
Let o(g) be the third derivative of -g**7/70 + g**6/8 - g**5/20 - 21*g**4/8 + 9*g**3 - 2*g**2 - 38. Factor o(c).
-3*(c - 3)**2*(c - 1)*(c + 2)
Suppose c = 4*j - 2, 0 = -4*j - c - 4*c - 10. Let w(f) be the first derivative of -3/8*f**2 + 1/16*f**4 - 1 + j*f**3 - 1/2*f. Factor w(r).
(r - 2)*(r + 1)**2/4
Let d = -10 + 15. Factor s**3 + s + 28 - d*s**2 - 28 + 3*s**2.
s*(s - 1)**2
Let r(c) be the first derivative of -1/10*c**6 - 3 - 9/10*c**4 + 0*c + 12/25*c**5 - 3/10*c**2 + 4/5*c**3. Factor r(w).
-3*w*(w - 1)**4/5
Let h(q) = q + 12. Let y be h(10). Let w = y - 94/5. Factor -6/5*t**3 + 4/5 + w*t**2 - 14/5*t.
-2*(t - 1)**2*(3*t - 2)/5
Let o = -4 + 8. Factor 2*y**3 - 3*y**2 + 0*y**2 + 8*y**o + 4 - 4*y - 7*y**4.
(y - 1)**2*(y + 2)**2
Factor -2/5*h**3 + 0*h + 0 + 2/5*h**2.
-2*h**2*(h - 1)/5
Factor -2099*s + 4*s**3 + 6*s**2 + 2*s**2 + 2099*s.
4*s**2*(s + 2)
Let n be 6/(-5)*-15*(-1)/(-3). Let y(z) be the third derivative of 0*z - 1/30*z**5 + 1/3*z**3 + 1/60*z**n + 2*z**2 - 1/12*z**4 + 0. Solve y(o) = 0.
-1, 1
Let z(g) be the second derivative of g**4/12 - 5*g**3/6 + 3*g**2 + g. Let i be z(4). Factor 0*o**2 - 3*o + 0*o + 2*o**i + 5*o.
2*o*(o + 1)
Suppose -5*i + 0*i + 5 = 5*n, n + 5*i + 3 = 0. Suppose -s = -2*s + 2. Find x such that 0 + 3 - s + x**2 + n*x = 0.
-1
Let u(v) be the third derivative of -v**8/336 - v**7/70 - v**6/120 + v**5/20 + v**4/12 + 2*v**2. Determine p so that u(p) = 0.
-2, -1, 0, 1
Let s(c) be the first derivative of -c**6/18 + c**4/3 + 2*c**3/9 - c**2/2 - 2*c/3 + 12. Factor s(g).
-(g - 2)*(g - 1)*(g + 1)**3/3
Suppose -3*c = 2*c - 10. What is n in -6*n**4 + 18*n**3 + 0*n**3 - 8*n - n + 0*n**3 + 12*n**c - 9*n**5 - 6 = 0?
-1, -2/3, 1
Determine h, given that 6/11*h - 6/11*h**3 + 0 - 2/11*h**2 + 2/11*h**4 = 0.
-1, 0, 1, 3
Let l(d) = -d + 1. Let b be l(-1). Solve 5*o**4 + 14*o**b - 4*o**4 - 15*o**2 = 0.
-1, 0, 1
Suppose -3*q + 0*q = 42. Let u = q + 29. Let 8 + 27*y + 243*y**3 + 270*y**2 + u*y + 42*y = 0. Calculate y.
-2/3, -2/9
Factor -21*x**3 + 19*x**3 + 0*x**5 + x**5 + 3*x**4 - 2*x**5.
-x**3*(x - 2)*(x - 1)
Let m(k) = 2*k**2 - 10*k + 14. Let s(g) = -2*g**2 + 10*g - 15. Let w(r) = 7*m(r) + 6*s(r). Solve w(q) = 0.
1, 4
What is c in -c**2 - 2*c**2 - 2*c**2 + 16*c + 32 + 7*c**2 = 0?
-4
Suppose 13*t - 65 = -0*t. Let s(z) be the first derivative of 0*z**4 - 4/55*z**t - 2 + 4/33*z**3 - 1/11*z**2 + 0*z + 1/33*z**6. What is o in s(o) = 0?
-1, 0, 1
Let i be -4 + 0/(-3) - 23. Let x = i - -27. Determine q so that 0 + 2/7*q**2 - 2/7*q**4 + x*q + 0*q**3 = 0.
-1, 0, 1
Factor 2/5*n**4 + 0*n**2 + 0*n - 4/5*n**3 + 0.
2*n**3*(n - 2)/5
Let z(a) = 9*a + 1. Let u be z(1). Let g be (-10)/(-25) + 16/u. Factor -2*d**g + 4*d**2 - d + 2*d**3 - 3*d.
