
5*(a - 36)*(a - 1)**2*(a + 1)
Let n(h) be the second derivative of 1/15*h**6 + 0 + 0*h**2 - h + 1/5*h**5 + 1/6*h**4 + 0*h**3. Factor n(b).
2*b**2*(b + 1)**2
Determine l, given that 135/4 - 69/8*l + 3/8*l**2 = 0.
5, 18
Let g(u) be the third derivative of -49*u**2 - 1/210*u**7 + 0*u**3 - 1/1008*u**8 + 1/36*u**4 - 1/360*u**6 + 0 + 1/60*u**5 + 0*u. Suppose g(j) = 0. What is j?
-2, -1, 0, 1
Let z = 302800 - 96593470/319. Let q = -14/29 - z. Factor 0*v**3 + 2/11*v**4 + 0 + q*v - 6/11*v**2.
2*v*(v - 1)**2*(v + 2)/11
Let o(t) be the second derivative of t**5/110 - t**4/33 - 13*t**3/33 - 10*t**2/11 + 48*t. Find x, given that o(x) = 0.
-2, -1, 5
Let x be (-14)/(-4) + (26 - 19 - 15/2). Let 0 + 6/7*w**x - 2*w**2 - 12/7*w = 0. What is w?
-2/3, 0, 3
Let o = -77 - -81. Factor o*z**3 + 8 - 8*z**2 + 7*z - 8*z**3 - 3*z.
-4*(z - 1)*(z + 1)*(z + 2)
Let n(q) be the third derivative of 19*q**5/4 + 55*q**4/12 + 5*q**3/6 + 87*q**2 + 1. Find c such that n(c) = 0.
-1/3, -1/19
Let l(a) be the third derivative of -a**6/72 - 11*a**5/60 - 23*a**4/36 + 4*a**3/3 + 89*a**2. Factor l(c).
-(c + 3)*(c + 4)*(5*c - 2)/3
Suppose -3*b - a = -42, 0 = 3*b + 3*a - a - 45. Suppose -5*i + b = -7. Solve -g**2 - 4*g**3 - 2*g**i + 11 + 8*g - 19 + 7*g**2 = 0.
-2, 1
Let f(b) be the third derivative of -b**7/420 - 77*b**6/240 - 531*b**5/40 - 4255*b**4/48 - 1369*b**3/6 + 11*b**2 + 29. Factor f(a).
-(a + 1)*(a + 2)*(a + 37)**2/2
Let a(u) be the first derivative of -1/18*u**4 + 0*u + 0*u**2 - 11 + 2/27*u**3. Solve a(w) = 0 for w.
0, 1
Suppose -5*q + 17 = -r, 6*q - 22 = -r + 5. Suppose 3/2 + 7/4*n - 3/4*n**2 - 3/4*n**r + 1/4*n**4 = 0. What is n?
-1, 2, 3
Let u(z) = -1 - 2*z**3 - 2*z - 11*z**2 - 6*z**3 + 2*z**3 - 9*z**3. Let l(v) = v**3 - v**2 + 1. Let k(f) = 5*l(f) + u(f). Factor k(w).
-2*(w + 1)**2*(5*w - 2)
Suppose -4*n**2 + 2*n + 2/3*n**3 + 20/3 = 0. Calculate n.
-1, 2, 5
Suppose 0 = -0*i - 2*i + 6. Let c = i - -3. Factor 0*l - 5 - l**2 + 3*l + 3 - c*l.
-(l + 1)*(l + 2)
Let r(v) = -6*v**2 - 212*v + 5832. Let m(s) = -10*s**2 - 210*s + 5832. Let t(p) = 2*m(p) - 3*r(p). Factor t(d).
-2*(d - 54)**2
Let u(w) = 2*w**3 - 748*w**2 + 95258*w - 4000752. Let i(b) = 6*b**3 - 2240*b**2 + 285775*b - 12002256. Let z(f) = 2*i(f) - 7*u(f). Let z(k) = 0. What is k?
126
Let s(z) = 2*z**4 - 2*z**3 + 2*z**2 + 2. Let p(x) = -x**3 - 1. Let g(w) = 2*p(w) + s(w). Find u, given that g(u) = 0.
0, 1
Let h be (1 - (-27)/(-12))/(-6 + 1). Suppose 3*x + 2 = 4*x. Find a such that 1/4*a**x + h*a - 1/4*a**3 - 1/4 = 0.
-1, 1
Suppose -45/2*c + 0 - 3/2*c**2 = 0. Calculate c.
-15, 0
Let k = 37 - 42. Let r(o) = -5*o**2 - 30*o - 25. Let s(m) = 5*m**2 + 30*m + 25. Let d(q) = k*s(q) - 6*r(q). What is c in d(c) = 0?
