2*t - 1/36*t**4 + l. Find j such that b(j) = 0.
-1, 0
Let m(c) be the third derivative of -c**6/10 + 13*c**5/20 + 13*c**4/8 - 2*c**3 + 11*c**2. Solve m(b) = 0.
-1, 1/4, 4
Factor 5 + 3*u**2 - 4*u**2 - 4.
-(u - 1)*(u + 1)
Let i(l) be the second derivative of 3*l**7/14 - 13*l**6/10 - l**5/10 + 47*l**4/6 + 19*l**3/2 + 9*l**2/2 - 13*l. Suppose i(r) = 0. Calculate r.
-1, -1/3, 3
Let z(w) be the third derivative of 3*w**6/64 - 31*w**5/160 + w**3/4 + 10*w**2. Solve z(m) = 0.
-1/3, 2/5, 2
Let d be 3/(-9) - 130/3. Let g = 44 + d. Let 1/3*u**2 - g*u - 2/3 = 0. Calculate u.
-1, 2
Let h be (-100)/(-16) + (-2)/8. Suppose 0*l - 8 - 12*l - h*l**2 - l**3 + 0*l = 0. Calculate l.
-2
Let u be (-2)/(5/(-2) + 2). Let l = 76 + -76. Solve l + t**3 + 0*t + 2/3*t**2 - 5/3*t**u = 0.
-2/5, 0, 1
Let a(k) be the third derivative of -1/3*k**3 + 0 - 1/8*k**4 - 1/60*k**5 + 0*k - k**2. Factor a(f).
-(f + 1)*(f + 2)
Suppose 3*b = -2*b + 50. Solve -10 - 4*t + 0*t + 8*t**3 - 14*t**2 + b = 0 for t.
-1/4, 0, 2
Suppose -8*l**2 + 3*l - 23 + 11*l**2 + 17 = 0. What is l?
-2, 1
Let z(l) be the second derivative of 2*l + 1/2*l**2 + 1/60*l**5 - 1/6*l**4 + 2/3*l**3 + 0. Let v(n) be the first derivative of z(n). Factor v(t).
(t - 2)**2
Let a be ((-12)/(-10))/(22/55). Suppose -1 + a*x + x - 4*x + x**2 = 0. Calculate x.
-1, 1
Let x(t) be the second derivative of -t**4/48 - t**3/48 - 53*t. Factor x(f).
-f*(2*f + 1)/8
Let x = -483359/240 + 2014. Let f(g) be the third derivative of 0 + 1/24*g**3 + 1/96*g**4 - 1/480*g**6 - g**2 - x*g**5 + 0*g. Suppose f(l) = 0. Calculate l.
-1, 1
Suppose -27 = -5*t + 4*y, 5*t - 4*y - 18 = 3*t. Let c be (16/(-12))/((-7)/t). Solve -c*d**2 + 2/7 + 2/7*d**4 + 0*d + 0*d**3 = 0.
-1, 1
Suppose 72/5*a - 12/5*a**2 - 54/5 - 8/5*a**3 + 2/5*a**4 = 0. Calculate a.
-3, 1, 3
Let h(o) be the first derivative of -o**3/3 - o**2/2 - 2. Factor h(s).
-s*(s + 1)
Let d be 70/(-20)*(-3)/42. Solve 1/4*l**3 - d - 1/4*l + 1/4*l**2 = 0.
-1, 1
Let b(g) = -9*g**4 - 15*g**3 - 12*g**2 - 8*g - 9. Let t = -11 - -7. Let h(i) = -5*i**4 - 8*i**3 - 6*i**2 - 4*i - 5. Let s(n) = t*b(n) + 7*h(n). Factor s(m).
(m + 1)**4
Let x be 1 - 4/(0 - 4). Let s(y) be the third derivative of 1/120*y**5 + 0 + 0*y - 2*y**x + 1/24*y**4 + 1/12*y**3. Factor s(a).
(a + 1)**2/2
Let t(i) = 6*i - 2. Let j be t(3). Let g = j - 8. Factor g*c**3 - 2 + 6*c**4 + 0 - 2*c**2 - 2*c**2 - 8*c.
2*(c - 1)*(c + 1)**2*(3*c + 1)
Let o be (-1)/(10/4 + -3). Let s(h) be the second derivative of -1/15*h**4 + 1/15*h**3 + o*h + 0*h**5 + 0 + 2/75*h**6 - 1/105*h**7 + 0*h**2. Factor s(g).
-2*g*(g - 1)**3*(g + 1)/5
Let a(y) = y**2 + 2*y - 2. Let w be a(-3). Let p be ((-12)/8)/(w/(-2)). Solve -8/5*o**2 - 8/5*o**p + 0*o - 2/5*o**4 + 0 = 0 for o.
-2, 0
Let p(c) be the first derivative of -c**3/5 - 3*c**2/2 - 10. Factor p(q).
