*a**2 - k*a**2 - 10*a**2 - 9*a = 0.
-2, -1
Let b = 12/77 + -103/1155. Let g(n) be the third derivative of 1/75*n**6 + 0 - 6*n**2 + 0*n + 1/10*n**4 - 3/50*n**5 - b*n**3. Factor g(k).
2*(k - 1)**2*(4*k - 1)/5
Let g(b) be the second derivative of 0 + 19*b + 0*b**2 - 2/3*b**3 + 1/3*b**4. Factor g(d).
4*d*(d - 1)
Let p(t) be the first derivative of -1/30*t**6 - 4/15*t**3 + 2/5*t + 2/25*t**5 + 1/10*t**4 - 1/10*t**2 - 32. Let p(v) = 0. Calculate v.
-1, 1, 2
Let 273*c + 59*c**3 - 18*c**4 - 36 - 53*c**2 - 313*c**2 + 88*c**3 = 0. Calculate c.
1/6, 1, 3, 4
Let c(y) = 2*y**4 - 52*y**3 - 600*y**2 + 1458*y. Let q(t) = 3*t**4 - 104*t**3 - 1207*t**2 + 2916*t. Let g(i) = -5*c(i) + 3*q(i). Solve g(n) = 0.
-27, 0, 2
Let -61/8*t**2 - 1/8*t**5 + 6 + 13/8*t**4 + 17/4*t - 33/8*t**3 = 0. What is t?
-1, 1, 6, 8
Let a(c) be the first derivative of 5*c**6/3 + 154*c**5/25 + 28*c**4/5 + 8*c**3/15 + 35. Solve a(f) = 0.
-2, -1, -2/25, 0
Let q be ((-3)/(-12))/((-16 - -15)/(-8)). Factor 0 + 2*y + 1/2*y**4 + 0*y**q - 3/2*y**3.
y*(y - 2)**2*(y + 1)/2
Let k(s) = 0 + 14*s**2 - 8*s**2 + 6 - s - 11*s**3. Let o(b) = 21*b**3 - 11*b**2 + b - 11. Let v(z) = -11*k(z) - 6*o(z). Solve v(a) = 0 for a.
-1, 0, 1
Let l = -41 - -44. Let w(a) be the second derivative of 0 - 1/50*a**5 - 2/15*a**4 + 0*a**2 + 4*a - 1/5*a**l. Factor w(x).
-2*x*(x + 1)*(x + 3)/5
Suppose 0 = 2*m - 1 - 5. Let 2 + 6*o**2 + o**3 - 5*o + 2*o**m - 8 + 2*o = 0. What is o?
-2, -1, 1
Let r = 42 - 46. Let j = -4/5 - r. Solve 64/5*u**2 + 0 - j*u - 28/5*u**3 = 0.
0, 2/7, 2
Let q be ((-8)/(-3))/((-12)/(-18)). Suppose q = 6*r - 5*r. Factor 2*a**5 + 4*a**3 - 10*a**4 - 2*a**r + 6*a**4.
2*a**3*(a - 2)*(a - 1)
Let k(i) be the third derivative of -i**8/1176 + 2*i**7/49 - 27*i**6/35 + 243*i**5/35 - 729*i**4/28 - 197*i**2 - i. Determine r so that k(r) = 0.
0, 3, 9
Let x(k) be the first derivative of -k**8/1008 + k**7/315 - k**6/360 - 17*k**2/2 - 20. Let g(w) be the second derivative of x(w). Suppose g(f) = 0. Calculate f.
0, 1
Suppose 0 = 7*a - 21 - 0. Let d(f) be the third derivative of 0*f + 0 + 1/18*f**4 + 1/9*f**3 + 1/90*f**5 + a*f**2. Determine k, given that d(k) = 0.
-1
Factor -12 + 31*r - 15*r**3 + 3*r**5 + 43*r**2 - 7*r - 46*r**2 + 3*r**4.
3*(r - 1)**3*(r + 2)**2
Suppose 48*j + 23*j = -1043 + 1185. Determine s, given that 20/3*s + 5/6*s**3 + 2 + 9/2*s**j = 0.
-3, -2, -2/5
Let m(p) = -5*p**5 + 23*p**4 + 78*p**3 + 106*p**2 + 41*p + 3. Let g(n) = -n**5 + 3*n**4 - n + 1. Let a(q) = 6*g(q) - 2*m(q). Let a(b) = 0. Calculate b.
-2, -1, 0, 11
Let p(h) = -h**2 - 26*h - 8. Let u(y) = 100*y + 4*y**2 - 17*y + 18 + 6 - 6*y. Let g(l) = -11*p(l) - 4*u(l). Let g(n) = 0. What is n?
-4, -2/5
Let d(t) = -15 + 3*t - t + t - t**2 + 2*t**2. Let c be d(-6). Factor 3/2*p**2 + 3/2 - c*p.
