**8 + 1/210*f**5 + 0*f. Factor v(p).
(p - 1)**3*(p + 1)**2/7
Let v(x) be the second derivative of -1/30*x**5 + x + 0*x**3 + 0 + 0*x**2 + 1/63*x**7 + 0*x**6 + 0*x**4. Solve v(k) = 0 for k.
-1, 0, 1
Let c(l) be the second derivative of -l**9/45360 + l**8/10080 - l**7/7560 + l**4/3 + 3*l. Let u(p) be the third derivative of c(p). Factor u(o).
-o**2*(o - 1)**2/3
Let r be 5/12 - 34/(-136). Find a such that 0*a + 0 - r*a**2 = 0.
0
Let z(g) = -6*g**5 + 22*g**4 - 4*g**3 + 16*g**2 + 16*g. Let s(t) = -2*t**5 + 7*t**4 - t**3 + 5*t**2 + 5*t. Let l(f) = 16*s(f) - 5*z(f). Factor l(v).
-2*v**3*(v - 2)*(v + 1)
Let q(f) = f**2. Let z(m) be the second derivative of -5*m**4/6 - 5*m**3/6 - m**2 - 2*m. Let t(u) = 21*q(u) + 3*z(u). Let t(b) = 0. What is b?
-1, -2/3
Let r = -18 - -23. Let s(h) be the third derivative of -h**2 - 1/24*h**4 + 0 + 0*h**3 + 1/240*h**6 - 1/120*h**r + 0*h. What is g in s(g) = 0?
-1, 0, 2
Let v(w) be the second derivative of -w**6/15 - w**5/10 - w. Factor v(n).
-2*n**3*(n + 1)
Suppose -2*x + g = 3*g + 6, -x = 5*g + 15. Let s be (-6 + 0)/(-5 + 3). Factor -p**2 + 1/2*p + 1/2*p**s + x.
p*(p - 1)**2/2
Let a = 403/1935 - -3/215. Let u(g) be the second derivative of 1/54*g**4 + 0 + 2*g - 1/27*g**3 - a*g**2. Factor u(b).
2*(b - 2)*(b + 1)/9
Let w(d) = -d**2 + 2*d + 3. Let h be (-3 - -5) + 3 + -3. Let s be w(h). Factor -1/2*m + 1/2 - 1/2*m**2 + 1/2*m**s.
(m - 1)**2*(m + 1)/2
Suppose -25/2 - 5*u - 1/2*u**2 = 0. Calculate u.
-5
Let o(q) be the third derivative of q**7/210 - q**6/40 + q**5/20 - q**4/24 - 19*q**2. Factor o(d).
d*(d - 1)**3
Let d(z) be the third derivative of -z**8/84 - 4*z**7/105 + 2*z**5/15 + z**4/6 - 11*z**2. Factor d(o).
-4*o*(o - 1)*(o + 1)**3
Let d = 76 - 74. Let u(n) be the first derivative of 0*n**2 + 4*n**4 + 6/5*n**5 + 4*n**3 - d*n + 3. Factor u(f).
2*(f + 1)**3*(3*f - 1)
Let 5/2*a**4 - 4*a - 1/2*a**2 - 2 + 1/2*a**5 + 7/2*a**3 = 0. What is a?
-2, -1, 1
Let v(p) be the second derivative of 1/60*p**5 - 1/180*p**6 - 1/6*p**3 + 0 + 0*p**4 + 0*p**2 - 2*p. Let s(t) be the second derivative of v(t). Factor s(g).
-2*g*(g - 1)
Let c = 17 - 9. Suppose 4*b = 2*r + 22, r + c = 5*b + 5*r. Factor m**b + 1/3*m**3 - 2/3*m**2 + 0*m + 0.
m**2*(m + 1)*(3*m - 2)/3
Let j be (-28)/5 + (-2)/5. Let q be j/(-4)*(-4)/(-3). Determine p so that -q*p**5 + p**5 + 6*p**3 - 5*p**3 = 0.
-1, 0, 1
Let m(r) be the first derivative of -r**3/5 - 3*r**2/10 + 6*r/5 + 7. Factor m(f).
-3*(f - 1)*(f + 2)/5
Let z(d) be the second derivative of -1/30*d**5 + 1/54*d**4 + 0 - 1/189*d**7 + 0*d**2 + 9*d + 0*d**3 + 1/45*d**6. Let z(g) = 0. Calculate g.
0, 1
Let o(p) be the first derivative of -p**7/21 - p**6/15 + p**5/10 + p**4/6 + 4*p + 5. Let f(q) be the first derivative of o(q). Factor f(a).