-3*q*(q + 5)/5
Suppose 0 = 4*q - s + 8 + 24, 0 = -2*q - 3*s - 30. Let r = q - -11. Factor 6*t - 9*t**r - 24*t**3 + 4*t + 4*t - 5*t**2 + 4.
-2*(t + 1)*(3*t - 2)*(4*t + 1)
Factor -9*y - 81/2 - 1/2*y**2.
-(y + 9)**2/2
Suppose 5*w - 4*m = -10, -9*m + 14 = 2*w - 7*m. Factor -4*u - 2/3 - 6*u**w.
-2*(3*u + 1)**2/3
Let n(f) be the second derivative of -f**7/14 - 7*f**6/90 + 11*f**5/60 + 7*f**4/36 - f**3/9 - 6*f - 1. Let n(b) = 0. What is b?
-1, 0, 2/9, 1
Let w(b) = -4*b**3 + 5*b**2 - b + 2. Let q(s) = s**2 - s + 1. Let x(o) = -6*q(o) + 3*w(o). Determine f so that x(f) = 0.
-1/4, 0, 1
Let n = 191/742 - -3/106. Determine y so that 4/7*y + 2/7*y**2 + 0 - n*y**4 - 4/7*y**3 = 0.
-2, -1, 0, 1
Let s be 4*(2 + 6/(-8)). Solve 2*m**2 - 5*m**2 - 4*m**3 + s*m**3 + 2*m = 0 for m.
0, 1, 2
Let t(j) = 5*j**3 + j**2 - 2*j + 1. Let v be t(1). Suppose 5 - r**3 - 6 - r**v + 2*r**4 + 1 = 0. Calculate r.
0, 1
Let r(n) = -5*n**3 - n**2 - 2*n. Let h(p) = -96 + 96 + 3*p + 6*p**3 + p**2. Let q(y) = 4*h(y) + 5*r(y). Factor q(x).
-x*(x - 1)*(x + 2)
Factor 0*p**4 + 1/3*p + 0 - 2/3*p**3 + 1/3*p**5 + 0*p**2.
p*(p - 1)**2*(p + 1)**2/3
Let o(t) be the third derivative of t**6/45 + 3*t**5/20 + t**4/6 + t**3/6 - t**2. Let m(b) be the first derivative of o(b). Let m(j) = 0. Calculate j.
-2, -1/4
Let j be (3/4)/(15/40). Let z(l) be the first derivative of -4*l - 3 - 2/3*l**3 - 3*l**j. Factor z(v).
-2*(v + 1)*(v + 2)
Let l(i) be the second derivative of i**6/15 + i**5/4 + 2*i**3/3 - 2*i**2 + 6*i. Let t(w) = -w**4 - w**3 - w + 1. Let m(f) = -l(f) - 4*t(f). Factor m(h).
h**3*(2*h - 1)
Let a(t) be the first derivative of -t**6/120 - t**5/20 - t**4/8 - t**3/6 + 5*t**2/2 - 5. Let z(d) be the second derivative of a(d). Solve z(b) = 0.
-1
Suppose -2*k**2 + 20*k - 20*k + k**3 = 0. What is k?
0, 2
Let i(p) = -p**3 - 4*p**2 + 19*p - 12. Let s be i(-7). Suppose 1/4*v**3 + 1/4*v**s + 0*v + 0 = 0. What is v?
-1, 0
Find n, given that -16/3 + 32/3*n + 20/3*n**4 - 4/3*n**5 - 28/3*n**3 - 4/3*n**2 = 0.
-1, 1, 2
Let f(k) = -3*k + 1. Let o be f(-1). Let 4*d**5 - 22*d**3 - 4*d**2 + 34*d**3 - o*d**4 - 8*d**4 = 0. What is d?
0, 1
Find s such that -24/7*s**3 + 0 - 18/7*s**4 + 0*s - 8/7*s**2 = 0.
-2/3, 0
Factor 2/5 - 1/5*r - 1/5*r**2.
-(r - 1)*(r + 2)/5
Suppose -11/3*x**3 - 2/3*x**4 + 8/3*x - 10/3*x**2 + 0 = 0. Calculate x.
-4, -2, 0, 1/2
Factor 3/8*m**4 + 9/8*m**2 - 27/8*m + 15/8*m**3 + 0.
3*m*(m - 1)*(m + 3)**2/8
Factor -2*l**2 + 0*l**2 - 12*l**3 + 11*l**3 - l.
-l*(l + 1)**2
Suppose 6*c - 10*c + 8 = 0. Suppose -r + 21 = -6. Factor 3*t**2 + 12*t + r - 8*t + 14*t + 0*t**c.
3*(t + 3)**2
Factor 0*m**2 + 1/2*m**3 + 0*m - 1/2*m**4 + 0.
