g**2 + 3*g**4 - 6*g**t - 5*g - 12*g**3 + 3*g**3 = 0.
0, 1, 2
Determine i, given that 162*i**3 + 432*i**4 + 81/4*i**2 + 0 + 384*i**5 + 0*i = 0.
-3/8, 0
Let d(f) be the first derivative of -5*f**3/3 - 25*f**2/2 + 70*f - 31. Determine p so that d(p) = 0.
-7, 2
Let b be 14/18 - 120/180. Suppose 0*s + b*s**2 - 1/9 = 0. What is s?
-1, 1
Factor 3*o**5 - 12*o - 4 + 2*o**5 - 3*o**5 - 8*o**2 + 12*o**4 + 2*o**5 + 8*o**3.
4*(o - 1)*(o + 1)**4
Let p(k) be the first derivative of -4/25*k**5 + 1/5*k**4 + 4/5*k**3 - 3 + 8/5*k - 2*k**2. Factor p(v).
-4*(v - 1)**3*(v + 2)/5
Let f(u) be the first derivative of -1/18*u**4 - 1/9*u**3 + 0*u**2 + 1 + u. Let q(k) be the first derivative of f(k). Factor q(j).
-2*j*(j + 1)/3
Let m(y) be the first derivative of -y**4/4 - y**3 - 3*y**2/2 - y + 4. Suppose m(i) = 0. What is i?
-1
Let i(j) = -5*j + 52. Let c be i(10). Factor 1/2*b**2 - c*b + 2.
(b - 2)**2/2
Let m(h) = -4*h**4 + 2*h**3 + 2. Let x(l) = -17*l**4 + 8*l**3 - l**2 + l + 9. Let b(w) = 9*m(w) - 2*x(w). Let b(y) = 0. Calculate y.
-1, 0, 1
Suppose -1/3*n**2 + 0*n + 1/3 = 0. Calculate n.
-1, 1
Determine d so that 0*d + 3/4*d**2 + 0 - 1/4*d**5 + 5/4*d**3 + 1/4*d**4 = 0.
-1, 0, 3
Let m(g) = 2 - g - 2 + 3. Let t(j) = j - 4. Let x(a) = -4*m(a) - 3*t(a). Let w(d) = -d**2 - 6*d + 1. Let l(k) = -w(k) - 6*x(k). Determine y so that l(y) = 0.
-1, 1
Let g = -9/2 + 31/6. Factor g*c**5 - 4/3*c**3 + 0*c**4 + 0*c**2 + 2/3*c + 0.
2*c*(c - 1)**2*(c + 1)**2/3
Let q(r) be the third derivative of 0*r + 0 - 1/4*r**3 - 1/360*r**5 - 1/24*r**4 + r**2. Factor q(a).
-(a + 3)**2/6
Let o(a) be the first derivative of 0*a + 4 + 2/3*a**3 - a**2. Factor o(q).
2*q*(q - 1)
Let k(c) be the first derivative of c**4/44 - 4*c**3/33 - c**2/22 + 4*c/11 - 14. Suppose k(r) = 0. Calculate r.
-1, 1, 4
Let m(w) be the second derivative of w**10/45360 + w**9/11340 + w**8/10080 + w**4/3 - w. Let j(c) be the third derivative of m(c). Factor j(b).
2*b**3*(b + 1)**2/3
Let z(f) be the second derivative of f**6/150 + f**5/20 + 3*f**4/20 + 7*f**3/30 + f**2/5 - 12*f. Factor z(i).
(i + 1)**3*(i + 2)/5
Suppose 6 + 18 = 2*v. Let -2*s**4 + 2*s + 0 + 8*s**3 - 2 + 6*s - v*s**2 = 0. Calculate s.
1
Let d(o) be the third derivative of -o**6/60 - o**5/10 - o**4/4 - o**3/3 - o**2. Find l, given that d(l) = 0.
-1
Let a(g) be the second derivative of -g**5/40 - g**4/24 + 2*g. Suppose a(k) = 0. Calculate k.
-1, 0
Let q(o) be the first derivative of 0*o**2 - 2/15*o**3 + 2/5*o - 5. Solve q(k) = 0 for k.
-1, 1
Find l such that -8*l**3 - 3*l**4 + 2*l**2 + 2*l**3 + 7*l**2 - 12 - 92*l + 104*l = 0.
-2, 1
Let h(n) be the third derivative of n**7/2520 - n**6/540 + n**5/360 + 5*n**3/6 + 8*n**2. Let s(z) be the first derivative of h(z). Factor s(b).
b*(b - 1)**2/3
Let u(v) be the first derivative of v**4 - 9*v - 1/5*v**5 + 2/3*v**3 - 11 - 6*v**2. Factor u(s).
