ppose -2 = -v + g. Find m, given that 0*m - 3/2*m**4 - 1/2*m**v - 3/2*m**3 - 1/2*m**2 + 0 = 0.
-1, 0
Suppose 0 = -4*c - 4*f + 24, -3*f + 25 = 5*c + 3. Factor -2/9*r + 2/9*r**c + 0.
2*r*(r - 1)/9
Factor -8*j**2 + j - 4*j**3 + 5*j - 2*j - 4 + 12.
-4*(j - 1)*(j + 1)*(j + 2)
Suppose 4*o = 12, 2 = 5*j + 4*o - 35. Let c = 4 + -1. Solve -j*h**3 + h**3 + 5*h**c + 0*h**3 = 0 for h.
0
Factor 63*j**2 - 15 + 11 + 3*j**4 - 36*j**3 + 4 - 30*j.
3*j*(j - 10)*(j - 1)**2
Let v(q) be the third derivative of -q**8/10080 - q**7/630 - q**6/90 + q**5/30 + 3*q**2. Let o(u) be the third derivative of v(u). Factor o(c).
-2*(c + 2)**2
Let j(b) be the first derivative of b**3/4 - 15*b**2/8 - 7. Let j(n) = 0. Calculate n.
0, 5
Let x = -90/13 - 2007/65. Let b = x + 38. Factor b*j**4 - 4/5*j**3 - 2/5*j + 0 + j**2.
j*(j - 2)*(j - 1)**2/5
Let y(u) = 2*u**2 - 12*u - 36. Let l(r) = r**2 + r - 1. Suppose 2*x - 1 = -4*j - 5, -5*j + 13 = -2*x. Let n(m) = j*y(m) - 4*l(m). Factor n(t).
-2*(t + 4)**2
Let y(j) = -j**3 - 12*j**2 + 50*j - 62. Let o(a) = a**3 - a - 1. Let l(r) = -2*o(r) - y(r). Factor l(w).
-(w - 4)**3
Let h(v) be the second derivative of v**4/66 + v**3/11 + 2*v**2/11 - 13*v. Let h(n) = 0. What is n?
-2, -1
Suppose -3*c = -c. Suppose c = -2*n + 3*y + 6, -5*n + 3*n = 2*y - 16. Suppose -n + 2*i - 4*i**2 + 6 + 2*i**3 = 0. Calculate i.
0, 1
Let a(x) be the first derivative of x**7/3360 - x**6/1440 - 4*x**3/3 - 4. Let o(p) be the third derivative of a(p). Factor o(w).
w**2*(w - 1)/4
Let g(m) be the first derivative of m**5/5 - m**4 + 2*m**3 - 2*m**2 + m - 7. Let g(n) = 0. Calculate n.
1
Let u(i) = 6*i**2 + 40*i + 96. Let a(k) = 4*k**2 + 27*k + 64. Let s(n) = 8*a(n) - 5*u(n). Factor s(q).
2*(q + 4)**2
Let v(u) be the third derivative of -u**6/180 + u**5/90 + 5*u**4/36 + u**3/3 + 7*u**2. Find i, given that v(i) = 0.
-1, 3
Let n(d) be the first derivative of 4/3*d**3 - 3 + 0*d + 2*d**4 + 4/5*d**5 + 0*d**2. Solve n(p) = 0.
-1, 0
Let g(i) = -4*i - 5 + 3*i + 5 - i**2. Let l(m) = 5*m**4 + 7*m**3 + 11*m**2 + 9*m. Let u(y) = 18*g(y) + 2*l(y). Factor u(k).
2*k**2*(k + 1)*(5*k + 2)
Suppose 8*b - 5*t - 6 = 4*b, 3*t - 2 = b. Let 0*c + 0 + 1/4*c**2 + 1/2*c**3 + 1/4*c**b = 0. Calculate c.
-1, 0
Let f(p) be the second derivative of -p**7/15120 + p**6/2160 - p**5/720 - p**4/6 - 6*p. Let m(v) be the third derivative of f(v). Suppose m(s) = 0. What is s?
1
Let z(k) be the first derivative of -k**3/21 + 4*k**2/7 - 16*k/7 - 2. Factor z(c).
-(c - 4)**2/7
Let i(y) be the second derivative of -y**2 + 0 - 2/3*y**3 + y - 1/6*y**4. Factor i(b).
-2*(b + 1)**2
Let p(o) = -9*o**5 - 9*o**4 + 4*o**3 + 4*o**2 - 4*o. Let q(x) = -80*x**5 - 80*x**4 + 35*x**3 + 35*x**2 - 35*x. Let b(d) = 35*p(d) - 4*q(d). Factor b(a).
5*a**4*(a + 1)
Let l(v) = 2*v**3 + 5*v**2 - 22*v + 12. Let b(u) = 7*u**3 + 15*u**2 - 67*u + 37. Let h(c) = -3*b(c) + 8*l(c). Factor h(p).
