ive of l**10/453600 + l**9/90720 + l**8/60480 + l**5/30 + 3*l**2. Let a(p) be the third derivative of x(p). Factor a(u).
u**2*(u + 1)**2/3
Suppose -12/5 - 39/5*t**3 - 48/5*t**4 + 24/5*t - 12/5*t**5 + 33/5*t**2 = 0. Calculate t.
-2, -1, 1/2
Let z(h) be the third derivative of -h**6/480 + h**4/24 + 6*h**2. Factor z(u).
-u*(u - 2)*(u + 2)/4
Let o(i) be the first derivative of -i**4/4 + i**3 + 2*i**2 + 2*i - 3. Let t be o(4). Determine s, given that 0*s**2 + 0 + 2*s**t - 2 = 0.
-1, 1
Suppose 0*k = 4*k - 24. Let x be -3 - (450/(-21))/k. Suppose 0 - 2/7*n**4 - x*n**3 + 0*n - 2/7*n**2 = 0. Calculate n.
-1, 0
Let i = 1 + -1. Let n be (-6 + (-12)/(-2))*(-2)/(-4). Factor i*m**2 + n - 1/4*m + 1/4*m**3.
m*(m - 1)*(m + 1)/4
Let x = 12 + -6. Let o(d) = -4*d**3 + 6*d**2 + 4*d + 3. Let u(r) = 4*r**3 - 5*r**2 - 3*r - 2. Let z(a) = x*u(a) + 4*o(a). Factor z(w).
2*w*(w - 1)*(4*w + 1)
Let z(s) be the first derivative of -s**6/30 + s**5/10 - s**4/12 + 4*s - 10. Let g(x) be the first derivative of z(x). Solve g(p) = 0.
0, 1
Let o(w) = -4*w**2 + 2 + w - w - 4*w. Let q(f) = f**2 - f - 1. Let k(x) = 11*x**2 - 2*x - 9. Let p(u) = k(u) - 6*q(u). Let n(d) = 3*o(d) + 2*p(d). Factor n(t).
-2*t*(t + 2)
Suppose -4*m = -0*m - 8. Let u(b) be the second derivative of b - 1/18*b**4 + 0 + 1/3*b**m - 1/30*b**5 + 1/9*b**3. Factor u(r).
-2*(r - 1)*(r + 1)**2/3
Suppose 0 = 2*b - 4, -5*j - 4*b + 28 + 0 = 0. Suppose m = -j*q - 14, m + 12 = -m - 4*q. What is x in 1/5*x**m + 1/5*x - 2/5 = 0?
-2, 1
Suppose 2*q + 2 = -3*q + 4*x, 2*q - 5*x + 11 = 0. Factor 0 - 2/5*d**q - 2/5*d.
-2*d*(d + 1)/5
Let v(b) = 12*b**3 - 24*b**2 + 12*b. Let w(r) = -4*r**3 + 8*r**2 - 4*r. Let s(q) = 3*v(q) + 10*w(q). Solve s(n) = 0 for n.
0, 1
Let r be (96/120)/((-2)/3 - -2). Suppose -r*s**2 + 3/5*s + 1/5*s**3 - 1/5 = 0. Calculate s.
1
Let v be ((-4)/16)/((-50)/40). Factor 0 + v*a**3 + 1/5*a + 2/5*a**2.
a*(a + 1)**2/5
Let r(j) = j**4 + j**3 - j**2. Let a(m) = -2*m**4 + 10*m**3 + 2*m**2 - 4*m. Let q(y) = -a(y) + 6*r(y). Factor q(c).
4*c*(c - 1)*(c + 1)*(2*c - 1)
Let y = -1443 - -47635/33. Let v = y + -26/99. Solve 0*p - 8/9*p**3 + 0 + v*p**4 + 8/9*p**2 = 0 for p.
0, 2
Let 0 - 2/21*a**5 + 4/21*a - 10/21*a**2 + 2/21*a**4 + 2/7*a**3 = 0. What is a?
-2, 0, 1
Let b(c) be the second derivative of c**4/24 + c**3/6 + c**2/4 - 4*c. Let b(o) = 0. What is o?
-1
Let w(r) be the first derivative of -r**5/20 + r**4/12 + r**3/6 - r**2/2 + 4*r + 2. Let m(t) be the first derivative of w(t). Find j such that m(j) = 0.
-1, 1
Factor 0 + 637/3*s**4 - 126*s**3 - 8/3*s - 343/3*s**5 + 92/3*s**2.
-s*(s - 1)*(7*s - 2)**3/3
Let h(o) be the second derivative of 0*o**4 - 1/98*o**7 + 0 + 0*o**3 - 1/70*o**6 + 0*o**5 + o + 0*o**2. Find j such that h(j) = 0.