-5, -1
Let q be 6172/48 - (-3 + (-39)/(-12)). Let c = -128 + q. Factor -2/3*k + 0*k**2 + c - 1/3*k**4 + 2/3*k**3.
-(k - 1)**3*(k + 1)/3
Let p(n) be the third derivative of -n**5/270 - 31*n**4/36 + 94*n**3/27 - 2*n**2 + 4. Solve p(w) = 0.
-94, 1
Let w = -125 - -259. Let u = 676/5 - w. Factor -1/5*y**2 - 9/5 + u*y.
-(y - 3)**2/5
Let s(v) be the first derivative of -5/12*v**2 - 12 - 1/15*v**5 - 1/2*v + 5/18*v**3 + 5/24*v**4. Find p, given that s(p) = 0.
-1, -1/2, 1, 3
Let t(u) be the third derivative of -u**8/112 - 2*u**7/35 + 4*u**5/5 + 2*u**4 + 382*u**2. Factor t(s).
-3*s*(s - 2)*(s + 2)**3
Let 5*z**3 + 9*z**2 + 3*z**4 - 13*z**3 + 3*z**5 - 7*z**3 + 0*z**5 = 0. Calculate z.
-3, 0, 1
Let y(k) be the first derivative of -k**4/60 - 2*k**3/15 - 3*k**2/10 + 4*k + 10. Let d(q) be the first derivative of y(q). Find t, given that d(t) = 0.
-3, -1
Suppose 0 = -0*q + 2*q - 6. Let u(t) be the first derivative of 2*t**5 + 8*t**3 + 22*t**3 + 11*t**4 - q + 20*t**2 - 8*t**3 + 5*t + 3*t. Factor u(x).
2*(x + 1)**2*(x + 2)*(5*x + 2)
Let s(b) be the second derivative of b**5/180 - 11*b**4/108 + 5*b**3/27 - 254*b. Determine y, given that s(y) = 0.
0, 1, 10
Let f be ((-2)/2)/(-2)*0/(-33). Let 16 - c**3 - 34*c + 23*c**2 - 3*c**2 + f*c**3 - c**3 = 0. Calculate c.
1, 8
Let z(w) = 14*w**3 + 8*w**2 - 17*w - 26. Let l(i) = 46*i**3 + 24*i**2 - 52*i - 80. Let c(t) = 3*l(t) - 10*z(t). Determine k, given that c(k) = 0.
-5, -1, 2
Let d(v) be the first derivative of v**6/3060 - v**5/510 + v**4/204 - 2*v**3 + 9. Let c(f) be the third derivative of d(f). Suppose c(s) = 0. Calculate s.
1
Let 5*r**4 - 144*r**3 - r**5 - 20*r**4 + 40*r**4 + 105 + 39 - 368*r + 344*r**2 = 0. What is r?
1, 2, 18
Let z(b) be the third derivative of -3*b**5/20 + 13*b**4/24 - 2*b**3/3 + 12*b**2 - 1. Factor z(y).
-(y - 1)*(9*y - 4)
Suppose -l - 2 - 2 = 0. Let t be (-6)/(-8)*(-16)/l. Find s, given that 2 - 2*s**3 - 3*s - t*s + 0*s**3 + 6*s**2 = 0.
1
Suppose -491 = 10*q - 511. Let l(x) be the second derivative of -1/24*x**4 - x**q + 1/3*x**3 + 6*x + 0. Suppose l(b) = 0. Calculate b.
2
Let v(j) be the third derivative of 6*j**7/35 + 79*j**6/30 + 15*j**5 + 63*j**4/2 - 36*j**3 - 2*j**2 - 46. Factor v(f).
4*(f + 3)**3*(9*f - 2)
Suppose 44*b - 41*b - 9 = 0. Factor -79*m**3 - 4*m + 160*m**b - 77*m**3.
4*m*(m - 1)*(m + 1)
Let k(i) = i**2 - 4*i - 43. Let w be k(-5). Factor -1/4*p**5 + 5/4*p**3 + 0*p - 1/4*p**4 - 3/4*p**w + 0.
-p**2*(p - 1)**2*(p + 3)/4
Let r = 22 + -19. Suppose 20 = 5*c, -r*u = -8*u - 2*c + 23. Find f such that f**2 + 3*f**4 + f**u - f + 0*f**4 - f**4 - 3*f**4 = 0.
-1, 0, 1
Let t be 0*(-7)/(-4 + 11). Factor -2/5*x**3 + 2/15*x**2 + t + 4/15*x.
-2*x*(x - 1)*(3*x + 2)/15
Suppose -21*a - a**2 + 9*a - 1058 - a**2 - 80*a = 0. What is a?
-23
Let d(h) = -2*h + 2. Let l(q) = -q + 1. Let p(f) = 2*d(f) - 3*l(f). Let n be p(-2). Suppose n*i + 6 + 2 + 2*i**2 + 5*i + 0 = 0. What is i?
