d n such that f(n) = 0.
-2, 0
Let y be ((-1)/(-2))/((-5)/(-50)). Suppose -3 = -4*g + 5*f, y = 2*g - 0*g + f. Determine m, given that g*m - 4*m**3 - 4 + 5 + 9*m**2 - 8*m = 0.
1/4, 1
Let i = -5/4 + 3/2. Let j(w) be the first derivative of 1/12*w**3 - 1 - i*w**2 + 1/4*w. Let j(n) = 0. What is n?
1
Let d = -324 - -2921/9. Factor 4/9 - d*z + 1/9*z**2.
(z - 4)*(z - 1)/9
Let j = -103/150 + 18/25. Let z(l) be the second derivative of 0 - j*l**6 - 1/2*l**2 + 0*l**3 + 1/6*l**4 + 0*l**5 + 2*l. Factor z(d).
-(d - 1)**2*(d + 1)**2
Suppose -1/2 - 5/4*w**2 - 7/4*w = 0. Calculate w.
-1, -2/5
Let q(d) = -d + 16. Let u be q(10). Suppose 0 = l - u + 1. Factor 8*r + 29*r**2 + 0*r**4 - l*r**2 + 6*r**4 - r**3 + 23*r**3.
2*r*(r + 1)*(r + 2)*(3*r + 2)
Solve 3 - 9/2*v**2 - 3/2*v + 3/2*v**3 + 3/2*v**4 = 0.
-2, -1, 1
Let u = -14/615 + 514/615. Let f = -6/41 + u. Factor -4/3*t**4 + 0*t**2 + 2/3*t**3 + 0 + f*t**5 + 0*t.
2*t**3*(t - 1)**2/3
Let a = 14 - 10. Suppose 0 = 5*u - 18 + 8. Factor 2/5*t**a - 2/5*t**5 + 0 + 0*t**u + 0*t**3 + 0*t.
-2*t**4*(t - 1)/5
Let r = 27/20 - 3/5. Let i = -190 - -381/2. Let -i - 5/4*b - r*b**2 = 0. What is b?
-1, -2/3
Let r = -6324/259 - -174/37. Let d = 20 + r. Find g such that 10/7*g**4 + 2/7*g - 6/7*g**3 - 4/7*g**5 + 0 - d*g**2 = 0.
-1/2, 0, 1
Let q(x) be the second derivative of 0 + 0*x**2 - 1/24*x**4 - 1/12*x**3 - 2*x. Let q(o) = 0. Calculate o.
-1, 0
Suppose 0 = 3*l + d - 30, 5*l - 5*d - 114 = -44. Factor -1 + l*a - 11*a + a**2.
(a - 1)*(a + 1)
Factor -24*w**2 - 15*w**5 - 27*w - 14*w**4 + 12*w**5 - 26*w**3 + 16*w - 2.
-(w + 1)**4*(3*w + 2)
Let x(w) = -w**2 - 2*w - 6. Let s(z) = -z + 1. Let u(j) = -2*s(j) - x(j). Factor u(b).
(b + 2)**2
Let k be (4/(-14))/((-13)/(819/108)). Factor -k*p**2 + 1/3 - 1/6*p.
-(p - 1)*(p + 2)/6
Let 40/3*c**2 + 16/3*c**3 + 17/3*c + 2/3 = 0. Calculate c.
-2, -1/4
Suppose -15 = 5*c, 4*i + 28 = c + 3*c. Let v = i - -12. Factor p**v + 1/2 + 9/4*p.
(p + 2)*(4*p + 1)/4
Solve 5*l - 3 - 1 - l - l**2 = 0 for l.
2
Let f(u) be the second derivative of -u**5/4 - u**4/4 + u**3/3 - 9*u. Suppose f(j) = 0. Calculate j.
-1, 0, 2/5
Let x(f) be the second derivative of 3*f**5/20 - f**3/2 - 5*f. Factor x(o).
3*o*(o - 1)*(o + 1)
Find q such that -5*q**2 + 7*q**3 - 19*q**2 - 3*q**4 - 37*q**3 - 51*q**2 = 0.
-5, 0
Let s be (-18)/(-140) - (-18)/(-30). Let w = 1/35 - s. What is h in 1/2 - 1/2*h**2 + w*h - 1/2*h**3 = 0?
-1, 1
Let j(p) be the third derivative of -p**8/672 + p**7/210 - p**6/240 + 2*p**2. Factor j(x).
-x**3*(x - 1)**2/2
Let o(w) = 40*w**3 + 88*w**2 + 56*w + 13. Let j(t) = 260*t**3 + 572*t**2 + 364*t + 84. Let y(n) = -5*j(n) + 32*o(n). Factor y(f).
-4*(f + 1)**2*(5*f + 1)
Let c(w) be the second derivative of -w**4/3 + 2*w**3/3 - 4*w. Factor c(l).
