 Factor -1/4*o + 3/4*o**2 - 3/4*o**3 + m + 1/4*o**4.
o*(o - 1)**3/4
Let h(o) be the first derivative of o**4 + 11*o**3/3 - 3*o**2/2 + 15. Determine f, given that h(f) = 0.
-3, 0, 1/4
Solve 104/5*k + 18/5*k**3 + 96/5*k**2 + 32/5 = 0.
-4, -2/3
Let z(d) = 3*d - 12. Let x be z(4). Let j(g) be the third derivative of 1/60*g**5 + 0*g**3 + g**2 + 0 + x*g - 1/24*g**4. Determine h, given that j(h) = 0.
0, 1
Let f(s) be the second derivative of s**5/10 - s**3 + 2*s**2 - 5*s. Factor f(a).
2*(a - 1)**2*(a + 2)
Let f(h) be the third derivative of 0*h + 0*h**3 + 1/240*h**5 + 0*h**4 + 1/480*h**6 + 0 - 3*h**2. Factor f(t).
t**2*(t + 1)/4
Factor -4*l + 48 - 48 + 4*l**2.
4*l*(l - 1)
Let q(r) = r**3 - r + 4. Let v(w) = -1. Suppose -3*y = -0*y - 51. Suppose 4 + 3 = -j - 2*m, -2*j - 5*m = y. Let b(s) = j*q(s) - 4*v(s). Factor b(l).
-l*(l - 1)*(l + 1)
Let i(v) be the second derivative of v**7/210 - v**6/120 - v**5/20 + 5*v**4/24 - v**3/3 + v**2 + 3*v. Let a(b) be the first derivative of i(b). Factor a(c).
(c - 1)**3*(c + 2)
Suppose -4*a = -10 - 2. Suppose 2 - 6 = -2*w. Suppose 0*s**w + 2/3*s - 2/3*s**a + 0 = 0. What is s?
-1, 0, 1
Let f be -1 - -5 - (-7 + 9). Let -8/3 - 54*d**3 - 78*d**f - 80/3*d = 0. Calculate d.
-1, -2/9
Factor -8/15*u + 4/5*u**2 + 2/15*u**4 + 2/15 - 8/15*u**3.
2*(u - 1)**4/15
Let v be 6/14 - (-66)/42. Let y(p) be the first derivative of 2*p - 2*p**2 - v + 2/3*p**3. Determine c so that y(c) = 0.
1
Suppose -4*d - o - 1 = -5, -4*d = 5*o + 12. Factor 6/5*r**d - 3/5*r + 0 + 9/5*r**3.
3*r*(r + 1)*(3*r - 1)/5
Let z(i) = i**2 + i - 1. Let a be z(-2). Let k be a - (2 + -2 - 2). Let -5*w**k - w**4 + 0*w - w - 3*w**2 + 0*w + 2*w**3 = 0. What is w?
-1, 0
Factor -4*b**2 - 7*b**2 + 3*b**2 - b**3 + 2*b**2.
-b**2*(b + 6)
Let q = 7/64 + 105/64. Let z be 35/(-20) - 4/(-1). Factor z*g**2 - q*g - 1/2.
(g - 1)*(9*g + 2)/4
Let i(v) be the first derivative of -v**7/21 + 4*v**6/15 - v**5/2 + v**4/3 + 3*v - 4. Let a(c) be the first derivative of i(c). Factor a(n).
-2*n**2*(n - 2)*(n - 1)**2
Let h = -36/11 - -83/22. Determine l, given that -h*l - 1 + l**2 + 1/2*l**3 = 0.
-2, -1, 1
Suppose 3*h + s + 25 = 2*s, -22 = 3*h + 2*s. Let x = 11 + h. Let 4*d**3 + 3*d - 2*d**x + d**3 - 7*d**3 + 1 = 0. What is d?
-1/2, 1
Let o(t) = 2*t + 10. Let g be o(-5). Suppose g*l + 1/5*l**3 + 0 - 1/5*l**4 + 0*l**2 = 0. What is l?
0, 1
Let b(k) = 2*k**4 + k**3 + 2*k**2 - 3*k + 3. Let v(t) = 18*t**4 + 10*t**3 + 18*t**2 - 26*t + 26. Let l(u) = 52*b(u) - 6*v(u). Suppose l(n) = 0. Calculate n.
-1, 0
Let o(x) = -8*x**2 - 4*x - 9. Let k(h) = 20*h**2 + 3*h - 14. Let i(r) = -7*r**2 - r + 5. Let y(z) = 17*i(z) + 6*k(z). Let n(g) = 2*o(g) + 14*y(g). Factor n(t).
-2*(t - 2)*(t - 1)
Let p(m) be the second derivative of -1/3*m**3 + m**2 + 0 + 5*m + 1/10*m**5 - 1/6*m**4. Let p(c) = 0. What is c?