-2
Factor 2/7*u**4 - 10/7*u + 6/7*u**2 + 10/7*u**3 - 8/7.
2*(u - 1)*(u + 1)**2*(u + 4)/7
Let g(a) be the third derivative of 0*a**3 + 1/32*a**4 - 39*a**2 + 0 + 1/240*a**5 + 0*a. Factor g(b).
b*(b + 3)/4
Let -126*q**4 + 123*q**4 + 11*q**2 + 18*q + 10*q**2 = 0. Calculate q.
-2, -1, 0, 3
Let x be 41/5 + 2/(-10). Let z = x - 5. Determine h so that 4*h**3 - 2*h - h**3 - z*h**3 - h**3 - 3*h**2 = 0.
-2, -1, 0
Let c = -512/9 - -1033/18. Let -2/3 + 13/6*q - c*q**2 = 0. What is q?
1/3, 4
Let l(t) = -t**3 + 17*t**2 - 31*t + 12. Let g be l(15). Let u be 0/((-4)/(-12)*-1*g). Factor -2/9*o**5 + 2/9*o**4 + 2/9*o**3 + u*o - 2/9*o**2 + 0.
-2*o**2*(o - 1)**2*(o + 1)/9
Let m = -2300 + 2305. Factor -3/2*w**3 + 3/2*w**2 + 0*w - 3/2*w**4 + 0 + 3/2*w**m.
3*w**2*(w - 1)**2*(w + 1)/2
Let h(m) be the second derivative of 12*m + m**4 + 0*m**2 - 1/4*m**5 - 2/3*m**3 + 0. Factor h(q).
-q*(q - 2)*(5*q - 2)
Let d(v) be the first derivative of -v**5 - 295*v**4/4 - 4495*v**3/3 - 4205*v**2/2 + 35. What is o in d(o) = 0?
-29, -1, 0
Determine c, given that -22/3*c + 40/3 + 1/3*c**2 = 0.
2, 20
Let o = -554/35 - -159/10. Let j(h) be the second derivative of -1/4*h**4 + o*h**7 + 0*h**2 - 3/20*h**5 + 0*h**3 + 0 + 1/10*h**6 + 2*h. Factor j(x).
3*x**2*(x - 1)*(x + 1)**2
Let u be (49 - 55) + (-1 - -10). Let q(v) = -v**3 - 5*v**2 - 6*v - 3. Let f be q(-4). Factor -1/2*y**2 + 1/2*y**f + 1/2*y**4 + 0*y - 1/2*y**u + 0.
y**2*(y - 1)*(y + 1)**2/2
Suppose -80*r**2 - 3 - 37*r - 298*r - 12 - 42 - 3 = 0. What is r?
-4, -3/16
Let l(p) be the third derivative of -p**6/90 - 8*p**5/45 - 11*p**4/18 + 40*p**3/9 - 426*p**2. Determine v so that l(v) = 0.
-5, -4, 1
Factor -4*j - j + 2*j**2 + 13 + 4*j**2 + 1 - 7*j**2.
-(j - 2)*(j + 7)
Let i(o) be the third derivative of 5*o**8/336 - 9*o**7/70 - 5*o**6/8 + 139*o**5/60 - 7*o**4/4 + 43*o**2. Solve i(g) = 0.
-3, 0, 2/5, 1, 7
Let h(c) be the first derivative of -c**4/2 - 58*c**3/3 - 224*c**2 - 392*c - 233. Factor h(g).
-2*(g + 1)*(g + 14)**2
Suppose -p + 5 = -7*p + 5. Suppose -4*k = -8*k. Determine m so that 0 + 2/5*m**3 + p*m**4 - 2/5*m**5 + 0*m**2 + k*m = 0.
-1, 0, 1
Suppose 2*w + 4*s = 48, -4*w + 6*w = 4*s + 32. Let b = -6 + w. Factor b*h**3 - 3*h**5 - 2 + 2*h**5 - 16*h**2 + 9*h + 2*h**5 - 6*h**4.
(h - 2)*(h - 1)**4
Suppose -30*t + 33 + 23 = -4. Solve -4/3*i**4 - 20/3*i + 13/3*i**3 - i**5 + 8/3 + t*i**2 = 0.
-2, 2/3, 1
Let m be 42/(-8) - (-5)/20. Let o(w) = w**2 + 6*w + 8. Let p be o(m). Factor -4*y**2 + 4*y**3 + 92*y - p*y**3 - 92*y.
y**2*(y - 4)
Let u be 2/8 - (-171)/36. Find x such that 26*x**4 - 9*x**3 + 29*x**4 - 49*x**4 + 3*x**u = 0.
-3, 0, 1
Factor 2*c**2 + 0 + 1/3*c**3 + 3*c.
c*(c + 3)**2/3
Find p, given that -16/9*p