-1, 0
Let v(s) be the third derivative of -s**7/2520 + s**6/720 + s**5/60 + s**4/6 + 4*s**2. Let n(p) be the second derivative of v(p). Find j, given that n(j) = 0.
-1, 2
Let t(v) be the first derivative of v**7/42 + v**6/15 + v**5/20 + 2*v + 3. Let f(m) be the first derivative of t(m). Factor f(n).
n**3*(n + 1)**2
Let j = 69421 + -486729/7. Let w = 112 + j. Factor -2/7*u**4 + 0*u**2 - w*u**3 + 0*u + 0.
-2*u**3*(u + 1)/7
Let b(a) be the second derivative of -a**7/11340 + a**4/3 + 2*a. Let m(z) be the third derivative of b(z). Suppose m(r) = 0. What is r?
0
Let s(n) be the second derivative of n**4/48 + n**3/24 - 2*n. Factor s(d).
d*(d + 1)/4
Let t be 2 + 40/(-18) - (-14)/63. Let q(n) be the third derivative of -1/120*n**6 - 2*n**2 + t*n + 0*n**3 + 0*n**5 + 0*n**4 - 1/210*n**7 + 0. Factor q(l).
-l**3*(l + 1)
Let q be (7/35)/((-9)/(-10)). Find k, given that -8/9*k**2 - 8/9*k - q*k**3 + 0 = 0.
-2, 0
Find p such that -15*p - p**2 - 14*p + 31*p = 0.
0, 2
Let k = 18 - 16. Let i = k + 1. Let -2/5*y**4 + 0 - 2*y**2 - 8/5*y**i - 4/5*y = 0. What is y?
-2, -1, 0
Let l(t) be the first derivative of t**7/1050 - t**6/300 + t**4/60 - t**3/30 + t**2 + 3. Let b(o) be the second derivative of l(o). Factor b(u).
(u - 1)**3*(u + 1)/5
Let p(i) be the first derivative of i**7/168 - i**6/40 + 3*i**5/80 - i**4/48 - i - 4. Let g(u) be the first derivative of p(u). What is k in g(k) = 0?
0, 1
Let k(c) = -c**3 + 12*c**2 - 10*c - 9. Let p be k(11). Let o(t) be the first derivative of 2/5*t - 2/25*t**5 + 2/5*t**2 - 1/5*t**4 - p + 0*t**3. Factor o(u).
-2*(u - 1)*(u + 1)**3/5
Let z(j) = -4*j**2 + 2*j - 3. Let s = 3 - 1. Let u(h) = 4*h**s + h - 2*h**2 + 5 - 4*h + 5*h**2. Let b(y) = 3*u(y) + 5*z(y). What is d in b(d) = 0?
-1, 0
Let r(p) be the first derivative of p**6/540 + p**5/90 - p**4/12 - p**3/3 + 4. Let u(f) be the third derivative of r(f). Determine k so that u(k) = 0.
-3, 1
Let v = -39 + 41. Factor 0*x + 0*x**v + 0*x**3 + 0 + 2/3*x**4 + 2/3*x**5.
2*x**4*(x + 1)/3
Let x(o) be the first derivative of 7*o**6/2 + 36*o**5/5 - 3*o**4 - 14*o**3 - 9*o**2/2 + 6*o + 2. Factor x(r).
3*(r - 1)*(r + 1)**3*(7*r - 2)
Let u(w) be the third derivative of 2*w**7/105 - w**6/15 + w**5/15 + 17*w**2. Solve u(j) = 0.
0, 1
Let u(h) be the first derivative of h**6/1260 - h**5/210 + h**4/84 + h**3/3 + 3. Let c(j) be the third derivative of u(j). Factor c(p).
2*(p - 1)**2/7
Let v(u) be the first derivative of 1 - 1/24*u**6 + 0*u**4 + 1/6*u**3 + 1/8*u**2 + 0*u - 1/10*u**5. Find h, given that v(h) = 0.
-1, 0, 1
Let q(i) = i**3 + i**2 + i + 1. Let t(g) = 13*g**3 + 13*g**2 + g - 3. Let p(k) = -3*q(k) - t(k). Determine u, given that p(u) = 0.
-1/2, 0
Let a(w) be the third derivative of -w**8/1680 + w**7/1050 + 7*w**6/600 - w**5/300 - w**4/20 - 6*w**2. Let a(p) = 0. What is p?
-2, -1, 0, 1, 3
Suppose 3*h + 2*v + 3 = -1, 5*v + 25 = 0. Let i(w) be the third derivative of 1/420*w**6 + w**h - 2/105*w**5 + 5/84*w**4 + 0 - 2/21*w**3 + 0*w. Factor i(g).
