
-c*(c - 6)*(c - 1)**2/3
Let o(a) = -12*a**2 + 1689*a - 238554. Let x(r) = 9*r**2 - 1690*r + 238560. Let d(y) = 2*o(y) + 3*x(y). Solve d(n) = 0 for n.
282
Find g, given that 44/3*g**3 - 4/3*g**4 + 52*g**2 + 164/3*g + 56/3 = 0.
-1, 14
Let t = 343 - 245. Let n be t/6 + (-2 + -2)/12. Factor 22*c**2 + 4*c - 9*c**2 - 8*c**2 + n*c.
5*c*(c + 4)
Suppose 2*c + 68*t - 65*t = -1, -4*c + 2*t = -22. Factor 0*k - 10/3*k**3 - 2/3*k**5 + 4/3*k**2 + 0 + 8/3*k**c.
-2*k**2*(k - 2)*(k - 1)**2/3
Let -4*f**3 - 74 + 2*f**3 + 317*f**2 + 29*f**2 - 434 + 162*f**2 + 2*f = 0. Calculate f.
-1, 1, 254
Suppose -3*z + 9*z = 18. Suppose 14 = 4*f + y, 2*f - 11 = -z*f + 2*y. Determine k so that 2*k + f*k**3 - 2*k**4 - 10*k**2 - 5*k - k - 11*k**3 = 0.
-2, -1, 0
Let c be (-8)/20*(-2590 - (-5 + 0)). Let v = -1034 + c. Let -4/5*m**2 + 0*m + v = 0. Calculate m.
0
Factor 0 + 24/5*h - 4/5*h**4 - 24/5*h**3 + 4/5*h**2.
-4*h*(h - 1)*(h + 1)*(h + 6)/5
Let z be (-36)/108 + (-12)/((-4536)/774). Factor -4/7*k**4 + 0 - z*k**3 + 12/7*k + 4/7*k**2.
-4*k*(k - 1)*(k + 1)*(k + 3)/7
Let b be 7/(-11) - 88/242. Let z be 325/75 + 4*b. Solve 0 - z*g + 1/3*g**2 = 0 for g.
0, 1
Let t be 2/(-6)*34/408*-27. Let r be (-12)/(-2) + -5*16/40. Find n, given that 3/4*n**r + 3/4*n**5 + 0 + 0*n - 3/4*n**3 - t*n**2 = 0.
-1, 0, 1
Let g(r) be the second derivative of -r**6/50 - 93*r**5/100 + 17*r**4/10 + 32*r**3/5 + 21*r - 70. Find n, given that g(n) = 0.
-32, -1, 0, 2
Let w(l) be the first derivative of -2*l**3/3 + 924*l**2 - 426888*l - 14752. Factor w(b).
-2*(b - 462)**2
Let i = 380 + -383. Let f be (-10)/(-125)*(-3 + -42)/i. Suppose -f*l - 4/5 - 2/5*l**2 = 0. What is l?
-2, -1
Suppose 280*l - 61*l = 219. Let y be (-76)/(-18) + (-4)/((-2)/(-2)). Factor l + 1/9*b**4 - y*b**2 + 4/9*b**3 - 4/3*b.
(b - 1)**2*(b + 3)**2/9
Let i(h) be the third derivative of -h**6/420 + 337*h**5/210 - 28891*h**4/84 + 27889*h**3/7 + 4088*h**2. Factor i(f).
-2*(f - 167)**2*(f - 3)/7
Let t(f) = f**3 - 19*f**2 - 4*f + 91. Let k be t(19). Suppose 4*s - 5*x - k = 0, -61*x = s - 65*x - 12. Factor s - 14/11*j**3 - 12/11*j + 34/11*j**2.
-2*j*(j - 2)*(7*j - 3)/11
Let z = -144511/3 + 48173. Factor -48 + 8/3*a**3 - 1/3*a**4 + z*a**2 - 32*a.
-(a - 6)**2*(a + 2)**2/3
Let p(y) = 3*y - 39. Suppose -2*t - 8 = 3*v - 25, -2*v - 6 = 0. Let g be p(t). Factor -u + g - 5/2*u**3 - 7/2*u**2.
-u*(u + 1)*(5*u + 2)/2
Let f(r) be the first derivative of 2*r**6/15 - 4*r**4 - 32*r**3/3 - 129*r + 61. Let b(c) be the first derivative of f(c). Factor b(i).
4*i*(i - 4)*(i + 2)**2
Let x(z) be the third derivative of -z**6/72 + 3*z**5/4 - 89*z**3/6 + 19*z**2 + 1. Let h(a) be the first derivative of x(a). Factor h(o).
-5*o*(o - 18)
Let s(o) be the first derivative of -2*o**3/3 + 540*o**2 - 3623. Factor s(c).
-2*c*(c - 540)
Suppose 68 + 102*n**2 + 143*n**5 - 116*n**3 - 103*n**3 - 1244 - 284*n**5 + 138*n**5 + 924*n + 48*n**4 = 0. What is n?
-2, 2, 7
Let b(v) be the third derivative of -v**7/210 - v**6/20 - 3*v**5/20 + v**4/6 + 2*v**3 - 10*v**2 - 6. Factor b(z).
-(z - 1)*(z + 2)**2*(z + 3)
Suppose 21*o + 30*o = 306. Suppose 3 = 2*h - 1. Factor -o*q**2 - 14