et p = -29/2 - b. Factor 1/2*o - 1 + p*o**2.
(o + 1)*(3*o - 2)/2
Suppose 4*b + y + 2 = 0, 2*b + 5*y - 5 = 3. Let s(a) = -9*a**2 + a - 1. Let t(h) = h**2 + h + 1. Let p(c) = b*t(c) - s(c). Factor p(j).
2*j*(4*j - 1)
Let z = -88 - -793/9. Let m(t) be the first derivative of 1/12*t**4 + 1/15*t**5 + 2 - 1/6*t**2 + 0*t - z*t**3. Let m(i) = 0. What is i?
-1, 0, 1
Let n(j) be the second derivative of j**5/180 - j**4/54 - j**3/18 + 13*j. What is h in n(h) = 0?
-1, 0, 3
Let g(h) = 7*h**2 + 5*h. Let m = -3 + 8. Let o(n) = 11*n**2 + 8*n. Let b(d) = m*o(d) - 8*g(d). Find p, given that b(p) = 0.
0
Factor 52*v**2 + 3*v**4 + 9 - 22*v**3 - 48*v + 6*v - 1 + 1.
(v - 3)**2*(v - 1)*(3*v - 1)
Let k(h) be the second derivative of -1/60*h**5 - 3/2*h**2 - 1/120*h**6 + 1/6*h**3 + h + 1/24*h**4 + 0. Let f(m) be the first derivative of k(m). Factor f(v).
-(v - 1)*(v + 1)**2
Suppose 0 = -0*r + r - 8. Let b be (-7 - -2)*r/(-10). Factor 2/3*p - 2*p**b - 2/3*p**2 + 0 - 10/3*p**3.
-2*p*(p + 1)**2*(3*p - 1)/3
Let v be 14/4 - 11/22. Factor 0 + 2/3*h**4 - 2/3*h - 2*h**v + 2*h**2.
2*h*(h - 1)**3/3
Suppose 4*d = -2*l + 2*d + 6, 3*d - 3 = -l. Let u(s) = -3*s**2 - 12*s - 3. Let b(f) = f - 1. Let z(a) = l*b(a) + u(a). Suppose z(m) = 0. Calculate m.
-2, -1
Let b = -20 - -28. Suppose u = b*u - 14. Factor -2/11*z + 2/11*z**3 + 2/11 - 2/11*z**u.
2*(z - 1)**2*(z + 1)/11
Let v be (-1)/(-18)*(-6)/(-4). Let d(p) be the second derivative of v*p**2 + 0 + 1/24*p**4 + 3*p + 1/12*p**3 + 1/120*p**5. Factor d(r).
(r + 1)**3/6
Let s be (6/4)/((-15)/(-40)). Suppose s*p - 5*p + 2 = 0. Solve 0 + 1/2*n**p + 0*n = 0 for n.
0
Let z = 54 + -50. Let m(j) be the first derivative of -4 + 2*j**z - 8/3*j**3 + 0*j + j**2. What is y in m(y) = 0?
0, 1/2
Let g(v) = 9*v**2 - 29*v + 3. Let q(p) = -17*p**2 + 57*p - 7. Let n(t) = 7*g(t) + 3*q(t). Suppose n(d) = 0. What is d?
0, 8/3
Let -2/5 + 4/5*y - 2/5*y**2 = 0. What is y?
1
Let z(o) be the third derivative of o**7/175 - 11*o**6/300 + 2*o**5/25 - o**4/15 - 9*o**2. Suppose z(k) = 0. Calculate k.
0, 2/3, 1, 2
Let p(z) be the second derivative of 0*z**3 - z + 1/48*z**4 + 0 + 0*z**2. Determine x, given that p(x) = 0.
0
Let y = -114 + 572/5. Find v, given that 8/5*v**3 - y - 6/5*v + 0*v**2 = 0.
-1/2, 1
Suppose 4*l - j = 15, 9 + 6 = l - 4*j. Factor -10*k - 3 + l + 9*k**2 + 4 - 3*k**2.
2*(k - 1)*(3*k - 2)
Let o be (1/5)/(12/(-636)). Let a = o + 11. Solve -a*l + 4/5 - 2/5*l**2 = 0 for l.
-2, 1
Let x(y) be the first derivative of -2/15*y**3 + 1 - 1/5*y**2 + 2/5*y + 1/10*y**4. Factor x(q).
2*(q - 1)**2*(q + 1)/5
Let j(k) be the second derivative of -4*k**6/15 + 2*k**5/5 - k**4/6 + 3*k. Let j(t) = 0. What is t?
0, 1/2
Let w(n) be the second derivative of -5*n**7/42 + n**6/6 + n**5/4 - 5*n**4/12 + 44*n. Factor w(g).
