
Let n = 3/145 + 269/1015. Factor 2/7 - 4/7*p + n*p**2.
2*(p - 1)**2/7
Let s(g) be the first derivative of -3 + 0*g + 1/3*g**3 + g**2. Factor s(l).
l*(l + 2)
Let c(p) = -49*p**3 - 90*p**2 - 49*p - 9. Let b(q) = q**3 - q - 1. Let y = -4 + 5. Let a(n) = y*b(n) - c(n). Factor a(u).
2*(u + 1)*(5*u + 2)**2
Let g(t) be the second derivative of -t**5/40 - t**4/24 - 3*t. Let g(y) = 0. What is y?
-1, 0
Let b(t) be the first derivative of 0*t + 1/5*t**5 - 1/2*t**6 - t**2 + 5/4*t**4 - 1/3*t**3 - 4. Let b(k) = 0. What is k?
-1, -2/3, 0, 1
Factor -3*c - 3*c + c - 5*c**2.
-5*c*(c + 1)
Suppose -4*o = 4*d + 44, -4*d - o - 46 = o. Let y = d - -16. Factor -8/7*i + 48/7*i**2 - 14*i**y - 6*i**3 + 0.
-2*i*(i + 1)*(7*i - 2)**2/7
Let v(c) = -5*c**3 + 20*c**2 + c - 16. Let a(s) = -5*s**3 + 20*s**2 + 2*s - 17. Let p(h) = -4*a(h) + 3*v(h). Let p(r) = 0. Calculate r.
-1, 1, 4
Let u = 16 + -10. Suppose -5*o = -4 - u. Factor -3*i**4 + 3*i**o - 7*i**2 - 2*i**5 - 2*i**4 + 3*i**2 - 4*i**3.
-i**2*(i + 1)**2*(2*i + 1)
Let w be -3 + ((-160)/6 - -1). Let o = w - -436/15. Solve -6/5*b**3 - 2/5*b**2 + o + 6/5*b = 0.
-1, -1/3, 1
Suppose 1 = -j - w + 7, -w = -4. Determine z, given that 3*z**2 + 5*z**4 - 3*z**j - 3*z**3 - 8*z**4 = 0.
-1, 0
Let d(u) be the first derivative of -u**4 + 8*u**2 + 28. Suppose d(b) = 0. Calculate b.
-2, 0, 2
Let j be (2 + -2)/(0 + -1). Let t(z) = -3*z - 12. Let c be t(-5). Solve -6/7*m**c + 6/7*m**4 + 0*m - 2/7*m**5 + j + 2/7*m**2 = 0 for m.
0, 1
Let j(w) be the first derivative of -2*w - 1/6*w**4 + 1/4*w**5 - 2 + 0*w**2 + 0*w**3. Let f(m) be the first derivative of j(m). Factor f(a).
a**2*(5*a - 2)
Suppose 3*g + b + 5 = 5*g, -2 = 2*b. Factor -5*u**2 + 11*u**2 - 4*u**g.
2*u**2
Let r(s) be the first derivative of -s**6/6 + s**5/5 + s**4/2 - 2*s**3/3 - s**2/2 + s + 25. Find g such that r(g) = 0.
-1, 1
Factor -7/3*v**2 + 16/3*v - 4/3.
-(v - 2)*(7*v - 2)/3
Suppose -2/7 + 11/7*q + 6/7*q**2 = 0. What is q?
-2, 1/6
Suppose 3*a - 408 = -a - 4*i, -5*a = 2*i - 498. Determine q so that -10 + 9*q**3 + 10 + a*q**5 - q**3 - 56*q**4 = 0.
0, 2/7
Let w(i) = 6*i**3 - 81*i + 87. Let v(c) = -3*c**3 + 40*c - 44. Let g(q) = 9*v(q) + 4*w(q). Factor g(d).
-3*(d - 2)**2*(d + 4)
Let p(r) be the first derivative of -2*r**3/3 - 3*r**2 - 2. Suppose p(o) = 0. Calculate o.
-3, 0
Factor -4/3 - 14/3*w + 6*w**2.
2*(w - 1)*(9*w + 2)/3
Let v(i) = 1. Let o(l) = l**3 + 2*l**2 - 2*l - 5. Let m(z) = -o(z) - 3*v(z). Let j be m(-3). Solve 2 - 2 - j*q + 3*q + q**2 + 1 = 0.
1
Let g(u) be the second derivative of u**7/168 - u**6/24 + 9*u**5/80 - 7*u**4/48 + u**3/12 - 2*u. Factor g(c).
c*(c - 2)*(c - 1)**3/4
Let k(i) be the second derivative of -i**5/20 + i**4/2 - 2*i**3 + 4*i**2 + 4*i. Factor k(p).
