2*c*(c - 1)**3*(c + 2)/7
Let a = 3 + 0. Let s(m) be the third derivative of -1/18*m**4 + 0*m**5 + 0 + 1/90*m**6 + 3*m**2 - 1/9*m**a + 1/315*m**7 + 0*m. Factor s(q).
2*(q - 1)*(q + 1)**3/3
Suppose -5*w - 5*d + 60 = 0, 2*w - 4 - 8 = d. Determine i, given that -3*i + w - 8 + 3*i**2 = 0.
0, 1
Let a = -38 - -41. Let b(z) = z**2 + 10*z + 11. Let n be b(-9). Determine u so that -2/5*u**n + 2/5 + 6/5*u**a - 6/5*u = 0.
-1, 1/3, 1
Let b = -43 + 43. Let w(y) be the third derivative of 0*y**4 + 1/420*y**7 + 0*y**6 + b*y**5 + 0*y + 3*y**2 - 1/672*y**8 + 0*y**3 + 0. Factor w(f).
-f**4*(f - 1)/2
Determine w so that 2/5*w**2 - 24/5*w + 72/5 = 0.
6
Let p = 18 + -16. Suppose -4*o = 5*a - 20, o + 5 = -3*a + p*o. Factor 0*k + 2*k**2 - 1/2*k**5 - 4*k**3 + 5/2*k**4 + a.
-k**2*(k - 2)**2*(k - 1)/2
Let k = 2 - 0. Factor -4*q**3 - q**4 + 0*q + 0*q**2 + 4*q - 5*q**4 + 6*q**k.
-2*q*(q - 1)*(q + 1)*(3*q + 2)
Let t(r) = -7*r**2 + r + 1. Let o be t(-1). Let z = -4 - o. Find b, given that -2 + 12*b + 4 + 5 - z - 7*b**2 = 0.
-2/7, 2
Let w be (-4)/(-28) - (-20)/7. Let 9*g**w + 3*g**5 + g**5 - g**5 - 3*g**2 - 9*g**4 = 0. What is g?
0, 1
Let g(a) = -1 - 2 + 9 + 5*a + 0 + 5*a**3 + 2*a**2. Let p(y) = 9*y**3 + 4*y**2 + 9*y + 11. Let w(v) = -11*g(v) + 6*p(v). Suppose w(z) = 0. What is z?
0, 1
Let h(t) be the first derivative of -10*t**5 + 30*t**4 - 92*t**3/3 + 12*t**2 - 2*t - 3. Let h(y) = 0. Calculate y.
1/5, 1
Let k(q) be the second derivative of -5/18*q**3 + 3*q + 0 + 1/9*q**4 - 1/60*q**5 + 1/3*q**2. Factor k(s).
-(s - 2)*(s - 1)**2/3
Let t(n) be the second derivative of n**8/10920 - n**7/1820 + n**5/195 + n**3/3 + 6*n. Let h(q) be the second derivative of t(q). Let h(z) = 0. Calculate z.
-1, 0, 2
Suppose 0*o + 12 = -4*l + 3*o, 2*o = -8. Let b = l + 8. Solve -1/2 - 3/2*r**b + 3/2*r + 1/2*r**3 = 0.
1
Let c(i) be the third derivative of -7*i**7/15 - 7*i**6/10 + 47*i**5/30 + 2*i**4 - 16*i**3/3 - 3*i**2 - 4*i. Factor c(z).
-2*(z + 1)**2*(7*z - 4)**2
Let t(v) = -2*v**4 + 10*v**3 - 26*v**2 + 14*v. Let n(g) = -8*g**4 + 39*g**3 - 105*g**2 + 55*g. Let y(x) = 2*n(x) - 9*t(x). Suppose y(b) = 0. Calculate b.
0, 2
Let y be (-75)/300*-1*(-2)/(-2). Factor -1/4*u**2 + 1/2 - y*u.
-(u - 1)*(u + 2)/4
Let w(k) be the second derivative of -k**5/10 - k**4/2 - 8*k. Determine f so that w(f) = 0.
-3, 0
Suppose 4*b = -2*f, 3*f - 2*b = 6 + 2. Let j be (4/10)/(f/10). Factor 2*s**2 - 3 + 2*s**j - s**2 - 3*s + 3*s**3.