2*d*(d - 1)*(d + 2)
Let w(x) be the first derivative of -x**4/4 - 2*x**3/3 - x**2/2 - 4. Factor w(h).
-h*(h + 1)**2
Factor -1/5*q**2 + 1/5*q + 2/5.
-(q - 2)*(q + 1)/5
Suppose 3/2*w + 0 + 9/2*w**2 + 3/2*w**4 + 9/2*w**3 = 0. Calculate w.
-1, 0
Factor -2*z - 10*z + 18 - 10 + 4*z**3.
4*(z - 1)**2*(z + 2)
Let r = 11 - 32/3. Solve 0 + 2/3*d**2 - r*d + d**3 = 0 for d.
-1, 0, 1/3
Let p(f) be the second derivative of 1/360*f**6 + 1/40*f**5 - 3*f + 1/12*f**4 + 0*f**2 + 1/6*f**3 + 0. Let w(r) be the second derivative of p(r). Factor w(a).
(a + 1)*(a + 2)
Let k(o) be the third derivative of o**7/42 + o**6/12 + o**5/12 + 13*o**2. Suppose k(m) = 0. What is m?
-1, 0
Let y(i) be the first derivative of -i**5/2 - i**4/2 + 4*i**3 - 4*i**2 - 3*i + 5. Let n(r) be the first derivative of y(r). Factor n(s).
-2*(s - 1)*(s + 2)*(5*s - 2)
Factor 8*g**2 + 5*g**4 - 28*g**2 + 0*g**4.
5*g**2*(g - 2)*(g + 2)
Factor 12*r**4 + 13*r - 3*r**5 + 2*r - 691*r**3 - 6 + 679*r**3 - 6*r**2.
-3*(r - 2)*(r - 1)**3*(r + 1)
Let p(u) be the first derivative of -3*u**5/20 - u**4/12 + u**3/2 + u**2/2 - 2*u - 2. Let m(x) be the first derivative of p(x). Factor m(w).
-(w - 1)*(w + 1)*(3*w + 1)
Let j(y) = y**3 - 4*y**2 + y - 1. Let a be j(4). Factor -3*q**3 - q**a + 8*q**2 - 8*q - q**3 + 3*q**3.
-2*q*(q - 2)**2
Let j(l) be the third derivative of 1/168*l**8 + 0*l**4 + 0*l**3 + 0*l + l**2 + 1/105*l**7 - 1/60*l**6 + 0 - 1/30*l**5. Factor j(n).
2*n**2*(n - 1)*(n + 1)**2
Let o be (12/(-18))/((-2)/6). Let w(d) be the first derivative of -1/3*d**3 + o*d**2 + 2 - 4*d. Factor w(x).
-(x - 2)**2
Let a(p) be the third derivative of 16*p**5/15 + 4*p**4 + 6*p**3 + 4*p**2. Factor a(z).
4*(4*z + 3)**2
Find x such that 2 + 26*x**2 - 26*x + 2 - 18*x**3 + 13*x**2 + x**2 = 0.
2/9, 1
Let h(c) be the first derivative of -c**5/40 + c**4/2 - 4*c**3 + c**2/2 + 2. Let q(i) be the second derivative of h(i). Factor q(w).
-3*(w - 4)**2/2
Let a(y) be the second derivative of -y**7/1575 + y**6/1800 - y**4/2 + y. Let c(z) be the third derivative of a(z). Factor c(h).
-2*h*(4*h - 1)/5
Let s(h) be the third derivative of -h**5/30 + h**4 - 12*h**3 + 22*h**2. Solve s(d) = 0 for d.
6
Let a(j) be the first derivative of 27*j**4/8 + 75*j**3/2 + 66*j**2 + 42*j - 29. Factor a(z).
3*(z + 7)*(3*z + 2)**2/2
Suppose -3*l - 10 = -16. Factor 4/5*z + 0 - 2/5*z**l.
-2*z*(z - 2)/5
Suppose -3*c - 2*c = -15, 3*c = 5*w + 9. Let g be ((2 - 3) + w)*-4. Factor 4*s**3 - 5*s**3 + g*s**4 + 3*s**3.
2*s**3*(2*s + 1)
Let u(b) = -b**3 - 2*b - 1. Suppose 4 = 3*g + 7. Let d be u(g). What is r in 1/2 + 1/2*r**d - r = 0?
1
Let y(a) be the second derivative of -a**6/6 + a**5/2 + 5*a**4/3 - 5*a**3/3 - 15*a**2/2 + 7*a. Factor y(u).
