Let z = -5 + 7. Suppose 0*i**4 + z*i**4 + 2*i**3 - 4*i**3 = 0. Calculate i.
0, 1
Factor -2 + 2 - 2267*i**2 + 2*i**3 + 2260*i**2 + 3*i.
i*(i - 3)*(2*i - 1)
Let x(g) be the third derivative of 0*g + 0 + 0*g**7 + 1/90*g**5 - 1/120*g**6 + 5*g**2 + 1/1008*g**8 + 0*g**4 + 0*g**3. Determine y so that x(y) = 0.
-2, 0, 1
Let c(t) = t + 1. Suppose -3 = -q - 0*d - 2*d, q + 5*d = 3. Let h be c(q). Factor 0 + 0*r**3 + 0*r**2 + 1/3*r**5 + 1/3*r**h + 0*r.
r**4*(r + 1)/3
Let l be -3*4/(-18)*6. Suppose 2*t = -3*t + 10. Let -3*w**2 - 5*w**5 - t*w - w**4 + 5*w**l - w**4 + 7*w**3 = 0. Calculate w.
-1, -2/5, 0, 1
Let o(q) be the second derivative of -6*q**7/7 + 22*q**6/15 + 7*q**5/5 - 11*q**4/3 + 4*q**3/3 + 3*q. Determine p, given that o(p) = 0.
-1, 0, 2/9, 1
Let x(a) = -a**3 - a**2 - 2. Let p be x(-2). Suppose p*j - 6 = -0*j. Factor j*q**2 - q + 0*q**2 - 2*q**2.
q*(q - 1)
Let p(u) = 4*u**3 - 5*u**2 + 4*u + 3. Let z(g) = 9*g**3 - 11*g**2 + 9*g + 7. Let r(q) = -7*p(q) + 3*z(q). Factor r(v).
-v*(v - 1)**2
Let i(v) be the second derivative of -v**5/60 + v**4/4 - 5*v**3/6 - 25*v**2/6 + 32*v. Solve i(y) = 0 for y.
-1, 5
Solve 9*z**2 + 4*z**3 - 10*z**2 - 3*z**3 = 0.
0, 1
Let i(m) = -2*m - 10. Let z be i(-8). Let b be z/3*(-1)/(-5). Factor 2/5*o - b*o**2 + 0.
-2*o*(o - 1)/5
Let u(o) be the first derivative of o**4/6 + 4*o**3/9 - o**2/3 - 4*o/3 + 7. Factor u(v).
2*(v - 1)*(v + 1)*(v + 2)/3
Let n(a) be the first derivative of a**6/80 + a**5/40 - 3*a**2 + 8. Let l(x) be the second derivative of n(x). Solve l(j) = 0.
-1, 0
Suppose 47 = 4*w - 5*j, -w - j = w - 41. Factor -2*x - w*x**4 - 12*x**3 - 24*x**3 + 6*x**3 - 10*x**2 - 4*x**2.
-2*x*(x + 1)*(3*x + 1)**2
Let v(z) be the second derivative of z**4/18 - 4*z**3/9 - 10*z. Determine k so that v(k) = 0.
0, 4
Let x(r) be the first derivative of -2*r**6/3 + 4*r**5/5 + 3*r**4/4 - 2*r**3/3 - r**2/2 - 3. Factor x(d).
-d*(d - 1)**2*(2*d + 1)**2
Let n(z) = -723*z**3 - 432*z**2 - 48*z - 12. Suppose 21 + 4 = 5*d. Let k(l) = 289*l**3 + 173*l**2 + 19*l + 5. Let h(o) = d*n(o) + 12*k(o). Factor h(c).
-3*c*(7*c + 2)**2
Let y(s) be the third derivative of s**5/20 - 2*s**4/3 + 5*s**3/6 + 51*s**2. Factor y(a).
(a - 5)*(3*a - 1)
Let x be ((-30)/(-50))/((-2)/(-10)). Let y(v) be the second derivative of 1/30*v**5 + 0*v**x - 1/18*v**4 + 0*v**2 + 0 - 2*v. Find c such that y(c) = 0.
0, 1
Let d(w) be the third derivative of w**6/280 - 9*w**5/140 + 3*w**4/7 - 8*w**3/7 + 15*w**2. Factor d(l).
3*(l - 4)**2*(l - 1)/7
Factor -1/3*h**3 - h**2 + 0 - 2/3*h.
-h*(h + 1)*(h + 2)/3
Suppose -3 = 18*s - 39. Suppose 0*z - 2/5*z**4 + 0 + 4/5*z**3 - 2/5*z**s = 0. Calculate z.
0, 1
Let m(r) be the third derivative of -r**5/180 + 4*r**2 + r. Factor m(k).
-k**2/3
Let h be (-1)/2*(-8 + 8). Let l(p) be the third derivative of 0*p + h*p**4 + p**2 + 1/18*p**3 - 1/180*p**5 + 0. Determine j so that l(j) = 0.
