**2
Let f be 6/10 + (-4)/(-10). Let i(c) be the first derivative of -2/5*c**2 + f + 2/5*c + 2/15*c**3. Factor i(a).
2*(a - 1)**2/5
Let b(y) be the first derivative of -y**7/40 + 3*y**6/40 - y**5/20 + 4*y**3/3 + 1. Let q(g) be the third derivative of b(g). Factor q(h).
-3*h*(h - 1)*(7*h - 2)
Let o(s) be the third derivative of -1/60*s**5 + 1/210*s**7 + 1/336*s**8 + 0*s**3 + 0 - 2*s**2 + 0*s - 1/120*s**6 + 0*s**4. Factor o(d).
d**2*(d - 1)*(d + 1)**2
Let o be 24/10 + 2/(-5). Factor 3*x - x**o + 2*x - 6*x.
-x*(x + 1)
Suppose 0 = -3*p - 0*p + 18. Suppose -3*r - 6 = -p*r. Factor -1/3*g**3 + 0*g**r + 0*g - 4/3*g**5 + 0 + 5/3*g**4.
-g**3*(g - 1)*(4*g - 1)/3
Let y = 122/3 - 40. Let c(z) be the second derivative of 0 - 1/5*z**5 + 2*z + 7/15*z**6 + 0*z**2 + y*z**3 - 7/6*z**4. Factor c(o).
2*o*(o - 1)*(o + 1)*(7*o - 2)
Let i(a) be the third derivative of -a**6/200 - a**5/75 + a**4/30 - 4*a**2. Solve i(f) = 0.
-2, 0, 2/3
Let c(q) be the second derivative of -1/30*q**4 - 1/50*q**5 - 7*q + 0 + 0*q**2 + 2/15*q**3. Suppose c(d) = 0. What is d?
-2, 0, 1
Suppose -17 = -12*r + 43. Let s(f) be the second derivative of 0 + 1/18*f**3 + 1/9*f**4 + 0*f**2 + 1/15*f**r - f. Factor s(n).
n*(2*n + 1)**2/3
Let j(b) be the first derivative of -b**5/5 + 5*b**4/4 - 3*b**3 + 7*b**2/2 - 2*b - 4. Factor j(a).
-(a - 2)*(a - 1)**3
Let r be (-1)/((-70)/(-20)) + 4/14. Factor -6/7*m - 3/7*m**2 + r.
-3*m*(m + 2)/7
Let g(l) be the third derivative of -l**9/1512 + l**8/168 - 2*l**7/105 + l**6/45 + l**3/2 - l**2. Let u(s) be the first derivative of g(s). Factor u(o).
-2*o**2*(o - 2)**2*(o - 1)
Let n(l) = l**3 - 7*l**2 - 8*l + 2. Let o(h) = -h**3 + 4*h**2 + 7*h - 2. Let m be o(5). Let c be n(m). Factor -r**c + r**3 + 50 - 50.
r**2*(r - 1)
Let w(x) be the third derivative of x**7/525 - x**6/300 - x**5/75 - 9*x**2. Solve w(p) = 0 for p.
-1, 0, 2
Let r be (3 - -1)/8*(-1 - -1). Let f(y) be the third derivative of 1/50*y**6 + 0 + r*y - y**2 - 1/30*y**4 + 0*y**3 - 1/150*y**5. Factor f(c).
2*c*(2*c + 1)*(3*c - 2)/5
Let g(b) = b**3 + 9*b**2 + 18*b + 2. Let t be g(-6). Solve -1/4*u + 1/4*u**t - 1/2 = 0 for u.
-1, 2
Let j = 77/50 + -3/2. Let m(k) be the first derivative of j*k**5 + 1/10*k**2 - 1 + 1/5*k**3 + 0*k + 3/20*k**4. Factor m(n).
n*(n + 1)**3/5
Let n(t) be the third derivative of 4*t**7/105 - t**6/12 + t**5/30 + 3*t**2. Find g, given that n(g) = 0.
0, 1/4, 1
Suppose -2*d + 3*d = 0. Suppose d = -w + 5*z - 3 + 23, -20 = w + 5*z. Solve -1/3*a**4 + 1/3*a**2 + w - 1/3*a + 1/3*a**3 = 0.
-1, 0, 1
Let o(l) = -43*l + 1. Let p be o(-1). Let q be (p/99)/((-2)/(-3)). Factor 4/3*a + 0 + 2/3*a**2 - q*a**3.
-2*a*(a - 2)*(a + 1)/3
Let i(c) be the second derivative of c**7/63 - c**5/15 + c**3/9 - 10*c. Factor i(p).
2*p*(p - 1)**2*(p + 1)**2/3
Suppose 2*f + 2*f - 92 = 0. Find c, given that -4*c**2 - 12*c**2 - 74*c**2 - 4 - 15*c - f*c = 0.
