 10*h. Let k(x) be the third derivative of -2*x**2 + h + 0*x**3 + 0*x**4 + 0*x + 2/105*x**5 - 1/245*x**7 + 1/1176*x**8 + 0*x**6. Factor k(q).
2*q**2*(q - 2)**2*(q + 1)/7
Suppose -5*r - 2*z + 315 = -0*z, 205 = 3*r - 2*z. Factor -46*t**4 - r*t**4 + 8*t**3 + 8*t**2 - 15*t**4.
-2*t**2*(7*t - 2)*(9*t + 2)
Let x = -1405/6 - -235. Let v(c) be the first derivative of 0*c + 2/3*c**3 + 2/3*c**2 + 2 - x*c**4. Let v(q) = 0. Calculate q.
-2/5, 0, 1
Let a be (0/16)/(3 - 0). Let i(h) be the second derivative of 1/4*h**4 + 1/2*h**2 + 1/2*h**3 - 2*h + a + 1/20*h**5. Suppose i(w) = 0. Calculate w.
-1
Let u = 53/40 + -9/8. Let b(o) be the second derivative of 0 + 4/3*o**2 - 11/18*o**4 + 4/9*o**3 - o - u*o**5 + 1/5*o**6. Factor b(m).
2*(m - 1)**2*(3*m + 2)**2/3
Let h(q) = q**3 - 7*q**2 - q + 10. Let i be h(7). Suppose i = 3*r - 3. Suppose -4/7*n**r + 2/7*n + 2/7*n**3 + 0 = 0. Calculate n.
0, 1
Let a(c) be the first derivative of -c**3/6 - 7*c**2/4 - 1. Factor a(i).
-i*(i + 7)/2
Factor 2/11 - 4/11*b + 2/11*b**2.
2*(b - 1)**2/11
Suppose -f = 2*v + 2*v + 1, 0 = -5*f - 5*v + 25. Suppose 4 - f = -w. Suppose 2*p**4 - 6*p**2 + 2*p**4 + 3*p**4 - 15*p**5 + 15*p**w - p**4 = 0. What is p?
-1, 0, 2/5, 1
Let d(m) be the first derivative of -m**5/6 + 5*m**3/9 - 5*m/6 - 28. Solve d(u) = 0 for u.
-1, 1
Let d(t) = -t**3 + t**2 - t - 1. Let s(k) = -2*k**4 + 7*k**3 - 5*k**2 + 3*k + 3. Let i(q) = -3*d(q) - s(q). Factor i(f).
2*f**2*(f - 1)**2
Let f(j) be the second derivative of -1/3*j**4 + 0*j**2 - 1/6*j**3 + 0 - j. Factor f(x).
-x*(4*x + 1)
Let c(q) be the first derivative of -q**4/72 + q**3/36 + 7*q + 8. Let p(b) be the first derivative of c(b). Factor p(d).
-d*(d - 1)/6
Solve 0 - 3/7*s**5 + 0*s**3 + 3/7*s**4 + 0*s**2 + 0*s = 0.
0, 1
Let i(y) = 2 - 7 - 4*y + 2 + y**3 - 2*y**3 + 6*y**2. Let n be i(5). Suppose b**3 + 1/2*b**4 + 0 + 1/2*b**n + 0*b = 0. What is b?
-1, 0
Let g(q) be the third derivative of 0*q + 1/210*q**5 + 0 + q**2 - 1/21*q**4 + 4/21*q**3. Suppose g(r) = 0. Calculate r.
2
Let i(j) be the first derivative of -2*j**5/45 - 2*j**4/9 - 8*j**3/27 + 7. Factor i(x).
-2*x**2*(x + 2)**2/9
Let p(a) = a**2 + 1. Let m be p(0). Let r(u) = u**2 + u + 1. Let h(b) = -3*b**2 + 3*b + 3. Let s(y) = m*h(y) + 5*r(y). Factor s(o).
2*(o + 2)**2
Let v(m) = m**3 - m**2 + m - 1. Let w(c) = c**4 - 4*c**3 + 4*c**2 - 2*c + 1. Let b(n) = -v(n) - w(n). Factor b(s).
-s*(s - 1)**3
Let p = -15 - 6. Let l(y) = -6*y**2 - 51*y. Let h(k) = -k**2 - 10*k. Let v(q) = p*h(q) + 4*l(q). Factor v(o).
-3*o*(o - 2)
Factor 201*g**3 - 6*g**2 + 2*g + 6 + g - 204*g**3.
-3*(g - 1)*(g + 1)*(g + 2)
Let c(p) be the first derivative of p**6/2 - 21*p**5/5 + 57*p**4/4 - 25*p**3 + 24*p**2 - 12*p - 1. Suppose c(y) = 0. Calculate y.