-1, 1
Let q(t) be the first derivative of -6/5*t**2 - 3/5*t**4 - 5 + 32/15*t**3 - 8/5*t. Factor q(c).
-4*(c - 2)*(c - 1)*(3*c + 1)/5
Let g(w) = 12*w**3 - 36*w**2 + 21*w - 2. Let a(o) = o**3 - o**2 - o. Let l(c) = 4*a(c) + g(c). Suppose l(q) = 0. What is q?
1/4, 2
Let h(k) be the third derivative of 7/540*k**6 - 1/36*k**4 + 1/90*k**5 - 2/27*k**3 + 0 + 1/315*k**7 + 2*k**2 + 0*k. Factor h(l).
2*(l + 1)**3*(3*l - 2)/9
Factor -6*y**3 - 3*y**2 - 8*y + 15*y**2 + 2*y**3.
-4*y*(y - 2)*(y - 1)
Let i = 12 + -8. Factor 2*g**2 - 6*g**2 + g**3 + 2*g**i + g**3.
2*g**2*(g - 1)*(g + 2)
Let 4 + 0*j**4 - 2*j**4 - 6*j**2 - 2*j - 2*j**3 + 4*j**3 + 4*j**4 = 0. What is j?
-2, -1, 1
Factor 1/4*a**2 + 1/2*a - 1/4*a**3 + 0.
-a*(a - 2)*(a + 1)/4
Suppose -1 = 3*j - 7. Suppose 0 = -2*o + 5*y + 6, 5*o + 5*y = -9 + 24. Factor 10*w - 2 - 4 + o - 2*w**j - w**2.
-(w - 3)*(3*w - 1)
Let h be ((-2)/4)/1 + (-11)/(-6). Suppose -h - 8/3*o**2 - 2/3*o**3 - 10/3*o = 0. Calculate o.
-2, -1
Let u = -52/7 + 628/77. Factor 98/11*q**4 - u*q - 48/11*q**2 + 0 - 42/11*q**3.
2*q*(q - 1)*(7*q + 2)**2/11
Solve 5*z**5 + 35*z**2 + 4*z + 34*z**4 + 45*z**3 - 7*z + 13*z - 9*z**4 = 0 for z.
-2, -1, 0
Let g be ((-105)/(-54) + -2)/((-75)/9). Let f(m) be the third derivative of -g*m**5 + 3*m**2 - 1/30*m**4 + 0 + 0*m - 1/15*m**3. Factor f(s).
-2*(s + 1)**2/5
Let c(t) be the first derivative of t**3/12 + t**2 + 7*t/4 + 45. Factor c(w).
(w + 1)*(w + 7)/4
Let t = 2 - 1. Let c(d) be the first derivative of 0*d**4 + 1/12*d**3 - 1/20*d**5 + 0*d**2 - t + 0*d. Suppose c(y) = 0. What is y?
-1, 0, 1
Find i such that 4/13*i**2 + 2/13*i**5 + 2/13 - 6/13*i + 4/13*i**3 - 6/13*i**4 = 0.
-1, 1
Let b = 84 - 35. Suppose 4*m - 39 = b. Suppose -4*y**3 + 4 - 10*y**3 - 5*y**2 + 37*y**2 - m*y = 0. Calculate y.
2/7, 1
Let p(j) be the first derivative of j**3/9 - 5*j**2/6 + 2*j - 16. Factor p(t).
(t - 3)*(t - 2)/3
Let u be (150/8)/(171/152). Factor -8/3*i - 32/3*i**2 - 10/3*i**3 + u*i**4 + 0.
2*i*(i - 1)*(5*i + 2)**2/3
Let -12/5 + 2/5*v**2 - 2/5*v = 0. Calculate v.
-2, 3
Factor -y**4 + 13*y**4 + 7*y**3 + 8*y**5 - y**3 - 2*y**3.
4*y**3*(y + 1)*(2*y + 1)
Let x be 10 - (-1 - 2 - 0). Factor -2*d**4 + x*d**4 - 9*d**3 + 8*d**5 + 3*d**2 - 11*d**5 - 2*d**4.
-3*d**2*(d - 1)**3
Factor 1/5*j**2 - 4/5*j + 0.
j*(j - 4)/5
Let m(v) be the second derivative of 0 - 8*v + 0*v**2 + 1/4*v**4 - 1/2*v**3. Solve m(j) = 0.
0, 1
Let u(y) be the second derivative of -y**5/15 - 4*y**4/9 - 7*y**3/6 - 3*y**2/2 - 4*y. Determine a, given that u(a) = 0.
-3/2, -1
Factor -d + 4*d**3 + 4 - 3*d + 19*d**2 - 23*d**2.
