*w + 2)/3
Let w be (0 + -16)*6/12. Let o be 1/(-2) + (-4)/w. Factor 0 + 2/5*t**3 + 2/5*t**2 - 2/5*t**5 - 2/5*t**4 + o*t.
-2*t**2*(t - 1)*(t + 1)**2/5
Factor 0*n**3 - 6*n**2 + n**3 - 3*n**3 - n**3.
-3*n**2*(n + 2)
Let q(k) be the third derivative of -k**10/453600 - k**9/60480 - k**8/30240 + k**5/30 + 3*k**2. Let n(p) be the third derivative of q(p). Factor n(v).
-v**2*(v + 1)*(v + 2)/3
Suppose 4 = -4*x - 0*x + 2*g, x + 2*g - 9 = 0. Suppose 5*u = -p + 10, 0 = -2*u - 4*p + 1 + 3. Factor 2*z**2 + z**5 - u*z**3 + 0*z**5 + 0*z**5 - z**4 + z - x.
(z - 1)**3*(z + 1)**2
Let x(o) be the first derivative of -4/3*o**2 + 4*o**5 - 23/6*o**4 + 3*o**6 - 196/27*o**3 + 4 + 16/9*o. Let x(s) = 0. What is s?
-1, -2/3, 2/9, 1
Let u be 3/9 - (-14)/(-42). Factor -2/3*v**2 - 2/3*v + u.
-2*v*(v + 1)/3
Let k(q) = q**2 - 9*q - 20. Let l be k(11). Factor 0*f**l - 4/3*f**4 + 0*f + 0 + 2/3*f**5 + 2/3*f**3.
2*f**3*(f - 1)**2/3
Let a(v) be the second derivative of -3*v**6/2 - 29*v**5/4 - 55*v**4/4 - 25*v**3/2 - 5*v**2 + 26*v. Solve a(b) = 0.
-1, -2/9
Let z = 21 - 15. Suppose z*b - 4*b - 10 = 0. Solve 0 + 8/5*a**2 - 8/5*a**4 - 1/5*a + 16/5*a**b - 3*a**3 = 0.
-1, 0, 1/4, 1
Let b(i) be the second derivative of 4/27*i**3 + 0 + 4*i + 1/54*i**4 + 1/3*i**2. Factor b(z).
2*(z + 1)*(z + 3)/9
Let z(u) be the third derivative of -5*u**7/63 - u**6/6 + 11*u**5/90 + u**4/3 - 4*u**3/9 + 6*u**2. Solve z(a) = 0 for a.
-1, 2/5
Let y(l) = l**3 + 2*l**2 - 3*l + 2. Suppose 5*f + 0 = -4*q - 3, 0 = 2*f - q + 9. Let k be y(f). Factor -4/9*o**k - 2/9*o + 0.
-2*o*(2*o + 1)/9
Let p(i) be the second derivative of -i**4/21 + i**3/21 + i**2/7 - 5*i. Determine c, given that p(c) = 0.
-1/2, 1
Let w(l) = l**2 + 40*l - 38. Let b be w(-41). Factor -6/5 + 3/5*v**b - 9/5*v + 0*v**2.
3*(v - 2)*(v + 1)**2/5
Determine t so that 2*t**2 + 0*t + t + 2*t**3 - 2*t - 3*t**3 = 0.
0, 1
Let g be ((-12)/(-110))/(8/(-10)). Let w = 29/110 - g. Let 6/5*n**3 - 2/5*n**4 + 0 + w*n - 6/5*n**2 = 0. What is n?
0, 1
Let a(m) be the first derivative of -m**6/120 + m**5/40 - m**4/48 + 4*m - 1. Let y(j) be the first derivative of a(j). Factor y(w).
-w**2*(w - 1)**2/4
Let w = 14/29 - 68/261. Solve 2/9*v**3 - 4/9*v**2 + 0 + w*v = 0.
0, 1
Let c(i) be the first derivative of -i**4/16 + i**3/6 + i**2/8 - i/2 + 22. Factor c(q).
-(q - 2)*(q - 1)*(q + 1)/4
Let r(q) be the second derivative of -q**4/48 + q**3/6 - 3*q**2/8 - 11*q. Let r(t) = 0. Calculate t.
1, 3
Let y(h) be the third derivative of h**6/720 - h**4/48 + h**3/18 + 22*h**2. Solve y(r) = 0 for r.
-2, 1
Suppose -4*j - 156 + 784 = 0. Let h = j - 1411/9. Factor -4/9*x - 2/9*x**2 - h.
-2*(x + 1)**2/9
Factor 5 - 269*m**2 + 314*m**2 - 1 + 25*m**3 + 24*m.