-5*(u - 3)*(u - 1)*(u + 1)**2
Let f be (-1 - (0 - 1))/(-1). Let w(u) be the third derivative of 2*u**2 + 0*u**3 + f - 1/30*u**5 + 0*u + 0*u**4 - 1/30*u**6. Find y such that w(y) = 0.
-1/2, 0
Let b(d) be the third derivative of d**7/70 + d**6/20 - d**4/4 - d**3/2 + 22*d**2. Factor b(i).
3*(i - 1)*(i + 1)**3
Let y = -60 + 112. Let u be y/72 + 2/(-4). Factor -2/9*o - 4/9*o**2 + 0 - u*o**3.
-2*o*(o + 1)**2/9
Let u(l) be the third derivative of l**5/60 - 5*l**4/24 + 29*l**2. Factor u(s).
s*(s - 5)
Let u be 52/14 - 14/(-49). Find z, given that -3*z**2 + 4*z**u - 6*z**3 + 3*z**2 + 2*z**3 = 0.
0, 1
Let u(d) be the third derivative of 1/15*d**5 + 0 + 0*d**3 + 1/105*d**7 - d**2 - 1/20*d**6 + 0*d**4 + 0*d. Factor u(t).
2*t**2*(t - 2)*(t - 1)
Let s = 7 + -2. Determine y so that 2*y**2 + y + y**s - 19 - 4*y**3 - y**4 + 18 + 2*y**3 = 0.
-1, 1
Let n(q) be the third derivative of -q**5/120 - q**4/8 - 5*q**3/12 + 5*q**2. Factor n(h).
-(h + 1)*(h + 5)/2
Let z(h) be the first derivative of 4*h**5/5 + 2*h**4 - 16*h**3/3 - 16*h**2 - 19. Factor z(s).
4*s*(s - 2)*(s + 2)**2
Let l(m) be the first derivative of 0*m - 1/3*m**3 - 1/2*m**2 + 4. Factor l(t).
-t*(t + 1)
Let w(r) = 4*r**3 - 2*r + 1. Let l(g) = -g**2 - 10*g - 8. Let v be l(-9). Let u be w(v). Determine b so that 2*b**3 - b**4 - 2*b**4 + 4*b**3 - u*b**2 = 0.
0, 1
Let w(m) be the third derivative of 0*m + 0*m**4 + 0 - 2*m**2 + 1/3*m**3 - 1/30*m**5. Factor w(v).
-2*(v - 1)*(v + 1)
Find r such that 4*r**3 + 74*r**2 + 0 - 66*r**2 + 0 = 0.
-2, 0
Factor -5*h**4 + 16*h**2 + h**4 + 3*h**3 - 193*h + h**3 + 177*h.
-4*h*(h - 2)*(h - 1)*(h + 2)
Let j(u) be the third derivative of -u**10/7560 - u**9/2520 - u**8/3360 - u**4/4 + 2*u**2. Let l(y) be the second derivative of j(y). Factor l(c).
-2*c**3*(c + 1)*(2*c + 1)
Let h = 364 + -5452/15. Let j = -1/5 + h. Let 2/3*z + j + 1/3*z**2 = 0. What is z?
-1
Let z(m) = -m. Let g be z(-5). Let d(h) be the second derivative of 0*h**2 + 0 - 1/2*h**4 + 3*h - 1/2*h**3 - 3/20*h**g. Suppose d(k) = 0. What is k?
-1, 0
Let m(g) be the first derivative of 3*g**4/4 + 6*g**3 + 18*g**2 + 24*g - 11. Suppose m(q) = 0. Calculate q.
-2
Suppose 5*m - 78 = 3*w, 0*w + 5*m = 2*w + 52. Let o be (39/w)/((-54)/8). Factor o - 14/9*x - 26/9*x**3 + 8/9*x**4 + 10/3*x**2.
2*(x - 1)**3*(4*x - 1)/9
Suppose 0*k = -6*k + 18. Suppose -2*w + 3*a = k, -3*w - 3 + 5 = 2*a. Suppose -1/3*q**2 - 1/3*q**3 + w*q + 0 = 0. What is q?
-1, 0
Suppose 10 + 8 = 3*r. Let l(t) be the first derivative of 1/5*t**5 + 1/2*t**2 - 2/9*t**3 - 1/3*t - 1/6*t**4 - 1/18*t**r - 1. Solve l(m) = 0 for m.
-1, 1
Let i(a) be the first derivative of -1/4*a**2 - 1/3*a**3 - 1/8*a**4 - 3 + 0*a. Find x, given that i(x) = 0.
-1, 0
Suppose 0 = -29*r + 25*r + 12. Determine b so that 0 - 1/2*b**r + 1/2*b**2 - 1/2*b**4 + 1/2*b**5 + 0*b = 0.
-1, 0, 1
Let l(m) be the second derivative of -m**4/24 - 3*m**3/4 + 43*m. Determin