u) be the first derivative of -u**4/16 - u**3/3 - 3*u**2/8 - 15. Factor f(i).
-i*(i + 1)*(i + 3)/4
Let o(c) be the second derivative of -c**7/2940 + c**6/420 - c**5/140 + c**4/84 - 2*c**3/3 - c. Let a(i) be the second derivative of o(i). Factor a(q).
-2*(q - 1)**3/7
Let a(r) be the second derivative of 0*r**3 + 1/21*r**7 + 0 + 1/3*r**4 + 0*r**2 - 1/10*r**5 - 2/15*r**6 + 9*r. Let a(m) = 0. What is m?
-1, 0, 1, 2
Let z be 91/35 - 4/(-10). Let i(r) be the second derivative of 0*r**2 - 7/15*r**6 + r - 1/5*r**5 + 2/3*r**z + 0 + 7/6*r**4. Let i(u) = 0. What is u?
-1, -2/7, 0, 1
Let v(m) = -4*m**3 - 16*m**2 + 2*m. Let y(j) = -17*j**3 - 63*j**2 + 9*j. Let b(l) = -18*v(l) + 4*y(l). Factor b(h).
4*h**2*(h + 9)
Let s(m) be the second derivative of -3*m**5/20 + m**4/2 - m**3/2 + 3*m. Factor s(p).
-3*p*(p - 1)**2
Let c(j) be the first derivative of j**6/120 - j**5/40 - j**4/4 + j**3 - 2. Let l(i) be the third derivative of c(i). Suppose l(p) = 0. Calculate p.
-1, 2
Factor -262*k**3 + 259*k**3 - 6*k**2 + 17*k - 8*k.
-3*k*(k - 1)*(k + 3)
Suppose 0 = 2*u - 3 - 5. Factor 5*k**2 + 7*k**u + 2*k**3 - 3*k**4 - 7*k**2.
2*k**2*(k + 1)*(2*k - 1)
Let o be (-6 - -3) + 13/3. Let h(g) = -g**2 + 5*g - 2. Let r be h(3). Find n, given that -14/3*n**2 - 2*n**r + 16/3*n**3 + o*n + 0 = 0.
0, 2/3, 1
Let q = 2143/129 + -12/43. Suppose 0 = -4*v + v + 6. Factor 4/3 - q*w**3 + 8*w + 7*w**v.
-(w - 1)*(7*w + 2)**2/3
Let x(s) = 2 - 4 + 1. Let r(h) = -5*h**2 + 3*h - 4. Let c(i) = 6*i**2 - 4*i + 4. Let a(f) = -6*c(f) - 7*r(f). Let q(l) = -a(l) - 6*x(l). Factor q(t).
(t - 2)*(t - 1)
Let d be (-34)/120 - (-15)/45. Let x(y) be the third derivative of -4*y**2 - d*y**6 + 1/3*y**4 + 0 + 0*y**3 + 0*y - 1/105*y**7 + 0*y**5. Factor x(z).
-2*z*(z - 1)*(z + 2)**2
Suppose j = -3*g + 9 - 0, -4*j = -3*g - 6. Let v(l) = -l + 7. Let q be v(5). Suppose g*w**q - 2*w - w**3 + w + 0*w = 0. Calculate w.
0, 1
Factor 1/2*h**4 + 0*h**2 - 1/2 - h + h**3.
(h - 1)*(h + 1)**3/2
Factor 9/5*i**2 + 16/5 + 1/5*i**3 + 24/5*i.
(i + 1)*(i + 4)**2/5
Let o(v) = -v**4 + 5*v**3 + 2*v**2 - 5*v - 1. Let m(g) be the second derivative of g**5/20 - g**3/6 - 3*g. Let k(b) = -5*m(b) + o(b). What is s in k(s) = 0?
-1, 1
Let l be (-4)/(-18)*126/960. Let s(b) be the third derivative of -1/96*b**6 - l*b**5 + 0*b**3 - 2*b**2 + 0 - 1/48*b**4 + 0*b. What is f in s(f) = 0?
-1, -2/5, 0
Factor -5*m - 9 + 8 - m**2 - 2 - 1.
-(m + 1)*(m + 4)
Let v be (-7 - 710/(-100))/(2/16). Find c, given that -v*c + 0 + 0*c**2 - 1/5*c**4 + 3/5*c**3 = 0.
-1, 0, 2
Let p = -16 - -21. Let d(w) be the third derivative of -1/210*w**7 + 1/60*w**6 + 0*w + 1/6*w**3 + 0 - 1/12*w**4 - w**2 + 0*w**p. Factor d(h).
-(h - 1)**3*(h + 1)
Let s(f) be the first derivative of -7*f**4/10 - 4*f**3/15 + 7*f**2/5 + 4*f/5 + 2. What is g in s(g) = 0?
