be the third derivative of t**5/180 - 15*t**2. Factor x(y).
y**2/3
Let x(c) be the first derivative of -c**5/5 - c**4 - 2*c**3/3 + 2*c**2 + 3*c - 33. Suppose x(n) = 0. What is n?
-3, -1, 1
Let u(i) = 11 + i - 8 - i**3 - 4. Let x(f) = f**4 + 6*f**3 - f**2 - 6*f + 5. Let k(l) = 10*u(l) + 2*x(l). Factor k(c).
2*c*(c - 1)*(c + 1)**2
Let x = 37 + -12. Let j = 76/3 - x. What is k in 2*k**2 + j*k**4 + 1/3 - 4/3*k - 4/3*k**3 = 0?
1
Let s = 5/4 - 1. Factor 0 + 0*t**3 + 1/4*t**5 + 0*t + s*t**4 + 0*t**2.
t**4*(t + 1)/4
Let y = -25 - -28. What is k in -2/9 + 4/9*k**4 + 2/3*k - 2/3*k**y - 2/9*k**2 = 0?
-1, 1/2, 1
Let x(d) be the second derivative of d**4/12 - 11*d**3/6 - 11*d**2/2 - d. Let t = 66 + -68. Let h(n) = 2*n + 2. Let b(u) = t*x(u) - 11*h(u). Factor b(a).
-2*a**2
Let d = -54 - -58. Factor 5/2*l**3 - 1/2*l**4 + 0 - d*l**2 + 2*l.
-l*(l - 2)**2*(l - 1)/2
Let s = 3 - 0. Let m(f) = 8*f + 0 + s*f**2 - 2 - 2*f**2 - 2. Let r(v) = 2*v**2 + 12*v - 6. Let q(z) = 8*m(z) - 5*r(z). Factor q(o).
-2*(o - 1)**2
Let a(g) be the first derivative of g**5/5 + 3*g**4/4 + g**3 + g**2/2 + 7. Factor a(v).
v*(v + 1)**3
Let g = -1079/12 + 90. Let o(n) be the third derivative of 0 - 1/60*n**5 + g*n**4 + 0*n - 2*n**2 - 1/6*n**3. Factor o(h).
-(h - 1)**2
Let k = -45/44 - -36/11. Find d such that 9/4*d**2 + k*d**3 + 3/4*d + 3/4*d**4 + 0 = 0.
-1, 0
Let t(c) = c**3 + c**2 + 12. Let b be t(0). Suppose 14 = 5*v + 5*k - 1, -k - b = -4*v. Factor -2/5*z**2 + 2/5 - 2/5*z**v + 2/5*z.
-2*(z - 1)*(z + 1)**2/5
Let l = 51 - 203/4. Factor -1/4*k**4 + 1/4*k - l*k**3 + 1/4*k**2 + 0.
-k*(k - 1)*(k + 1)**2/4
Let x = 30/49 - 16/49. What is m in 2/7*m**2 - x*m + 0 = 0?
0, 1
Let -2/7*u**5 + 2/7*u + 4/7*u**4 - 4/7*u**2 + 0*u**3 + 0 = 0. Calculate u.
-1, 0, 1
Let w(i) be the third derivative of i**7/4200 - i**6/450 + i**5/120 - i**4/60 - 5*i**3/6 - 2*i**2. Let k(s) be the first derivative of w(s). Factor k(d).
(d - 2)*(d - 1)**2/5
Suppose 0 = -3*d - 49*t + 53*t, -5*d = 5*t. Solve d + 1/2*v**2 - 1/2*v = 0.
0, 1
Let m(a) be the first derivative of 4*a**5/25 + a**4 + 4*a**3/5 - 18*a**2/5 + 41. Factor m(b).
4*b*(b - 1)*(b + 3)**2/5
Let d = 0 - 2. Let v be (-3)/d*(-20)/(-15). Factor -2 - u**3 + 3*u + 2*u**3 + 3*u**v + 3.
(u + 1)**3
Let z be ((-2)/3)/((-2)/15). Suppose -z*b = -b - 20. Factor 3*x**4 + 2*x**b - x**4 - 4*x**5 - 4*x**4.
-2*x**4*(x + 1)
Let a be (-2)/(-5) - (55/75)/11. Determine c, given that -a*c**5 + 0*c**4 + c**3 + 0*c + 2/3*c**2 + 0 = 0.
-1, 0, 2
Let l(h) = 2*h**2 + 13*h + 6. Let j be l(-6). Factor -4/13*b**2 + j + 2/13*b**3 + 0*b.
2*b**2*(b - 2)/13
Let k = -4 + 8. Suppose -5*g + 10 = s, -k*g + s + 6 = -2. Determine u so that u**g - 6 + u + 6 = 0.
-1, 0
Factor 0 - 3/5*j**3 - 12/5*j**2 + 12/5*j + 3/5*j**4.
