m(n) = 4*n**3 - n**2 - 2*n + 2. Let h be m(1). Factor 2*y**3 - 2*y**3 + y**h + y**2.
y**2*(y + 1)
Let f(s) be the third derivative of -1/360*s**6 - 1/630*s**7 + 0*s + 1/72*s**4 + 0*s**3 - 8*s**2 + 0 + 1/180*s**5. Factor f(i).
-i*(i - 1)*(i + 1)**2/3
Suppose 0 - 30/7*f**3 + 66/7*f**2 - 8*f**4 + 20/7*f = 0. Calculate f.
-5/4, -2/7, 0, 1
Let w(l) be the second derivative of -l**7/1260 + l**6/540 + l**3/6 + 4*l. Let x(v) be the second derivative of w(v). Solve x(o) = 0.
0, 1
Factor -59/5*j**2 - 2/5 + 36/5*j**4 - 23/5*j + 48/5*j**3.
(j - 1)*(j + 2)*(6*j + 1)**2/5
Let o = 5/14 + 1/252. Let v(p) be the second derivative of 1/6*p**2 + p + o*p**3 + 11/72*p**4 + 0. Factor v(i).
(i + 1)*(11*i + 2)/6
Suppose -7*z - 4 = -3*z. Let b be (z/(-1) - 9)/(-3). Factor 2/3 - 8/3*p**3 - 2/3*p**2 + b*p.
-2*(p - 1)*(p + 1)*(4*p + 1)/3
Let g be (-4)/7 - (-54)/21. Factor 3/2*o**g - 1/2*o**3 + 0*o - 2.
-(o - 2)**2*(o + 1)/2
Let m(o) be the first derivative of 3*o**5/20 - 3*o**3/2 - 3*o**2 - 2*o + 2. Let y(n) be the first derivative of m(n). Factor y(p).
3*(p - 2)*(p + 1)**2
Let f be 4/(-6) + 10/6. Suppose 2*k - 5*t + f = -0, k - 7 = -5*t. Factor -1 - i**3 + k*i**2 + 1.
-i**2*(i - 2)
Factor -r**2 - 2*r**4 - r**4 - 8*r**3 - 3*r**2 - r**4.
-4*r**2*(r + 1)**2
Find g, given that 0 + 0*g - 4/13*g**2 - 14/13*g**3 - 10/13*g**4 = 0.
-1, -2/5, 0
Find w, given that -2/7 - 2/7*w**3 - 6/7*w - 6/7*w**2 = 0.
-1
Factor 6/7*n - 4/7 + 6/7*n**4 + 6/7*n**2 - 2*n**3.
2*(n - 1)**3*(3*n + 2)/7
Let c be 1224/510*5/2. Find y, given that 5*y**3 + 1/2 + 3*y + 3/2*y**4 + c*y**2 = 0.
-1, -1/3
Let d = 6 - 3. Suppose d - 13 = -5*j. Factor -g**4 + 10*g**3 - 7*g**3 - g**j - g**4.
-g**2*(g - 1)*(2*g - 1)
Factor 5*d**2 - 4*d**2 + 0*d**2 + 3*d - d.
d*(d + 2)
Let o(g) be the second derivative of 7*g**5/60 + g**4/12 - 3*g**2/2 - 9*g. Let m(f) be the first derivative of o(f). Factor m(b).
b*(7*b + 2)
Let h(a) be the first derivative of -a + 0*a**2 + 1/3*a**3 - 3. Factor h(l).
(l - 1)*(l + 1)
Factor -2/5*t**2 - 44/5*t - 242/5.
-2*(t + 11)**2/5
Let h be (1/(-3))/((-4)/(1 + 23)). Solve 0 + 1/5*o + 4/5*o**h + 3/5*o**3 = 0.
-1, -1/3, 0
Suppose 3*n - 8 = -2. Let x(j) = 100*j**3 - 120*j**2 - 149*j - 37. Let p(t) = -50*t**3 + 60*t**2 + 74*t + 18. Let w(s) = n*x(s) + 5*p(s). Factor w(i).
-2*(i - 2)*(5*i + 2)**2
Factor -3*g**2 + 6*g + 4*g**2 + 2*g**2 + 0 - 9.
3*(g - 1)*(g + 3)
Find g such that 4*g**4 + 28*g**2 - 9*g - g**5 - 22*g**3 + 4 + 4*g**4 - 9*g + g = 0.
1, 4
Let x(y) = -16*y + 20. Let a be x(-11). Let t be 4/(-18) + a/315. Factor 0*q - 2/5*q**2 + t.
-2*(q - 1)*(q + 1)/5
Find a, given that 2/3*a**2 + 0 + 8/3*a = 0.
-4, 0
Let d be 80/(-6) - 18/27. Let z(x) = -x**2 - 9*x + 18. Let a(s) = 4*s**2 + 46*s - 90. Let h(v) = d*z(v) - 3*a(v). Factor h(k).