-2*a**2*(a - 1)*(a + 1)**2
Suppose 0 = -5*h - 2*p - 2, h + 2*p + 2 = -2*h. Let r(u) be the third derivative of -u**2 + 0 + h*u - 1/210*u**5 + 1/21*u**3 + 0*u**4. Factor r(a).
-2*(a - 1)*(a + 1)/7
Suppose z + 2 = 2*z. Factor -5*n**2 + 2*n**z - 2*n**2 + 7*n**2.
2*n**2
Factor -3/2*t**2 - 5/2*t**3 - 1/2*t**4 + 2 + 5/2*t.
-(t - 1)*(t + 1)**2*(t + 4)/2
Let r(x) be the first derivative of -x**6/40 + 3*x**5/5 - 6*x**4 + 32*x**3 - 2*x**2 + 4. Let n(c) be the second derivative of r(c). Factor n(g).
-3*(g - 4)**3
Let z = 0 - 2. Let g be (-209)/(-380) - z/10. Find m, given that -m**5 + g*m**3 + 5/4*m**4 - 5/4*m**2 + 0 + 1/4*m = 0.
-1, 0, 1/4, 1
Factor -8/3*c**4 + 4*c**3 - 8/3*c**2 + 2/3*c + 0 + 2/3*c**5.
2*c*(c - 1)**4/3
Let s(z) be the second derivative of -z**6/225 + z**5/150 - 3*z. Factor s(u).
-2*u**3*(u - 1)/15
Let f(n) = -n**2 + 16*n - 47. Let t(k) = 3*k**2 - 49*k + 140. Let q(r) = 7*f(r) + 2*t(r). Let q(c) = 0. Calculate c.
7
Let n(h) be the second derivative of -h**5/120 - 5*h**4/12 - 25*h**3/3 - 250*h**2/3 + 16*h. Factor n(v).
-(v + 10)**3/6
Let l(c) be the first derivative of -c**4/4 - c**3 - 3*c**2/2 - c + 3. Find j such that l(j) = 0.
-1
Let r be (-6)/(-8) + 630/(-40). Let s be (-7)/r + 6/(-45). Factor -4/3 - s*y**2 + 4/3*y.
-(y - 2)**2/3
Let k(b) be the first derivative of -b**5 + 10*b**3/3 - 5*b + 1. Factor k(f).
-5*(f - 1)**2*(f + 1)**2
Let t(q) be the third derivative of -q**6/72 - q**5/18 - 5*q**4/72 + q**2 + 24. What is g in t(g) = 0?
-1, 0
Suppose g = -g + 8. Suppose -5*b - 2*k = -11 - 15, g*k - 12 = 0. Determine j, given that 0*j**4 - 2 + 4*j**2 - j**b - j**4 = 0.
-1, 1
Let y(b) = 8*b**5 - 24*b**4 + 4*b**3 + 16*b**2 - 20*b. Let x(i) = -i**4 - i**3 - i - 1. Let f(h) = -4*x(h) + y(h). Determine u, given that f(u) = 0.
-1, 1/2, 1
Suppose 0 + 12 = 4*i, -5*m = 4*i - 22. Factor -4/7*u**m + 2/7*u**4 + 0*u + 0*u**3 + 2/7.
2*(u - 1)**2*(u + 1)**2/7
Let o(m) be the first derivative of -2*m**3/33 + 6*m**2/11 - 18*m/11 + 3. Factor o(q).
-2*(q - 3)**2/11
Let m(y) = 8*y**3 + 5*y**2 - 8*y - 5. Suppose 3*c + 8 = -c. Let j(t) = -4*t**3 - 2*t**2 + 4*t + 2. Let s(r) = c*m(r) - 5*j(r). Factor s(o).
4*o*(o - 1)*(o + 1)
Let j(k) be the second derivative of k**8/1344 - k**7/210 + k**6/80 - k**5/60 + k**4/96 + 3*k**2 + 10*k. Let f(v) be the first derivative of j(v). Factor f(a).
a*(a - 1)**4/4
Let v(s) = -5*s - 22. Let p be v(-5). Let b(f) be the second derivative of 5/2*f**4 + f**2 + 0 - 7/3*f**p + 4*f + 4/15*f**6 - 13/10*f**5. Factor b(w).
2*(w - 1)**3*(4*w - 1)
Find n, given that -1/5*n**2 - n + 1/5*n**3 - 3/5 = 0.
-1, 3
Let h(d) be the second derivative of -d**4/12 - d**3/2 - d**2 + 2*d. Factor h(g).
-(g + 1)*(g + 2)
Let u(k) = k. Let h be u(7). Let b be 16/h + 8/(-28). Factor -3*m - 4*m - 4*m**b - 2 + 2*m**2 + 3*m.
