*g + 1/5 = 0. What is g?
-1, 1
Suppose -g + 33 + 12 = 3*h, -4*h = -g + 10. Let x be 24/g*5/2. Factor -1 + x*w**3 + 6*w - 6*w**2 + 0 - 1.
2*(w - 1)**3
Factor -44*y**2 - 82*y + 45*y + 45*y.
-4*y*(11*y - 2)
Solve 2*k**2 + 0 - 8/3*k**3 + 0*k = 0.
0, 3/4
Suppose -38*f + 18 = -29*f. Let t(w) = -w**3 + 5*w**2 + 2*w - 6. Let n be t(5). Suppose -3*z**2 - 1 + f*z - n*z**2 + 6*z**2 = 0. Calculate z.
1
Let o = 2/1145 - -11428/12595. Suppose -4/11 + 34/11*r**3 - 42/11*r**2 + 2*r - o*r**4 = 0. Calculate r.
2/5, 1
Factor -2*o**2 + o**2 - 1 - 3*o**2 + 5.
-4*(o - 1)*(o + 1)
Let s = 361/19470 - 1/295. Let a(d) be the second derivative of 0*d**3 + 0 + s*d**4 + d + 1/55*d**5 - 1/55*d**6 + 0*d**2. Factor a(h).
-2*h**2*(h - 1)*(3*h + 1)/11
Let d(s) = 2*s**2 - 9*s - 3. Let k be d(5). Solve -2*p**4 + 5*p**k - 12*p**3 - 5*p**2 - 6*p**2 + 9 + 12*p - p**4 = 0.
-3, -1, 1
Let y = -13 + 18. Let h(r) be the third derivative of 0*r**3 - 2*r**2 + 0*r + 1/420*r**6 + 0 + 0*r**4 + 0*r**y. Let h(x) = 0. Calculate x.
0
Let i be (0 - 7/3)*(-8)/28. Determine n, given that -2*n**2 - 2/3 + i*n**3 + 2*n = 0.
1
Let g = 4555154/5607 + 19/801. Let u = g - 811. Factor 20/7*v**3 + u*v + 10/7*v**4 + 2/7*v**5 + 2/7 + 20/7*v**2.
2*(v + 1)**5/7
Let s(b) be the first derivative of b**4/36 - 4*b + 1. Let d(o) be the first derivative of s(o). Factor d(w).
w**2/3
Let p(y) be the second derivative of -1/18*y**4 + 0*y**3 + 0 - 3*y + 0*y**2. Let p(i) = 0. What is i?
0
Suppose -5*d + 3*z = -3*d + 2, 5*d + z - 12 = 0. Let r(u) be the first derivative of 2 + 8/3*u**3 + 0*u**d + 0*u + 2*u**4 - 6/5*u**5. Factor r(b).
-2*b**2*(b - 2)*(3*b + 2)
Suppose 23 + 5 = 7*b. Suppose u = -b*u + 4*r, 2*u - r = 0. Factor 2/7*p**3 + 2/7*p**4 + u*p + 0 - 4/7*p**2.
2*p**2*(p - 1)*(p + 2)/7
Let b(h) be the second derivative of -h**6/6 + 3*h**5/4 - 5*h**4/4 + 5*h**3/6 + 2*h. Find u such that b(u) = 0.
0, 1
Let f(v) be the third derivative of -1/24*v**4 + 0 + 1/60*v**5 + 4*v**2 - 1/6*v**3 + 1/120*v**6 + 0*v. Factor f(x).
(x - 1)*(x + 1)**2
Let y = -2234/153 - -252/17. Determine x so that -2/3*x**2 - y - 2/3*x - 2/9*x**3 = 0.
-1
Let q(b) = 10*b**2 + 32*b + 16. Let l(a) = 2*a**2 + 6*a + 3. Let m(n) = -16*l(n) + 3*q(n). Suppose m(f) = 0. What is f?
0
Let m(f) be the second derivative of f**6/195 - f**4/78 + 4*f. Suppose m(k) = 0. Calculate k.
-1, 0, 1
Let y(d) = -9*d**4 + 3*d**3 + 18*d**2 - 21*d + 9. Let p(q) = 5*q**4 - 2*q**3 - 9*q**2 + 10*q - 4. Let o(z) = 9*p(z) + 4*y(z). Find i, given that o(i) = 0.
-1, 0, 2/3, 1
Let t(h) be the second derivative of h**4/9 + 10*h**3/9 + 8*h**2/3 + 18*h. Suppose t(l) = 0. Calculate l.
-4, -1
Suppose -2*f - 20 = 3*f. Let s be (0 - -2)/((-2)/f). Find y such that -2*y**4 - 8*y**3 + 14*y**5 - 6*y**3 - 2*y**4 + s*y**2 = 0.