1, 2
Let b(z) = 6*z**5 + 4*z**4 + 6*z**3 - 4*z. Let i(r) = 17*r**5 + 12*r**4 + 17*r**3 - 11*r. Let f(c) = 11*b(c) - 4*i(c). Solve f(s) = 0 for s.
-1, 0
Let v(x) be the first derivative of -5 + 3/4*x**4 + 3/25*x**5 + 21/10*x**2 + 6/5*x + 9/5*x**3. Let v(g) = 0. What is g?
-2, -1
Factor 12 + 3*s**2 - 16*s**5 + 13*s**5 - 3*s**4 - 35*s + 11*s + 15*s**3.
-3*(s - 1)**3*(s + 2)**2
Let f(l) be the second derivative of l**5/20 - 5*l**4/12 + 4*l**3/3 - 2*l**2 + 12*l. Solve f(h) = 0.
1, 2
Let k(g) be the third derivative of -2*g**5/15 - g**4/2 + 4*g**3/3 + 4*g**2. Find p, given that k(p) = 0.
-2, 1/2
Let k = 5 + -3. Let -7*q**4 + q**4 - 2*q + 4*q**2 + 2*q**3 + k*q**2 = 0. What is q?
-1, 0, 1/3, 1
Let z(l) = 3*l**2 - 6*l + 1 - 1 + 10*l. Let u(t) = t**2 + t. Let d(w) = 4*u(w) - z(w). Solve d(c) = 0.
0
Let p(h) be the first derivative of -2*h**3/21 + h**2 + 21. Factor p(a).
-2*a*(a - 7)/7
Let d(g) = 3*g**2 - 45*g - 48. Let w(s) = 4*s**2 - 68*s - 72. Let x(u) = -8*d(u) + 5*w(u). Determine h, given that x(h) = 0.
-1, 6
Factor 0 - 1/8*x**4 + 5/8*x**2 - 1/8*x**5 + 3/8*x**3 + 1/4*x.
-x*(x - 2)*(x + 1)**3/8
Let a = 2 - 0. What is x in -x**a + 7*x - 2*x + x - 5*x = 0?
0, 1
Let x be (0 - -3 - 3)/1. Suppose -z + 3*q + 17 = 0, x*q = z + 5*q + 15. Factor -7*d**2 + 2 + d - z*d - d.
-(d + 1)*(7*d - 2)
Let m(f) be the first derivative of 1/26*f**4 - 1/13*f**2 + 0*f + 0*f**3 - 5. Factor m(t).
2*t*(t - 1)*(t + 1)/13
Let n = -15 + 14. Let s be (n/(-2))/(-10 - -11). Factor 1/2*h**3 + 0*h**2 - s*h + 0.
h*(h - 1)*(h + 1)/2
Let m(r) be the first derivative of 25*r**4 + 140*r**3/3 + 22*r**2 + 4*r - 2. What is j in m(j) = 0?
-1, -1/5
Factor -3*t - 15 - 6*t**2 - 3*t**2 + 20*t + 31*t.
-3*(t - 5)*(3*t - 1)
Let z be ((-3)/9*0)/(0 + -1). Let g(p) be the third derivative of 1/60*p**4 + 0 + p**2 + 1/150*p**5 + z*p - 2/15*p**3. Suppose g(r) = 0. Calculate r.
-2, 1
Let u(t) be the second derivative of t**7/525 - t**6/120 + t**5/75 - t**4/120 - 2*t**2 - 4*t. Let l(s) be the first derivative of u(s). Factor l(m).
m*(m - 1)**2*(2*m - 1)/5
Let b(s) be the third derivative of s**7/1680 - 7*s**6/720 + s**5/16 - 3*s**4/16 + 2*s**3/3 + 2*s**2. Let q(w) be the first derivative of b(w). Factor q(g).
(g - 3)**2*(g - 1)/2
Suppose p + 4 + 2 = v, -5*v + 3*p + 26 = 0. Suppose -2*l - v = -5*h, -5*h + l - 5*l = -22. Factor 2/3*d**h - 2/3 + 0*d.
2*(d - 1)*(d + 1)/3
Let q be 11 + -2 - 4/2. Suppose 3*r + 1 - q = 0. Suppose 1 + z**2 - 3*z**2 + 3*z**r - 2 = 0. Calculate z.
-1, 1
Suppose -q - 8 = -w + 4*w, -2*q = -5*w - 28. Let z(l) be the first derivative of 1/2*l**2 + 1/2*l + 0*l**3 - 1/4*l**q - 1/10*l**5 + 1. Factor z(g).
-(g - 1)*(g + 1)**3/2
Let h(y) = -y**2 + y - 1. Suppose -2*x = 0, -3*s + 5*x = -2*s + 14. Let c(q) = 6*q**2 - 8*q + 7. Let v(m) = s*h(m) - 2*c(m). Find n, given that v(n) = 0.
