*d**3/27 - d**2/9 - 2. Factor x(h).
-2*h*(h + 1)*(4*h - 1)**2/9
Let r(g) be the second derivative of g**8/336 - g**7/70 + g**6/60 - 2*g**2 - 4*g. Let o(s) be the first derivative of r(s). Determine x, given that o(x) = 0.
0, 1, 2
Let f(t) be the third derivative of t**7/420 - t**5/60 - t**3/3 + t**2. Let z(l) be the first derivative of f(l). Let z(p) = 0. What is p?
-1, 0, 1
Let t(u) be the third derivative of u**7/16380 - u**6/4680 - 3*u**4/8 + u**2. Let s(n) be the second derivative of t(n). Factor s(g).
2*g*(g - 1)/13
Factor 14/5*f**2 - 18/5*f**3 - 2/5*f**5 + 2*f**4 + 0 - 4/5*f.
-2*f*(f - 2)*(f - 1)**3/5
Factor 0 - 3/2*j**3 + 0*j - 3/4*j**4 - 3/4*j**2.
-3*j**2*(j + 1)**2/4
Suppose -2*p + 16 = p + 2*o, p - o - 7 = 0. Suppose -p*v - 2*h = -v + 2, 0 = 4*h + 4. Factor -3/2*r**5 + 0 + 1/2*r - 3*r**3 + v*r**2 - 4*r**4.
-r*(r + 1)**3*(3*r - 1)/2
Let b = -7 + 11. Suppose -b = -o, 0 = 3*i - 4*i - 3*o + 12. Factor 1/2*n**2 - 3/4*n**3 + 0 + i*n + 1/4*n**4.
n**2*(n - 2)*(n - 1)/4
Let k(j) = -j**4 + j**2 + j - 1. Let t(f) = 4*f**4 - f**3 - 4*f**2 - 2*f + 3. Let v(i) = -6*k(i) - 2*t(i). Factor v(r).
-2*r*(r - 1)**2*(r + 1)
Let d(o) be the first derivative of -7*o**3/3 + 20*o**2 + 12*o - 48. Factor d(g).
-(g - 6)*(7*g + 2)
Factor -2/11*n**4 - 2/11 + 0*n + 4/11*n**2 + 0*n**3.
-2*(n - 1)**2*(n + 1)**2/11
Let p(v) = -6*v**2 + 3. Let t(k) = -k**2 + 1. Let x(c) = -3*p(c) + 21*t(c). Determine o, given that x(o) = 0.
-2, 2
Suppose 0 = t + 4*b - 47, t + 2*b - 37 = 3*b. Suppose 3*z = -h + t, z + 85 = 6*z - 5*h. Factor 3*j**2 + 14 + j**4 - z - j - 3*j**3.
j*(j - 1)**3
Let y be 46/144 - 1/4. Let u(s) be the third derivative of -2/45*s**5 + 0 - 2*s**2 - 1/18*s**3 + y*s**4 + 1/90*s**6 + 0*s. Find a, given that u(a) = 0.
1/2, 1
Factor -1/2*k**3 + 0 - 3/2*k**2 + 2*k.
-k*(k - 1)*(k + 4)/2
Let w be (30/18)/(5/6). Suppose 1/4*v**5 + 0*v + 3/4*v**4 + 1/4*v**w + 3/4*v**3 + 0 = 0. Calculate v.
-1, 0
Let m(p) be the second derivative of 4*p - 1/8*p**2 + 0 - 1/20*p**5 + 1/6*p**3 + 1/30*p**6 - 1/16*p**4. Factor m(o).
(o - 1)*(o + 1)*(2*o - 1)**2/4
Let j(a) be the first derivative of 1/10*a**4 - 2 + 0*a**2 + 2/15*a**3 + 0*a. Determine n so that j(n) = 0.
-1, 0
Solve 4/11*h**3 + 0 + 0*h - 2/11*h**2 = 0 for h.
0, 1/2
Let u(f) = f**3 - 5*f**2 - 7*f + 7. Let c be u(6). Let r be ((-1)/3)/(c/(-6)). Find w, given that -6*w**2 + w + 4*w**2 - w**r - 4*w**3 = 0.
-1, 0, 1/4
Let o be (-6)/3*(0 + 6). Let w = o - -61/5. Factor w*h + 0 - 2/5*h**2 + 1/5*h**3.
h*(h - 1)**2/5
Suppose 3*f = 4*f - 8. Suppose f = 3*k + 23. Let g(b) = 4*b**3 + 9*b**2 - 4*b + 5. Let z(h) = -h**2 + h - 1. Let d(u) = k*z(u) - g(u). Factor d(n).
-n*(2*n + 1)**2
Determine r so that r + 0 + 1/4*r**2 = 0.
-4, 0
Let k(r) = -3*r**4 - 2*r**3 + 5*r**2 - 5*r. Let t(s) = 3*s**4 + s**3 - 4*s**2 + 4*s. Let p(l) = -4*k(l) - 5*t(l). Factor p(f).
