**2 + 9*j + 10. Let f be s(-8). Suppose -f*m**2 + 2*m + 2/3*m**3 - 2/3 = 0. Calculate m.
1
Let n(r) be the first derivative of 5*r**3/3 - 2*r**2 - r - 33. Let w(h) = -h**2 + 1. Let d be (-2)/7 + (-9)/(-7). Let y(s) = d*n(s) + 3*w(s). Factor y(t).
2*(t - 1)**2
Let s(y) = y**2 - y + 3. Let j be s(0). Factor j*k**3 - 4*k**3 + 2*k**4 - 3*k**4.
-k**3*(k + 1)
Determine y so that -3*y**3 + 7*y - 6*y**2 + 4*y - 14*y = 0.
-1, 0
Let u = -39/2953 - 3327680/26577. Let i = -125 - u. Suppose -4/9 + 2/3*h - i*h**2 = 0. Calculate h.
1, 2
Let -17*x + 4*x**3 - x**3 + 14*x = 0. Calculate x.
-1, 0, 1
Let k(q) be the third derivative of 2*q**2 + 0 + 0*q**3 + 1/30*q**5 + 0*q**4 + 0*q. Factor k(t).
2*t**2
Let w = -320 + 322. Factor -1/8*o**3 + 0*o - 1/8*o**w + 0.
-o**2*(o + 1)/8
Suppose -2 - 1 + 60*s**2 - 5*s + 4 - 6 = 0. Calculate s.
-1/4, 1/3
Suppose -11 = -4*v + 9. Suppose 48*t**5 - 4*t**3 + 42*t**5 + t**4 - t**2 - 86*t**v = 0. Calculate t.
-1, -1/4, 0, 1
Let q(s) be the second derivative of s**4/42 - 5*s. Let q(m) = 0. Calculate m.
0
Suppose -3*t = -5*s + 2*t + 35, 3*s - t - 17 = 0. Factor 2*o**s - o**5 + 2*o**4 - o**4.
o**4*(o + 1)
Let i(b) be the first derivative of 2/3*b**3 + 0*b - 2/5*b**5 + 2/3*b**2 - 1/9*b**6 + 1 - 1/6*b**4. Suppose i(t) = 0. What is t?
-2, -1, 0, 1
Let t(x) be the third derivative of -1/210*x**5 + 0 + 1/14*x**4 - 3/7*x**3 + 4*x**2 + 0*x. Find d such that t(d) = 0.
3
Let w(n) be the first derivative of n**3/6 + 3*n**2/4 + 43. Factor w(p).
p*(p + 3)/2
Let a(m) be the third derivative of -1/15*m**5 - 1/30*m**6 + 1/3*m**3 + 1/105*m**7 + 1/12*m**4 + 0*m + 0 + 1/168*m**8 - 2*m**2. Find v such that a(v) = 0.
-1, 1
Suppose 0 = 16*l - 19*l + 9. Let -2 + 17/2*p**2 + 13/4*p**l - 13/2*p**4 - 5*p + 7/4*p**5 = 0. Calculate p.
-1, -2/7, 1, 2
Let u(r) be the first derivative of r**6/2 + 3*r**5/5 - 8. Find m, given that u(m) = 0.
-1, 0
Let u(t) be the second derivative of 0 - 1/210*t**7 + 4*t + 0*t**3 + 0*t**2 - 1/150*t**6 + 1/100*t**5 + 1/60*t**4. Factor u(f).
-f**2*(f - 1)*(f + 1)**2/5
Let b(a) be the first derivative of -5/8*a**4 + 7/6*a**3 + 2*a**2 - 2*a + 4. Factor b(o).
-(o - 2)*(o + 1)*(5*o - 2)/2
Let a(m) be the first derivative of -5*m**4/2 + 16*m**3/3 - m**2 - 4*m - 48. Find q such that a(q) = 0.
-2/5, 1
Suppose 52*r = 48*r + 20. Let c = 14/15 + -2/15. Factor -2/5*k**r + 4/5*k**2 - 2/5 - 2/5*k + c*k**3 - 2/5*k**4.
-2*(k - 1)**2*(k + 1)**3/5
Let v = -22 - -19. Let u(b) = b + 3. Let x be u(v). Factor 0*k**4 - 1/2*k**5 + k**3 + 0*k**2 + x - 1/2*k.
-k*(k - 1)**2*(k + 1)**2/2
Let v = 17 + -17. Solve -18/5*b**4 + 2*b**2 - 6/5*b**3 + v - 2/5*b = 0.
-1, 0, 1/3
Let n(w) be the third derivative of -w**7/10080 - w**6/2880 + w**4/24 - w**2. Let y(x) be the second derivative of n(x). Determine z, given that y(z) = 0.
