the third derivative of -1/12*m**4 + 0*m + 1/9*m**3 + 1/30*m**5 + 2*m**2 - 1/180*m**6 + 0. Suppose z(n) = 0. Calculate n.
1
Suppose -13 = -4*s - 5. Suppose -s*y = -7*y + 10. Find q, given that -2/3*q**3 - 1/3 + 1/3*q**5 + 1/3*q - 1/3*q**4 + 2/3*q**y = 0.
-1, 1
Suppose -2*q - 21 = -z - 27, 3*z = 0. Find r such that 10/3*r**2 - 6 - 2/3*r**q - 2*r = 0.
-1, 3
Let b(k) be the second derivative of k**9/3024 - k**8/840 + k**6/180 - k**5/120 - k**3/3 + 2*k. Let h(z) be the second derivative of b(z). Factor h(s).
s*(s - 1)**3*(s + 1)
Suppose 3*q = 367 + 104. Let p = q - 1095/7. What is r in 2/7*r - 2/7*r**5 - p*r**2 + 0*r**3 + 4/7*r**4 + 0 = 0?
-1, 0, 1
Let u be (-3)/3 + (14 - 3). Let l be u/12*4/5. Suppose -1/3*h**3 + 0 + l*h**2 - 1/3*h = 0. What is h?
0, 1
Factor -1/11*p**3 + 1/11*p**2 - 1/11 + 1/11*p.
-(p - 1)**2*(p + 1)/11
Let h(c) be the third derivative of -8*c**2 + 0*c - 1/36*c**4 - 1/18*c**3 + 0 + 1/60*c**5. Factor h(r).
(r - 1)*(3*r + 1)/3
Let l(z) = -z**2 - 2*z + 2. Let k be l(-2). Determine r so that 4 + 0*r**k + r**2 - 5 = 0.
-1, 1
Suppose n - 4 = -3*n. Let i(s) be the first derivative of 2/3*s**3 + 0*s**2 + 0*s - s**4 - n. Let i(u) = 0. What is u?
0, 1/2
Let o(j) be the first derivative of j**6/1980 + j**5/660 - j**4/66 + j**3/3 + 4. Let g(u) be the third derivative of o(u). Determine d, given that g(d) = 0.
-2, 1
Determine p so that 18*p - 10*p**3 - 5*p + 16*p**2 - 8*p**2 + 9*p + 4 = 0.
-1, -1/5, 2
Let f = -22 - -22. Let n(m) be the second derivative of 1/36*m**4 - 1/90*m**6 + 0*m**2 + 1/18*m**3 + f - 2*m - 1/60*m**5. Factor n(g).
-g*(g - 1)*(g + 1)**2/3
Let s be (-12)/(-15)*40/16. Determine v, given that 0 - 1/4*v**3 + 1/4*v + 1/4*v**4 - 1/4*v**s = 0.
-1, 0, 1
Let f be 4*30/24 + (-10)/8. Determine l so that 51/4*l**4 + 3*l**2 + 0*l - 12*l**3 + 0 - f*l**5 = 0.
0, 2/5, 1, 2
Let s = 2/325 - -632/2925. Let h be (-10)/(-15)*((-50)/15 + 5). What is z in h*z**2 + s*z**3 + 8/9 + 16/9*z = 0?
-2, -1
Let s(u) be the first derivative of 4*u**5/5 + 3*u**4/2 - u**2 + 5. Factor s(n).
2*n*(n + 1)**2*(2*n - 1)
Factor -5*p - 5 - 15*p**2 + 5*p**3 + 10*p + 8*p + 2*p.
5*(p - 1)**3
Let d(a) = -a - 4. Let j be d(-9). Suppose 0 = i - 3*n + 13, 4*n = -i - 4*i + 30. What is r in 1/4*r**4 - 1/2*r**i - 1/4*r**j + 1/2*r**3 + 1/4 - 1/4*r = 0?
-1, 1
Let v(u) be the first derivative of 6*u**4 - 12*u**3 + 9*u**2 - 3*u + 2. Factor v(j).
3*(2*j - 1)**3
Let q(d) be the first derivative of 7*d**4/32 - 9*d**3/4 + 6*d**2 + 4*d - 28. Factor q(w).
(w - 4)**2*(7*w + 2)/8
Let l(d) = -d**4 + 11*d**3 - 3*d**2 - 11*d + 10. Let o(y) = -y**4 + 10*y**3 - 3*y**2 - 10*y + 9. Let n(f) = 5*l(f) - 6*o(f). Factor n(j).
(j - 4)*(j - 1)**2*(j + 1)
Let t(z) be the first derivative of -1 - 2/15*z**5 + 0*z - 2/3*z**2 - 4/9*z**3 + 7/12*z**4. Factor t(x).