-2/9, -1/5
Let y = 1115/2 - 557. Let f(z) = -z**3 - 2*z**2 - z + 1. Let t be f(-2). Let y*n**4 - 1/4*n + 0*n**t + 1/4*n**5 - 1/2*n**2 + 0 = 0. What is n?
-1, 0, 1
Let k(c) be the third derivative of -c**5/150 + c**4/10 - 3*c**3/5 + 3*c**2. Factor k(i).
-2*(i - 3)**2/5
Suppose 5*h - 16 = 4. Factor 2*y**3 - 2*y + 7*y**3 - 2*y**5 - 5*y**3 - h*y**2 + 2*y**4 + 2.
-2*(y - 1)**3*(y + 1)**2
Let z(p) = -20*p**2 + 44*p - 8. Let m(j) = -7*j**2 + 15*j - 3. Let i(h) = 16*m(h) - 5*z(h). Factor i(k).
-4*(k - 1)*(3*k - 2)
Let o(b) be the first derivative of b**7/42 + b**6/15 - b**4/6 - b**3/6 - 2*b - 3. Let q(f) be the first derivative of o(f). Factor q(z).
z*(z - 1)*(z + 1)**3
Let r(b) = -b - 1. Let v(n) = -n**2 - 9*n + 9. Let i(p) = -2*p**2 - 14*p + 13. Let k(c) = 5*i(c) - 7*v(c). Let d(o) = -k(o) - 2*r(o). Factor d(x).
3*x*(x + 3)
Let v(x) be the second derivative of -x**6/10 + 9*x**5/10 - 3*x**4 + 4*x**3 - 37*x. Let v(a) = 0. Calculate a.
0, 2
Let q be (27/(-675))/((-6)/5 + 1). Solve 0 + q*r**2 + 1/5*r**3 + 0*r = 0 for r.
-1, 0
Let c be ((-12)/9)/((-4)/6). Suppose 0 = -b - c*b + 6. Solve 1 - m - m**3 - m - m**b + 3*m = 0.
-1, 1
Let w(n) be the first derivative of 2*n**3/39 - 2*n/13 - 4. Let w(q) = 0. What is q?
-1, 1
Let a(u) be the first derivative of 2*u**6/21 - 8*u**5/35 + 8*u**3/21 - 2*u**2/7 - 9. Factor a(p).
4*p*(p - 1)**3*(p + 1)/7
Suppose 2*i - 8 = -2*d, i + 5 = 4*i - 4*d. Let s(n) be the third derivative of 1/90*n**5 + 2*n**2 + 1/27*n**i - 1/36*n**4 - 1/540*n**6 + 0*n + 0. Factor s(w).
-2*(w - 1)**3/9
Let q(x) be the third derivative of x**7/70 + x**6/10 + 3*x**5/20 - x**4/2 - 2*x**3 - 6*x**2. Factor q(t).
3*(t - 1)*(t + 1)*(t + 2)**2
Let x(u) be the first derivative of -9*u**5/20 - 7*u**4/16 + u**3/6 + 41. Factor x(s).
-s**2*(s + 1)*(9*s - 2)/4
Let p(a) be the second derivative of a**8/448 - a**7/140 + a**5/40 - a**4/32 + 5*a**2/2 + 2*a. Let j(h) be the first derivative of p(h). Factor j(g).
3*g*(g - 1)**3*(g + 1)/4
Let d(h) be the second derivative of h**6/180 - h**5/120 - h**4/72 + h**3/36 + 8*h. Factor d(i).
i*(i - 1)**2*(i + 1)/6
Suppose 4*f = 5*n + 15, n = -5*f - 4*n - 15. Factor 0 - t**5 + 0*t + f*t**2 + 1/2*t**4 + 1/2*t**3.
-t**3*(t - 1)*(2*t + 1)/2
Factor 0*y + 231*y**5 - 10*y**2 - 5*y - 226*y**5 + 0*y + 10*y**4.
5*y*(y - 1)*(y + 1)**3
Let x = 158 - 2369/15. Let m(d) be the second derivative of -1/20*d**5 + 0*d**4 + 3*d + 0*d**2 + x*d**6 - 1/42*d**7 + 0 + 0*d**3. Factor m(h).
-h**3*(h - 1)**2
Let 3*z**2 + 4*z**2 - 28*z - 2*z**2 - z**2 + 24 = 0. What is z?
1, 6
Suppose -4*g = 20 - 32. Suppose -2/5*n**g + 2*n - 2/5*n**2 - 6/5 = 0. What is n?
-3, 1
Let u(g) be the first derivative of g**4/22 + 6*g**3/11 + 24*g**2/11 + 32*g/11 - 7. Factor u(z).