3*(p - 1)**2/2
Let 55*z**4 - 3969*z**3 - z**5 - 4*z**5 - 160*z**2 + 3869*z**3 = 0. Calculate z.
-1, 0, 4, 8
Let c(f) be the third derivative of f**6/75 + f**5/25 - 17*f**4/30 + 8*f**3/5 - 15*f**2. Determine l so that c(l) = 0.
-4, 1, 3/2
Suppose -6/7*f**3 + 46/7*f**2 - 2 - 26/7*f = 0. Calculate f.
-1/3, 1, 7
Let x(f) be the second derivative of -5/2*f**4 - 10/3*f**3 - 11*f - 1/12*f**6 + 0*f**2 + 0 - 3/4*f**5. Factor x(b).
-5*b*(b + 2)**3/2
Let b = 50 - 34. Suppose 4*x - b = 0, 4*x + 17 = 3*n - 21. Factor -4*h**2 - 10*h**4 + n*h**3 + 0*h**5 + 2*h**5 + 4*h - 10*h**2.
2*h*(h - 2)*(h - 1)**3
Let c = 1/2795 + 209/16770. Let v(t) be the third derivative of 8*t**2 + c*t**4 + 0 + 0*t**3 + 0*t - 1/780*t**6 - 1/390*t**5. Find w such that v(w) = 0.
-2, 0, 1
Factor -4*t + 3*t - 40 - 6*t + 3*t**2 + 4*t + 4.
3*(t - 4)*(t + 3)
Factor 2*r**3 - 487*r**2 + 250*r**2 + 297*r**2 - 112*r - 5*r**3 + r**3.
-2*r*(r - 28)*(r - 2)
Suppose -114*f - 8*f - 10 - 85*f**2 + 27*f = 0. What is f?
-1, -2/17
Let f(o) = -o**2 - 11*o - 10. Let q(d) = -10*d**2 - 100*d - 90. Let u(x) = 55*f(x) - 6*q(x). Factor u(l).
5*(l - 2)*(l + 1)
Let f(n) be the third derivative of -n**6/480 + 17*n**5/240 - 7*n**4/12 + 13*n**3/6 + 37*n**2. Suppose f(b) = 0. What is b?
2, 13
Let m(l) be the third derivative of -2*l**5/75 + l**4/20 + 9*l**3/5 - 2*l**2 + 56. Factor m(a).
-2*(a - 3)*(4*a + 9)/5
Let i(s) = s + 55*s**3 - 110*s**3 + 54*s**3 - 1. Let v(o) = 8*o**3 - 4*o**2 - 8*o + 10. Let n(h) = 12*i(h) + 2*v(h). Find f, given that n(f) = 0.
-1, 1, 2
Let c be (30/(-9) - -2)/(27/(1053/(-260))). Factor d - 4/5 - c*d**2.
-(d - 4)*(d - 1)/5
Let l = 11 - 8. Suppose -l*t = -0*t - 9. Find x such that -4*x**3 + 6*x**2 + 9*x + 3*x**2 + 3*x**3 + 4*x**t + 3 = 0.
-1
Let b be 12 - 11 - (-29)/1. Suppose -22 = 2*r - b. Factor 9*h**r - 28*h**3 + 4 - 18*h**3 - 26*h + 54*h**2 + 5*h**4.
2*(h - 1)**3*(7*h - 2)
Let t(q) be the third derivative of q**6/720 - 23*q**5/60 + 15*q**4/4 - 134*q**3/9 - 6*q**2 - 13. Factor t(l).
(l - 134)*(l - 2)**2/6
Let k(o) be the third derivative of -1/6*o**3 + 1/60*o**6 + 1/210*o**7 + 0*o + 0 - 13*o**2 - 1/12*o**4 + 0*o**5. Solve k(s) = 0.
-1, 1
Let m(l) be the first derivative of -3*l**6/8 + 33*l**5/20 + 53*l**4/16 - 43*l**3/4 - 30*l**2 - 25*l + 546. Factor m(n).
-(n + 1)**3*(3*n - 10)**2/4
Let z(f) be the first derivative of -2*f**3/45 - 7*f**2/15 - 4*f/5 - 168. Factor z(m).
-2*(m + 1)*(m + 6)/15
Suppose 13*c - 62 = 16. Suppose -5*u + c = -2*u. Factor -8/7*q + 8/7 + 2/7*q**u.
2*(q - 2)**2/7
Let l(m) = m**2 + 9*m + 43. Let i be l(-8). Let w = 37 - i. Factor 1 - 1/2*h - 1/2*h**w.
-(h - 1)*(h + 2)/2
Let y(o) = -3*o**4 - 9*o**3 + 18*o**2 + 24*o - 20. Let a(k) = -k**4 - 3*k**3 + 6*k**2 + 8*k - 6. Let n(x) = -10*a(x) + 3*y(x). Factor n(q).
q*(q - 2)*(q + 1)*(q + 4)
Let d(h) be the second derivative of -h**6/45 + h**5/6 - 2*h**4/9 - 787*h. Find b such that d(b) = 0.