-3*f**3*(f - 1)
Let d(l) be the first derivative of -l**6/6 - l**5 - 3*l**4/2 + 4*l**3/3 + 4*l**2 + 5. Factor d(r).
-r*(r - 1)*(r + 2)**3
Let w(i) be the third derivative of i**8/168 - 11*i**7/315 + i**6/12 - i**5/10 + i**4/18 + 6*i**2. Factor w(o).
2*o*(o - 1)**3*(3*o - 2)/3
Let d(r) = 5*r**2 - 4*r - 7. Let u(n) = -9*n**2 + 7*n + 13. Let o(z) = 11*d(z) + 6*u(z). Let c be o(1). Factor 0 + 1/2*f**2 + c*f.
f**2/2
Let s(k) be the third derivative of -5*k**2 + 1/120*k**6 + 0*k + 0*k**3 - 2/105*k**7 - 1/24*k**4 + 1/15*k**5 + 0. Let s(a) = 0. Calculate a.
-1, 0, 1/4, 1
Let k be (-12)/(-5) - 2/5. Let d be 30/12 + k/(-4). Suppose -2*g**d - g - g**2 - 2*g + 6*g**3 = 0. Calculate g.
-1/2, 0, 1
Let w be (-1 - -7)*2/66. Let i = -1/343 - -1383/3773. Factor w*l - i*l**3 - 2/11*l**4 + 4/11*l**2 - 2/11 + 2/11*l**5.
2*(l - 1)**3*(l + 1)**2/11
Solve -n**3 + 4*n**4 + 24*n**2 + 4 - 6*n**3 - 16*n - 9*n**3 = 0 for n.
1
Let l(r) = r + 7. Let o be l(-6). Suppose 6*g - 3*g**2 - o + 0*g + 1 = 0. What is g?
0, 2
Let a(j) be the first derivative of 2*j**3/27 + 2*j**2/9 + 2*j/9 - 10. Suppose a(x) = 0. Calculate x.
-1
What is b in 5*b**4 + 5*b**4 - 4*b**4 + 2*b**5 + 4*b**3 = 0?
-2, -1, 0
Let y be (3 + (-9)/(-5))*-10. Let k = y - -193/4. Suppose -k*f**2 + 0 - 1/4*f = 0. What is f?
-1, 0
Let m(r) be the first derivative of -r**3/21 - 5*r**2/7 - 25*r/7 - 8. Factor m(p).
-(p + 5)**2/7
Let s = 2 + -6. Let d(q) = q**4 - 5*q**3 + 4*q**2 - 4*q + 4. Let u(k) = -k**4 + 6*k**3 - 5*k**2 + 5*k - 5. Let i(h) = s*u(h) - 5*d(h). Let i(j) = 0. What is j?
0, 1
Let b(i) be the first derivative of -3*i**4/4 - 4*i**3 - 3*i**2/2 + 1. Let u(n) = -3*n**3 - 11*n**2 - 2*n + 1. Let j(l) = 5*b(l) - 6*u(l). Factor j(f).
3*(f - 1)*(f + 1)*(f + 2)
Let b = 17 + -8. Let u be (1 + -4)/b*-6. Suppose -2/7*k**u + 0 - 2/7*k**3 + 0*k + 4/7*k**4 = 0. What is k?
-1/2, 0, 1
Let w be 2*1 + (7 - 1). Factor -g**2 + 8*g - w*g.
-g**2
Let l(q) be the third derivative of 9*q**8/4480 - q**7/112 - q**6/15 - 3*q**5/20 + q**4/8 - 4*q**2. Let v(y) be the second derivative of l(y). Solve v(d) = 0.
-2/3, 3
Let x(i) = 5*i**4 - 3*i**5 + 6*i**3 + 1 - 7 + i**5 + 7*i**5 + 6*i. Let k(y) = 4*y**5 + 4*y**4 + 5*y**3 + 5*y - 5. Let b(t) = -6*k(t) + 5*x(t). Factor b(h).
h**4*(h + 1)
Let g = 6 + 0. Factor -s - 2*s - 27*s**2 + g + 24*s**2.
-3*(s - 1)*(s + 2)
Let z(k) = 11*k**4 + 7*k**3 + 9*k**2 + 9*k + 9. Let t(j) = -5*j**4 - 3*j**3 - 4*j**2 - 4*j - 4. Let u(h) = -9*t(h) - 4*z(h). Factor u(n).
n**3*(n - 1)
Suppose -3*c = -5*c. Let o(l) be the second derivative of 1/50*l**5 - 1/15*l**3 + 0*l**4 + 2*l + 0*l**2 + c. Suppose o(n) = 0. Calculate n.
-1, 0, 1
Let q be (8 + 0)*(-12)/(-8). Suppose -a = 3*a - q. Find g, given that -g - g**3 + g**4 + 2*g**a + g = 0.