3*j*(j - 2)*(j - 1)*(j + 2)/5
Let b(h) = 3*h + 12. Let u be b(-3). Suppose 2/9*p**2 - 2/9*p**u + 0*p + 2/9*p**5 + 0 - 2/9*p**4 = 0. Calculate p.
-1, 0, 1
Let y(n) be the second derivative of n**8/13440 + n**7/5040 - n**6/720 - n**4/12 - 4*n. Let w(r) be the third derivative of y(r). Factor w(i).
i*(i - 1)*(i + 2)/2
Suppose 4*d - s = 5*d, -2*d + 5*s + 28 = 0. Factor 3*j**2 - 5*j**2 + j**d - 3*j**4 + 4*j**3.
-2*j**2*(j - 1)**2
Let g(m) be the second derivative of 0*m**2 + 2/21*m**3 + 0 - m - 1/14*m**4. Factor g(c).
-2*c*(3*c - 2)/7
Solve -4*r + 4*r - 2*r**2 - 3*r**3 + r**4 + 4*r**2 = 0 for r.
0, 1, 2
Suppose -w - 9 = -3*s - 22, -7 = -4*w - 3*s. Let v = -986 - -989. Factor 0*g**w - 8/7*g**v + 4/7*g**2 - 4/7 + 2/7*g**5 + 6/7*g.
2*(g - 1)**3*(g + 1)*(g + 2)/7
Let a(d) be the first derivative of d**5/45 + 5*d**4/36 + d**3/9 - 5*d**2/18 - 4*d/9 - 16. Let a(c) = 0. Calculate c.
-4, -1, 1
Let g(t) be the second derivative of -2*t**6/15 - t**5/5 + t**4/3 + 2*t**3/3 + 4*t + 3. What is h in g(h) = 0?
-1, 0, 1
Factor 7/5*n + 2 + 1/5*n**2.
(n + 2)*(n + 5)/5
Factor -1 - 1/2*q**2 - 3/2*q.
-(q + 1)*(q + 2)/2
Let t(i) be the first derivative of -121*i**3/15 + 22*i**2/5 - 4*i/5 + 17. Factor t(r).
-(11*r - 2)**2/5
Let d(q) be the third derivative of q**7/630 - q**5/60 - q**4/36 + 26*q**2. Suppose d(x) = 0. What is x?
-1, 0, 2
Suppose 2*s + 19 = 3*q, 2*s = 4*q - 6 - 18. Let r(h) = 4*h**2 + 4*h + 4. Let o(u) = 9*u**2 + 7*u + 8. Let z(y) = q*r(y) - 2*o(y). Factor z(j).
2*(j + 1)*(j + 2)
Let s(v) = v**4 - v**3 + v**2 + 1. Let u(l) = 3*l**4 + 6*l**2 - 6*l + 9. Let q(d) = -6*s(d) + u(d). Find g, given that q(g) = 0.
-1, 1
Let k = 9 - 15. Let h = -4 - k. Suppose -b**h + 2 - 2*b + 0*b**2 - b**2 + 2*b**3 = 0. Calculate b.
-1, 1
Let n be (-3 - 478/(-160))*16/(-12). Let t(a) be the third derivative of 0*a + a**2 - 1/8*a**4 - 1/3*a**3 - n*a**5 + 0. Solve t(x) = 0 for x.
-2, -1
Let m = 19 - 14. Solve 5*x**4 + 8*x - 3*x**4 - 6 - 3*x**3 - m*x**3 + 4*x**2 = 0.
-1, 1, 3
Suppose 0 = -l + 4*j + 6, 3*l = -2*l - j + 9. Factor 4/5*o - 2/5 - 2/5*o**l.
-2*(o - 1)**2/5
Let b = -3/305 - -3071/2135. Suppose -4*h - 5 = -2*v + 3, -3*v + h + 7 = 0. Let 16/7*o**v - b*o**3 - 2/7*o - 4/7 = 0. What is o?
-2/5, 1
Let p be -4 + -4*(-34)/32. Determine r so that 0 - p*r**2 + 3/4*r = 0.
0, 3
Let h(p) be the third derivative of p**6/360 - p**5/45 + p**4/72 + p**3/3 + 16*p**2. Solve h(q) = 0.
-1, 2, 3
Suppose 0 = -5*x + c + 6, 3*c + 1 - 3 = 5*x. Let g = 39/5 + -38/5. Factor -1/5 + 0*p**x - 2/5*p**3 + 2/5*p + g*p**4.
(p - 1)**3*(p + 1)/5
Suppose 0 = 5*y - 4*y + 3*y. Let l(j) be the second derivative of -4*j - 1/60*j**4 + y*j**2 + 0 + 1/15*j**3. Factor l(w).
-w*(w - 2)/5
Let a be 1/(-5)*-5*(-2)/(-6). Find z such that 2/3*z - a*z**2 + 0 = 0.
0, 2
Factor k**3 - 4*k**3 - 3*k + 6*k**2 + 0*k**3.