2*(z + 1)*(z + 4)**2/11
Let t(d) = -23*d + 4*d**2 - 5*d + 10*d - 3*d**2 + 2. Let h be t(18). Find k such that 5/2*k**4 + 9/2*k**h + 6*k**3 + k + 0 = 0.
-1, -2/5, 0
Suppose -9*a + 6 = 2*c - 10*a, -4*a - 15 = -5*c. Suppose 2/11*t**c + 2/11*t**2 + 0 + 0*t = 0. Calculate t.
-1, 0
Let t(h) be the third derivative of -11*h**8/84 + 4*h**7/105 + 11*h**6/30 - 2*h**5/15 - 3*h**2. Let t(b) = 0. What is b?
-1, 0, 2/11, 1
Let j(f) be the first derivative of 2*f**3/15 - 2*f**2 + 29. Factor j(o).
2*o*(o - 10)/5
Let c(p) be the third derivative of -p**7/56 + 3*p**6/160 + 7*p**5/80 - 3*p**4/32 - p**3/4 + 13*p**2. Let c(b) = 0. What is b?
-1, -2/5, 1
Let a be (-21)/(-2)*(-6)/(-42). Factor -45/2*r**2 + 39/2*r**3 - 6*r**4 - a + 21/2*r.
-3*(r - 1)**3*(4*r - 1)/2
Factor -1/4*y + 0*y**2 + 1/2*y**3 + 0*y**4 - 1/4*y**5 + 0.
-y*(y - 1)**2*(y + 1)**2/4
Let x(n) be the first derivative of n**7/840 + n**6/480 - n**5/240 - n**4/96 + n**2/2 + 1. Let y(t) be the second derivative of x(t). Factor y(g).
g*(g - 1)*(g + 1)**2/4
Let d(r) be the second derivative of r**4/12 + r**3 + 9*r**2/2 + 6*r. Solve d(i) = 0 for i.
-3
Factor 0*g**4 + 9*g**3 - 3*g**4 + 0*g**2 - 3*g**2 - 3*g**2.
-3*g**2*(g - 2)*(g - 1)
Let z(y) be the third derivative of y**6/150 - y**5/25 + y**4/10 - 2*y**3/15 - 4*y**2. Determine v, given that z(v) = 0.
1
Suppose 4*h + x - 7 = 0, 2*h + x - 4*x = 21. Let d be (3 - 3) + -3 + h. Determine y so that 2/7*y + 2/7*y**2 - 2/7*y**3 - 2/7*y**4 + d = 0.
-1, 0, 1
Let k(s) = -s**3 - s**2 - s - 1. Let r be k(-1). Factor r*d + 0*d**2 + 0 + 3/5*d**4 + 1/5*d**5 + 2/5*d**3.
d**3*(d + 1)*(d + 2)/5
Factor 2*x**2 + 4*x**3 + 0*x**4 - 2*x**4 + x**5 + 0*x**4 - 2*x**4 - 5*x + 2.
(x - 2)*(x - 1)**3*(x + 1)
Let u be 8/20 + 36/10. Factor -10*c**3 + 0*c**3 + 14*c**2 + u*c - 8*c.
-2*c*(c - 1)*(5*c - 2)
Suppose -14*p - 15 = -19*p. Let j(x) be the second derivative of -1/24*x**4 + 1/4*x**2 + 0 + 0*x**3 + p*x. Find g, given that j(g) = 0.
-1, 1
Let w = 5 + -1. Suppose -x + 14 = 3*d, 2*x = d - x + 2. Factor -4*t**w - t**d + 3*t**4.
-2*t**4
Let r be 1/3 + 4/(-3). Let o be (r/3)/((-15)/270). Factor 22/3*h**3 + 7/3*h - 13/3*h**4 - 1/3 + h**5 - o*h**2.
(h - 1)**4*(3*h - 1)/3
Let 3*b**3 - 4*b**2 - 4*b**5 + b + 0*b**5 + 5*b**4 - b**2 = 0. Calculate b.
-1, 0, 1/4, 1
Let z(w) = -7*w**3 + 12*w**2 + 40*w + 3. Let b(y) = y**3 - 1. Let l(j) = 3*b(j) + z(j). Factor l(v).
-4*v*(v - 5)*(v + 2)
Let u(b) be the second derivative of 0 + 1/2*b**2 - b + 1/120*b**6 + 1/6*b**3 - 1/16*b**4 - 1/40*b**5. Factor u(a).
(a - 2)**2*(a + 1)**2/4
Find b such that -1/2*b**2 + 0 + b = 0.
0, 2
Let -14*r**4 + 13*r**2 - 6*r - 53*r**2 - 62*r**3 - 2*r + 16*r**3 = 0. Calculate r.
-2, -1, -2/7, 0
Find c, given that