-x*(x - 2)**2*(2*x + 1)/3
Let c(t) = t**3 - 6*t**2 - 5*t - 4. Let d be c(7). Factor -9*o - o**3 + d*o**3 - 3*o**2 + 3 + 0.
3*(o - 1)*(o + 1)*(3*o - 1)
Suppose 5*u = 2*o + u + 6, 0 = 3*o - 3*u. Factor -5*g**2 - o + 2*g**2 - 2 + 2 - 6*g.
-3*(g + 1)**2
Let n be (4/(-34) - (-60)/510)/(-1). Solve 0*x**2 + 1/3*x - 1/3*x**3 + n = 0.
-1, 0, 1
Let 2/5*q**2 + 0 - 4/5*q**3 + 0*q + 2/5*q**4 = 0. What is q?
0, 1
Let c(f) be the third derivative of -f**6/90 + f**5/60 + f**3/2 + 2*f**2. Let x(i) be the first derivative of c(i). Factor x(p).
-2*p*(2*p - 1)
Let t = 6 + -2. Let a(b) be the second derivative of 0 - 1/50*b**5 - b + 1/5*b**3 + 0*b**t + 2/5*b**2. Factor a(f).
-2*(f - 2)*(f + 1)**2/5
Let n(b) be the third derivative of -b**11/582120 - b**5/20 - 8*b**2. Let z(o) be the third derivative of n(o). Determine q, given that z(q) = 0.
0
Let q be (-1)/(3/9) - -1. Let r(f) = f**3 + 4*f**2 + 3*f + 1. Let c be r(q). Factor -o**2 + c*o**4 + o**4 + 2*o**3 - 5*o**4.
-o**2*(o - 1)**2
Let g be 24/(-30) - 28/(-10). Let z(c) be the second derivative of 0*c**3 + 0*c**5 - 1/6*c**4 + 0 - g*c + 1/15*c**6 + 0*c**2. Factor z(l).
2*l**2*(l - 1)*(l + 1)
Let h(p) be the second derivative of 0*p**3 + 0 + 1/20*p**4 + 1/100*p**5 + 0*p**2 + 3*p. Solve h(a) = 0.
-3, 0
Let t(p) be the first derivative of 0*p**2 + 0*p + 3 + 1/12*p**3. Factor t(y).
y**2/4
Let x(w) be the first derivative of 6*w**5/5 + w**4/2 - 2*w**3 - w**2 + 42. Factor x(m).
2*m*(m - 1)*(m + 1)*(3*m + 1)
Let r(v) be the first derivative of -2*v**3/3 - 6*v**2 - 18*v - 6. Factor r(o).
-2*(o + 3)**2
Suppose -15/2*q + 5/2*q**2 + 5 = 0. Calculate q.
1, 2
Suppose -n + 16 = n. What is u in 6*u**2 + 3 - u**5 + n*u**3 - 4*u**3 - 9*u**4 - 9*u + 4*u**5 + 2*u**3 = 0?
-1, 1
Let f(p) be the first derivative of 4/21*p**3 - 3/14*p**4 - 1/42*p**6 + 4/35*p**5 - 1/14*p**2 + 0*p + 3. Factor f(t).
-t*(t - 1)**4/7
Let s(l) be the second derivative of 0 + 1/12*l**4 + 0*l**3 + 3*l + 1/20*l**5 + 0*l**2. Factor s(d).
d**2*(d + 1)
Let u(y) = y**2 + 0 - y - 4*y**3 - 4 + 5 + 5*y**3. Let g(h) = -6*h**3 - 8*h**2 + 6*h. Let w(s) = g(s) + 4*u(s). Factor w(a).
-2*(a - 1)*(a + 1)*(a + 2)
Let l(m) = 3*m**2 + 3*m. Suppose -2*v - 3*f = -0*f + 6, 4*f = -v - 3. Let t be l(v). Factor -2*k**4 - t*k**2 + 0*k**4 + 8*k + 10*k**3 + 2*k**2.
-2*k*(k - 2)**2*(k - 1)
Let b(v) be the first derivative of 1/5*v**2 - 2/15*v**3 + 1 + 0*v. Find c, given that b(c) = 0.
0, 1
Let d(o) = -o**3 + 3*o**2 + 3*o + 4. Let l be d(4). Suppose 2*s - 4*t - 4 = l, 4*s = 4*t + 1 + 7. Factor -9/5*i - 9/5*i**s - 3/5 - 3/5*i**3.
-3*(i + 1)**3/5
Let m(t) = -4*t**2 + 4*t + 5. Let x(j) = 5*j**2 - 5*j - 6. Let o(f) = 4*m(f) + 3*x(f). Find q such that o(q) = 0.