-(s - 3)**2*(s + 1)**2
Let x(q) be the third derivative of -q**8/20160 + q**7/2520 - q**5/90 + q**4/12 + 2*q**2. Let d(t) be the second derivative of x(t). Let d(m) = 0. What is m?
-1, 2
Determine u, given that -34*u + 18*u + 3*u**2 - 20 + u**2 = 0.
-1, 5
Let a(i) be the third derivative of i**7/140 + i**6/40 - 3*i**2. Factor a(o).
3*o**3*(o + 2)/2
Suppose 0*q + 2*q = -4*q. Factor q*r - 1/6*r**3 + 0 - 1/6*r**2.
-r**2*(r + 1)/6
Let h(z) = 1 - z + 4*z + z**2 - 3*z. Let i(q) = -2*q**2 - 2*q - 2. Let v(p) = 3*h(p) + i(p). Factor v(j).
(j - 1)**2
Let g(t) be the third derivative of -t**7/1470 + t**6/840 + t**5/420 - t**4/168 - 6*t**2. Factor g(c).
-c*(c - 1)**2*(c + 1)/7
Let o be 6 + (-5 - -1) + 2. Suppose -2*g = 2*k - o*k, -g + 5*k - 8 = 0. Determine v so that -2*v**2 - 5*v + 4*v**g + 3*v + 0*v = 0.
0, 1
Let w(h) be the third derivative of h**5/360 + h**4/72 + h**3/36 - 11*h**2. Factor w(v).
(v + 1)**2/6
Let r(t) = -5*t**2 - 2*t - 2. Let l be r(-2). Let a(c) = -3*c**3 + 3*c - 2. Let y(o) = 13*o**3 - 13*o + 9. Let n(d) = l*a(d) - 4*y(d). Factor n(m).
2*m*(m - 1)*(m + 1)
Let z(x) = -21*x**3 + 231*x**2 + 15*x - 15. Let t(v) = 3*v**3 - 33*v**2 - 2*v + 2. Let g(n) = 15*t(n) + 2*z(n). Factor g(r).
3*r**2*(r - 11)
Suppose -9/4 + 2*q**3 - 11/2*q**2 + 6*q - 1/4*q**4 = 0. What is q?
1, 3
Let j(z) be the first derivative of -4*z**5/15 + z**4 - 4*z**3/9 - 2*z**2 + 8*z/3 + 31. Solve j(l) = 0 for l.
-1, 1, 2
Let k be (-8)/36 - 40/(-18). Factor 0*t**5 - 2*t**2 - t**5 - 3*t**3 + t**k - 3*t**4.
-t**2*(t + 1)**3
Let r be ((-20)/(-24))/((-20)/(-36)). Factor -3/2*l + r*l**3 - 1/2*l**4 - 1/2*l**2 + 1.
-(l - 2)*(l - 1)**2*(l + 1)/2
Let b(l) be the first derivative of -5*l**4/38 - 6*l**3/19 - 3*l**2/19 + 2*l/19 - 4. Factor b(y).
-2*(y + 1)**2*(5*y - 1)/19
Solve -6*w**3 + 9*w**3 + 2*w**2 + w**2 + 3*w**2 = 0.
-2, 0
Let j = -47253 + 10631974/225. Let p = j - -1/225. Let 2/9*x**3 - p*x - 4/9 + 4/9*x**2 = 0. What is x?
-2, -1, 1
Let k(t) be the second derivative of -t**7/84 + t**5/10 - t**4/12 - t**3/4 + t**2/2 + 5*t. Factor k(s).
-(s - 1)**3*(s + 1)*(s + 2)/2
Find g such that -2/7*g**4 + 0*g**2 + 4/7*g**3 + 2/7 - 4/7*g = 0.
-1, 1
Let a(t) be the third derivative of t**6/240 - t**5/120 - t**4/24 + 20*t**2. Determine w, given that a(w) = 0.
-1, 0, 2
Let g(m) = -6*m**2 + 8. Let c(u) = -2*u**2 + 3. Let w(k) = 8*c(k) - 3*g(k). Find r, given that w(r) = 0.
0
Let p(f) be the third derivative of f**7/420 + f**6/180 - f**5/60 - f**4/12 + f**3/6 - f**2. Let y(q) be the first derivative of p(q). Factor y(i).
2*(i - 1)*(i + 1)**2
Let y = 5 - 1. What is l in 3*l**2 + y*l**4 - 16*l**3 - 3*l**4 - l + 13*l**3 = 0?
0, 1
Let n = 119/2 + -57. Let -2 - n*k**2 - 4*k - 1/2*k**3 = 0. What is k?
-2, -1
Let c be (-72)/(-44) + 32/88. Let -4/3*u - 2/3 + 2*u**c = 0. What is u?
