is o in n(o) = 0?
-1, 3
Factor -74 + 32*p - 41 + 3*p**2 - 50 - 43*p + 29*p.
3*(p - 5)*(p + 11)
Suppose 5*d - 25 = 2*q, -13*q + 17*q - 25 = -5*d. Let s(v) be the first derivative of 0*v**2 + q*v + 7 - 1/6*v**3 - 1/16*v**4. Factor s(f).
-f**2*(f + 2)/4
Let j = 46139 - 599805/13. Factor -j*x**2 + 0 - 2/13*x.
-2*x*(x + 1)/13
Suppose -2*t = -6*t + 72. What is u in t*u - 5*u**2 - 9*u + 20*u**3 + 0*u**2 - 89*u + 20 = 0?
-2, 1/4, 2
Let k(j) = -23*j**3 + 316*j**2 - 88*j + 5. Let v(b) = -68*b**3 + 948*b**2 - 264*b + 16. Let o(x) = -16*k(x) + 5*v(x). Factor o(r).
4*r*(r - 11)*(7*r - 2)
Factor 32/15*t**2 + 46/5*t + 12 + 2/15*t**3.
2*(t + 3)**2*(t + 10)/15
Let q(y) be the second derivative of y**4/48 + 4*y**3/3 + 31*y**2/8 + 126*y. Solve q(u) = 0.
-31, -1
Let z(y) be the first derivative of 3*y**5/10 + 19*y**4/4 + 107*y**3/6 + 17*y**2 - 18*y + 47. Factor z(v).
(v + 2)**2*(v + 9)*(3*v - 1)/2
Suppose -55 = -3*l + 23. Let s be 238/l - (-6)/(-39). Find v such that v**2 - 16*v - 2*v**2 + 8*v + s*v = 0.
0, 1
Let a(i) be the third derivative of 1/6*i**4 + 0 - 4/9*i**3 + 0*i + 17*i**2 - 1/45*i**5. Factor a(v).
-4*(v - 2)*(v - 1)/3
Suppose -3*z + 1 = -2. Let b = 186 - 184. Factor 5*f**2 - f**4 + 0*f**4 - 3*f**b - z.
-(f - 1)**2*(f + 1)**2
Let b = 54 - 45. Let o be (2/10)/(b/(-117)) - -3. Factor 2*r - 2/5*r**3 + o*r**2 + 6/5.
-2*(r - 3)*(r + 1)**2/5
Let b(v) be the third derivative of -v**7/420 - v**6/120 + v**5/30 + v**4/24 - v**3/4 + 2*v**2 - 20. Determine f so that b(f) = 0.
-3, -1, 1
Let d(p) be the third derivative of p**8/756 - 2*p**7/315 - p**6/270 + p**5/45 - 21*p**2 - 2. Suppose d(q) = 0. Calculate q.
-1, 0, 1, 3
Suppose -21*m + 1386*m**2 - m**3 - 2*m**3 - 27*m - 1362*m**2 = 0. What is m?
0, 4
Factor 886*s**2 + 48*s**4 + 1250*s + 114*s**2 + 2*s**5 + 300*s**3 - 8*s**4.
2*s*(s + 5)**4
Let k(q) be the second derivative of 0*q**4 + 0*q**3 + 1/105*q**6 + 3*q + 10 + 0*q**2 - 1/70*q**5. Factor k(h).
2*h**3*(h - 1)/7
What is v in 1/10*v**2 + 3/2*v + 7/5 = 0?
-14, -1
Let m(l) be the second derivative of l**6/600 - l**5/200 - l**4/20 - 14*l**3/3 + l. Let t(z) be the second derivative of m(z). Factor t(i).
3*(i - 2)*(i + 1)/5
Suppose 0 = z - 2*a - 25, -6*z + z = -a - 89. Let j = z - 14. Suppose -h**4 + 7*h**2 - j*h**2 - 4*h**2 + h**2 = 0. Calculate h.
-1, 0, 1
Let i = -250 + 280. Let l be ((-56)/35)/((-132)/i). Determine a, given that -l*a - 2/11*a**3 + 0 + 6/11*a**2 = 0.
0, 1, 2
Suppose 0 = -13*b + 487 - 461. Factor 1/3 - 3/2*j**b - 7/6*j.
-(j + 1)*(9*j - 2)/6
Let r be (-1 - 15)/(-2)*(-402)/(-536). Let l(i) be the third derivative of 0*i**4 + 0*i**3 + 0*i + 0 + 5*i**2 - 1/60*i**r - 1/30*i**5. Factor l(d).
-2*d**2*(d + 1)
Let p = 70 - 70. Let w(s) be the first derivative of -1/3*s**3 + p*s**2 + 0*s + 3. Factor w(m).