-1, 2
Suppose -33 - 7 = -4*y. Factor -y*t**5 - 2*t**4 + 13*t**5 - t + 6*t**3 - 7*t**4 + t**4.
t*(t - 1)**3*(3*t + 1)
Let v(j) be the second derivative of 1/5*j**3 + 1/25*j**6 - 1/105*j**7 + 4*j - 1/5*j**2 - 1/25*j**5 - 1/15*j**4 + 0. Solve v(d) = 0.
-1, 1
Let l(q) = q**4 + 2*q**3 - q**2 - q. Let v(y) = -12*y**4 - 28*y**3 + 20*y**2 + 52*y + 24. Let n(w) = -8*l(w) - v(w). What is f in n(f) = 0?
-3, -1, 2
Let h(j) be the third derivative of j**7/5040 - j**5/240 - j**4/12 - 3*j**2. Let g(t) be the second derivative of h(t). Factor g(k).
(k - 1)*(k + 1)/2
Let b = 23 + -19. Let p(u) be the second derivative of 1/30*u**6 - 1/10*u**5 + 1/3*u**3 + 0 + 0*u**b - 1/2*u**2 + u. Let p(s) = 0. What is s?
-1, 1
Let b(q) be the third derivative of -1/420*q**7 + 0 + 0*q**3 + 0*q**5 - 1/240*q**6 + 0*q**4 + 3*q**2 + 0*q. Suppose b(d) = 0. Calculate d.
-1, 0
Let o be (-1)/(-3) + (-10)/120. Determine u, given that 0*u**2 + 0 + u**4 + o*u**3 + 0*u = 0.
-1/4, 0
Let r(z) be the second derivative of z**8/20160 + z**7/3024 + z**6/1440 + 7*z**4/12 + z. Let v(i) be the third derivative of r(i). Let v(u) = 0. What is u?
-3/2, -1, 0
Factor -8/3 + 4/3*f - 1/3*f**3 + 2*f**2 - 1/3*f**4.
-(f - 2)*(f - 1)*(f + 2)**2/3
Determine o so that -15/2*o**3 + 3*o + 0 - 9/2*o**2 = 0.
-1, 0, 2/5
Let j(r) be the third derivative of -r**2 + 0*r + 0*r**4 + 1/330*r**6 + 0 - 1/330*r**5 - 1/1155*r**7 + 0*r**3. Factor j(u).
-2*u**2*(u - 1)**2/11
Let -8*y - 2*y**3 - 4 + 4*y**4 + 12*y**3 + 0 - 2*y**3 = 0. What is y?
-1, 1
Suppose 5*a + 5*w - 20 = 0, 3*a - 7 = -w + 1. Solve -x**a - 1 - 3*x + 1 + 4*x = 0 for x.
0, 1
Let m(l) be the third derivative of -1/6*l**4 + 0 - 1/3*l**3 + l**2 - 1/30*l**5 + 0*l. Solve m(w) = 0 for w.
-1
Let v(f) be the first derivative of -4/3*f + 2 - 2/9*f**3 + f**2. Solve v(m) = 0.
1, 2
Let r(f) be the first derivative of f**5/2 + f**4 + f**3/6 - f**2/2 + 5. Determine o so that r(o) = 0.
-1, 0, 2/5
Suppose 3*a + a = 0. Factor 2*y**3 - y**3 + y**5 + a*y**4 - 2*y**4.
y**3*(y - 1)**2
Let n(i) = i**3 - 6*i**2 - 7*i. Let x be n(7). Let v be (8/(-6))/4 - -1. Factor -4/3*l**3 + v*l**2 + 0*l + x + 2/3*l**4.
2*l**2*(l - 1)**2/3
Let s(i) be the third derivative of -i**7/70 + 3*i**6/40 + 3*i**5/20 - 7*i**4/8 - 3*i**3 + 31*i**2. Determine a so that s(a) = 0.
-1, 2, 3
Let b(v) be the third derivative of v**6/160 - v**4/32 - 44*v**2. What is l in b(l) = 0?
-1, 0, 1
Suppose -6*l = -l + w - 2, 0 = 4*l - 5*w + 10. Let d be (-7)/14*l/1. Factor -1/4*z**4 - 1/4*z**5 + d + 1/4*z**2 + 0*z + 1/4*z**3.
-z**2*(z - 1)*(z + 1)**2/4
Factor -8*j**3 - 13*j**2 + 2*j**2 + 5*j**3 - 4*j**2.
-3*j**2*(j + 5)
Let m(w) = -w**2 - w - 1. Let j = 0 + -3. Let l(n) = -n**3 + n**2 + 2*n + 1. Let q(d) = j*l(d) - 3*m(d). Find t such that q(t) = 0.
-1, 0, 1
Let t = 2 - 3. Let f = 2 - t. Suppose n + f*n**2 + n**2 - 