3*(s - 1)*(s + 1)**2
Let z = -19 + 23. Let l(v) be the first derivative of -4/21*v**3 + 2 + 0*v**2 + 0*v - 6/35*v**5 - 5/14*v**z. What is a in l(a) = 0?
-1, -2/3, 0
Let y(b) be the first derivative of 0*b**3 + 2 - 1/30*b**6 + 0*b**5 + 0*b**2 + 2*b + 1/12*b**4. Let s(p) be the first derivative of y(p). Factor s(z).
-z**2*(z - 1)*(z + 1)
Let t(c) be the first derivative of 4*c - 3 + 8/3*c**3 - 5*c**2 - 1/2*c**4. Find k, given that t(k) = 0.
1, 2
Suppose -2*q - 1 + 11 = 3*g, 5*g - 8 = q. Solve 2/5*r**g + 2/5 - 4/5*r = 0.
1
Let g(s) = -3*s**2 - 3*s - 8. Let o(b) = b**3 + b**2 - 1. Let c(w) = 5*g(w) - 40*o(w). Let c(n) = 0. Calculate n.
-1, -3/8, 0
Factor 0 + 0*l**2 + 0*l - 2/3*l**4 + 2/3*l**3.
-2*l**3*(l - 1)/3
Let k(l) be the first derivative of -l**4/4 + l**3 - l**2 - 20. Factor k(t).
-t*(t - 2)*(t - 1)
Let u = -210 - -2941/14. Let q(k) be the first derivative of 0*k**3 + 2 + 0*k + 1/7*k**2 - u*k**4. Factor q(p).
-2*p*(p - 1)*(p + 1)/7
Suppose 4*x + 5*h = 96, 2*x + 3*x + 3*h - 107 = 0. What is u in x*u**3 + 7*u**2 + 17*u**3 + 14*u**2 - 21*u - 6 = 0?
-1, -1/4, 2/3
Let v(w) be the third derivative of -w**5/20 - w**4/12 - 5*w**3/6 + 2*w**2. Let d(s) = 5*s**2 + 3*s + 8. Let u(n) = 5*d(n) + 8*v(n). Let u(b) = 0. What is b?
0, 1
Suppose 2*g - 3*b - 3 = -1, b = 2*g - 6. Factor 1/3*j**3 + 0*j**2 - 2/3*j**g + 0*j + 0 + 1/3*j**5.
j**3*(j - 1)**2/3
Let w = 203 + -141. Suppose -w - 2*z**2 + 62 + 2*z**3 - 3*z**3 = 0. Calculate z.
-2, 0
Let z(f) be the first derivative of -2*f**5/5 + 4*f**3/3 - 2*f - 2. Factor z(d).
-2*(d - 1)**2*(d + 1)**2
Suppose 0*f + 0 - 4/3*f**4 + 14/3*f**3 + 4/3*f**2 - 14/3*f**5 = 0. Calculate f.
-1, -2/7, 0, 1
Let w(n) be the first derivative of n**5/40 - n**4/6 + 5*n**3/12 - n**2/2 - 4*n - 2. Let z(x) be the first derivative of w(x). Determine k so that z(k) = 0.
1, 2
Factor 25*c**3 + 5*c + c**2 - 26*c**2 - 5*c**3.
5*c*(c - 1)*(4*c - 1)
Let v(d) be the second derivative of -d**8/10080 + 7*d**4/12 - 3*d. Let c(r) be the third derivative of v(r). Factor c(z).
-2*z**3/3
Let u(f) be the second derivative of -4/3*f**3 - 1/45*f**6 - 1/5*f**5 + f - 13/18*f**4 - 4/3*f**2 + 0. Factor u(j).
-2*(j + 1)**2*(j + 2)**2/3
Let y(g) = -g. Let h be y(-2). Let c be 5 - h*(-9)/(-6). Determine t, given that -1/4*t**c + 0 - 1/4*t = 0.
-1, 0
Let i(j) be the third derivative of -j**5/120 + 5*j**4/48 + j**3/2 - 13*j**2. Factor i(u).
-(u - 6)*(u + 1)/2
Let z be (6 - (-2 - -5))*6/18. Factor -3/2*w - z - 1/2*w**2.
