**2 = 0.
-1, -1/2, 0, 2/3
Let t be (-6)/2 + -2 + -1. Let i(m) = 15*m**4 - 9*m**3 + 15*m**2 + 13*m. Let g(w) = 7*w**4 - 4*w**3 + 7*w**2 + 6*w. Let o(a) = t*i(a) + 13*g(a). Factor o(u).
u**2*(u + 1)**2
Let m(c) be the third derivative of 0*c - 1/120*c**5 + 1/24*c**4 - 1/12*c**3 + 6*c**2 + 0. Factor m(k).
-(k - 1)**2/2
Suppose 0 = 5*c - 24 - 1. Let z be (13 - c)*1/18. Find m, given that -2/9*m**4 - 10/9*m**2 + 0 + 8/9*m**3 + z*m = 0.
0, 1, 2
Let w = 27 - 24. Find i such that i - w*i**2 - 2*i + 2*i**2 + 2*i = 0.
0, 1
Let l be ((-3)/2)/(20/(-40)). Let p(f) be the first derivative of 1/6*f**4 + 2 + 0*f**2 + 0*f - 2/9*f**l. Factor p(g).
2*g**2*(g - 1)/3
Let n(d) be the third derivative of -5*d**8/3696 + d**7/770 + 7*d**6/1320 - d**5/220 - d**4/132 + 27*d**2. Solve n(w) = 0.
-1, -2/5, 0, 1
Suppose 0*o - 10 = 4*t - 2*o, 3*t + 20 = 4*o. Suppose t = -n + 14. Find b, given that -3*b**2 - b**2 - 6*b**2 - 6*b**4 - 2*b - n*b**3 = 0.
-1, -1/3, 0
Suppose -5*z + 198 = -4*d, 2*z - 4 = -0*z. Let m = d + 47. Factor -1/2*a + 3/4*a**2 + m - 1/4*a**3.
-a*(a - 2)*(a - 1)/4
Let a(v) be the first derivative of v**4/20 + 2*v**3/15 + v**2/10 + 2. Suppose a(k) = 0. What is k?
-1, 0
Let w(i) be the first derivative of 1/3*i**3 - 1/240*i**5 + 1/96*i**4 + 0*i**2 - 1 + 1/1440*i**6 + 0*i. Let f(s) be the third derivative of w(s). Factor f(l).
(l - 1)**2/4
Factor 27*p**2 - 33*p - 30*p**3 + 12*p**5 + 19*p**2 + 3*p**4 - 13*p**5 + 9 + 6*p**4.
-(p - 3)**2*(p - 1)**3
Let n(g) = -6*g**2 - 3. Let l(t) = -39*t**2 - 7*t - 21. Let c(v) = 20*v**2 + 4*v + 11. Let o(d) = -5*c(d) - 3*l(d). Let w(x) = 8*n(x) + 3*o(x). Factor w(j).
3*j*(j + 1)
Let y be ((-3)/(-4))/((-3)/36). Let p = -5 - y. What is s in 7*s - 2*s**p + 2 + 0 + s**3 - s**5 + s**3 + 8*s**2 = 0?
-1, 2
Let i(c) = 2*c**2 + 20*c + 10. Let w(b) = b**2 + 13*b + 7. Let s(q) = 5*i(q) - 8*w(q). Suppose s(x) = 0. Calculate x.
-1, 3
Factor 3*j**5 + 28*j - 6*j**4 - 74 - 59 + 37 + 48*j**2 - 24*j**3 + 20*j.
3*(j - 2)**3*(j + 2)**2
Let c(k) be the third derivative of k**8/112 - k**7/35 + k**6/40 - 9*k**2. Factor c(b).
3*b**3*(b - 1)**2
Let h = -625 + 2481/4. Let w = 61/12 + h. Determine q so that -8*q**2 - 3*q - 16/3*q**3 - w = 0.
-1, -1/4
Let a(x) be the first derivative of x**7/126 - x**6/30 + x**5/20 - x**4/36 - 3*x - 3. Let t(w) be the first derivative of a(w). Factor t(c).
c**2*(c - 1)**3/3
Let j(z) be the first derivative of 3*z**4/8 - z**3 - 3*z**2/4 + 3*z - 13. Factor j(i).
3*(i - 2)*(i - 1)*(i + 1)/2
Let s(u) be the first derivative of -u**6/3 - 6*u**5/5 - 25. Suppose s(m) = 0. What is m?
-3, 0
Let h(a) be the third derivative of a**8/560 - 3*a**7/350 + a**6/100 + 20*a**2. Determine o, given that h(o) = 0.
0, 1, 2
Solve 0*k + 0 + 1/9*k**4 + 1/9*k**3 + 0*k**2 = 0 for k.