2*(g - 2)*(g - 1)**2/7
Let m(p) = -7*p**2 - 11. Let h(q) = 13*q**2 - q + 21. Let s(c) = 6*h(c) + 11*m(c). Let s(f) = 0. What is f?
1, 5
Suppose 3*y - 25 = -5*m, 2*m = -y - 4*y + 29. Solve -2/9*t**m - 4/9*t + 2/3 = 0 for t.
-3, 1
Suppose 0 = -3*k + c + 22, k - 10 = -0*k + 3*c. Suppose -5*r + k*r = 0. Let 0*m + 1/3*m**2 + r - 1/3*m**3 = 0. What is m?
0, 1
Let y be 0 - -3 - (-7 - 204/(-21)). Determine r so that -2/7*r**2 + 0 - y*r = 0.
-1, 0
Let k(x) be the third derivative of 0*x**4 + 0 + 0*x**5 + 3*x**2 + 1/600*x**6 - 1/1050*x**7 + 0*x + 0*x**3. What is o in k(o) = 0?
0, 1
Suppose -1/9*u**2 + 0 + 1/9*u = 0. Calculate u.
0, 1
Suppose 0*m + m = 0. Factor -2*y**3 + 4*y - 2*y**3 - y**2 - 1 + m*y**2 + 2*y**2.
-(y - 1)*(y + 1)*(4*y - 1)
Find w, given that -28*w + 544 - 608 - 4*w**2 - 4*w = 0.
-4
Let z be (-2 - 2)*5/(-4). Suppose -2*f + 14 = 3*x, -x = x + z*f - 24. Factor 2/3*b + 2/3*b**x - 4/3.
2*(b - 1)*(b + 2)/3
Factor j + 52*j**2 + 20*j**3 - 22 + 15*j + 6.
4*(j + 1)*(j + 2)*(5*j - 2)
Let u(a) be the third derivative of -a**8/112 - 3*a**2. Factor u(j).
-3*j**5
Let t(m) be the second derivative of m**6/60 + 3*m**5/20 + m**4/24 - 2*m**3 + 4*m**2 - 19*m. Determine f so that t(f) = 0.
-4, 1
Let y(k) = k**2 - 21*k - 7. Let u(j) = 2*j**2 - 22*j - 6. Let a(q) = -5*u(q) + 6*y(q). Solve a(m) = 0.
-3, -1
Let h = -16 - -7. Let k(t) = t**2 + 10*t + 12. Let l be k(h). Factor -r**2 + 7*r**2 + 0*r**3 + 2 - 6*r - 2*r**l.
-2*(r - 1)**3
Let w be 49/(-14)*10/(-28) + 1. Factor 0*x + x**5 - w*x**4 + 0 - 1/4*x**2 + 3/2*x**3.
x**2*(x - 1)**2*(4*x - 1)/4
Suppose -4*u + q = u - 11, u - 3 = q. Suppose -7 = -u*s + 3. Determine t, given that -2/3*t**2 + 1/3 - 1/3*t + 2/3*t**3 - 1/3*t**s + 1/3*t**4 = 0.
-1, 1
Suppose 3*o = 66 - 6. Suppose -3*x - 2*d = -o, -x + d = -0*d. Factor -3*j**4 - 2*j**2 + 4*j**x + j**4.
2*j**2*(j - 1)*(j + 1)
Factor 10/3*d - 2/3*d**2 + 4.
-2*(d - 6)*(d + 1)/3
Let x = -35 + 37. Factor 0*d**x - 4/7*d**3 + 4/7*d + 0.
-4*d*(d - 1)*(d + 1)/7
Let o(d) be the first derivative of -d**6/480 - d**5/60 - 5*d**4/96 - d**3/12 - d**2/2 - 2. Let l(f) be the second derivative of o(f). Factor l(x).
-(x + 1)**2*(x + 2)/4
Let u(b) be the first derivative of -1/2*b - b**3 - 1/10*b**5 - 1/2*b**4 - b**2 + 5. Factor u(f).
-(f + 1)**4/2
Let m(f) be the third derivative of 0*f + 0*f**3 - 1/210*f**7 + 0 + 0*f**4 - 1/120*f**6 + f**2 - 1/180*f**5 - 1/1008*f**8. Factor m(k).
-k**2*(k + 1)**3/3
Solve -8/3 + 8*c**2 - 4/3*c**3 - 8/3*c**4 - 4/3*c = 0 for c.
-2, -1/2, 1
Let v(s) be the first derivative of -s**4/24 + s**3/6 - s**2/4 + s/6 - 15. Solv