-1, 0, 2/7, 1
Let k be (-1)/4 + 18/8. Determine x so that 5*x - 6*x**k - 2*x**2 + 12*x**3 + x + 2*x**5 - 4*x - 8*x**4 = 0.
0, 1
Suppose -5*f - 6*q + 18 = -3*q, 2*f = -5*q + 11. Let l(g) be the second derivative of 1/30*g**4 - 1/15*g**f + 0 + 0*g**2 - 2*g. Factor l(k).
2*k*(k - 1)/5
Let u(x) be the first derivative of x**4/4 + 4*x**3 + 24*x**2 + 3*x + 2. Let d(z) be the first derivative of u(z). Factor d(h).
3*(h + 4)**2
Let j be (-4)/(1*4/2). Let r be (-2 - j) + (2 - 0). Factor -3/4*f**3 - 1/4*f**4 - 3/4*f**r + 0 - 1/4*f.
-f*(f + 1)**3/4
Determine a, given that 2/7*a**2 + 10/7 - 12/7*a = 0.
1, 5
Determine p so that -16 + 11 + 23*p**2 - 18*p**2 = 0.
-1, 1
Let g(i) be the first derivative of i**7/105 + i**6/15 + i**5/10 - i**4/3 - 4*i**3/3 + i**2 - 2. Let d(v) be the second derivative of g(v). Solve d(h) = 0.
-2, -1, 1
Let i be 8/(-3)*9/(-2). Let k be 1/(2*(-2)/i). Let y(h) = 4*h**2 + 4*h - 6. Let t(n) = -5*n**2 - 5*n + 7. Let o(p) = k*y(p) - 2*t(p). Factor o(u).
-2*(u - 1)*(u + 2)
Let v(y) be the second derivative of -y**8/336 + y**6/120 + y**2 + 2*y. Let g(q) be the first derivative of v(q). Factor g(a).
-a**3*(a - 1)*(a + 1)
Let r be (-5)/(-10) + (-241)/442. Let p = r - -2280/1547. Factor -2/7*f**5 + 2/7 + 10/7*f**4 + 20/7*f**2 - 20/7*f**3 - p*f.
-2*(f - 1)**5/7
Let g(z) be the first derivative of 2/3*z + 0*z**2 - 2 - 2/9*z**3. Factor g(j).
-2*(j - 1)*(j + 1)/3
Factor -144*b**2 + b**4 + 9*b + 36*b**3 - 4*b**4 + 183*b.
-3*b*(b - 4)**3
Let f(k) = -12*k**2 + 1056*k - 6304. Let a(n) = n**2 - 96*n + 573. Let r(s) = -32*a(s) - 3*f(s). Factor r(m).
4*(m - 12)**2
Let l(b) = 2*b**3 + 5*b**2 - 3*b + 4. Let u be l(3). Let w be (-2)/9 + u/18. Determine z, given that -2*z**2 + w*z**3 - z**5 + 2*z**4 + z**5 - 5*z**5 = 0.
-1, 0, 2/5, 1
Suppose 5*h = z - 2, -z - 2*h - 10 = -6*z. Suppose z*w = 3*k + 4*w - 21, -w = 0. Let -4*m + 6*m - m**2 - k*m**2 = 0. Calculate m.
0, 1/4
Let i(v) be the first derivative of 3*v**4/8 + 3*v**3/2 - 3*v**2/4 - 9*v/2 - 6. Find j, given that i(j) = 0.
-3, -1, 1
Let t(g) be the second derivative of g**4/54 - 4*g**3/9 + 4*g**2 + 14*g. Factor t(o).
2*(o - 6)**2/9
Let j(x) be the first derivative of -3 + 3*x - 3/4*x**4 - x**3 + 3/2*x**2. Factor j(v).
-3*(v - 1)*(v + 1)**2
Let f(k) = 5*k. Let u(m) = -m**2. Let g(w) = -f(w) - u(w). Find x such that g(x) = 0.
0, 5
Let z = -5 + 9. Let -3*j**4 + 3*j**3 + 3*j**2 + 4*j**z - j**5 - 4*j**4 - 4*j**3 + 2*j = 0. Calculate j.
-2, -1, 0, 1
Let j(u) be the first derivative of u**6/15 - 2*u**4/5 - 4*u**3/15 + 3*u**2/5 + 4*u/5 + 3. Factor j(c).
2*(c - 2)*(c - 1)*(c + 1)**3/5
Let l(j) = 6*j**4 + 10*j**3 + 7*j**2 + 3*j + 5. Let y(d) = -3*d**4 - 5*d**3 - 3*d**2 - d - 2. Let s(w) = -6*l(w) - 15*y(w). Factor s(q).