2*(k - 3)**2
Let m(w) be the second derivative of w**8/336 - w**6/120 - w**2 + 2*w. Let u(t) be the first derivative of m(t). Factor u(c).
c**3*(c - 1)*(c + 1)
Factor 6*d**2 + 10*d**3 - 4 - 8*d - 4 - 12*d**3 - 2*d**4 + 6*d**3.
-2*(d - 2)**2*(d + 1)**2
Factor -4/3*w**2 - 1/3 - 1/6*w**5 + 1/3*w**4 + 7/6*w + 1/3*w**3.
-(w - 1)**4*(w + 2)/6
Let g(m) be the first derivative of m**4 - 2/3*m**3 - 2/5*m**5 + 0*m**2 + 10 + 0*m. Factor g(w).
-2*w**2*(w - 1)**2
Let l(t) be the first derivative of -t**6/80 - t**5/10 - t**4/4 + 5*t**2/2 - 4. Let o(g) be the second derivative of l(g). Suppose o(y) = 0. What is y?
-2, 0
Let b(g) be the third derivative of -g**7/70 - g**6/20 + g**4/4 + g**3/2 + 16*g**2. Factor b(c).
-3*(c - 1)*(c + 1)**3
Let t(y) be the third derivative of y**5/60 - y**4/24 - y**3 - 3*y**2. Factor t(h).
(h - 3)*(h + 2)
Let z(f) be the first derivative of 2/3*f + 2/15*f**5 - 1/9*f**6 - 4/9*f**3 - 1/3*f**2 + 3 + 1/3*f**4. Determine g so that z(g) = 0.
-1, 1
Let y = 124/3 + -41. Let g(q) be the first derivative of -3/2*q**2 + 3/4*q**4 - y*q**3 - 1/5*q**5 - 2 + 2*q. Determine p, given that g(p) = 0.
-1, 1, 2
Let g(s) be the second derivative of s**8/168 - s**7/35 + s**6/20 - s**5/30 - 3*s**2/2 + 2*s. Let n(k) be the first derivative of g(k). Factor n(d).
2*d**2*(d - 1)**3
Factor 0 + 0*f**2 - 1/3*f**4 - 2/3*f**3 + 1/3*f**5 + 0*f.
f**3*(f - 2)*(f + 1)/3
Let g be 6/2 - 214/72. Let c(n) be the third derivative of 1/630*n**7 + 1/180*n**6 + n**2 + 0*n - g*n**4 + 0*n**5 - 1/18*n**3 + 0. Factor c(s).
(s - 1)*(s + 1)**3/3
Let z(k) be the third derivative of k**5/240 + k**4/96 + k**2. Suppose z(u) = 0. What is u?
-1, 0
Let p = -8 - -10. Let g(a) = -9*a**2 + 23*a**2 + 12*a**p - 17. Let h(k) = -9*k**2 + 6. Let l(b) = 6*g(b) + 17*h(b). Suppose l(w) = 0. Calculate w.
0
Let t be (-2)/7 + 12/42. Suppose 4*i - 3*i - 4 = t. Let 2/5*f**i + 0 - 2/5*f**3 - 2/5*f**2 + 2/5*f = 0. What is f?
-1, 0, 1
Let y(g) be the third derivative of g**6/100 + g**5/150 - g**4/20 - g**3/15 - 3*g**2. Find f, given that y(f) = 0.
-1, -1/3, 1
Factor -2/13*r**2 + 0 - 2/13*r**3 + 2/13*r**4 + 0*r + 2/13*r**5.
2*r**2*(r - 1)*(r + 1)**2/13
Let q = 17/6 + -13/6. Suppose i**4 - 1/3 - 2/3*i**2 - q*i**3 + i - 1/3*i**5 = 0. Calculate i.
-1, 1
Let g be 3 + (2 + (-8)/4)/(-2). Suppose 2/5*v**g + 0 + 2/5*v**4 + 0*v**2 + 0*v = 0. What is v?
-1, 0
Let f(o) be the first derivative of o**6/420 - o**5/210 - o**4/84 + o**3/21 + o**2/2 + 3. Let u(c) be the second derivative of f(c). What is v in u(v) = 0?
-1, 1
Suppose 0 = 2*a - 7 - 17. Solve 6 - 6 + 9*d - a*d**3 - 6 + 8*d**2 + 3*d**5 - 2*d**2 = 0.
-2, -1, 1
Suppose -60*l + 72*l - 39 + 24*l + 3*l**2 = 0. What is l?
-13, 1
Suppose 5*n = -5*t, -4 = -2*n + 3*t + 6. Solve -106*f**n - 56*f**2 - 24*f - 48*f - 12 + 4 = 0.
-2/9
Suppose -i - 3*z + 1 = 0, -4*i - 3*z + 25 - 3 = 0. Let n = i - 4. Factor 2 - 4*t + n*t**2 - 8 + 7*t.