-5*(p - 1)**2*(p + 3)
Let i(r) be the third derivative of r**9/181440 + r**8/60480 + r**5/60 + 2*r**2. Let o(f) be the third derivative of i(f). Factor o(c).
c**2*(c + 1)/3
Find k such that 0 - 1/3*k**3 - 1/3*k + 2/3*k**2 = 0.
0, 1
Let r = -6 + 9. Let w(y) be the second derivative of 0 + 1/48*y**4 - 1/6*y**r + y + 1/2*y**2. Suppose w(d) = 0. Calculate d.
2
Factor -48 + 9*f**2 + 3/2*f**3 + 0*f.
3*(f - 2)*(f + 4)**2/2
Let n be (-416)/(-68) - 4/34. Factor 3/2*y**2 + 0*y - n.
3*(y - 2)*(y + 2)/2
Let m = 634 - 1267/2. Factor 0 - m*n**2 - 1/2*n.
-n*(n + 1)/2
Suppose s = 4*i + 107 - 29, 3*s + 13 = -i. Let p = -37/2 - i. Factor -1/2*v**2 + 0 + p*v.
-v*(v - 1)/2
Find v, given that -1/3 + 13/6*v + 11/6*v**4 - 13/6*v**3 - 3/2*v**2 = 0.
-1, 2/11, 1
Let f(y) = -3*y + 6. Let v be f(-6). Factor -24 - l**5 + v - 5*l**4 - 4*l**2 - 8*l**3.
-l**2*(l + 1)*(l + 2)**2
Factor -15 + 27 + 48*f + 26*f**3 + 69*f**2 + 9*f**4 + 16*f**3.
3*(f + 1)**2*(f + 2)*(3*f + 2)
Let p(g) be the third derivative of 0*g**3 + 3*g**2 - 1/320*g**6 + 0 + 0*g - 1/80*g**5 - 1/64*g**4. Solve p(a) = 0 for a.
-1, 0
Let t(h) be the second derivative of h**7/189 - h**5/45 + h**3/27 - h. Find u such that t(u) = 0.
-1, 0, 1
Let i(a) be the first derivative of -4*a + 2/3*a**3 + 2 - a**2. Factor i(q).
2*(q - 2)*(q + 1)
Suppose 5*r - 19 = -a - 62, 0 = -4*r + 4*a - 20. Let c be ((-5)/(-1))/((-44)/r). Factor 4/11*v**5 + c*v**4 + 2/11*v**2 + 8/11*v**3 + 0*v + 0.
2*v**2*(v + 1)**2*(2*v + 1)/11
Let r = 27 + -13. Suppose 5*p - r = 6. Let -5*k**4 - 10*k**p + 6*k**2 + 5*k**3 + k**3 + 3*k**3 = 0. What is k?
-2/5, 0, 1
Solve -1/6*u**3 + 0 + 0*u**2 + 0*u = 0.
0
Let h be (-1)/((-10)/4) - 119/1785. Let 0*p + h*p**4 + 0*p**2 - 1/3*p**3 + 0 = 0. What is p?
0, 1
Let f(a) be the first derivative of -2 - 9/2*a - 1/6*a**3 + 3/2*a**2. Factor f(w).
-(w - 3)**2/2
Solve -8/5*j**3 + 2/5*j**4 + 2*j**2 + 0 - 4/5*j = 0 for j.
0, 1, 2
Find v, given that -4/3 - 2*v + 2/3*v**2 + 2*v**3 + 2/3*v**4 = 0.
-2, -1, 1
Suppose -m = -5*c + 37 - 15, -3*m = 4*c - 10. Factor 3*d**2 + c*d**3 - 4*d**4 - 4*d**5 + 2*d**2 - d**2.
-4*d**2*(d - 1)*(d + 1)**2
Let a = 20 + -14. Suppose u + u = a. Factor 6*s**2 - u - s**3 - s**3 - 5.
-2*(s - 2)**2*(s + 1)
Suppose 0 = n - 6*n + 25. Let x(r) be the third derivative of 2*r**2 + 0*r**4 + 1/30*r**n + 0*r - 1/3*r**3 + 0. What is w in x(w) = 0?
-1, 1
Let v(u) = -u**4 + 21*u**3 - 77*u**2 + 80*u - 23. Let m(h) = -h**4 + h**3 - h**2 + 1. Let o(j) = 5*m(j) - v(j). Factor o(z).
-4*(z - 1)**3*(z + 7)
What is d in -2/5*d**2 - 26/5 + 28/5*d = 0?
1, 13
Let y(b) be the second derivative of b**4/42 - 4*b**3/21 + 4*b**2/7 - 18*b. Let y(q) = 0. What is q?
2
Let n(z) be the second derivative of -z**4/54 + 2*z**3/27 + 8*z**2/9 - z - 6. Factor n(s).