-1, 0
Suppose -4*h + 42 = -h. Let t be ((-2)/(-10))/(h/28). Let 2/5*s**3 + 0*s**2 + 0 - t*s = 0. Calculate s.
-1, 0, 1
Let g be (-10*3)/(-5) + -2. Let w(f) be the first derivative of -1 + 0*f - 7/5*f**5 + 9/4*f**g + 1/2*f**2 - 5/3*f**3 + 1/3*f**6. Let w(m) = 0. Calculate m.
0, 1/2, 1
Let a(o) be the second derivative of 0 - 9*o - 1/14*o**4 - 3/70*o**5 - 1/21*o**3 + 0*o**2 - 1/105*o**6. Factor a(q).
-2*q*(q + 1)**3/7
Suppose 15 = -0*x + 5*x. Let q(j) = -j**3 + 2*j**2 + 3*j. Let n be q(x). Find s, given that -6*s**3 + n*s**3 + 2*s**3 + 5*s**3 = 0.
0
Let x(f) be the first derivative of 0*f + 5 + 3*f**3 + 3/4*f**4 + 3*f**2. Factor x(d).
3*d*(d + 1)*(d + 2)
Let z(d) be the second derivative of 3/4*d**4 - 9/20*d**5 - 5*d + 0*d**2 + 1/10*d**6 + 0 - 1/2*d**3. Factor z(q).
3*q*(q - 1)**3
Let w(n) be the first derivative of n**7/126 - n**5/60 + 4*n + 2. Let k(l) be the first derivative of w(l). Factor k(x).
x**3*(x - 1)*(x + 1)/3
Let j(n) be the third derivative of n**3 + 0*n - 2*n**2 - 5/112*n**8 + 0 - 5/8*n**4 + 1/4*n**6 - 1/5*n**5 + 1/35*n**7. Find u such that j(u) = 0.
-1, 2/5, 1
Let a(p) = p**2 + 9*p + 2. Let i be a(-8). Let m be (-1)/3*9/i. Suppose m*f - 1/2*f**2 + 0 = 0. Calculate f.
0, 1
Suppose -5*f - 3*f = -32. Let w(m) be the third derivative of 0*m - 1/18*m**3 + 0*m**f + 0 - 3*m**2 + 1/180*m**5. Factor w(x).
(x - 1)*(x + 1)/3
Let i be 3 + (0 - (-1 + -8)). Suppose -4 = -4*t + i. Find s, given that 6*s**2 + 3*s**3 + 0*s**4 + 2*s**t - 2*s - 9*s**3 = 0.
0, 1
Factor -4 + 2 - 109*p**2 + 111*p**2.
2*(p - 1)*(p + 1)
Determine h so that 8*h + 0*h**2 + 9*h**2 - 11*h**2 - 6 = 0.
1, 3
Let b be (-6)/(-21)*-1677 - -1. Let s = b + 479. Determine r so that 2/7*r**3 + s*r + 18/7 - 10/7*r**2 = 0.
-1, 3
Suppose -7/4*y - 5/4*y**3 + 1/4 + 11/4*y**2 = 0. What is y?
1/5, 1
Determine f so that -13 - 3*f + 0*f + 22 - 3*f**2 - 3 = 0.
-2, 1
Let p(n) be the first derivative of n**4/4 + n**3/3 - n**2/2 - n + 11. Let p(z) = 0. What is z?
-1, 1
Let 18/5*v - 3/5*v**2 + 0 = 0. Calculate v.
0, 6
Let i(s) be the second derivative of -1/180*s**6 + 0*s**5 - s**2 + 0*s**3 + 0 + 2*s + 0*s**4. Let k(r) be the first derivative of i(r). Factor k(d).
-2*d**3/3
Let b(l) = -4*l**4 + 3*l**3 - 15*l**2 + 11. Let m(z) = z**4 - z**3 + 4*z**2 - 3. Let d = -7 - 15. Let c(v) = d*m(v) - 6*b(v). Let c(k) = 0. What is k?
-1, 0
Find v, given that -22*v**5 - 9*v**4 + 6*v + 20*v**5 - 21*v**3 + 9*v**2 + 17*v**5 = 0.
-1, -2/5, 0, 1
Factor 1/5*z**2 - 2/5 + 1/5*z.
(z - 1)*(z + 2)/5
Let g = -176 - -182. Let p(d) be the second derivative of -2*d - 1/10*d**5 + 1/30*d**g + 1/3*d**3 + 0*d**4 - 1/2*d**2 + 0. Factor p(k).
(k - 1)**3*(k + 1)
Let y(f) be the first derivative of f**3/9 - f**2/3 - 6. Determine z, given that y(z) = 0.
0, 2
Let i(h) be the first derivative of 4*h**3/3 + 4*h**2 - 32*h - 22. Factor i(p).