-1, 0
Suppose -4*j - 215 = 5*d, -6 = -4*j - 26. Let o = -271/7 - d. What is h in 12/7*h**3 + 2/7*h**5 - 8/7*h**4 + 0 - 8/7*h**2 + o*h = 0?
0, 1
Let n(j) = 4*j**2 + 2*j. Let t(r) = -4*r**2 + 4*r + 4*r**2 + 7*r**2. Let u(h) = -5*n(h) + 3*t(h). Suppose u(i) = 0. What is i?
-2, 0
Let i be (-6)/(-2) - 477/(-265). Suppose 81/5 - 3/5*u**4 - i*u**3 - 54/5*u**2 + 0*u = 0. Calculate u.
-3, 1
Let s(w) = -31*w**5 - 60*w**4 - 23*w**3 + w**2 + 5*w - 5. Let x(c) = -c**5 - c**3 - c**2 - c + 1. Let p(k) = -s(k) - 5*x(k). Factor p(r).
4*r**2*(r + 1)*(3*r + 1)**2
What is l in -4/9*l - 2/9*l**2 + 0 = 0?
-2, 0
Let a(b) be the first derivative of b**4/2 + 4*b**3 + 3*b**2 + 4*b - 2. Let t(z) = -z**2 + z. Let v(h) = a(h) + 4*t(h). Let v(s) = 0. Calculate s.
-2, -1
Factor 0*s**4 + 0 - 2/9*s - 2/9*s**5 + 0*s**2 + 4/9*s**3.
-2*s*(s - 1)**2*(s + 1)**2/9
Find u such that -3/2 + 9/4*u**2 - 3/4*u**4 - 3/4*u**3 + 3/4*u = 0.
-2, -1, 1
Let y be (-8)/10 - (3 + -4 + 0). Determine z so that 1/5*z**3 - y*z**2 + 1/5 - 1/5*z = 0.
-1, 1
Let b(v) be the third derivative of v**8/10080 - v**7/1890 + v**6/1080 - v**5/30 - 6*v**2. Let k(p) be the third derivative of b(p). Factor k(a).
2*(a - 1)*(3*a - 1)/3
Let a(c) = 5*c**4 - 35*c**3 + 10*c**2 + 30*c - 15. Let u(x) = -x**5 - 5*x**4 + 34*x**3 - 10*x**2 - 29*x + 15. Let y(p) = 4*a(p) + 5*u(p). Solve y(n) = 0.
-3, -1, 1
Let g = 17 - 14. Suppose -19 + 4 = -5*r. Factor 2 + 3*f**2 + r*f**2 - 6*f - 3*f**g + f**3.
-2*(f - 1)**3
Let u = -6/227 + -23363/681. Let k = 35 + u. Determine a so that 2/3*a**2 + 0 - k*a = 0.
0, 1
Let h(d) be the third derivative of d**5/330 + d**4/44 - 2*d**2. Factor h(g).
2*g*(g + 3)/11
Let t(d) = -12*d**4 - 10*d**3 + 7*d**2 - 13*d + 6. Let s(f) = -f**4 - f**3. Let r(i) = -22*s(i) + 2*t(i). Factor r(a).
-2*(a - 2)*(a - 1)**2*(a + 3)
Let m be (8/15 + (-2)/3)*-3. Factor 0 - 2/5*k**3 + 2/5*k**4 + 2/5*k - m*k**2.
2*k*(k - 1)**2*(k + 1)/5
Suppose l - 3*i + 8 = -0*l, -5*l = 2*i - 28. Factor l*x**5 - 4*x**2 - 2*x**4 + 6*x**4 - 2*x**5 - 2*x.
2*x*(x - 1)*(x + 1)**3
Let w(q) = -180*q**3 + 390*q**2 - 219*q + 9. Let x(s) = -18*s**3 + 39*s**2 - 22*s + 1. Let f(o) = 2*w(o) - 21*x(o). Let f(b) = 0. Calculate b.
1/6, 1
Let s(q) = -4*q**2 - q + 3. Let o(f) = f**2 - 1. Let k(h) = 5*o(h) + s(h). Find b such that k(b) = 0.
-1, 2
Let h(d) = -6*d**2 + 2. Suppose -6 = 3*f - 3*g, -f - 3*g + 8*g - 14 = 0. Suppose 0*q + 12 = -3*q. Let s(w) = w. Let i(c) = f*h(c) + q*s(c). Factor i(z).
-2*(z + 1)*(3*z - 1)
Let j(o) = -o**2 - 8*o + 3. Let p be j(-8). Let v(b) be the first derivative of 2/3*b**p - 1/3*b**6 - 3/2*b**4 + 0*b + 6/5*b**5 + 0*b**2 - 1. Factor v(q).
-2*q**2*(q - 1)**3
Suppose 2/3 + 0*a - 2/3*a**2 = 0. Calculate a.
-1, 1
Let z = -1