-m**2
Factor -22*g - 8*g**2 + 4*g + 24 + 6*g + 4*g**3 - 8*g.
4*(g - 3)*(g - 1)*(g + 2)
Let h be 3 - -6*(-2)/4. Suppose 0 = 5*q + 3*w - 11, q + 2*w + 2*w + 8 = h. Solve a**3 - q*a**3 + a**3 = 0 for a.
0
Let i(t) be the third derivative of -31*t**2 + 0*t - 4/27*t**3 - 1/270*t**5 + 1/27*t**4 + 0. Factor i(l).
-2*(l - 2)**2/9
Suppose -16 = -3*b + 2. Let f**4 - 63*f**5 - 51*f**2 + 6 + 99*f**3 - 36*f + 7*f**4 + 31*f**4 + b = 0. Calculate f.
-1, -2/3, 2/7, 1
Let u(j) be the third derivative of j**7/70 + j**6/20 - 3*j**5/20 + 96*j**2. Factor u(l).
3*l**2*(l - 1)*(l + 3)
Let v = -68 + 68. Let b be v*5*4/40. Factor -2/9*i - 2/9*i**3 + b + 4/9*i**2.
-2*i*(i - 1)**2/9
Let r(y) be the second derivative of 2*y + 1/8*y**4 - 1/2*y**2 + y**3 - 1/20*y**5 + 0. Let k(m) be the first derivative of r(m). Factor k(g).
-3*(g - 2)*(g + 1)
Let 80/7*d**3 - 1/7*d**5 - 24/7*d**4 - 79/7*d + 54/7 - 30/7*d**2 = 0. What is d?
-27, -1, 1, 2
Let n(b) be the first derivative of -b**7/735 - 17*b**6/1260 - b**5/105 + 2*b**3 - 10. Let l(s) be the third derivative of n(s). Let l(i) = 0. Calculate i.
-4, -1/4, 0
Let l(s) be the third derivative of 1/6*s**4 - 1/3*s**3 - 5*s**2 + 1/120*s**5 - 1/120*s**6 + 0*s + 0. Factor l(n).
-(n - 2)*(n + 2)*(2*n - 1)/2
What is m in 23/4*m**2 + 1/4*m**5 - 25/2*m - 7/4*m**4 + 9/4*m**3 + 6 = 0?
-2, 1, 3, 4
Let t = -329845/113 + 2919. Let c = 783/452 + t. Solve -1/4*w**3 - c*w + 3/4 + 5/4*w**2 = 0 for w.
1, 3
Let g(r) be the second derivative of r**6/6 + 5*r**5/4 + 10*r**4/3 + 10*r**3/3 - 4*r - 20. Suppose g(f) = 0. Calculate f.
-2, -1, 0
Let j = 157 - 99. Let o = j + -58. Solve 2/3*m + 8/3*m**4 + o + 10/3*m**2 + 16/3*m**3 = 0 for m.
-1, -1/2, 0
Let m(f) be the third derivative of f**6/60 + 11*f**5/30 + 6*f**2 + 9. Factor m(c).
2*c**2*(c + 11)
Let u(z) = -z**2 + 1. Let i(h) = 2*h**2 + 3. Let q(n) = 3*n**2 - n + 2. Let s(d) = 4*i(d) - 6*q(d). Let f(k) = 4*s(k) - 36*u(k). Factor f(b).
-4*(b - 3)**2
Let f(k) be the third derivative of 3*k**5/8 - 5*k**4/24 + 419*k**2. Let f(u) = 0. Calculate u.
0, 2/9
Let b(f) be the first derivative of f**3/3 + f**2/2 - 6*f - 44. Solve b(r) = 0 for r.
-3, 2
Let y(g) = 23*g**3 - 48*g**2 + g + 8. Let r(x) = 8*x**3 - 16*x**2 + 3. Let p(d) = 8*r(d) - 3*y(d). Find f such that p(f) = 0.
0, 1/5, 3
Let d(l) be the first derivative of -30*l**2 - 33/2*l**4 - 3*l**5 - 33*l**3 + 17 - 12*l. Determine z, given that d(z) = 0.
-2, -1, -2/5
Factor -28/3*d**3 + 256/3 + 2/3*d**4 - 320/3*d + 48*d**2.
2*(d - 4)**3*(d - 2)/3
Let b(l) be the second derivative of 5*l**7/42 - l**6/6 - 3*l**5/2 + 35*l**4/6 - 55*l**3/6 + 15*l**2/2 - 47*l. Determine z, given that b(z) = 0.
-3, 1
Let l be (-76)/(-315) - 10/45. Let d(o) be the third derivative of 0*o + 0 + 1/15*o**6 - 1/3*o**4 + 0*o**5 - l*o**7 - 7*o**2 + 2/3*o**3. Factor d(h).