-1, 1
Let x = 733050047/345 + -2124781. Let t = -10/69 + x. Find g such that t*g**3 - 22/5*g - 32/5*g**4 + 28/5*g**2 + 4/5 + 14/5*g**5 = 0.
-1, 2/7, 1
Let p = -2 - -7. Suppose 0 = -t + p*t. Factor -2/3*i**2 + 0*i + t.
-2*i**2/3
Let h(a) be the first derivative of a**4/12 - a**3/3 + a + 2. Let k(i) be the first derivative of h(i). Factor k(b).
b*(b - 2)
Factor 4 - 4 - 4*a + 16*a**2 + 2*a**3 + 18*a.
2*a*(a + 1)*(a + 7)
Suppose -4*v - v + 10 = 0. Let p(r) = 7*r**3 + 1 + 4*r**3 + 2 - 24*r**2 - 20*r. Let z(t) = -t**3 - t + 1. Let i(q) = v*p(q) - 10*z(q). Factor i(d).
2*(d - 2)*(4*d + 1)**2
Suppose h + 3*h + 18 = 5*l, 4*l + 4*h = 0. Determine d so that -21/2*d**3 - 3/4*d**5 - 27/4*d - 9/2*d**4 - 3/2 - 12*d**l = 0.
-2, -1
Determine f, given that -3*f + f**2 + 115 - 55 - 58 = 0.
1, 2
Let i(n) be the first derivative of -2/9*n**3 + 4/3*n - 2 + 1/3*n**2. Factor i(s).
-2*(s - 2)*(s + 1)/3
Factor -8*q**3 + 2*q**4 - 4*q**2 - 6*q**4 + 0*q**4.
-4*q**2*(q + 1)**2
Let h(f) be the second derivative of 8*f - 4/5*f**5 - 4/15*f**6 + 0 + 0*f**3 + 2/21*f**7 + 0*f**2 + 8/3*f**4. Factor h(o).
4*o**2*(o - 2)**2*(o + 2)
Factor 0 + 2/7*n**2 - 2/7*n**4 + 4/7*n**3 - 4/7*n.
-2*n*(n - 2)*(n - 1)*(n + 1)/7
Let i(u) be the third derivative of u**7/3780 + u**6/810 + u**5/540 - 2*u**3/3 - 3*u**2. Let p(z) be the first derivative of i(z). Factor p(j).
2*j*(j + 1)**2/9
Let n(c) be the second derivative of -c**6/6 - 3*c**5/4 - 5*c**4/12 + 5*c**3/2 + 5*c**2 - 8*c. Suppose n(v) = 0. What is v?
-2, -1, 1
Let h be (0 + -2)*-3 + 2. Let j = h + -5. Factor -2*u**3 - 4 + 2*u**2 + 2 + u**j + 2*u - u**3.
-2*(u - 1)**2*(u + 1)
Factor 0 + 0*l + 2/9*l**3 + 4/9*l**2.
2*l**2*(l + 2)/9
Let n(g) = -g + 8. Let v be n(5). Let p(u) be the second derivative of 0 + 3*u - 1/6*u**4 + u**2 + 0*u**v. Factor p(x).
-2*(x - 1)*(x + 1)
Suppose -3*n + r + 1 = 0, -n - 3 = -4*n + 3*r. Solve -y**3 + 1/3*y**5 + 2/3*y**2 + 0*y + n + 0*y**4 = 0.
-2, 0, 1
Let j = -179/20 + 189/20. Factor -11/4*n**2 - j*n + 0 + 1/2*n**3 + 11/4*n**4.
n*(n - 1)*(n + 1)*(11*n + 2)/4
Let z(g) be the second derivative of -g**5/90 + g**4/54 - 3*g. Factor z(y).
-2*y**2*(y - 1)/9
Let q(t) be the first derivative of t**4/54 - 2*t**3/27 + t**2/9 + 5*t + 7. Let l(x) be the first derivative of q(x). Solve l(v) = 0.
1
Let r(l) be the third derivative of 0*l**3 + 1/28*l**7 - 5*l**2 + 0*l**4 + 0 + 0*l**5 + 0*l + 1/40*l**6. Factor r(x).
3*x**3*(5*x + 2)/2
Let w(z) = -z - 1. Let j be w(-3). Find a, given that 3*a**4 + 6*a**3 + 8*a**2 - 11*a**2 + 6*a**j = 0.
-1, 0
Let x = -9 + 11. Let q(o) be the third derivative of -1/120*o**5 - 3*o**x + 0*o**4 + 1/12*o**3 + 0*o + 0. Find i such that q(i) = 0.
-1, 1
Determine f, given that 1/4*f**5 + 0*f + 0 + 1/2*f**3 + 5/8*f**4 + 1/8*f**2 = 0.
