7 + 1641/2785. Let 0*r**2 + 0*r + 2/5*r**3 + 0 - i*r**4 = 0. What is r?
0, 2/3
Let o = 1667/11 - 152. Let m = o - -37/33. Find d such that 0 + m*d + 2/3*d**2 = 0.
-1, 0
Let k(j) be the third derivative of j**8/1344 + j**7/140 + 7*j**6/240 + j**5/15 + 3*j**4/32 + j**3/12 + 10*j**2. Factor k(h).
(h + 1)**4*(h + 2)/4
Factor 27/2*n**4 + 0*n + 0 - 9*n**3 - 6*n**5 + 3/2*n**2.
-3*n**2*(n - 1)**2*(4*n - 1)/2
Let o(m) = 11*m**2 - 13*m + 13. Let w(c) = -5*c**2 + 6*c - 6. Let f(n) = -6*o(n) - 13*w(n). Factor f(h).
-h**2
Let f(b) be the third derivative of -b**9/37800 + b**8/8400 - b**7/6300 - b**4/8 - 3*b**2. Let k(o) be the second derivative of f(o). Factor k(h).
-2*h**2*(h - 1)**2/5
Let x(a) be the first derivative of 2*a**3/27 + 2*a**2/9 - 10. Let x(o) = 0. What is o?
-2, 0
Let s(g) be the second derivative of -g**9/15120 - g**8/3360 + g**6/360 + g**5/120 - 5*g**4/12 + 5*g. Let z(j) be the third derivative of s(j). Factor z(n).
-(n - 1)*(n + 1)**3
Let g(p) be the third derivative of -p**8/560 + 3*p**7/350 + p**6/200 - 3*p**5/100 - 17*p**2. Let g(o) = 0. What is o?
-1, 0, 1, 3
Let t(n) be the first derivative of 12/5*n**4 + 3 + 27/25*n**5 + 14/5*n**3 + 1/5*n**6 + 9/5*n**2 + 3/5*n. Factor t(o).
3*(o + 1)**4*(2*o + 1)/5
Let p(f) be the first derivative of f**6/60 - f**4/24 + 6*f + 4. Let u(r) be the first derivative of p(r). Factor u(o).
o**2*(o - 1)*(o + 1)/2
Let h(d) = 4*d**4 - 7*d**3 + 3*d**2 + 5*d. Let r(t) = 0*t - 15*t**4 + 6*t**3 + 0*t - 2*t**2 + 11*t**4 - 4*t. Let p(i) = -4*h(i) - 5*r(i). Solve p(g) = 0 for g.
-1/2, 0, 1
Suppose 0*q + 2*q = 6. Factor 7*k**2 - k**2 + 0*k - 4*k + 0*k**q - 2*k**3.
-2*k*(k - 2)*(k - 1)
Let m(s) be the first derivative of -s**4/24 - s**3/18 + s**2/6 + 6. Determine h so that m(h) = 0.
-2, 0, 1
Let b(l) be the second derivative of 2*l**7/273 - l**6/13 + 14*l**5/65 - 7*l**4/39 - 2*l**3/13 + 5*l**2/13 + l + 11. Suppose b(c) = 0. Calculate c.
-1/2, 1, 5
Let q(l) = 2*l**2 + 8*l - 5. Let i be q(-7). Find k such that -8 + 3*k + 35*k - 125*k**2 + 34*k - i*k**2 = 0.
2/9
Let u(y) be the third derivative of -y**5/450 - y**4/45 - 36*y**2. Let u(z) = 0. What is z?
-4, 0
Let n(s) be the first derivative of 3*s**4/16 - s**3 + 9*s**2/8 + 5. Factor n(j).
3*j*(j - 3)*(j - 1)/4
Let v = 9607/20 + -480. Let z(s) be the first derivative of 5/16*s**4 + 1 + 1/2*s**2 + 4/3*s**3 - v*s**5 + 0*s. Solve z(j) = 0.
-1, -2/7, 0, 2
Let h(y) be the first derivative of 9 - 10/3*y**2 + 1/3*y**4 - 4/3*y**3 - 8/3*y + 4/15*y**5. Factor h(w).
4*(w - 2)*(w + 1)**3/3
Factor -23 - 3*v**2 - 24*v - 7 - 18.
-3*(v + 4)**2
Let x = 2131/3720 + -35/62. Let g(y) be the third derivative of -x*y**5 - 1/16*y**4 - 1/6*y**3 + 0*y + y**2 + 0. Factor g(j).
-(j + 1)*(j + 2)/2
Let x = 26 - -23. Let f = 445/9 - x. Factor -2/9*b**4 + f*b**2 + 0*b + 0*b**3 - 2/9.
-2*(b - 1)**2*(b + 1)**2/9
Suppose -24/7*r + 36/7 + 4/7*r**2 = 0. Calculate r.