-1, 0
Let -t**4 - 6*t**3 + t - 7*t**4 + t + 19*t**2 - 15*t**2 + 8*t**5 = 0. Calculate t.
-1/2, 0, 1
Let i(n) be the second derivative of 3*n**5/16 - 7*n**4/16 + n**3/4 - 5*n. Factor i(a).
3*a*(a - 1)*(5*a - 2)/4
Let u(p) = -25*p + 77. Let a be u(3). Suppose 1/6 + 1/6*t**4 + 2/3*t + t**a + 2/3*t**3 = 0. Calculate t.
-1
Let t(n) be the third derivative of -n**8/168 - 4*n**7/315 + 7*n**6/180 + 2*n**5/45 - n**4/9 + 14*n**2. Suppose t(q) = 0. What is q?
-2, -1, 0, 2/3, 1
Let c = -19 - -1. Let t be (2/6)/((-3)/c). Find z such that t*z**2 + 5*z + 5*z**2 + 5*z**3 - 3*z = 0.
-1, -2/5, 0
Let r be 1/4*(-36)/(-27) + 1. Suppose -r*m**3 + 1/3*m**4 - 4/3 + 4/3*m + m**2 = 0. Calculate m.
-1, 1, 2
Let m = -21 - -24. Factor 5*k**5 - 6 + m*k**2 + 0*k**4 - 3*k**4 + 2*k + 6 - 7*k**3.
k*(k - 1)**2*(k + 1)*(5*k + 2)
Suppose -2*p - 25 = -25. Let q(r) be the second derivative of p*r**3 + 1/24*r**4 - 1/60*r**6 + 0 + 0*r**2 + 2*r + 0*r**5. Factor q(d).
-d**2*(d - 1)*(d + 1)/2
Factor 1/6*m**2 + 4/3*m + 8/3.
(m + 4)**2/6
Let y = 32 - 29. Factor -b - b**2 - 1/3*b**y - 1/3.
-(b + 1)**3/3
Let d(g) = -g**5 + g**4 - g**3 + g**2. Let o(v) = 3*v**5 + 2*v**3 - 4*v**2 - v. Let u(i) = -2*d(i) - o(i). Factor u(j).
-j*(j - 1)*(j + 1)**3
Let b = -10 - -24. Let o be (-4)/b + 90/21. Factor 12*x + 2 + 5*x**2 - o*x**2 + 17*x**2.
2*(3*x + 1)**2
Determine v so that 10*v**2 - 6*v + 12*v**2 + 0*v + 6*v**3 + 10*v**4 - 32*v**3 = 0.
0, 3/5, 1
Suppose 0 = -m - 0*n - 4*n + 3, 4*m - 12 = -n. Factor -15/2*h**2 - 6 - 12*h - 3/2*h**m.
-3*(h + 1)*(h + 2)**2/2
Let g = -22 + 22. Let z(o) be the first derivative of -3*o**3 + g*o + 2 - 3/2*o**2. Let z(w) = 0. Calculate w.
-1/3, 0
Let t(a) be the first derivative of 3*a**4/16 + a**3/2 - 5. Factor t(q).
3*q**2*(q + 2)/4
Let b(n) be the third derivative of -n**5/60 - n**4/4 - 14*n**2. Find v, given that b(v) = 0.
-6, 0
Let x be (-7)/63*0 + (-1)/(-5). Find k such that 1/5 - 2/5*k + x*k**2 = 0.
1
Let i(t) be the third derivative of -1/60*t**6 + 0 + 4*t**2 + 0*t**3 + 0*t**5 + 0*t + 1/12*t**4. Factor i(u).
-2*u*(u - 1)*(u + 1)
Let c(s) = -s**2 + 7*s. Let u be c(7). Let v(w) be the first derivative of 1/2*w**3 + 3/2*w**4 + u*w - 2 - 1/2*w**2 + 7/10*w**5. Factor v(x).
x*(x + 1)**2*(7*x - 2)/2
Suppose 2*a + 2*g = -2, -g = -5*g - 12. Let j(d) be the first derivative of -1/2*d**a + 3 + d + 1/12*d**3. Factor j(w).
(w - 2)**2/4
Let a(m) = -m**2 + 62*m - 81. Let u(n) = -21*n + 27. Let d(f) = -3*a(f) - 8*u(f). Solve d(j) = 0 for j.
3
Let i(l) be the first derivative of 0*l + 0*l**2 + 6 - 2/9*l**3 + 2/15*l**5 + 0*l**4. Factor i(k).
2*k**2*(k - 1)*(k + 1)/3
Let p(c) be the third derivative of -2/3*c**3 + 0*c - 1/30*c**5 - 1/4*c**4 - 3*c**2 + 0. Factor p(j).
-2*(j + 1)*(j + 2)
Let t(d) be the second derivative of 0 + 0*d**2 + 0*d**3 - 4*d - 1/60*d**5 + 0*d**4. Factor t(n).