3*q*(q + 1)**2*(3*q - 1)
Let v be 18*((-87)/84 - -1). Let x = v - -101/70. What is k in 2/5*k**3 + 2/5*k**2 + 0 + 0*k - x*k**4 = 0?
-1/2, 0, 1
Let a(f) = -2*f**2 - 12*f + 12. Let g = -5 - -6. Let w(u) = -u + 3*u**2 - 4*u**2 - 2 + 3. Let d(v) = g*a(v) - 4*w(v). Factor d(j).
2*(j - 2)**2
Let v(u) be the second derivative of -u**6/27 - 4*u**5/45 - u**4/54 + 2*u**3/27 - 27*u. Factor v(l).
-2*l*(l + 1)**2*(5*l - 2)/9
Let h(q) be the third derivative of q**5/60 - q**4/8 + q**3/3 - 11*q**2. Let h(s) = 0. Calculate s.
1, 2
Let u(t) be the first derivative of t**4/2 - 8*t**3/3 + 5*t**2 - 4*t - 17. Let u(z) = 0. Calculate z.
1, 2
Factor 32 - 32/9*y**3 - 128/3*y + 176/9*y**2 + 2/9*y**4.
2*(y - 6)**2*(y - 2)**2/9
Let c = -1/123 - -44/369. Let w(z) be the first derivative of 0*z + c*z**2 - 2 - 2/27*z**3. Let w(i) = 0. Calculate i.
0, 1
Suppose -2*h - 108 = 3*b - h, -2*b - 3*h = 79. Let j be -5*(-7)/(b/(-2)). Factor -6/7*q**3 - 6/7*q**4 + 0*q + 0 - 2/7*q**j - 2/7*q**5.
-2*q**2*(q + 1)**3/7
Suppose 15 = l - 1. Suppose 4*i = z - 18, -2*i - l = -0*z - 4*z. Let 0*h**z + h - 1/3*h**3 + 2/3 = 0. Calculate h.
-1, 2
Let a be 0/2 + 4 + 0. Factor s**3 + a*s**2 - 3*s**3 + s**4 - s**2 - 2*s**2.
s**2*(s - 1)**2
Let f be ((-8)/24)/(25/(-15)). Factor -f - 1/5*h**2 - 2/5*h.
-(h + 1)**2/5
Let o(b) be the third derivative of 9*b**7/14 - 9*b**6/4 + 3*b**5 - 5*b**4/3 - 20*b**2 + b. Determine p, given that o(p) = 0.
0, 2/3
Let i(m) = -8*m**2 + 21*m - 8. Let k(r) = 52*r**2 - 136*r + 52. Let a(v) = -32*i(v) - 5*k(v). Factor a(p).
-4*(p - 1)**2
Let g(b) be the first derivative of 1 + 2/3*b**2 + 2/9*b**3 + 2/3*b. Solve g(d) = 0.
-1
Let b(a) be the first derivative of -7 + 3*a**3 + 0*a - 3*a**2 - 3/5*a**5 + 0*a**4. Factor b(o).
-3*o*(o - 1)**2*(o + 2)
Suppose 0 = -2*l + 4*v - 12, 5*l + 2*v - 6 = -0. Suppose l - 1/3*i**3 + 2/3*i + 1/3*i**2 = 0. What is i?
-1, 0, 2
Let w be ((-3)/(-6))/(1/6). Factor 27*n**3 - 24*n**2 - 13*n**3 - w*n - 5*n.
2*n*(n - 2)*(7*n + 2)
Let l(b) be the first derivative of -5*b**4/4 + 35*b**3/3 - 20*b**2 - 80*b + 34. Factor l(n).
-5*(n - 4)**2*(n + 1)
Let m(k) be the second derivative of 5*k**4/48 + 5*k**3/24 - 8*k. Factor m(o).
5*o*(o + 1)/4
Let h = 41 - 35. Let g(t) be the second derivative of -3*t**3 + 0 - 4/5*t**h + 4*t + 2*t**2 + 5/3*t**4 + 2/5*t**5 + 5/21*t**7. Factor g(z).
2*(z - 1)**3*(z + 1)*(5*z - 2)
Suppose 3/5*q**2 - 3/5*q**3 + 3/5*q - 3/5 = 0. Calculate q.
-1, 1
Let w(y) be the third derivative of y**5/480 + y**4/48 - 5*y**3/48 - 22*y**2. Suppose w(x) = 0. Calculate x.
-5, 1
Let y(w) be the third derivative of -w**7/70 + 4*w**6/5 - 96*w**5/5 + 256*w**4 - 2048*w**3 - 11*w**2. Suppose y(g) = 0. Calculate g.
8
Determine t so that 0 + 2/7*t + 2/7*t**2 = 0.
-1, 0
Let w(x) be the second derivative of -x**7/1680 + x**5/240 + x**3/6 - 3*x. 