-m**3*(m - 1)/2
Let k(a) = -60*a**2 - 274*a + 86. Let y(u) = 12*u**2 + 55*u - 17. Let f(z) = 2*k(z) + 11*y(z). Let f(n) = 0. What is n?
-5, 1/4
Let u be (1/1)/((-1)/3). Let x(d) = -3*d**4 - 11*d**3 - 4*d**2 + d - 3. Let y(s) = s**3 - s**2 - s + 1. Let w(q) = u*y(q) - x(q). Factor w(t).
t*(t + 1)**2*(3*t + 2)
Let k(v) be the first derivative of v**7/1155 - v**6/330 + v**5/330 - 7*v**2/2 - 1. Let p(n) be the second derivative of k(n). Determine u so that p(u) = 0.
0, 1
Let l(j) = 0*j + j**2 - 4*j + 3*j. Let s(p) = -14*p**2 + 16*p. Let n(m) = -12*l(m) - s(m). Suppose n(i) = 0. What is i?
0, 2
Let f(n) be the third derivative of n**5/20 - 3*n**4/8 + n**3 - 24*n**2. Factor f(o).
3*(o - 2)*(o - 1)
Let s(c) be the first derivative of -c**8/10080 + c**7/5040 + c**6/2160 - c**5/720 - 3*c**3 + 9. Let k(f) be the third derivative of s(f). Factor k(b).
-b*(b - 1)**2*(b + 1)/6
Let u = -348/7 + 50. Factor -4/7*t**3 + 2/7*t + u*t**2 + 0.
-2*t*(t - 1)*(2*t + 1)/7
Let f = 533/3 - 175. Let w(j) be the first derivative of 1 + 18*j**3 + f*j + 12*j**2. Factor w(y).
2*(9*y + 2)**2/3
Let v(b) be the first derivative of b**4/8 + b**3/2 + 3*b**2/4 + b/2 + 11. Factor v(o).
(o + 1)**3/2
Let -2/5*n**2 + 2/5*n + 0 = 0. What is n?
0, 1
Find z such that -2*z**4 - 18*z**3 + 9*z**3 + 5*z**3 - 2*z**2 = 0.
-1, 0
Let i(c) be the first derivative of c**4/102 - 2*c**3/17 + 9*c**2/17 - c - 6. Let z(j) be the first derivative of i(j). Let z(k) = 0. Calculate k.
3
Let o = -4 - -4. Let j be o + 0 + (-6)/(-2). Solve 10/7*b**4 + 0 - 10/7*b**2 + 4/7*b - 4/7*b**j = 0 for b.
-1, 0, 2/5, 1
Let x(a) be the second derivative of -a**4/10 + 4*a**3/15 - a**2/5 - 2*a. Factor x(n).
-2*(n - 1)*(3*n - 1)/5
Suppose 0 = 4*g - 7 - 1. Let t(l) be the third derivative of 0*l + 1/420*l**6 - 4/21*l**3 + 4*l**g + 2/21*l**4 - 1/42*l**5 + 0. Let t(z) = 0. What is z?
1, 2
Let k(o) be the third derivative of o**8/756 + o**7/210 + o**6/180 + o**5/540 + 2*o**2. Factor k(m).
m**2*(m + 1)**2*(4*m + 1)/9
Let s(g) = 15*g**2 + 39*g + 25. Let w(h) = -8*h**2 - 20*h - 12. Let z(l) = 4*s(l) + 7*w(l). Factor z(x).
4*(x + 2)**2
Let t be ((-133)/(-35) + -3)*10/4. Let n(z) be the first derivative of -1/12*z**6 + 0*z**t + 0*z**3 + 3/20*z**5 - 1/16*z**4 - 1 + 0*z. Factor n(m).
-m**3*(m - 1)*(2*m - 1)/4
Suppose 0*n = -n + 2. Suppose -n*z + 0*z = 0. What is u in 0*u**3 + 0*u + z - 1/4*u**4 + 1/4*u**2 = 0?
-1, 0, 1
Let q(x) = x**3 - 5*x**2 - 6*x + 4. Let f be q(6). Suppose f = 5*o - 6. Solve 2*t + 2 + 2 - 6 - 2*t**3 + 2*t**o = 0.
-1, 1
Factor 0*l + 3/2*l**3 + 3/2*l**4 + 0 + 0*l**2.
3*l**3*(l + 1)/2
Let c = 64 + -61. Let p(g) be the second derivative of 0 + 0*g**2 + c*g + 0*g**3 - 1/30*g**5 - 1/90*g**6 - 1/36*g**4. Factor p(h).
-h**2*(h + 1)**2/3
Factor -16/9*t + 0 + 4/3*t**3 + 2/9*t**5 + 8/9*t**2 - 10/9*t**4.
2*t*(t - 2)**3*(t + 1)/9
Suppose -5*a - 5*v = 6