-(p - 2)**3
Let x(b) = 1. Let z(w) = 4*w**4 - 4*w**3 - 4*w**2 + 4*w + 24. Let l(q) = 24*x(q) - z(q). Determine u, given that l(u) = 0.
-1, 0, 1
Let n(c) be the first derivative of 4/3*c**3 + 2*c**4 + 0*c - 10 + 4/5*c**5 + 0*c**2. Factor n(a).
4*a**2*(a + 1)**2
Let a(r) be the first derivative of 4*r**5/5 + 3*r**4 + 4*r**3 + 2*r**2 + 17. Let a(p) = 0. Calculate p.
-1, 0
Let n(m) = -35*m**2 + 190*m - 140. Let c(k) = -5*k**2 + 27*k - 20. Let z(h) = 15*c(h) - 2*n(h). Suppose z(g) = 0. Calculate g.
1, 4
Factor 2*x + 2 - 6 + 2*x + 12 - 4*x**2.
-4*(x - 2)*(x + 1)
Let n(w) = 2*w**2 + 12. Let h(i) = i. Let b(z) = -10*h(z) - n(z). Factor b(y).
-2*(y + 2)*(y + 3)
Let z(j) be the third derivative of 2/9*j**3 + 11/90*j**5 - 1/60*j**6 - 13/315*j**7 + 1/4*j**4 + 3*j**2 - 1/84*j**8 + 0*j + 0. Suppose z(c) = 0. What is c?
-1, -2/3, -1/2, 1
Let a(p) be the third derivative of p**8/80640 + p**7/20160 - p**6/1440 - 7*p**5/60 + p**2. Let l(r) be the third derivative of a(r). Factor l(v).
(v - 1)*(v + 2)/4
Solve 8 - 18 - 8*o**2 + 3*o**2 - 15*o = 0 for o.
-2, -1
Suppose 2*z - 10 = z. Let u = z - 8. Solve 1/2*x**u + 2*x + 2 = 0.
-2
Suppose -2*t + t + 15 = 4*a, t - 10 = -3*a. Let w be a/(-6)*(-32)/20. Factor -2/3 - 2/3*c**2 + w*c.
-2*(c - 1)**2/3
Let q(i) be the first derivative of 2*i**3/3 + 5*i**2/2 + 3*i - 11. Let q(s) = 0. What is s?
-3/2, -1
Suppose 0 = 2*c + u - 18, 11 = c + 4*u - 5. Factor 2*n**4 - 3*n**3 - 6*n**3 + n**3 + c*n**2.
2*n**2*(n - 2)**2
Factor -c + 2 + 10*c**2 + 2 + 15*c.
2*(c + 1)*(5*c + 2)
Factor 1/10*n - 1/5*n**2 + 0 + 1/10*n**3.
n*(n - 1)**2/10
Let v be (-7)/(-9) + (-2)/(-9). Let b = 5 - v. Let -6*w**3 - 8*w**3 - w**3 - w**4 - 2*w**b + 6*w**5 - 6*w**2 = 0. Calculate w.
-1, -1/2, 0, 2
Let y(h) be the third derivative of h**8/72 + h**7/63 - h**6/90 - 11*h**2. Factor y(t).
2*t**3*(t + 1)*(7*t - 2)/3
Suppose 0 = -5*r - r + 30. Let q be (-1)/(-3) + r/15. Factor q - 1/3*s**3 + s**2 + 5/3*s - 1/3*s**4.
-(s - 2)*(s + 1)**3/3
Let n(b) be the second derivative of 1/4*b**5 + 7/6*b**3 + 0 - 3/4*b**4 - b**2 + b - 1/30*b**6. Let n(q) = 0. What is q?
1, 2
Suppose -4*s + 25 = -4*v + 9, -s + 2*v + 6 = 0. Determine g so that -368/7*g**s - 32/7 - 32*g + 304/7*g**3 - 50*g**5 + 670/7*g**4 = 0.
-2/5, -2/7, 1, 2
Let q(f) = f**2 + 2*f - 3. Let v be q(-3). Let u(g) be the second derivative of v - 2/21*g**3 - 1/42*g**4 - 2*g - 1/7*g**2. Factor u(m).
-2*(m + 1)**2/7
Let c(p) be the first derivative of p**4/28 + p**3/7 - 3. Factor c(k).
k**2*(k + 3)/7
Let r(a) be the first derivative of 0*a**2 - 2/21*a**3 + 0*a - 1. Factor r(l).
-2*l**2/7
Let y(f) be the third derivative of f**5/90 + f**4/9 - 5*f**3/9 - 19*f**2. Determine p so that y(p) = 0.
-5, 1
Let r(k) be the second derivative of 3*k**4/4 + 5*k**3/6 - 2*k**2 - k. Let b(q) = 22*q**2 + 12*q - 10. Let a(s) = 5*b(s) - 12*r(s). Find d, given that a(d) = 0.