-3*k*(k - 1)**2
Let s(n) = n**4 - n**3 - n**2 + 1. Let t(a) = -6*a**4 - a - 4 + 10*a**2 + 8*a**3 - 3 - 4*a**2. Let i(m) = -14*s(m) - 2*t(m). Factor i(o).
-2*o*(o - 1)*(o + 1)**2
Let x be (6/(-4))/((-3)/8). Suppose 3*o**5 + o**4 - 14*o**4 + x*o**4 - 9*o + 3 + 6*o**2 + 6*o**3 = 0. What is o?
-1, 1
Let j(v) be the third derivative of 1/300*v**5 + 0*v + 1/15*v**3 + 1/40*v**4 + 0 + 4*v**2. Determine c so that j(c) = 0.
-2, -1
Let a(s) = -s - 2*s**4 + 4*s**4 + 4*s**2 - 2*s**3 - 1 + s**2 - 3*s**2. Let v(d) = d**4 + d**3 - d**2 - 1. Let j(n) = a(n) - v(n). Find u such that j(u) = 0.
0, 1
Suppose 0*m - 10 = -2*m. Solve x**2 - 6*x**3 + 2*x**4 + 4*x**3 - 3*x**4 - 4*x**m + 6*x**5 = 0 for x.
-1, 0, 1/2, 1
Solve 2*m + 0*m - 2*m**3 + 0*m**4 - 4*m**4 + 2*m**4 + 2*m**2 = 0 for m.
-1, 0, 1
Let z(h) be the first derivative of -h**6/105 + h**5/35 - 2*h**3/21 + h**2/7 - 2*h + 2. Let f(g) be the first derivative of z(g). Factor f(x).
-2*(x - 1)**3*(x + 1)/7
Factor -6/7*y + 3/7*y**4 + 0 - 3/7*y**2 + 6/7*y**3.
3*y*(y - 1)*(y + 1)*(y + 2)/7
Factor 0 - s + 1/3*s**2.
s*(s - 3)/3
Let k(d) be the first derivative of d**6/27 - 4*d**5/45 + d**4/18 - 28. Factor k(r).
2*r**3*(r - 1)**2/9
Let r = 9 + -7. What is z in 4*z + 3*z + 5*z - 16*z**r + 4 = 0?
-1/4, 1
Let c = -29/16 + 273/80. Factor 8/5*d - 2/5*d**2 - c.
-2*(d - 2)**2/5
Let v(m) = m**5 + 7*m**4 - 3*m**3 - 7*m**2 + 2*m - 6. Let s(k) = -2*k**5 - 15*k**4 + 6*k**3 + 15*k**2 - 4*k + 13. Let a(g) = -6*s(g) - 13*v(g). Factor a(o).
-o*(o - 1)**2*(o + 1)*(o + 2)
Let f(j) = -j**2 + 3*j + 4. Let n be f(5). Let k = 6 + n. Suppose -1/4*d + 0*d**2 + 1/4*d**3 + k = 0. What is d?
-1, 0, 1
Suppose -3*q + 0 = -3. Suppose -26 = -5*v - q. Factor 0*c**4 - 2/5*c + 4/5*c**3 - 2/5*c**v + 0 + 0*c**2.
-2*c*(c - 1)**2*(c + 1)**2/5
Let c(n) be the second derivative of n**5/140 - n**4/84 - 5*n**3/42 - 3*n**2/14 + 4*n + 5. Find o, given that c(o) = 0.
-1, 3
Determine y, given that 62*y**3 - 31*y**3 - 28*y**3 - 9*y**2 = 0.
0, 3
Let j(o) be the first derivative of 0*o + 1 + 2/27*o**3 + 1/18*o**4 - 2/45*o**5 - 1/9*o**2. Solve j(c) = 0.
-1, 0, 1
Let r = -2/621 - -2494/3105. Factor -6/5 + r*y + 2/5*y**2.
2*(y - 1)*(y + 3)/5
Let u = -1/27 + 7/27. Factor -u*h**4 + 0 - 4/9*h**2 + 2/3*h**3 + 0*h.
-2*h**2*(h - 2)*(h - 1)/9
Let r = -97 - -97. Let j be 102/105 - (-4)/(-10). Factor r + 2/7*v - 2/7*v**5 + 0*v**3 + 4/7*v**2 - j*v**4.
-2*v*(v - 1)*(v + 1)**3/7
Suppose 133*w = 128*w + 10. Let 2/3 - f + 1/3*f**w = 0. What is f?
1, 2
Let b(x) be the first derivative of -x**4 - 8*x**3 - 18*x**2 + 12. Factor b(t).
-4*t*(t + 3)**2
Let m = 3/142 - -127/710. Let -1/5*o + 0 - m*o**2 = 0. Calculate o.
-1, 0
Suppose -19*z + 13*z + 18 = 0. Suppose -3*n**4 - 3/4*n**5 + 0*n + 0 + 0*n**2 - z*n**