3
Let k = 165 - 163. Factor 2*b**3 + 6/7*b**5 + 0*b + 16/7*b**4 + 0 + 4/7*b**k.
2*b**2*(b + 1)**2*(3*b + 2)/7
Let t(u) = -4*u. Let n be t(-3). Suppose 2*c = -0*y + 2*y, -4*y = -n. Factor z - 4*z**2 + 3*z + 4 + 2*z - 6*z**c.
-2*(z - 1)*(z + 1)*(3*z + 2)
Let t(r) be the third derivative of -r**5/180 - r**4/48 - r**3/36 + 2*r**2 - 29*r. Factor t(c).
-(c + 1)*(2*c + 1)/6
Let d(m) be the second derivative of -3/2*m**3 + 5*m + 3/2*m**2 - 3/20*m**5 + 3/4*m**4 + 0. Factor d(j).
-3*(j - 1)**3
Let m be 0 + 24/11 + 662/(-3641). Factor -4/7*b**3 + 12/7*b + 8/7 + 0*b**m.
-4*(b - 2)*(b + 1)**2/7
Let b be (-2)/8 + 9/4. Suppose 0*u = u + 2*w + 6, -3*w = 3*u + 9. Factor -2/7*y**3 + 0 + 4/7*y**4 - 2/7*y**5 + 0*y + u*y**b.
-2*y**3*(y - 1)**2/7
Let j(x) = x**3 + x**2 + x - 5. Let k be j(0). Let d be k/20 + 2/8. Factor -1/3*q**3 + 0 + d*q**2 + 0*q.
-q**3/3
Let v(z) be the first derivative of 3 - 4/17*z**2 - 8/17*z - 2/51*z**3. Factor v(o).
-2*(o + 2)**2/17
Let c(f) be the third derivative of -f**7/2520 - f**6/540 - f**5/360 + f**3/2 - f**2. Let i(l) be the first derivative of c(l). Solve i(p) = 0 for p.
-1, 0
Factor 2/15 - 2/5*o - 2/15*o**3 + 2/5*o**2.
-2*(o - 1)**3/15
Let a = 114 + -5128/45. Let b(p) be the first derivative of 2/9*p**2 - 3 + 0*p**3 - 2/9*p + a*p**5 - 1/9*p**4. Factor b(n).
2*(n - 1)**3*(n + 1)/9
Suppose 5*k + 2*s - 4 = 0, 14 = 7*k - 3*k - 2*s. Factor 2*z**2 + 0 + 2/3*z**4 - 2/3*z - k*z**3.
2*z*(z - 1)**3/3
Let s(l) be the second derivative of l**4/6 - 15*l. Factor s(y).
2*y**2
Let o(p) be the second derivative of p**7/84 - 11*p**6/60 + 43*p**5/40 - 73*p**4/24 + 14*p**3/3 - 4*p**2 + 29*p. Determine y so that o(y) = 0.
1, 4
Let q(a) be the third derivative of 5*a**2 + 0 + 0*a**6 - 1/12*a**4 + 2/105*a**7 + 1/168*a**8 + 0*a**3 + 0*a - 1/15*a**5. Factor q(x).
2*x*(x - 1)*(x + 1)**3
Let z be -3 + (-2 - -4) - 48/(-40). Let z*l**3 - 1/5*l + 1/5*l**2 + 0 - 1/5*l**4 = 0. What is l?
-1, 0, 1
Let p = -95/4 + 951/40. Let r(u) be the third derivative of -2*u**2 - 1/24*u**4 + 1/224*u**8 + 0*u + 1/60*u**7 + 1/80*u**6 + 0*u**3 + 0 - p*u**5. Factor r(f).
f*(f + 1)**3*(3*f - 2)/2
Let i = -794/5 - -159. Factor 1/5*o**5 - 3/5*o**4 - i*o**2 + 3/5*o**3 + 0*o + 0.
o**2*(o - 1)**3/5
Let b be 16 + -5 + 2/2. Factor 4*p**4 + 2*p**4 + b*p**2 + p**3 - 3*p**4 + 11*p**3.
3*p**2*(p + 2)**2
Let x(o) be the second derivative of -o**7/1680 + o**6/720 + o**5/120 - o**3/6 - o. Let y(z) be the second derivative of x(z). Solve y(d) = 0 for d.
-1, 0, 2
Let z = 6 - 4. Let a(v) = -v**2 + 6*v - 1. Let g be a(5). Factor 2*u**z + u**g + 2*u**3 + 0*u**3 - u**2.
u**2*(u + 1)**2
Let d(b) = 2*b. Let k be d(2). Let i(f) = 2*f**2 - 5*f - 4. Let x be i(k). Let 2*u**2 + 14/3*u**4 + x*u**3 - 4/3*u + 0 = 0. What is u?