-1, 1
Solve -4*m**3 + m**3 + m**5 + 2*m**4 + 2*m**5 - 2*m**2 = 0.
-1, -2/3, 0, 1
Let x(f) be the first derivative of 0*f - 5 + 1/9*f**3 + 0*f**2 - 1/12*f**4. Factor x(j).
-j**2*(j - 1)/3
Let x(b) be the first derivative of 3*b**5/25 + b**4/2 + b**3/5 - 6*b**2/5 - 4*b/5 - 21. Factor x(t).
(t - 1)*(t + 2)**2*(3*t + 1)/5
Let c = 70 - 70. Solve 0*t - t**3 - 1/2*t**4 - 1/2*t**2 + c = 0 for t.
-1, 0
Let y(o) be the second derivative of -1/20*o**5 + 1/6*o**3 + 1/30*o**6 + 2*o + 0*o**2 + 0 - 1/12*o**4. Factor y(n).
n*(n - 1)**2*(n + 1)
Let f(q) be the second derivative of -q**6/40 + 3*q**5/80 + q**4/16 - q**3/8 - 13*q. Factor f(a).
-3*a*(a - 1)**2*(a + 1)/4
Let f = 7 + 0. Let 1 - 4*s + s**3 + f*s + 0 + 3*s**2 = 0. What is s?
-1
Let u be (-4 - (-19 + 11))/1. Find y, given that y**u - 1/2 - 1/4*y**5 + 5/4*y - 1/2*y**2 - y**3 = 0.
-1, 1, 2
Let t(c) = -c**2 + c - 1. Let p(q) be the second derivative of -7*q**4/12 + 5*q**3/6 - 2*q**2 + q. Let a(u) = p(u) - 6*t(u). Solve a(m) = 0.
-2, 1
Let y = -44 - -44. Factor 1/3*t**3 + 0 - 2/3*t**4 + y*t + 1/3*t**5 + 0*t**2.
t**3*(t - 1)**2/3
Let g be (1/(-2))/(2/4). Let y = 3 + g. Determine p so that -6*p**2 + 1 - 4*p - p**4 - y - p**3 - 3*p**3 = 0.
-1
Let g(w) = w - 3. Let m(i) = i - 3. Let p(d) = -3*g(d) + 4*m(d). Let x be p(5). Factor 0*o**x + 0*o - 2/3*o**3 + 0.
-2*o**3/3
Let d be ((-18)/(-10))/(-3)*330/(-99). Let -8/3 - 2/3*q**d - 8/3*q = 0. What is q?
-2
Let g(t) be the third derivative of -t**6/360 - t**5/180 + t**4/72 + t**3/18 - 8*t**2. Factor g(q).
-(q - 1)*(q + 1)**2/3
Let w = 23 + -21. Factor 0 + 0*j + 2/5*j**w - 4/5*j**3 + 2/5*j**4.
2*j**2*(j - 1)**2/5
Factor -1/4*p**3 + 0 + 1/4*p + 1/4*p**2 - 1/4*p**4.
-p*(p - 1)*(p + 1)**2/4
Let o(d) be the third derivative of d**7/105 + d**6/10 + 2*d**5/5 + 5*d**4/6 + d**3 + 8*d**2. Find j, given that o(j) = 0.
-3, -1
Let i(v) = 5*v**3 - 2*v**2 + 4. Let s(q) = -14*q**3 + 6*q**2 + q - 13. Let h(m) = -11*i(m) - 4*s(m). Factor h(n).
(n - 2)**2*(n + 2)
Factor 18/7*l - 3/7*l**3 + 0 - 15/7*l**2.
-3*l*(l - 1)*(l + 6)/7
Let x(v) = -5*v**2 - 81*v - 12. Let a be x(-16). Factor -2/3*r - 7/3*r**a + r**2 + r**3 + r**5 + 0.
r*(r - 1)**3*(3*r + 2)/3
What is r in -14/9*r**3 + 16/9*r + 4/9*r**4 - 8/9 + 2/3*r**2 = 0?
-1, 1/2, 2
Let t(i) = 6 - 2 - i**2 - 3*i + 5*i. Let d be t(3). Factor -2*r**4 + 3*r**4 - 2*r**3 + 2*r + 0 - d.
(r - 1)**3*(r + 1)
Let n = 2 - 26. Let z be (-3)/(-4) - (-2)/n. Determine l, given that 0*l + z - 2/3*l**2 = 0.
-1, 1
Let r = -4/17 + 78/187. Factor -2/11*c**3 + 2/11 - 2/11*c**2 + r*c.
-2*(c - 1)*(c + 1)**2/11
Suppose 2*y + 3*d - 13 = 0, 2*y + d = 4 + 3. Suppose x = 4*l - 2 - 0, -4 = -4*l + y*x. What is s in -2 - s**3 + l*s**3 + 2 - 3*s**2 + 4 = 0?
-2,