-4*l*(l - 1)
Let j(i) be the second derivative of 2*i - 1/80*i**5 + 0*i**2 + 1/60*i**6 - 1/168*i**7 + 0*i**3 + 0*i**4 + 0. Factor j(c).
-c**3*(c - 1)**2/4
Suppose 2*p = -n - 8, -5*n + 12 = -4*p - 18. Suppose h - n = -0*h. Determine l so that h*l**3 + 12*l + 6*l**4 - 12*l = 0.
-1/3, 0
Let c(b) be the third derivative of -1/735*b**7 + 0*b + 2*b**2 + 0 + 0*b**5 + 0*b**4 + 0*b**3 + 1/420*b**6. Factor c(q).
-2*q**3*(q - 1)/7
Suppose 0 = 2*d - u + 6*u - 25, d - 4*u + 20 = 0. Suppose d = 5*o - 2*o - 12. Find g, given that -1/4*g**3 + 0 - 1/4*g**2 + 1/4*g**o + 1/4*g = 0.
-1, 0, 1
Solve -3/4*b**2 + 0 + 3/2*b = 0 for b.
0, 2
Suppose 5*f = 4*v + 1, 0*v + f = 5*v - 4. Suppose z - v = -0*z. Factor -j**2 + 7/2*j - 7/2*j**3 + z.
-(j - 1)*(j + 1)*(7*j + 2)/2
Suppose 2*a + 5 = 5*s, -4*a - 2*s = -4*s - 14. Let m(f) be the third derivative of -3*f**2 + 0 + 0*f**3 + 1/120*f**a + 0*f + 1/48*f**4. Factor m(y).
y*(y + 1)/2
Suppose 5*o + 196 = 216. Let w(c) be the third derivative of 1/3*c**3 - 1/60*c**5 + 0*c + o*c**2 + 0 + 1/24*c**4. Factor w(y).
-(y - 2)*(y + 1)
Let g be (6/(-14))/(60/(-105)). Factor -g*n**2 + 3/4*n**3 - 3/4*n + 3/4*n**4 + 0.
3*n*(n - 1)*(n + 1)**2/4
Let n = -307/24 - -105/8. Factor -1/3*l + 2/3*l**3 + 0*l**4 + 0*l**2 + 0 - n*l**5.
-l*(l - 1)**2*(l + 1)**2/3
Factor -2/7*d**2 + 4/7*d + 0.
-2*d*(d - 2)/7
Let g(m) be the first derivative of m**6/300 - m**4/60 - 2*m**2 + 6. Let u(n) be the second derivative of g(n). Factor u(i).
2*i*(i - 1)*(i + 1)/5
Let f(u) be the third derivative of 1/660*u**6 + 0*u**3 + 3*u**2 + 0 + 1/1155*u**7 + 0*u - 1/132*u**4 - 1/330*u**5. Factor f(d).
2*d*(d - 1)*(d + 1)**2/11
Let r = 29 + -29. Let s(y) be the first derivative of -1 + 1/8*y**4 + 0*y + r*y**2 - 1/6*y**3. Let s(a) = 0. What is a?
0, 1
Factor 2/7*b + 0 + 2/7*b**4 - 2/7*b**3 - 2/7*b**2.
2*b*(b - 1)**2*(b + 1)/7
Suppose -5*i = 20, 3*i + 3 + 3 = -2*t. Factor -3*n**t + n + 2*n + 0*n.
-3*n*(n - 1)*(n + 1)
Suppose 0 = -0*o + o - 2. Factor -2*u**4 + 2*u**2 - 2*u**o + u**4.
-u**4
Let p be 1/((6/9)/2). Factor 2*k**2 + 0*k**2 + 2*k**2 - p*k**2.
k**2
Let l(s) be the first derivative of -2*s**5/45 + s**4/18 + 19. Let l(m) = 0. Calculate m.
0, 1
Let v(h) be the second derivative of h**6/35 + h**5/70 - h**4/21 + 12*h. Suppose v(u) = 0. Calculate u.
-1, 0, 2/3
Suppose -5*h = -t + 8, 0*t + 4*h = 5*t - 19. Suppose 4 = t*u + 2*l - 2, 0 = 4*u - 5*l - 8. Solve 6*c**2 - c - 1 + 3 - 5*c - u*c**3 = 0 for c.
1
Let n = 0 + 0. Let u = 48 + -45. Factor -2/3*s**u + 2/3*s + 0 + n*s**2.
-2*s*(s - 1)*(s + 1)/3
Suppose 8 = -a + 2*m, 11 = -a + 5*m - 12. Factor -2 + 0*p**2 + 2*p**2 + 0 - 3*p**a - 3*p.
-(p + 1)*(p + 2)
Let u = -1 + 5. Suppose -2*d**u - 2*d + 4*d + 2*d**2 - 3*d**3 + d**3 = 0. Calculate d.