-1, 0, 2/7
Let a(y) be the first derivative of -y**2/2 + y + 5. Let z(h) = 6*h**2 - 6*h + 9. Let c(d) = -9*a(d) + z(d). Factor c(b).
3*b*(2*b + 1)
Suppose -20 = 4*d + 2*o, 2*o = -0*d - 3*d - 16. Let v be d/(-2) - -2 - 2. Solve -v*s**2 + 2*s**2 + 0*s**2 + 2*s**2 = 0.
0
Let a(z) = -z**2 + 47*z - 130. Let r be a(3). Factor 0 - 2/3*u**3 - 2/3*u**r + 2/3*u**4 + 2/3*u.
2*u*(u - 1)**2*(u + 1)/3
Let n be 65/70 - 6/14. Let g(b) = -b**2 - 8*b + 13. Let f be g(-9). Solve j - 1/2 + n*j**f - j**3 + 0*j**2 = 0 for j.
-1, 1
Let f(d) be the second derivative of d**5/50 + d**4/15 + d**3/15 - 2*d. Factor f(g).
2*g*(g + 1)**2/5
Let -5*j**4 + 7*j - 27*j - 20*j**3 + 216 - 22*j**2 - 221 - 8*j**2 = 0. What is j?
-1
Let r(s) = 6*s**5 - 18*s**4 - 4*s**3 + 10*s**2 + 10*s + 10. Let w(q) = -q**5 + q**4 - q**2 - q - 1. Let u(a) = r(a) + 10*w(a). Find x such that u(x) = 0.
-1, 0
Let b(r) = -r**2. Let a(g) = -6*g**2 + 1. Let q(x) = -a(x) + 5*b(x). Factor q(n).
(n - 1)*(n + 1)
Let d(l) = -3*l + 12. Let r be d(9). Let n be (24/30)/((-6)/r). Solve 0*v + 2/5*v**4 + 18/5*v**n - 12/5*v**3 + 0 = 0.
0, 3
Let h(c) be the second derivative of c**7/280 - c**6/40 + c**4/2 + 5*c**3/6 - c. Let k(m) be the second derivative of h(m). Find y such that k(y) = 0.
-1, 2
Determine t so that -4/3*t**2 + 2/3*t**3 + 0 + 2/3*t = 0.
0, 1
Find y such that -1/3 + 1/3*y**2 + 1/3*y**3 - 1/3*y = 0.
-1, 1
Suppose 6*y = 3*y - 6. Let s = y - -4. Factor 18/13*a**s + 54/13*a + 54/13 + 2/13*a**3.
2*(a + 3)**3/13
Let v = -110 - -110. What is o in v - 1/5*o**4 + 1/5*o**2 - 1/5*o + 1/5*o**3 = 0?
-1, 0, 1
Determine z so that 3/4*z**4 + 0 - 3/4*z + 9/4*z**2 - 9/4*z**3 = 0.
0, 1
Let z(v) = -2*v**2 - 2*v + 4. Let n(b) = -b**2 - 3*b + 4. Let a(j) = -4*n(j) + 3*z(j). Factor a(m).
-2*(m - 2)*(m - 1)
Let o(n) be the first derivative of n**5/20 + 5*n**4/16 + 3*n**3/4 + 7*n**2/8 + n/2 - 16. Factor o(g).
(g + 1)**3*(g + 2)/4
Suppose -f = -4*g + 7 - 27, 28 = 2*f - 5*g. Factor -4*w**2 + 4*w + 12*w**3 - 4*w**f + 7*w**2 - 15*w**2.
-4*w*(w - 1)**3
Let t(q) = 2*q**4 - 6*q**3 - 2*q**2 + 6*q - 6. Let j(o) = 5*o**4 - 12*o**3 - 4*o**2 + 13*o - 13. Let x(f) = -6*j(f) + 13*t(f). Factor x(d).
-2*d**2*(d + 1)*(2*d + 1)
Let f(q) = -q**2 - 5*q + 2. Let s be f(-5). Suppose -4*n + s*n = 0. Factor m - 4*m**3 - 2 + 3*m + n*m**4 + 2*m**4.
2*(m - 1)**3*(m + 1)
Let a(h) = 5*h - 1. Let u be a(1). Let z(m) be the third derivative of 1/10*m**3 + 0*m + 1/100*m**5 + u*m**2 + 1/20*m**4 + 0. What is k in z(k) = 0?
-1
Let z(d) = -d**3 + 11*d**2 - 18*d + 2. Let w be z(9). Factor -1/2*o - 1 + 3/2*o**w.
(o - 1)*(3*o + 2)/2
Let y be -3*2*1/(-3). Determine i, given that 3*i**5 + i**3 + 2*i + 26*i**3 