-2*(m + 1)**2
Factor 4/3*n + 8/3*n**3 + 0 + 10/3*n**2 + 2/3*n**4.
2*n*(n + 1)**2*(n + 2)/3
Let x = 5 - 1. Let w be 10/x - 12/(-8). Factor 4*s**3 - 4*s - w*s + 4 + 2*s - 2*s**3.
2*(s - 1)**2*(s + 2)
Suppose -4*b + 28 = -0*s + 4*s, 0 = b - 4. Suppose 15 = y + s*o, -2*o + 0*o + 10 = 2*y. Factor -2*t**5 + y*t**5 - 12*t**3 - 2*t + t**2 - 8*t**4 - 9*t**2.
-2*t*(t + 1)**4
Let b(v) be the second derivative of v**5/5 - 7*v**4/3 + 10*v**3 - 18*v**2 + v. Determine y, given that b(y) = 0.
1, 3
Let c(p) be the third derivative of p**6/140 + 4*p**5/105 + p**4/28 - 2*p**3/21 - 2*p**2. Factor c(v).
2*(v + 1)*(v + 2)*(3*v - 1)/7
Let p(z) = -z**3 - 5*z**2 - 6*z - 6. Let v be p(-4). Let o = 202/3 + -67. Suppose -1/6 - o*m - 1/6*m**v = 0. Calculate m.
-1
Let u(k) be the second derivative of -1/40*k**5 - 1/60*k**6 + 0*k**3 + 1/84*k**7 + 0*k**2 - 3*k + 1/24*k**4 + 0. Solve u(p) = 0 for p.
-1, 0, 1
Let k = -4 - -3. Let f be ((-1)/k)/(1/7). Solve i**3 - f - i - i**2 + 7 + i**4 = 0 for i.
-1, 0, 1
Let r(i) be the first derivative of -i**4/28 + i**3/21 + i**2/14 - i/7 + 9. Factor r(s).
-(s - 1)**2*(s + 1)/7
Suppose -7*c + 5 = 5. Find o such that -2/13*o**2 + 0*o + c = 0.
0
Suppose 2*n = 3*n + 3*d + 9, 0 = 3*d + 12. Let c(m) be the second derivative of -1/18*m**4 + m + 1/9*m**n + 0 + 2/3*m**2. Factor c(r).
-2*(r - 2)*(r + 1)/3
Let a(n) = -n - 1. Let c be a(-3). Determine v so that 4*v**5 + c - 4*v**2 + 4*v**3 + 2*v**4 - 6*v**5 - v - v = 0.
-1, 1
Let u(n) = n - 2*n + 2 + 2*n. Let j be u(0). Factor 4 - 2 - 3 - 2*s + 2*s**j - 3*s**2.
-(s + 1)**2
Let n be 4/10 - 28/(-5). Suppose -2*h + n = h. Find c, given that -6*c**4 + 13*c**h - 7*c**2 + 4*c**3 - 3*c - c = 0.
-1, 0, 2/3, 1
Let w = -1/85 + 87/170. Find v such that 1 + 0*v**2 - 3/2*v + w*v**3 = 0.
-2, 1
Suppose 0 = -3*k - 2 + 14. Let p(s) be the first derivative of 0*s + 2 + 3*s**3 + 7/4*s**k + s**2. Factor p(f).
f*(f + 1)*(7*f + 2)
Suppose -1/5*m**3 + 1/5*m**2 + 0 + 0*m = 0. What is m?
0, 1
Let t be 3/5 - (-2)/5. Let b = 2 + t. Find l, given that 2*l + b*l**3 - l**3 + l**5 - l**2 - 5*l**3 + l**4 = 0.
-2, -1, 0, 1
Let k(s) be the second derivative of s**7/840 - s**6/480 - s**2 + 2*s. Let u(a) be the first derivative of k(a). Suppose u(v) = 0. Calculate v.
0, 1
Let s(z) be the second derivative of 1/5*z**2 - 1/60*z**4 - 3*z - 1/10*z**3 - 1/150*z**6 + 0 + 3/100*z**5. Factor s(p).
-(p - 2)*(p - 1)**2*(p + 1)/5
Let m(c) = c**3 - c**2 + c - 1. Let y(b) = -2*b**4 + 4*b**2 - 12*b + 10. Let s(x) = 6*m(x) + y(x). Factor s(g).
-2*(g - 2)*(g - 1)**2*(g + 1)
Let j be (1/(-21)*-2)/(13/39). Let x(h) = -h**3 - 4*h**2 + 3*h - 7. Let l be x(-5). Factor -2/7*t**2 + 2/7 - 2/7*t**l + j*t.
-2*(t - 1)*(t + 1)**2/7
Let j(g) be the third derivative of g**7/168 - g**6/60 - 19*g**5/240 -