-1, 0, 1
Factor 48*l**2 - 56*l**3 - 13*l**2 - 30*l + 51*l**3.
-5*l*(l - 6)*(l - 1)
Let y(n) be the first derivative of 1/12*n**4 + 2*n**2 + 3 + 8/3*n + 2/3*n**3. Factor y(k).
(k + 2)**3/3
Let b(x) be the second derivative of -1/6*x**3 + 0*x**2 + 0 + 1/12*x**4 - 2*x. Let b(a) = 0. What is a?
0, 1
Let o = -799/3 + 267. Find m, given that o + m - 1/3*m**3 + 0*m**2 = 0.
-1, 2
Let z(f) be the second derivative of -1/5*f**2 - 2*f + 1/30*f**3 + 1/60*f**4 + 0. Factor z(x).
(x - 1)*(x + 2)/5
Let z(h) = 4*h**4 + 21*h**3 + 29*h**2 + 16*h + 9. Let q(p) = -p**3 - p**2 - 1. Let d(x) = 5*q(x) + z(x). Factor d(j).
4*(j + 1)**4
Let o be 12/(-40)*12/(-3). Find w, given that -o*w**2 - 2/5 + 2/5*w**3 + 6/5*w = 0.
1
Let w(k) = -2*k. Let a be w(-3). Factor -56*h**2 - 32*h - 2*h**5 + a*h**2 - 38*h**3 - 4*h**5 - 14*h**4 + 4*h**5 - 8.
-2*(h + 1)**3*(h + 2)**2
Let l(j) be the third derivative of -j**5/12 + 5*j**3/6 - 13*j**2. Suppose l(i) = 0. What is i?
-1, 1
Let q(s) be the first derivative of -9*s**5/40 - 3*s**4/8 - s**3/8 - 17. What is g in q(g) = 0?
-1, -1/3, 0
Let u(f) be the second derivative of -4*f - 5/3*f**3 + 2*f**2 + 0 - 1/10*f**5 + 2/3*f**4. Determine w, given that u(w) = 0.
1, 2
Let 2/3*s**2 - 2/3*s**3 - 2/3 + 2/3*s = 0. What is s?
-1, 1
Let u(t) be the second derivative of t**6/6 - 5*t**4/3 + 20*t. Factor u(y).
5*y**2*(y - 2)*(y + 2)
Suppose -99/2*d**2 - 27 + 135/2*d + 29/2*d**3 - 3/2*d**4 = 0. What is d?
2/3, 3
Let y(s) = s**3 - s**2 + 1. Suppose -u + 0*u = 1. Let w be y(u). Let j(p) = -p**2 + 9*p - 2. Let t(q) = -q**2 + q - 1. Let o(x) = w*j(x) + 4*t(x). Factor o(m).
-(m + 1)*(3*m + 2)
Suppose 2/7*y - 4/7 + 2/7*y**2 = 0. What is y?
-2, 1
Solve 10/13*w**3 + 14/13*w**4 - 18/13*w**2 - 10/13*w + 4/13 = 0 for w.
-1, 2/7, 1
Suppose -t - 3 = 3*i, 0*t + 5*t = 15. Let g be i/56 + 14/49. Factor -g*a**2 + 0 + 0*a.
-a**2/4
Let q(s) = 8*s**2 - 43*s + 45. Let p(y) = 4*y**2 - 22*y + 22. Let w(r) = -5*p(r) + 2*q(r). Factor w(h).
-4*(h - 5)*(h - 1)
Determine y so that -2*y**2 - 2*y**3 - 461*y + 461*y - 24*y**2 = 0.
-13, 0
Let s(z) be the first derivative of 1/3*z**2 + 11/18*z**3 + 1 + 1/4*z**4 - 4*z. Let l(n) be the first derivative of s(n). Suppose l(m) = 0. Calculate m.
-1, -2/9
Let h(f) = -f**2 + 13*f + 3. Let q(u) = 14*u**2 - 1. Let t be q(-1). Let a be h(t). Factor 1/3*o**2 - 2/3*o**a + 0 + 1/3*o.
-o*(o - 1)*(2*o + 1)/3
Let d be (-2)/(-6) + (-33)/(-9). Let y(b) = -3*b - 3. Let o be y(-2). Factor 11*x**o - 9*x**3 + 12*x**3 - d*x**2.
2*x**2*(7*x - 2)
Let s(r) = r**2 - 4*r + 3. Let g be s(4). Let -2*l**3 - l + 5*l**g - 2*l**3 = 0. What is l?
-1, 0, 1
Factor 6/5 + 22/5*g - 8/5*g**2.
-2*(g - 3)*(4*g + 1)/5
Determine d so that 0 + 8/11*d + 50/11*d**3 - 40/11*d**2 = 0.
0, 2/5
Let z(s) be the third derivative of -2*s**2 - 5/144*s**4 + 1/180*s**5 - 1/2016*s**8 +