-1, -2/7, 1
Let m(r) be the first derivative of 3*r**5/5 - 5*r**3 + 12*r - 17. Find g such that m(g) = 0.
-2, -1, 1, 2
Factor 16/3*s + 0*s**3 + 4*s**2 + 2 - 2/3*s**4.
-2*(s - 3)*(s + 1)**3/3
Let r(b) be the second derivative of 1/12*b**4 - 1/18*b**3 + 1/12*b**5 + 0*b**2 - 1/30*b**6 - 2*b + 0 - 2/63*b**7. What is o in r(o) = 0?
-1, 0, 1/4, 1
Let s(p) be the third derivative of p**11/332640 + p**10/75600 + p**9/60480 + p**5/60 + 4*p**2. Let g(x) be the third derivative of s(x). Factor g(v).
v**3*(v + 1)**2
Suppose -20 = -2*c - 3*c. Suppose -c*x = -13 + 5. What is m in 0*m**x - m - m**2 + 2*m = 0?
0, 1
Let p(o) = -2*o**3 - 8*o**2 + 2*o. Let d(n) = -2*n**3 - 9*n**2 + 3*n. Suppose -7*s = -9*s + 10. Let x(m) = s*p(m) - 4*d(m). Solve x(u) = 0 for u.
-1, 0
Let l = 3 - -2. Suppose -l*z + 4*z = -2. What is u in -2 + z*u**2 - 3*u - 2*u**2 + 2*u**2 + 2*u**3 + u = 0?
-1, 1
Suppose -17*r + 23*r - 24 = 0. What is m in -4/5*m**r + 0 + 2*m**5 - 8/5*m + 32/5*m**2 - 6*m**3 = 0?
-2, 0, 2/5, 1
Let f = -332 - -332. Factor f + 3/4*c**2 - 3/4*c.
3*c*(c - 1)/4
Suppose -4*j - 2*a + 6 = 0, 4*a - 2*a = -3*j + 2. Suppose 5*k - j*k = 2. What is q in 0 + 1/2*q**3 - 1/2*q + 0*q**k = 0?
-1, 0, 1
Suppose -f + 18 = -4*o, 0 = -2*f - 5*o + 2*o - 8. Factor -1/2*h**4 + 0 - h - 5/2*h**2 - f*h**3.
-h*(h + 1)**2*(h + 2)/2
Let z(v) be the second derivative of -v**5/80 - 5*v**4/48 + 20*v + 2. Solve z(o) = 0 for o.
-5, 0
Let l(j) be the third derivative of -j**8/336 + j**7/210 + j**6/120 - j**5/60 - j**2. Factor l(a).
-a**2*(a - 1)**2*(a + 1)
Suppose 2*n = 3*n - 3. Factor -7*d**n + d + 5*d**2 + 7*d**3 + 4*d**3.
d*(d + 1)*(4*d + 1)
Suppose -h - 8 = -5*h. Let u(l) = -4*l. Let w be u(-1). Let h*k**4 - 2*k**2 + 4*k**4 - 4*k**w - 4*k**3 + 4*k = 0. Calculate k.
-1, 0, 1, 2
Let y(k) be the first derivative of -15*k**6/14 - 27*k**5/35 + 19*k**4/14 + 4*k**3/7 - 4*k**2/7 - 6. Find x such that y(x) = 0.
-1, -2/3, 0, 2/5, 2/3
Suppose 3 = f - 3. Let b(i) = -i**4 + 2*i**3 + 2. Let y(h) = -2*h**4 + 3*h**3 + 3. Let k(p) = f*b(p) - 4*y(p). Factor k(g).
2*g**4
Let w(l) be the third derivative of l**6/40 + l**5/10 + 7*l**2. Factor w(i).
3*i**2*(i + 2)
Let t(p) be the first derivative of p**3/6 + p**2/4 - p - 6. Factor t(v).
(v - 1)*(v + 2)/2
Let d(o) = 5 + 5 - 9 + 8 + o. Let v be d(-7). Factor n**4 + 2 + n**3 - v*n**2 - 2.
n**2*(n - 1)*(n + 2)
Let w(y) be the first derivative of -2 + 5/4*y**2 + 1/10*y**5 - 1/8*y**4 - 1/2*y**3 - y. Factor w(b).
(b - 1)**3*(b + 2)/2
Factor -15/2*j**3 + 1/2*j**5 + 5*j**2 - 36 + 0*j**4 + 30*j.
(j - 2)**3*(j + 3)**2/2
Let l(r) be the second derivative of 0 - 1/24*r**4 + r - 1/4*r**3 - 1/2*r**2. Factor l(h).