-1/3, 1
Let z = 1059/5 - 211. Let b(w) be the first derivative of 1/6*w**6 + 5/4*w**4 + 0*w**2 + 0*w + 2/3*w**3 + 3 + z*w**5. What is j in b(j) = 0?
-2, -1, 0
Let h be 2 - (1 + -1)/2. Let a(x) = -3*x - h*x**2 - 3 + x + 2*x**4 - 2*x**5 + 4*x. Let t(n) = -n**5 + n - 1. Let k(w) = -a(w) + 3*t(w). Factor k(m).
-m*(m - 1)*(m + 1)**3
Factor 0 + 5*t - 1 - 3 - 10*t**2 + 9*t.
-2*(t - 1)*(5*t - 2)
Suppose 28*x - 189 = 21*x. Find l, given that 147/5*l**4 - 84/5*l**3 - 12/5 - x*l**2 + 84/5*l = 0.
-1, 2/7, 1
Let q(m) be the third derivative of -m**6/120 + 7*m**5/60 - 5*m**2 + 2*m. Determine g, given that q(g) = 0.
0, 7
Determine u, given that -3469 + 0*u**3 - 2*u**3 - 2*u**2 + 2*u + 3471 = 0.
-1, 1
Let f(j) be the first derivative of 65*j**4/4 - 25*j**3 - 60*j**2 + 20*j + 41. Factor f(y).
5*(y - 2)*(y + 1)*(13*y - 2)
Let c(h) = 2*h**2 - 3*h - 6. Let r(z) = -z**2 + 4*z + 7. Let y(b) = -2*c(b) - 3*r(b). Find g, given that y(g) = 0.
-3
Let -3/5*n**4 + 9/5*n**2 + 0 + 0*n**3 - 6/5*n = 0. What is n?
-2, 0, 1
Let g(r) be the first derivative of -1/24*r**6 + 0*r - 1/6*r**3 + 3/16*r**4 - 1 + 0*r**5 + 0*r**2. Factor g(d).
-d**2*(d - 1)**2*(d + 2)/4
Let t = 54 - 48. Let o(z) be the first derivative of 0*z + 0*z**3 + 0*z**2 - 1/4*z**4 + 2 - 2/5*z**5 - 1/6*z**t. Factor o(g).
-g**3*(g + 1)**2
Let b = 31 + -26. Let f(m) be the third derivative of 0 + 2*m**2 - 1/60*m**6 + 0*m + 1/12*m**3 - 1/40*m**b + 1/24*m**4 + 1/105*m**7. Factor f(x).
(x - 1)**2*(2*x + 1)**2/2
Factor 2/3*s**2 + 1/9*s**3 + 4/3*s + 8/9.
(s + 2)**3/9
Let n be (-7)/(-1 - -2) - 1. Let a be (-26)/n - 9/(-12). Suppose 2*p**2 - p**3 - a*p**2 + 2*p - 3*p = 0. Calculate p.
-1, 0
Let c be (-392)/(-18) - 4/(-18). Let x be c/42 + 8/24. Factor -x*b - 2/7 - 6/7*b**2 - 2/7*b**3.
-2*(b + 1)**3/7
Let c(p) = 4*p**4 - 2*p**3 - 6*p**2 + 2*p + 6. Let u(f) = 3*f + 5*f**4 - 2*f**3 - 6*f**2 - 3 - f + 10 + 0*f. Let x(l) = -3*c(l) + 2*u(l). Factor x(w).
-2*(w - 2)*(w - 1)*(w + 1)**2
Suppose -5*q + 14 = 3*c, -26 = -4*q + 7*c - 2*c. Factor -2/3*m - 1/2*m**q + 0 - 2*m**2 - 11/6*m**3.
-m*(m + 1)*(m + 2)*(3*m + 2)/6
Let q(o) be the third derivative of -o**8/16 + 3*o**7/7 - 29*o**6/40 - 11*o**5/10 + 9*o**4/2 - 4*o**3 + 14*o**2. Find x, given that q(x) = 0.
-1, 2/7, 1, 2
Let m(k) = 4*k**4 + 8*k**3 + 10*k**2 + 12*k + 6. Let g(p) = -4*p**4 - 9*p**3 - 11*p**2 - 11*p - 5. Let v(t) = 6*g(t) + 5*m(t). Factor v(o).
-2*o*(o + 1)**2*(2*o + 3)
Let s(p) = 2*p - 2. Let x be s(2). Let l be (-1)/(-5)*1 + (-6)/(-30). What is v in -l + 2/5*v**3 - 2/5*v + 2/5*v**x = 0?
-1, 1
Factor 0*q + 0*q**2 - 5*q**3 + 0 - 15/2*q**4 - 5/2*q**5.
-5*q**3*(q + 1)*(q + 2)/2
Solve x**2 + 0 + x + 1