-5*g**2*(g - 1)**2*(g + 1)
What is t in 0 - 8/5*t + 2/5*t**2 - 4/5*t**5 + 2*t**4 + 24/5*t**3 = 0?
-1, 0, 1/2, 4
Let d(u) be the third derivative of 3*u**2 - 1/30*u**5 + 1/3*u**4 - 4/3*u**3 + 0 + 0*u. Factor d(m).
-2*(m - 2)**2
Let m(c) be the second derivative of -c**7/105 - c**6/75 + c**5/50 + c**4/30 - 24*c. Factor m(t).
-2*t**2*(t - 1)*(t + 1)**2/5
Let n = 67/84 + -5/7. Let y(l) be the second derivative of -1/30*l**6 + 0 + 1/3*l**2 - 1/6*l**3 - n*l**4 + 2*l + 7/60*l**5. Suppose y(r) = 0. What is r?
-2/3, 1
Factor 0 + 0*k**2 + 8/7*k**4 + 4/7*k**3 + 0*k.
4*k**3*(2*k + 1)/7
Solve 0 - 2*n**3 - 2/3*n**4 + 0*n - 4/3*n**2 = 0 for n.
-2, -1, 0
Let g(d) be the second derivative of 5*d**4/12 + 5*d**3/3 + 5*d**2/2 - d. Suppose g(u) = 0. Calculate u.
-1
Suppose 0 = h - 2*h + 4. Let r(n) be the third derivative of 2/3*n**3 + 1/30*n**5 + 0 + 0*n + 1/4*n**h + 2*n**2. Factor r(l).
2*(l + 1)*(l + 2)
Let v(t) be the first derivative of -t**7/14 - t**6/5 + t**4/2 + t**3/2 + 4*t - 3. Let x(h) be the first derivative of v(h). Find f, given that x(f) = 0.
-1, 0, 1
Suppose -342*h + 338*h + 8 = 0. Let 0*b - 8/7 + 2/7*b**h = 0. What is b?
-2, 2
Let d = 6 - 11/2. Let -2*v + d + 3/2*v**2 = 0. Calculate v.
1/3, 1
Let t(k) be the third derivative of 0*k**3 + 0 + 0*k + 0*k**4 + 1/120*k**6 + 1/60*k**5 + 3*k**2. Suppose t(v) = 0. What is v?
-1, 0
Let z = 9 + -6. Let q(x) = -4*x**3 - 3*x**2 + x + 2. Let l(k) = 5*k**3 + 3*k**2 - 2*k - 3. Let c(j) = z*q(j) + 2*l(j). Factor c(o).
-o*(o + 1)*(2*o + 1)
Let g(q) be the second derivative of -q**7/42 - q**6/10 - q**5/20 + q**4/4 + q**3/3 + 8*q. Solve g(c) = 0 for c.
-2, -1, 0, 1
Let y(t) = -3*t**3 - 15*t**2 + 39*t - 33. Let u(p) = 6*p**3 + 30*p**2 - 78*p + 64. Let h(x) = 6*u(x) + 11*y(x). Factor h(k).
3*(k - 1)**2*(k + 7)
Let i(d) = 2*d**3 - 8*d + 16. Let y(b) = -4*b**3 - b**2 + 16*b - 32. Let x(q) = -9*i(q) - 4*y(q). Factor x(f).
-2*(f - 2)**2*(f + 2)
Determine a so that -1/5*a**2 + 6/5*a - 9/5 = 0.
3
Suppose 3*t = 6*t + 15. Let b = -9/2 - t. Solve -b*y**5 + 1/2*y**4 + 0 + 0*y**3 + 0*y + 0*y**2 = 0 for y.
0, 1
Let y(t) be the third derivative of t**9/60480 - t**8/8960 + t**7/3360 - t**6/2880 - t**4/12 - 2*t**2. Let c(z) be the second derivative of y(z). Factor c(f).
f*(f - 1)**3/4
Let v(d) = 3*d - 15. Suppose -j - 4*s = 7, 2*j + 2 = -2*s + 6. Let k be v(j). Find h, given that -2/3*h**3 - h**2 + k*h + 1/3 = 0.
-1, 1/2
Let i(m) = -3*m**3 + 9*m**2 - 6. Let d(h) = -8*h**3 + 26*h**2 - h - 17. Let j(w) = -6*d(w) + 17*i(w). Solve j(b) = 0 for b.
-2, 0, 1
Let a(s) be the second derivative of s**8/672 - s**7/420 + s**2/2 + s. Let k(y) be the first derivative of a(y). Suppose k(p) = 0. Calculate p.
0, 1
Let k(g) be the first derivative of g**4/18 + 10*g**3/27 + g**2/3 - 2*g - 4. Factor k(q).