0, 1, 4
Suppose -4*n + 35 = -5*u + 57, -12 = -3*u + 2*n. Factor -2/3 - 4/3*p + 4/3*p**3 + 2/3*p**4 + 0*p**u.
2*(p - 1)*(p + 1)**3/3
Let u = 3 + -1. Let s(r) = -2*r**3 + 40*r**2 - 3*r + 60. Let f be s(20). Factor -3 + f*k + 3/4*k**u.
3*(k - 2)*(k + 2)/4
Let y(t) be the second derivative of 3*t**5/5 - 163*t**4/3 - 556*t**3/3 - 224*t**2 - 2*t - 15. Let y(k) = 0. Calculate k.
-1, -2/3, 56
Let w(i) = 5*i**2 + 131*i. Let k(n) = -17*n**2 - 392*n. Let b(d) = -2*k(d) - 7*w(d). Factor b(l).
-l*(l + 133)
Suppose -r + 3*q + 1 = 0, -2*q = 2*q - 4. Factor 62*a**3 - 100*a**2 + 25*a - 14*a**3 + 4*a - 5*a + 28*a**r.
4*a*(a - 1)*(a + 3)*(7*a - 2)
Let x(u) be the first derivative of 14 + 3/2*u**2 + u**3 - 9/4*u**4 + 0*u - u**6 - 3*u**5. Suppose x(n) = 0. Calculate n.
-1, 0, 1/2
Factor 651*u**4 + u**5 - 321*u**4 - 5*u**2 - 5*u**3 - 2*u**3 + 6*u - 325*u**4.
u*(u - 1)**2*(u + 1)*(u + 6)
Factor -6/5*d + 17/5*d**2 - 7/5*d**4 + 16/5*d**3 + 0.
-d*(d - 3)*(d + 1)*(7*d - 2)/5
Factor -23/5*v - 24/5 + 1/5*v**2.
(v - 24)*(v + 1)/5
Factor -26 + t**2 - 13*t - 2*t**2 - 32 + 46.
-(t + 1)*(t + 12)
Suppose 7*a - a = 18. Suppose 6*r**3 - 3*r**5 - 7*r**3 + 7*r**3 - a*r = 0. What is r?
-1, 0, 1
Let p(n) = 9*n**2 + 4*n - 4. Let h(a) = -11*a**2 - 4*a + 5. Let z(d) = 4*h(d) + 5*p(d). Determine j, given that z(j) = 0.
-4, 0
Suppose 0*y + 3*y - 3 = 0. Suppose 4*o - 11 = y. Suppose 4*w**2 - 3*w**2 + 3*w**4 + 2*w**o - 7*w**2 - 5*w**3 = 0. Calculate w.
-1, 0, 2
Let i be 2*(8/4 + -1). Let b(w) = 2*w**3 - 4*w**2 + 2*w. Let q be b(i). Factor -q - 4*v + 3*v**2 + 4*v**3 - 2*v**4 + v**4 + 2*v**4 + 0*v**4.
(v - 1)*(v + 1)*(v + 2)**2
Let m = 9 - 4. Let 4*f**2 + 3*f**2 - m*f**3 - 3*f**2 + 6*f**2 = 0. What is f?
0, 2
Let h be (-384)/(-1728) - 10/(-9). What is d in 0*d + 0 + 2/3*d**5 - 8/3*d**4 - h*d**2 + 10/3*d**3 = 0?
0, 1, 2
Let d be 11/77*7/8. Let l(q) be the third derivative of q**3 - 1/20*q**5 + 0*q + 0 + 3*q**2 + d*q**4. Solve l(j) = 0 for j.
-1, 2
Let z(c) be the second derivative of -c**6/195 + 183*c**5/130 - 3721*c**4/26 + 226981*c**3/39 - 71*c - 2. Find v, given that z(v) = 0.
0, 61
Let r = 496 + -491. Let g(b) be the first derivative of 0*b**2 + 0*b + 0*b**3 + 0*b**4 - 2 - 2/15*b**r. Factor g(k).
-2*k**4/3
Let w(y) be the first derivative of -y**4/12 - y**3 - 9*y**2/2 - 59*y + 7. Let d(h) be the first derivative of w(h). Factor d(z).
-(z + 3)**2
Suppose 0 = 5044*n - 5051*n. Let o + 1/3*o**3 + n + 4/3*o**2 = 0. Calculate o.
-3, -1, 0
Let q(y) = -y**2. Let j = 36 - 31. Let z(s) = -4*s**2 - 8*s + 12. Let k(p) = j*q(p) - z(p). Suppose k(a) = 0. What is a?
2, 6
Suppose -4*x + 48 = -2*d, -d + 33 = -2*d - x. Let 