-1, -1/2, 0
Let x(g) be the third derivative of 3/392*g**8 + 0*g + 37/420*g**6 - 2/49*g**7 - 2/21*g**5 + 0 - 2*g**2 + 0*g**3 + 1/21*g**4. Factor x(v).
2*v*(v - 1)**2*(3*v - 2)**2/7
Suppose o - 56 = 5*o. Let f = -11 - o. Let -l - 11/2*l**2 + 11/2*l**4 + l**f + 0 = 0. What is l?
-1, -2/11, 0, 1
Factor 21/4*b**3 + 3/4*b**4 + 15/4*b + 0 + 33/4*b**2.
3*b*(b + 1)**2*(b + 5)/4
Let g(l) be the first derivative of 25*l**5 - 75*l**4/2 - 55*l**3/3 + 30*l**2 + 20*l + 6. Let g(z) = 0. What is z?
-2/5, 1
Let h(r) be the first derivative of 3*r**5/5 - 2. Factor h(l).
3*l**4
Let f(m) = -9*m**3 - 38*m**2 - 79*m + 397. Let a(s) = 4*s**3 + 20*s**2 + 40*s - 198. Let z(q) = -10*a(q) - 4*f(q). Factor z(r).
-4*(r - 2)*(r + 7)**2
Let o be 1/5*(-48)/(-36). Let l = 1/15 + o. Factor 0*f - l*f**3 + 0*f**2 + 0.
-f**3/3
Let a(f) = -4*f**2 + 24*f - 4. Let r(q) = -q**2 + 5*q - 1. Let c(s) = -3*a(s) + 16*r(s). Factor c(x).
-4*(x - 1)**2
Suppose 7*j - 4*j - 18 = 0. Let y be (j/(-21))/(3/(-7)). Solve y*a**3 - 2/3*a**2 + 0*a + 0 = 0 for a.
0, 1
Let q = -41 + 41. Determine f, given that -1/3*f**5 + 2/3*f**4 + q - 1/3*f**3 + 0*f + 0*f**2 = 0.
0, 1
Suppose -3*v**2 - 2 + 18*v - 1 - 24*v + 0*v**2 = 0. What is v?
-1
Suppose 0 = -0*u - u + 5. Let f = -23/5 + u. Factor -f*d**2 + 0 - 2/5*d.
-2*d*(d + 1)/5
Let z(r) be the second derivative of -3*r**5/40 - r**4/8 + r**3/4 + 3*r**2/4 + 16*r + 2. Factor z(t).
-3*(t - 1)*(t + 1)**2/2
Factor 5*s + 12*s + 14*s - 16*s**2 - 11*s - 4.
-4*(s - 1)*(4*s - 1)
Find c such that 6/5 - 4/5*c - 2/5*c**2 = 0.
-3, 1
Let q(p) be the first derivative of p**5/40 - p**4/24 - p**3/6 - 2*p - 4. Let r(x) be the first derivative of q(x). Determine c so that r(c) = 0.
-1, 0, 2
Suppose -l + 0 - 2 = 0, 2*a + 4*l = 40. Find f, given that 9*f**5 + 24*f**4 + 5 + 3*f**3 - 15 + 10 - 12*f - a*f**2 = 0.
-2, -1, -2/3, 0, 1
Factor t + 0 - 1/3*t**3 + 2/3*t**2.
-t*(t - 3)*(t + 1)/3
Let d(s) be the third derivative of 0*s**4 + 0 + 0*s**3 + 0*s - 2*s**2 + 1/30*s**5. Factor d(l).
2*l**2
Let k(h) = 3*h**5 - 18*h**4 - 21*h**3 - 18*h**2 - 18*h - 18. Let z(t) = t**4 + t**3 + t**2 + t + 1. Let u(g) = k(g) + 18*z(g). Factor u(s).
3*s**3*(s - 1)*(s + 1)
Let k(r) = 3*r - 33. Let m be k(11). Solve -1/8*y + 1/8*y**3 + 0*y**2 + m = 0 for y.
-1, 0, 1
Let m = -18 + 18. Let w(g) be the first derivative of 1/10*g**4 + 0*g + 0*g**3 + m*g**2 - 1. Find y, given that w(y) = 0.
0
Let l(r) = 3*r. Let u be l(1). Factor -32/7 - 16/7*v**u - 64/7*v - 2/7*v**4 - 48/7*v**2.
-2*(v + 2)**4/7
Let s = 1 - -1. Let x(o) be the third derivative of 0*o + 1/240*o**5 - 1/96*o**4 + s*o**2 - 1/24*o**3 + 0 + 1/480*o**6. Factor x(v).
(v - 1)*(v + 1)**2/4
Suppose -2*n + 2*v = -0*v - 10, -25 = 4*n + 5*v. Factor 0*g**3 - 3*g**3 +