3*(t - 1)*(t + 2)
Let a(p) be the first derivative of 2/7*p - 10/21*p**3 - 4 - 1/7*p**2 - 3/14*p**4. Factor a(g).
-2*(g + 1)**2*(3*g - 1)/7
Let c(v) = -21*v**5 + 15*v**4 + 9*v**3 - 24*v**2 + 3*v + 9. Let k(a) = -5*a**5 + 4*a**4 + 2*a**3 - 6*a**2 + a + 2. Let z(t) = 2*c(t) - 9*k(t). Factor z(x).
3*x*(x - 1)**3*(x + 1)
Suppose -5*i - r = 3, -i = 4*r - 0*r + 12. Let o(w) be the third derivative of 0*w**4 + 0*w**6 + 0*w + i*w**3 + 0*w**5 + 0 - 2*w**2 - 1/420*w**7. Factor o(g).
-g**4/2
Let k(m) be the second derivative of 0*m**3 + 1/2*m**2 - 1/12*m**4 + 0 - 3*m. Suppose k(v) = 0. What is v?
-1, 1
Suppose 2*q - 14 = 2*g, 2*g = q - 0 - 10. Let l be (-9)/(-6)*q/3. Factor 2*c**3 + 0*c**l - 4*c**3 + c**2 - 3*c**4 + 0*c**4.
-c**2*(c + 1)*(3*c - 1)
Let k = -1 - -5. Suppose 2*o - 2*f = o + 9, -k*o + 4*f = -28. Solve v**o - v**3 - 4*v + 4*v = 0 for v.
-1, 0, 1
What is j in 0*j**4 - 9/4*j**3 + 0 + 3/2*j**2 + 3/4*j**5 + 0*j = 0?
-2, 0, 1
Let h = -8 - -4. Let p(z) = -5*z**2 + 1. Let g(m) = -6*m**2 + 1. Let a = -10 - -15. Let t(q) = a*p(q) + h*g(q). What is n in t(n) = 0?
-1, 1
Suppose 0*w = 2*w - 10. Suppose -w*y + 24 = -4*u + 5*u, -4 = -3*u + 2*y. Find c such that -6*c**3 + 6*c**u + 2*c**2 - 5*c**5 + c**5 + 2*c**5 = 0.
0, 1
Let n = -451 + 1354/3. Let -1/3*p**4 + 1/3*p**3 + n*p**2 + 0 - 1/3*p**5 + 0*p = 0. What is p?
-1, 0, 1
Let b = -6 - -14. Suppose 12*u - b = 8*u. Factor 1/2*m + 0 + 1/2*m**u.
m*(m + 1)/2
Let m(x) = 3*x + 26. Let h be m(-8). Let r(z) be the third derivative of -1/60*z**6 + 1/12*z**4 + 0 - 1/3*z**3 - z**h + 1/30*z**5 + 0*z. Factor r(t).
-2*(t - 1)**2*(t + 1)
Let d be 6/(-1)*1/(-2). Let y be 39/6 - 3 - d. Factor b**2 - y*b**3 + 0 - 1/2*b.
-b*(b - 1)**2/2
Suppose 0 = 2*b + 2*g - 20, -3*g + g = 3*b - 25. Find u, given that 2*u**5 - u**2 - 4*u**b + 5*u**2 + 4*u**3 - 2*u**4 - 2 - 2*u = 0.
-1, 1
Let y = -4479 - -13550/3. Let r = y + -37. Suppose 2/3*s + 2/3*s**2 - r*s**4 + 0 - 2/3*s**3 = 0. Calculate s.
-1, 0, 1
Let d be (-44)/10 - (-6)/(-10). Let g(h) = -2*h**3 - 5*h**2 + 11*h + 1. Let w(c) = c**2 - c - 1. Let p(m) = d*w(m) - g(m). Factor p(x).
2*(x - 1)**2*(x + 2)
Suppose 4*s = 3*s - s. Let z be (-1)/(-1) + 0 + 1. Factor 1/2*m**4 - 1/2*m**5 + 0*m + s - 1/2*m**z + 1/2*m**3.
-m**2*(m - 1)**2*(m + 1)/2
Let v = 214 + -209. Let 3/5*k**4 - 3/5*k**3 + 0 - 3/5*k**2 + 0*k + 3/5*k**v = 0. What is k?
-1, 0, 1
Let v(w) be the first derivative of -3*w**5/5 + 9*w**4/4 - 2*w**3 + 1. Factor v(c).
-3*c**2*(c - 2)*(c - 1)
Suppose 3*k = k - 16. Let h be 9/(-5) - 24/k. Suppose -2*o + h*o**2 + 4/5 = 0. Calculate o.
2/3, 1
Let w(g) be the first derivative of -g**3/3 - 4*g**2 + 11*g + 2. Let 