4*(p - 2)*(p + 4)
Let v(t) be the first derivative of 4/15*t**5 - 3*t + 2/3*t**3 - 2/3*t**4 - 1/3*t**2 + 2. Let g(d) be the first derivative of v(d). Factor g(l).
2*(2*l - 1)**3/3
Suppose -p + 8 = 2*f, -14 = 3*f - 3*p - 2*p. Let d be (0 + -1)/(-5 - 133/(-28)). Let 0 + 0*b + 4/9*b**d + 2/9*b**3 + 0*b**f + 2/9*b**5 = 0. Calculate b.
-1, 0
Suppose -5*i + 4 + 26 = 0. Suppose i*p - 16 = 2*p. Solve x**4 + 4*x**p - x**2 - 4*x**4 = 0.
-1, 0, 1
Let p(o) be the third derivative of -o**7/420 - o**6/120 + o**5/30 + o**4/24 - o**3/4 + 18*o**2. Factor p(q).
-(q - 1)**2*(q + 1)*(q + 3)/2
Let n = 582 - 580. Factor 0*v - 32/9*v**5 + 0 - 2/9*v**3 + 0*v**n + 16/9*v**4.
-2*v**3*(4*v - 1)**2/9
Let x = 1 - -1. Let p be 0 + ((-1)/4)/(2/(-10)). Factor 0*o + o**3 + 0 + 1/2*o**5 + 1/4*o**x + p*o**4.
o**2*(o + 1)**2*(2*o + 1)/4
Factor 4/3*o**3 - 10/3*o**2 + 0 + 2/3*o**4 - 4*o.
2*o*(o - 2)*(o + 1)*(o + 3)/3
Let g = 11 + -9. Suppose c = -0*w - 4*w + g, 0 = -2*c + 4*w + 4. Solve -2*t**3 - 24*t**2 + 24*t**c - 6*t**4 = 0 for t.
-1/3, 0
Let g = 18301/60 + -305. Let t(q) be the third derivative of 0*q + 0*q**3 + 1/60*q**4 + 0 - g*q**5 - q**2. Factor t(y).
-y*(5*y - 2)/5
Let h(m) = m**3 - 4*m**2 + 2*m. Let b be h(3). Let g(t) = -t - 3. Let f be g(b). Factor -c**3 - 2*c**2 + f*c**3 + 2*c**3 + c.
c*(c - 1)**2
Let r be (-312)/(-22) - (-2)/(-11). Let a be 4/r + (-38)/(-14). Factor -2/7*o**a + 0 + 0*o**2 + 2/7*o.
-2*o*(o - 1)*(o + 1)/7
Suppose r + 4*p = 0, 3*r + 3*p - 4*p = 13. Find f, given that 2/5*f**5 + 0 + 0*f**r + 0*f**2 + 2/5*f - 4/5*f**3 = 0.
-1, 0, 1
Let d = -105 + 107. Factor -15/2*c**2 - 13/4*c - 1/2 - d*c**4 - 7*c**3.
-(c + 2)*(2*c + 1)**3/4
Let z(t) be the second derivative of -t**5/25 - 4*t**4/15 + 28*t. Factor z(h).
-4*h**2*(h + 4)/5
Let t(v) = -4*v**3 + 6*v**2 - 2*v + 3. Let a be 2 - (2 - -2) - -5. Let d(q) = q**2 - 1. Let b(x) = a*d(x) + t(x). Factor b(l).
-l*(l - 2)*(4*l - 1)
Let v = -13 - -23. Suppose 5*k - v*k + 10 = 0. Factor -5/2*u**3 - 6*u**k - 9/2*u - 1.
-(u + 1)**2*(5*u + 2)/2
Let n(z) be the third derivative of z**10/30240 + z**9/15120 - z**8/6720 - z**7/2520 - z**4/24 + z**2. Let k(t) be the second derivative of n(t). Factor k(l).
l**2*(l - 1)*(l + 1)**2
Determine t, given that -2/3*t**3 + 0*t - 1/6*t**4 + 0*t**2 + 0 = 0.
-4, 0
Let u(b) = b**2 - 6*b + 7. Let f be u(2). Let t(n) = -4*n - 2. Let p be t(f). Factor 0*v**3 + 0*v - 2/11 - 2/11*v**4 + 4/11*v**p.
-2*(v - 1)**2*(v + 1)**2/11
Let u = -20 - -22. Determine j so that -2/7*j**u + 0 + 2/7*j**4 + 0*j + 2/7*j**5 - 2/7*j**3 = 0.
-1, 0, 1
Let i(p) be the first derivative of p**4/6 - 2*p**3/9 - 9. Factor i(l).
2*l**2*(l - 1)/3
Let r(g) be the third derivative of g