4*(d - 1)**2*(d + 1)
Let t(m) be the second derivative of m**5/15 - 8*m**3/9 + 39*m. Factor t(i).
4*i*(i - 2)*(i + 2)/3
Let -3 + 10*g + 5*g - 21*g**2 + 15*g**3 - 6*g**3 = 0. What is g?
1/3, 1
Let j = 41 + -39. Let l(w) be the third derivative of 0*w + 1/420*w**6 + 0*w**3 + 3*w**j + 0*w**4 + 0 + 1/1176*w**8 + 0*w**5 - 2/735*w**7. Factor l(z).
2*z**3*(z - 1)**2/7
Suppose -4*k = k. Suppose k*z**2 + 2 - z + 4*z + 0 + z**2 = 0. What is z?
-2, -1
Let y(l) be the first derivative of -l**6/39 + 8*l**5/65 - 3*l**4/13 + 8*l**3/39 - l**2/13 - 5. Suppose y(n) = 0. Calculate n.
0, 1
Let s(h) = -20*h**3 + 52*h**2 + 8*h - 88. Let b(d) = -d**3 + d**2 - d - 1. Let l(w) = -24*b(w) + s(w). Find q, given that l(q) = 0.
-4, 1
Factor 36*k - 24*k**2 + 20/3*k**3 - 18 - 2/3*k**4.
-2*(k - 3)**3*(k - 1)/3
Let l(x) be the third derivative of x**8/2520 - x**7/1575 - x**6/900 + x**5/450 - x**2. What is r in l(r) = 0?
-1, 0, 1
Let o(w) = 7*w. Let p be o(2). Let l be 4/p + (-10)/35. Determine h so that 1/4*h**2 + l*h + 0 = 0.
0
Let l(d) be the second derivative of -3*d**5/140 + 3*d**3/14 - 3*d**2/7 - 6*d. Suppose l(u) = 0. Calculate u.
-2, 1
Solve 18/13 - 12/13*t + 2/13*t**2 = 0 for t.
3
Let q(b) be the second derivative of b**7/168 - b**6/60 - 3*b**5/80 + b**4/12 + b**3/6 + 10*b. Factor q(h).
h*(h - 2)**2*(h + 1)**2/4
Let -1/4*s**5 + 1/2*s**3 - 1/2*s**2 + 1/4*s**4 + 1/4 - 1/4*s = 0. Calculate s.
-1, 1
Find i such that -2/3*i**4 - 2*i**3 + 4/3 - 2/3*i**2 + 2*i = 0.
-2, -1, 1
Suppose 3*q + 0*q = -51. Let i = q - -24. Factor -i*t**2 + 4 - t**3 + 0*t + 6*t**2 - 3 + t.
-(t - 1)*(t + 1)**2
Let 86 - 86 - c**2 + c = 0. Calculate c.
0, 1
Let u be 2 - (2 + (-32)/(-330)). Let h = 10/33 - u. Factor h*b - 2/5*b**2 + 0.
-2*b*(b - 1)/5
Let t(q) be the second derivative of q**4/96 - 5*q**3/48 + q**2/4 - 14*q. Determine w so that t(w) = 0.
1, 4
Let o(z) be the third derivative of 1/4*z**4 + 0*z - 2/3*z**3 + 0 - 1/30*z**5 + z**2. Find s, given that o(s) = 0.
1, 2
Let t(s) = 3*s - 63. Let p be t(23). Factor -9/2 + p*c**2 + 3/2*c.
3*(c + 1)*(4*c - 3)/2
Suppose -5*f - 68 = -8. Let r be 12/63*(-14)/f. Factor 2/9*g**4 + r*g**5 - 4/9*g**3 + 2/9 - 4/9*g**2 + 2/9*g.
2*(g - 1)**2*(g + 1)**3/9
Let r(d) be the third derivative of -1/30*d**5 - 10*d**2 + 0 + 0*d + 1/10*d**6 + 0*d**4 - 3/35*d**7 + 0*d**3. Factor r(y).
-2*y**2*(3*y - 1)**2
Let q(a) be the second derivative of a**6/450 - a**5/120 + a**4/120 + a**3/6 + 3*a. Let c(b) be the second derivative of q(b). Let c(r) = 0. What is r?
1/4, 1
Factor 9*v**3 + 3*v**3 + 8*v**2 - 8*v - 14*v**3.
-2*v*(v - 2)**2
Let z = 23 - 22. Let m be -4 - (z - 2)*7. Factor 0 + 2/9*y + 2/9*y**m + 4/9*y**2.
2*y*(y + 1)**2/9
Let m(g) be the second derivative of -g**4/102 - 2*g**3/51 + 11*g. Solve m(y) = 0 for y.
-2, 0
Let f(m) be the first derivative of -1/3*m**4 + 3/40*m**5 - 1/2*m**2 + 7/12*m**3 + 2*m - 2. Let