(m + 1)*(5*m + 2)**2
Let j(z) be the second derivative of z**10/60480 - z**8/6720 + z**6/1440 - z**4/6 + z. Let t(m) be the third derivative of j(m). Factor t(x).
x*(x - 1)**2*(x + 1)**2/2
Let k be ((10/3)/10)/(3/24). Suppose 4/3 - k*c**3 + 0*c**4 - 4/3*c**2 + 2/3*c**5 + 2*c = 0. What is c?
-1, 1, 2
Let q = -335/6 - -56. Let p(l) be the first derivative of 0*l - q*l**2 - 4/15*l**5 - 1/2*l**4 - 4/9*l**3 - 1/18*l**6 + 1. Find r such that p(r) = 0.
-1, 0
Let j(t) be the third derivative of -1/210*t**7 + 2/15*t**3 + 3*t**2 - 23/600*t**6 + 2/15*t**4 + 1/240*t**8 + 1/300*t**5 + 0 + 0*t. Solve j(o) = 0.
-1, -2/7, 1, 2
Let c(f) be the first derivative of -2/33*f**3 - 2/55*f**5 - 2 + 1/11*f**4 + 0*f**2 + 0*f. Factor c(u).
-2*u**2*(u - 1)**2/11
Let s(p) be the first derivative of -2*p**3/9 + p**2 + 8*p/3 - 7. Factor s(n).
-2*(n - 4)*(n + 1)/3
Let g(h) = -h**3 - 5*h**2 + 4*h + 2. Let o be g(-6). Let m be 48/126 - (-4)/o. Factor -4/9*w + m*w**3 + 0 + 2/9*w**2.
2*w*(w + 1)*(3*w - 2)/9
Let c be (0/7)/(1 - 3). Factor 2/5*g**2 + c + 2/5*g.
2*g*(g + 1)/5
Let y = -91/40 - -12/5. Let w(z) be the second derivative of -3/80*z**5 + 2*z - y*z**3 + 0 - 1/8*z**4 + 0*z**2. Determine f so that w(f) = 0.
-1, 0
Suppose 0 = t + 2 + 1. Let m(a) = 8*a**2 - 10*a + 5. Let u(c) = -c**3 + 16*c**2 - 19*c + 9. Let x(p) = t*u(p) + 5*m(p). Factor x(d).
(d - 1)**2*(3*d - 2)
Let p(t) = t**3 - 6*t**2 + 5*t - 2. Let n be p(5). Let b be n*6/(-4)*1. Factor 1/5*x**2 + 1/5*x**b - 1/5 - 1/5*x.
(x - 1)*(x + 1)**2/5
Let k(s) be the second derivative of -s**5/80 + s**3/8 + s**2/4 + 8*s. Factor k(w).
-(w - 2)*(w + 1)**2/4
Let b = -33353/3360 + 139/14. Let s(m) be the third derivative of -b*m**6 + 0 + 0*m**3 + 1/840*m**7 + 0*m**5 + 0*m + 0*m**4 + 2*m**2. Factor s(v).
v**3*(v - 1)/4
Let a(u) be the first derivative of u**6/720 + u**5/80 + u**4/24 - u**3 - 1. Let c(k) be the third derivative of a(k). Factor c(l).
(l + 1)*(l + 2)/2
Let s = -5 - -5. Let y = 5 - s. Let z(a) = a**3 + 8*a**2 + 13*a - 2. Let l(x) = 7*x**2 + 14*x - 3. Let d(u) = y*z(u) - 4*l(u). What is p in d(p) = 0?
-1, -2/5
Let s(m) be the first derivative of m**6/240 - m**5/60 - m**4/48 + m**3/6 + m**2/2 + 4. Let h(o) be the second derivative of s(o). Factor h(r).
(r - 2)*(r - 1)*(r + 1)/2
Let w(t) = t**3 - 7*t**2 - 8*t + 2. Let f be w(8). Let c be ((-24)/(-75))/(f/10). Factor c + 8/5*b + 2/5*b**2.
2*(b + 2)**2/5
Factor -12 - 1/3*y**2 + 4*y.
-(y - 6)**2/3
Let b(c) = 39*c**4 + 105*c**3 - 12*c**2 - 105*c - 27. Let t(m) = -3*m**4 - 8*m**3 + m**2 + 8*m + 2. Let y(h) = -2*b(h) - 27*t(h). Factor y(w).
3*w*(w - 1)*(w + 1)*(w + 2)
Let x be (-3)/(-12) + 3/(-12). Factor 8*d**2 + 14*d + x - 8*d + 12*d + 4.
2*(d + 2)*(4*d + 1)
Let h(i) = 9*i**5 - 4*i**4 - 2*i**3 + 3*i**2 + 3*i. Let d(w) = w**4 + w**2 + w. Let z(q) = -3*d(q) + h(q). Let z(l) = 0. Calculate l.