-1, 0
Suppose -2*g + 5*t + 27 = 0, -2 = -3*g + 5*t + 31. Let x(a) = -a**3 + 9*a**2 - 9*a - 5. Let w(j) = -j**2 + j + 1. Let f(i) = g*w(i) + x(i). Factor f(p).
-(p - 1)**3
Let r(f) be the second derivative of -f**8/1470 - f**7/980 + f**6/1260 + f**3/6 + f. Let w(z) be the second derivative of r(z). Suppose w(h) = 0. Calculate h.
-1, 0, 1/4
Suppose 0 = -0*y - y. Suppose 3*u + y*u = -3*b + 9, 10 = -5*b. Determine a, given that -u*a**3 + a**4 + 2*a**3 + 0*a**4 + 0*a**4 + 2*a**2 = 0.
0, 1, 2
Factor -4/13 - 2/13*n**2 - 6/13*n.
-2*(n + 1)*(n + 2)/13
Let t be (-9)/(-2*12/8). Let q(l) be the second derivative of -l + 1/48*l**4 + 1/80*l**5 + 0 + 0*l**2 - 1/12*l**t. Factor q(h).
h*(h - 1)*(h + 2)/4
Let y be 45/(-10) + 2 + (-6)/(-2). Let v(h) be the first derivative of y*h**4 - 3 + 0*h + 0*h**2 - 2/3*h**3. Factor v(z).
2*z**2*(z - 1)
Suppose 5*l + 7 - 2 = 0. Let g = 1 + l. Factor 1/2*h - 1/2*h**3 + g - 1/2*h**4 + 1/2*h**2.
-h*(h - 1)*(h + 1)**2/2
Suppose 1 = -4*t + 9. Find n, given that -6*n**3 + 3*n**4 + 17*n**t - 17*n**2 = 0.
0, 2
Let v = -1 + 3. Let g = 4 + -4. Suppose g*y**2 + 8 - 10 + v*y**2 = 0. Calculate y.
-1, 1
Let n(o) = o**2 - 4*o - 5. Let z = -9 - -4. Let l(k) = 7*k - 3. Let f(d) = 4*d - 2. Let i(j) = -5*f(j) + 3*l(j). Let c(u) = z*i(u) - n(u). Solve c(m) = 0.
-1, 0
Let l = -1 + 5. Factor 7*u**l + 15*u**3 + 15*u**2 + 3*u**2 - 12*u - 4*u**4 - 24.
3*(u - 1)*(u + 2)**3
Let d(q) be the first derivative of q**3/3 - 3*q**2 + 9*q - 4. Suppose d(t) = 0. Calculate t.
3
Determine j so that -3/5*j**2 - 12/5*j + 0 = 0.
-4, 0
Factor -3/5*p + 3/5*p**2 + 2/5*p**3 - 2/5.
(p - 1)*(p + 2)*(2*p + 1)/5
Let w(h) = 9*h**4 - 57*h**3 + 48*h**2 - 33*h. Let r(l) = l**4 - 7*l**3 + 6*l**2 - 4*l. Let u(t) = -33*r(t) + 4*w(t). Factor u(a).
3*a**2*(a - 1)*(a + 2)
Suppose -r = -16*r + 60. Suppose 2*c = -2*z - 4, z + 13 = -5*c - 5. Factor -2/9 - 20/9*k**z - 10/9*k - 10/9*k**r - 20/9*k**3 - 2/9*k**5.
-2*(k + 1)**5/9
Factor 5/3*k**2 - 100/3*k + 500/3.
5*(k - 10)**2/3
Let a be (5/4 + -1)*0/1. Let u(d) be the third derivative of 1/36*d**3 - 1/48*d**4 + 0*d + a + d**2 - 1/90*d**5. Factor u(s).
-(s + 1)*(4*s - 1)/6
Let u(d) = -8*d**3 - 16*d**2 - 8*d. Let c(y) = 12*y**3 + 24*y**2 + 12*y. Let z(f) = 5*c(f) + 7*u(f). Factor z(k).
4*k*(k + 1)**2
Suppose 0 = -6*r + 11*r - 15. Determine v so that v**5 - 3*v**5 + 4*v**3 - 5*v**3 + r*v**3 = 0.
-1, 0, 1
Let v(g) = 3*g**4 + 4*g**3 - 2*g - 1. Let a(i) = -i**4 - i**3. Let r(q) = 10*a(q) + 5*v(q). What is x in r(x) = 0?
-1, 1
Let x be (15 - 3) + 12/4. Factor x*n - 15*n + n**3 - n**4.
-n**3*(n - 1)
Let v = -1 + 4. Solve 4*a - 2*a + v*a**2 - a**4 + 0*a = 0.
-1, 0, 2
Factor 0 - 3/2*f**2 + 3*f - 3/2*f**3.
-3*f*(f - 1)*(f + 2)/2
Let i(o) be the first derivative of -o**6/24 