-2*(s - 4)*(s + 2)/9
Let u(m) be the second derivative of -m**4/42 + 2*m**3/7 - 9*m**2/7 + 16*m. Find r such that u(r) = 0.
3
Let l(h) be the second derivative of 3*h**6/10 + 21*h**5/20 + h**4/12 - 3*h**3/2 + h**2 - 4*h. Let l(x) = 0. What is x?
-2, -1, 1/3
Suppose f = -c - 6 + 5, 3 = -f. Let 0 + c*l**4 - 9/2*l**3 - 1/2*l + 3*l**2 = 0. Calculate l.
0, 1/4, 1
Let g(o) be the second derivative of 5*o**7/84 + o**6/4 + o**5/4 - 4*o. Let g(l) = 0. Calculate l.
-2, -1, 0
Factor 0*h**2 + 3/5*h**3 + 0 + 0*h.
3*h**3/5
Suppose -3 - 3 = -2*v. Factor 10*p**2 + 6*p**2 + 6*p**4 - 3*p + v*p**3 - 22*p**2.
3*p*(p - 1)*(p + 1)*(2*p + 1)
Let x(z) be the second derivative of z**6/6 - z**5/4 - 5*z**4/4 + 5*z**3/6 + 5*z**2 - 12*z. Factor x(v).
5*(v - 2)*(v - 1)*(v + 1)**2
Factor 2*n**2 - 8/9*n + 2/9*n**4 - 8/3 + 4/3*n**3.
2*(n - 1)*(n + 2)**2*(n + 3)/9
Let q(z) = -z**4 - z**3 + 3*z**2. Let r(v) = v**3 - v**2 - 1. Suppose 4*j - 4*h + 12 = 0, 3*j - 4*h = -7 - 6. Let b(l) = j*q(l) + r(l). Factor b(p).
-(p - 1)**2*(p + 1)**2
Let d(c) = 0*c + 10 - 6*c + 4*c**2 - 3*c**2 - 3. Let t be d(5). Determine h so that 4*h**2 + h**3 - t*h**2 - 3*h**3 = 0.
0, 1
Let a be 4 + (-3)/(24/31). Let b(f) be the second derivative of 1/60*f**6 - 1/24*f**3 + 1/16*f**4 - a*f**2 + 1/16*f**5 + 0 - f. Factor b(u).
(u + 1)**3*(2*u - 1)/4
Let v(w) = w**5 + 2*w**4 + 4*w**3 - 14*w**2 - 13*w - 8. Let g(p) = p**3 - p**2 - p - 1. Let l(q) = 30*g(q) - 5*v(q). Factor l(x).
-5*(x - 2)*(x + 1)**4
Let k(g) be the second derivative of 9*g**5/20 - 13*g**4/4 + 13*g**3/2 - 9*g**2/2 + 47*g. Let k(n) = 0. Calculate n.
1/3, 1, 3
Let r(q) be the third derivative of 0*q**3 - 1/70*q**7 + 0*q + 3*q**2 + 1/12*q**4 + 7/60*q**5 + 1/60*q**6 + 0. Factor r(h).
-h*(h - 2)*(h + 1)*(3*h + 1)
Let u be 20/12 + 2/(-3). Let x be (-1 + 3)/(u/4). Find w such that 4*w**3 - 12*w**2 - x - 1/2*w**4 + 16*w = 0.
2
Factor 0*o**2 - 1/8*o**3 + 0*o + 0 - 1/8*o**4.
-o**3*(o + 1)/8
Suppose 25 - 3 = 11*g. Let 2/5*b - 1/5*b**g - 1/5 = 0. Calculate b.
1
Let t(g) = -g**2 - g. Let l(m) = m**3 + 3*m**2 + 3*m. Let o(z) = -l(z) - 3*t(z). Suppose o(f) = 0. Calculate f.
0
Let w = 3631 + -7091/2. Let y = w + -84. What is o in 3*o - y*o**2 - 3/2 = 0?
1
Suppose 50/3*n**3 - 30*n**2 - 8/3 + 16*n = 0. What is n?
2/5, 1
Let b = 62/111 + 4/37. Let 2/9*r**3 + 4/9 + 0*r**2 - b*r = 0. What is r?
-2, 1
Let b(m) be the first derivative of -2*m**5/5 - 7*m**4/8 - m**3/3 + m**2/4 - 13. Factor b(r).
-r*(r + 1)**2*(4*r - 1)/2
Suppose 3 = 2*g + 3*v - 20, 3*g = 5*v - 13. Let -12*q**4 + 32*q**g - 20*q**2 + 8*q**4 - 8 + 2*q**3 + 34*q**3 - 36*q = 0. Calculate q.
-1, -2/7, 1
Let n(p) be the second derivative of 5*p**4/12 - 10*p**