-2/9, 0, 1
Suppose 0 = c - 3*c. Let h(j) be the second derivative of -1/30*j**6 + 1/6*j**3 + 0*j**2 + 1/12*j**4 - 2*j - 1/20*j**5 + c. Factor h(f).
-f*(f - 1)*(f + 1)**2
Let u(j) = 11*j**2 + 96*j + 399. Let c(s) = -s**2 - s + 1. Let x(r) = -6*c(r) - u(r). Find w such that x(w) = 0.
-9
Suppose 3*p = -10*p + 2*p. Let n(t) be the third derivative of -1/72*t**4 - 2*t**2 - 1/9*t**3 + 1/360*t**6 + p*t + 1/90*t**5 + 0. Solve n(o) = 0 for o.
-2, -1, 1
Let j(x) be the first derivative of -6/5*x**2 + 12/25*x**5 - 8/15*x**3 + 2/15*x**6 + 10 - 4/5*x + 2/5*x**4. Find m such that j(m) = 0.
-1, 1
Let s = 4021/5 - 804. Factor 1/5*o**3 + 3/5*o**2 + 0 - 3/5*o**4 - 2/5*o + s*o**5.
o*(o - 2)*(o - 1)**2*(o + 1)/5
Factor -9*d**2 - 6*d**2 + d**3 + 5*d**4 - 6*d**3 + 5*d - 24 + 34.
5*(d - 2)*(d - 1)*(d + 1)**2
Suppose 2*i - 4*m = -3*i - 30, -7 = -4*i - 3*m. Let v = 0 - i. Factor -f**4 - 2*f**2 - v*f**5 + 3*f**5 - f + 3*f**4.
f*(f - 1)*(f + 1)**3
Factor -6*j**2 - 48*j**4 - 164*j**5 + 7*j**2 + 10*j**3 + 38*j**5 + 3*j**2.
-2*j**2*(3*j + 1)**2*(7*j - 2)
Let m(g) be the first derivative of -4*g**3/3 - 3*g**2 - 8*g + 3. Let s(n) = n**2 + n + 1. Let w(v) = m(v) + 6*s(v). Factor w(h).
2*(h - 1)*(h + 1)
Factor -x**3 + 2*x**3 + 4*x - 4*x - x.
x*(x - 1)*(x + 1)
Let y(u) be the second derivative of u**7/189 + 2*u**6/45 - 8*u**5/45 + u**4/27 + 5*u**3/9 - 8*u**2/9 - 22*u. Suppose y(w) = 0. Calculate w.
-8, -1, 1
Let y(p) = -6*p**5 - 8*p**4 + 6*p**3 + 4*p**2 - 8*p - 4. Let v(o) = -13*o**5 - 17*o**4 + 12*o**3 + 7*o**2 - 16*o - 9. Let x(h) = -4*v(h) + 9*y(h). Factor x(l).
-2*l*(l - 1)**2*(l + 2)**2
Let b(q) be the third derivative of q**7/175 - q**6/150 - q**5/50 + q**4/30 - 3*q**2. Solve b(a) = 0.
-1, 0, 2/3, 1
Let v(b) be the second derivative of -1/8*b**4 + 1/20*b**6 + 0 + 0*b**3 - 3/40*b**5 + 0*b**2 + 6*b + 1/28*b**7. Suppose v(h) = 0. Calculate h.
-1, 0, 1
Let z be 294/210*2/7. What is d in 0 - z*d + 1/5*d**2 = 0?
0, 2
Let v(m) = -12*m + m**2 - 6*m**2 - 6 + 3*m**2 - 4*m**2. Let l(u) = -2*u**2 - 4*u - 2. Let r be ((-3)/(-6))/(1/(-34)). Let z(n) = r*l(n) + 6*v(n). Factor z(k).
-2*(k + 1)**2
Suppose -2*u - 8 = 5*c - 0*u, -4*u = -4*c + 16. Factor 2/5 + 3/5*g + c*g**2 - 1/5*g**3.
-(g - 2)*(g + 1)**2/5
Let z = 152/3 + -50. Let 1/3*d - 1/3*d**3 + z - d**2 + 1/3*d**4 = 0. Calculate d.
-1, 1, 2
Suppose 0 = -s, 3 = -2*x + 5*s + 13. Suppose -3*i - 3*f = -18, 6*i - i - x*f = 0. Factor -7*w**2 - 4*w**3 + 16*w - 6*w - 4 - w**2 + 6*w**i.
2*(w - 2)*(w - 1)**2
Let y(h) be the first derivative of -2*h**5/15 - h**4/6 + 2*h**3/9 + h**2/3 - 18. Factor y(r).
-2*r*(r - 1)*(r + 1)**2/3
Suppose 0 = 4*v - z - 80, 3*v - 4*v + 3*z = -31. Determine r, given that v - 19 - 3*r**5 - 3*r + 6*r**3 = 0.
-1, 0, 1
Let m(b) be the first derivative of b**8/840