-4*(h - 1)**3*(h + 1)
Determine k so that -2/11*k**3 - 12/11 - 8/11*k**2 + 2*k = 0.
-6, 1
Let t be (34/(-119))/(-2 - -1). Factor 2/7*z**2 - 4/7 - t*z.
2*(z - 2)*(z + 1)/7
Let i = -3 + 7. Let b be (-1)/i - 174/(-24). Factor -5*s + 4*s**4 + 0*s**5 - 8*s**2 - 4*s**5 + b*s + 8*s**3 + 4 - 6*s.
-4*(s - 1)**3*(s + 1)**2
Suppose -2*t + 6 = 4. Let w be (1 + 0/(-1))/(2/t). Factor 1/4*m**3 + 1/4*m - w*m**2 + 0.
m*(m - 1)**2/4
Let t = -1/5760 - -42241/5760. Let t*b**3 + 0 + 56/3*b**4 + 0*b + 2/3*b**2 = 0. Calculate b.
-1/4, -1/7, 0
Suppose p = -j - 4*p + 468, -4*p + 1404 = 3*j. Let g be j/33 + (-4)/22. Factor -g*h**2 + 7*h**3 + 2*h**2 + 8*h + h**3 - 2*h**4 - 2.
-2*(h - 1)**4
Suppose 7*l**2 + 5*l**2 - 38*l**3 - 4*l**4 + 6*l**2 - 6*l**2 + 6*l**5 + 0*l**2 + 16 + 56*l = 0. Calculate l.
-2, -1, -1/3, 2
Let i = 61 + 14. Suppose i = 4*g - 77. Find s, given that -3*s**2 + s + 3*s**3 - s**4 + g - 38 = 0.
0, 1
Let z(o) be the third derivative of o**6/120 - 2*o**5/15 - 19*o**4/24 - 5*o**3/3 + 81*o**2 - o. Determine a, given that z(a) = 0.
-1, 10
Solve -6/5*g**4 - 8 - 26/5*g**3 + 2/5*g**5 + 22/5*g**2 + 48/5*g = 0 for g.
-2, 1, 5
Determine h, given that -20/9*h**3 - 2/9*h**4 - 40/9*h + 0 - 58/9*h**2 = 0.
-5, -4, -1, 0
Let h(s) be the third derivative of s**5/150 + s**4/10 + s**3/3 + 2*s**2 - 37. Let h(d) = 0. What is d?
-5, -1
Let t = 11906/15 - 2380/3. Factor -11/5*h**2 - 14/5*h**3 + t + h.
-(h + 1)*(2*h - 1)*(7*h + 2)/5
Factor 140/3*l + 0 + 2/3*l**2.
2*l*(l + 70)/3
Factor -1452*n - 4153 - 752 - 66*n**2 - 5743 - n**3.
-(n + 22)**3
Let z(t) = -2*t. Let m(g) = 4*g**2 + 23*g + 3. Let k(p) = 5*m(p) + 40*z(p). Factor k(j).
5*(j + 1)*(4*j + 3)
Let f = -5825 + 5828. What is c in 22/5*c**2 - 2*c + 26/5*c**f - 6/5*c**4 + 0 = 0?
-1, 0, 1/3, 5
Suppose -2*b - 3*b = -5. Let y be (0 - b)/(12/(-6)). Find d, given that 0 - 3*d**3 - 9/4*d**4 - 1/4*d**2 + y*d = 0.
-1, -2/3, 0, 1/3
Let k(b) be the first derivative of -42/5*b**5 + 0*b - 5 - 686/3*b**3 + 147/2*b**4 + 0*b**2 + 1/3*b**6. Factor k(i).
2*i**2*(i - 7)**3
Let y(f) be the second derivative of -f**7/273 + 7*f**6/195 - 9*f**5/65 + 11*f**4/39 - f**3/3 + 3*f**2/13 + 28*f - 2. Find d such that y(d) = 0.
1, 3
Factor 0 + 16/5*t**3 - 2/5*t**4 - 34/5*t**2 + 4*t.
-2*t*(t - 5)*(t - 2)*(t - 1)/5
Let d be (-12)/(-9) - 2 - -1. Let t = 1540/3 + -513. What is y in 0*y - d + t*y**2 = 0?
-1, 1
Let r(h) be the first derivative of -2*h**3/33 - 18*h**2/11 - 34*h/11 + 55. Factor r(t).
-2*(t + 1)*(t + 17)/11
Let g = -225 - -677/3. Let y(p) be the first derivative of 2*p + g*p**3 + 2*p**2 - 4. Factor y(v).
2*(v + 1)**2
Factor -3/2*n**3 + 32*n**2 + 40/3 - 122/3*n.
-(n - 20)*(3*n - 2)**2/6
Let h(o) be the first derivative of -o**3/4 + 9*o**2/8 - 