-n**3/3
Let m(d) = -d**3 + 11*d**2 + d - 9. Let y be m(11). Factor -9*v**2 + v**5 + 4*v - 6*v**3 + 3*v**3 + y*v**4 + 5*v**2.
v*(v - 1)**2*(v + 2)**2
Let s(l) be the second derivative of l**4/4 + 5*l**3/2 + 9*l**2 - 10*l. Determine m so that s(m) = 0.
-3, -2
Let f(d) be the second derivative of 0*d**6 - 1/21*d**7 + 0 + 0*d**2 + 1/5*d**5 - 1/3*d**3 - 2*d + 0*d**4. Factor f(h).
-2*h*(h - 1)**2*(h + 1)**2
Let r = -805 - -2417/3. Factor -2/3*l + 4/3*l**3 + 2/3*l**4 - r*l**5 + 2/3 - 4/3*l**2.
-2*(l - 1)**3*(l + 1)**2/3
Let s(p) be the third derivative of p**6/24 + p**5/4 + 5*p**4/8 + 5*p**3/6 + 2*p**2. Factor s(n).
5*(n + 1)**3
Let b = 3 + -1. Factor 6*n**2 - 3*n**b + 2*n**2 - 3*n**2 + 2 - 4*n.
2*(n - 1)**2
Let l(k) be the first derivative of 5 + 2/3*k**3 + k**2 + 0*k. Let l(i) = 0. Calculate i.
-1, 0
Let y(w) be the second derivative of 0*w**2 + 0*w**6 + 4*w + 1/147*w**7 + 0 + 0*w**3 - 1/21*w**4 - 3/70*w**5. Let y(u) = 0. Calculate u.
-1, 0, 2
Determine o, given that 0*o**2 - 1/5*o**3 + 2/5 + 3/5*o = 0.
-1, 2
Let z be 3/(-8)*290/15. Let o = z - -211/28. Factor 2/7 - 4/7*n + o*n**2.
2*(n - 1)**2/7
Let p(s) = -2*s**4 - 2*s**3 - s**2. Let q(w) = w**4 + w**3 + w**2. Let f(g) = -3*p(g) - 5*q(g). Determine n, given that f(n) = 0.
-2, 0, 1
Let s(k) = -k**3 - 4*k**2 + 5*k + 7. Let l be s(-5). Find p such that 2*p**4 + l*p**3 - 3*p**4 + 2*p**2 + 6*p**4 = 0.
-1, -2/5, 0
Factor 4/3*w**2 + 0 + 8/3*w**3 + 16/3*w**5 + 0*w - 28/3*w**4.
4*w**2*(w - 1)**2*(4*w + 1)/3
Suppose w - 46 = -44. Determine q so that 4/3*q**w - 2/3*q**3 + 0 - 2/3*q = 0.
0, 1
Let s = -7 - -13. Let q = -9 + s. Let o(c) = -c**2 - 2*c + 3. Let z(p) = -3*p**2 - 5*p + 8. Let b(y) = q*z(y) + 8*o(y). Let b(d) = 0. Calculate d.
0, 1
Let h(g) be the first derivative of -1/7*g**2 + 1 + 0*g + 1/14*g**4 + 0*g**3. Factor h(j).
2*j*(j - 1)*(j + 1)/7
Let w = 22/5 - 4. Let f(m) be the first derivative of -2/15*m**3 + 3 + w*m + 0*m**2. Factor f(n).
-2*(n - 1)*(n + 1)/5
Let u = -103/340 - -6/17. Let z(m) be the first derivative of u*m**5 + 0*m - 1/12*m**3 + 1/8*m**2 - 2 - 1/16*m**4. Determine a so that z(a) = 0.
-1, 0, 1
Let l = -9 - -15. Suppose -6*i = -3*i - l. Factor 3/5*u**3 + 7/5*u - 2/5 - 8/5*u**i.
(u - 1)**2*(3*u - 2)/5
Let v(n) = 2*n**3 - 2*n**2 - 2*n - 6. Let d(p) = 3*p**3 - 3*p**2 - 3*p - 7. Let z(f) = -f**2 - 8*f - 2. Let h be z(-7). Let b(g) = h*v(g) - 4*d(g). Factor b(x).
-2*(x - 1)**2*(x + 1)
Let u(i) be the third derivative of i**8/336 - i**7/70 + i**6/60 + i**5/30 - i**4/8 + i**3/6 + 55*i**2. Suppose u(b) = 0. Calculate b.
-1, 1
Suppose 2*v - 16 = -4*i, -5 = -23*i + 20*i + 2*v. Suppose 4/5*w - 4/5*w**i - 8/5*w**2 + 8/5 = 0. What is w?
-2, -1, 1
Let x(a) be the second derivative o