2*(q - 1)*(q + 3)**2/9
Let g(w) be the first derivative of -w**6/6 - 3*w**5/5 + w**4/2 + 2*w**3 - w**2/2 - 3*w + 46. Find s such that g(s) = 0.
-3, -1, 1
Let d(s) = -s**2 - s. Let i(v) = -3*v**3 + v**2. Let r(g) = -2*d(g) + 2*i(g). Factor r(x).
-2*x*(x - 1)*(3*x + 1)
Let k = -170/11 + 180/11. Factor -8/11*i**3 + 2/11*i**4 + 0 + k*i**2 - 4/11*i.
2*i*(i - 2)*(i - 1)**2/11
Let m(f) be the second derivative of -f**5/10 + 3*f**4/2 - 9*f**3 + 27*f**2 - 4*f. Factor m(n).
-2*(n - 3)**3
Suppose 0*i**2 - 22*i + 4*i**2 + 34*i = 0. Calculate i.
-3, 0
Let m(z) = -3*z**2 + 7*z + z**2 + 5 + 3*z**2. Let v be m(-7). Suppose 1/5*d**v + 0*d + 1/5*d**3 + 0*d**2 - 2/5*d**4 + 0 = 0. Calculate d.
0, 1
Let v be (8 - -1)/3*3. Suppose -2*h + v = 5*o, 5*o - 1 = 2*h - 0. Suppose -4*a**h + 4*a**3 + 0*a**4 + 6*a**2 + 2*a**4 = 0. What is a?
-1, 0
Let k be 13 - (2*-2)/2. Suppose k = 5*i + 5. What is t in 4*t - 5*t**2 - t**i + 4*t**2 + 0*t**2 = 0?
0, 2
Let k be ((-1)/4)/((-6)/12). Let o(a) be the second derivative of 1/4*a**3 - 3*a + 1/12*a**4 - k*a**2 + 0. Factor o(h).
(h + 2)*(2*h - 1)/2
Suppose 4*t = -8*t + 36. Factor -1/3 + 1/6*n**t - 1/6*n + 1/3*n**2.
(n - 1)*(n + 1)*(n + 2)/6
Let v = -519 + 521. Solve 0 - 1/4*g**v + 0*g = 0.
0
Let i be (1*6)/(12/20). Factor i*x**3 + 0 + 2*x**2 + 17/2*x**4 + 2*x**5 + 0*x.
x**2*(x + 2)**2*(4*x + 1)/2
Let p be (-3)/6 + 15/6. Let x(c) be the first derivative of 0*c**3 - p - 1/5*c**5 + 1/4*c**4 + 0*c**2 + 0*c. Factor x(v).
-v**3*(v - 1)
Suppose o - d = 8, -3*o = 5*d - 2*d. Factor -2*h**5 + 8*h**3 - 3*h - 3*h + o + h**4 - h**4 - 4*h**2.
-2*(h - 1)**3*(h + 1)*(h + 2)
Let z(b) be the second derivative of -b**5/60 - b**4/18 + b**3/18 + b**2/3 - b - 31. Factor z(x).
-(x - 1)*(x + 1)*(x + 2)/3
Let i(c) = -3*c**3 - 2*c**2 + 7*c - 6. Let d(v) = 2*v**3 + 3*v**2 - 7*v + 7. Let m(u) = -4*d(u) - 5*i(u). Solve m(z) = 0 for z.
-1, 2/7, 1
Let g(n) be the first derivative of 4*n**5/5 + n**4 - 4*n**3/3 - 2*n**2 - 1. Factor g(f).
4*f*(f - 1)*(f + 1)**2
Let r(l) = l**3 + 6*l**2 + 6*l + 7. Let k be r(-5). What is n in -3*n**3 + n**4 + 3*n**4 - 3*n**4 + 0*n**3 + 2*n**k = 0?
0, 1, 2
Suppose 15 = 6*n - 5*n. Let a be (-51)/(-15) - 6/n. Find p, given that -4/7*p**4 + 0 + 0*p**2 + 0*p - 2/7*p**a - 2/7*p**5 = 0.
-1, 0
Suppose 7 + 3 = p. Suppose p = k + 2*k - 2*c, 0 = -k + 2*c + 6. Determine f, given that -1/4 + 3/4*f**4 + 3/4*f - 1/2*f**3 - 1/2*f**k - 1/4*f**5 = 0.
-1, 1
Let o(h) be the first derivative of -h**7/480 + h**6/720 + 7*h**5/480 - h**4/48 + 2*h**3/3 + 3. Let j(x) be the third derivative of o(x). Factor j(t).
-(t - 1)*(t + 1)*(7*t - 2)/4
Let q(d) be the first derivative of -3 + 0*d**3 + 0*d - 1/8*d**4 + 0*d**2. Factor q(f).
-f**3/2
Let p(u) be the first derivative of -1/3*u**2 + 0*u +