-(h + 1)*(h + 2)/2
Let z(j) = -j**2 + 3*j + 10*j**3 - 11*j**3 - 2*j + j**4. Let b(c) = -10*c**4 + 9*c**3 + 12*c**2 - 11*c. Let i(s) = 2*b(s) + 22*z(s). Solve i(h) = 0.
0, 1
Let l(g) be the first derivative of -g**6/180 - g**5/60 + 2*g - 1. Let a(x) be the first derivative of l(x). Factor a(q).
-q**3*(q + 2)/6
Let b(k) be the third derivative of k**8/2352 - k**7/1470 - k**6/280 + k**5/420 + k**4/84 - 7*k**2. Factor b(s).
s*(s - 2)*(s - 1)*(s + 1)**2/7
Let x(l) = -22*l**2 + 32*l + 12. Let n(k) = 65*k**2 - 96*k - 35. Let o(p) = 4*n(p) + 11*x(p). Solve o(z) = 0 for z.
-2/9, 2
Solve 8/5*c**3 - 22/5*c**2 + 2*c + 4/5 = 0.
-1/4, 1, 2
Let u(n) be the second derivative of -3*n + 1/30*n**6 + 3/4*n**4 + 0 - 7/6*n**3 + n**2 - 1/4*n**5. Let u(r) = 0. Calculate r.
1, 2
Factor -28/5*z - 36/5*z**2 - 4/5*z**4 - 4*z**3 - 8/5.
-4*(z + 1)**3*(z + 2)/5
Let s(r) be the first derivative of -3 + 2/15*r**3 + 0*r + 1/10*r**2 + 1/20*r**4. Factor s(g).
g*(g + 1)**2/5
Let m(d) be the third derivative of 1/8*d**4 + d**2 - 1/5*d**3 + 0 - 3/100*d**5 + 1/350*d**7 - 1/200*d**6 + 0*d. Determine o, given that m(o) = 0.
-2, 1
Factor 12/5 - 16/5*i + 4/5*i**2.
4*(i - 3)*(i - 1)/5
Let q(p) be the first derivative of 2*p**5/55 - p**4/11 - 10*p**3/33 + 6*p**2/11 - 38. Factor q(f).
2*f*(f - 3)*(f - 1)*(f + 2)/11
Let k(o) be the first derivative of o**4/6 - o**3/3 - o + 2. Let z(n) be the first derivative of k(n). Factor z(x).
2*x*(x - 1)
Let x(n) be the third derivative of n**9/60480 - n**8/13440 + n**4/8 + 2*n**2. Let h(t) be the second derivative of x(t). Find i such that h(i) = 0.
0, 2
Let w = 13/2 - 37/6. Let q(m) be the first derivative of -2/15*m**5 - 1/9*m**6 + 2 + 4/9*m**3 + w*m**4 - 1/3*m**2 - 2/3*m. Suppose q(u) = 0. What is u?
-1, 1
Solve -3*d**3 + d**2 + 20*d - 24*d - 4 + 4*d**3 = 0.
-2, -1, 2
Let c(l) be the first derivative of l**4/30 - 4*l**3/45 + l**2/15 - 6. Factor c(s).
2*s*(s - 1)**2/15
Let u = 553/24 - -31/24. Let v = 25 - u. Factor 0 - 4/3*l**2 + 2/3*l**3 + v*l.
2*l*(l - 1)**2/3
Let k be -4*4/(-8)*1. Find w such that k*w**4 - 3*w**3 + 3*w**2 - w - w**4 + 0*w**4 = 0.
0, 1
Let w(m) be the second derivative of m**6/160 - 3*m**5/40 + 9*m**4/32 - 3*m**2/2 + 5*m. Let x(y) be the first derivative of w(y). Factor x(l).
3*l*(l - 3)**2/4
Let o(r) be the third derivative of r**6/120 - r**3 - r**2. Let h(y) be the first derivative of o(y). Factor h(l).
3*l**2
Solve -4*t**2 + 0*t**2 - 12*t + 32*t = 0 for t.
0, 5
Factor 324*i + 54*i**2 + 641 - 4*i**3 + 7*i**3 + 7.
3*(i + 6)**3
Let i(z) be the third derivative of -z**8/1260 - z**7/105 - z**6/150 + 7*z**5/450 - 61*z**2. Find t, given that i(t) = 0.
-7, -1, 0, 1/2
Let d(l) be the first derivative of 4*l**6/27 - 2*l**5/5 - l**4/9 + 2*l**3/3 - 2*l**2/9 - 4. Suppose d(a) = 0. Calculate a.
-1, 0, 1/4, 1, 2
Let k(p) be the first derivative of -p**4/24 - p**3/