-(w + 1)*(w + 2)/2
Let y(z) be the first derivative of z**6/180 - z**5/45 - z**4/36 + 2*z**3/9 - 2*z**2 + 1. Let q(l) be the second derivative of y(l). Solve q(h) = 0 for h.
-1, 1, 2
Let u(g) be the second derivative of -g**4/8 + 3*g**2 + 2*g. What is j in u(j) = 0?
-2, 2
Factor -6/5*q - 4/5 + 0*q**2 + 2/5*q**3.
2*(q - 2)*(q + 1)**2/5
Suppose -62 = -3*a - 3*z - z, 0 = -5*z + 25. Suppose 5*k - 20 = 4*r - 6*r, -3*k = -4*r + a. Factor 3/2*c - 1 - 1/2*c**k.
-(c - 2)*(c - 1)/2
Suppose 0*d + 5*d - 4*j = 1891, 2*d + 2*j = 760. Let 39*w**2 + 55*w**4 + 180*w**3 + 89*w**2 + 16*w - d*w**4 = 0. What is w?
-2/9, 0, 1
Let r(a) = 2*a - 15. Let u(n) = 5*n - 44. Let x(o) = 8*r(o) - 3*u(o). Let k be x(-6). Solve 10*y**3 - 2*y**4 - k*y**2 + 8*y**4 - 8*y**5 + 2*y - 4*y = 0.
-1, -1/4, 0, 1
Factor p**5 - 4*p**2 - 6*p - 2 + 6*p**4 + 17*p**3 + p**5 - 13*p**3.
2*(p - 1)*(p + 1)**4
Let x(i) be the third derivative of -9*i**8/112 - 6*i**7/35 + i**6/5 + 7*i**5/10 + i**4/8 - i**3 - 15*i**2. Solve x(l) = 0.
-1, -2/3, 1/3, 1
Let -26*i**2 - 6*i**3 - 48*i - 32 - 1/2*i**4 = 0. What is i?
-4, -2
Suppose -3*u = u - 12, -5*u = -4*x - 7. Let f(n) be the second derivative of 0*n**3 + 0*n**4 + 0*n**x + n + 0 + 1/75*n**6 - 1/50*n**5. What is q in f(q) = 0?
0, 1
Suppose -231*o**4 - 120*o**3 + 105*o**2 - 25*o + 114*o**4 + 137*o**4 = 0. Calculate o.
0, 1/2, 5
Let a(h) = 244*h - 244*h - 12*h**3 + 10*h**2 - 24*h**4. Let d(o) = 8*o**4 + 4*o**3 - 3*o**2. Let p(x) = -3*a(x) - 10*d(x). Factor p(r).
-4*r**3*(2*r + 1)
Let k be -1*(2 + 0/(-5)). Let s be k*(-4 - (-195)/50). Find j, given that -s + 2/5*j - 1/5*j**2 = 0.
1
Let p(h) be the second derivative of -2*h**6/105 + 4*h**5/35 - 4*h**4/21 + 9*h. Factor p(y).
-4*y**2*(y - 2)**2/7
Suppose 0 = -3*m + 46 - 40. Determine j, given that 0 - 4/3*j**m + 0*j**3 - 2/3*j + 2/3*j**5 + 4/3*j**4 = 0.
-1, 0, 1
Let n(g) be the first derivative of 2*g**5/55 + 3*g**4/22 - 2*g**3/33 - 3*g**2/11 - 20. Let n(v) = 0. What is v?
-3, -1, 0, 1
Suppose 0 - 1/4*p - 1/4*p**2 = 0. What is p?
-1, 0
Let w(h) = 3*h**3 + 10*h**2 + 8*h + 3. Let j(x) = 1 - x**3 - 3*x - 2*x + 5*x. Let m(z) = -j(z) + w(z). Solve m(t) = 0 for t.
-1, -1/2
Let x = -54 + 21. Let p be (-16)/x + (-4)/(-22). Solve 0 - 2/3*u**3 - 4/3*u**4 + p*u**2 + 0*u = 0 for u.
-1, 0, 1/2
Suppose -2*c + 0 = -8. Let t(l) be the first derivative of 0*l**3 - 2/5*l**5 + 2 - 2*l**2 + l**c + 2*l. Factor t(a).
-2*(a - 1)**3*(a + 1)
Let q = -623 - -625. Factor -8/5 - 4/5*k + 4/5*k**q.
4*(k - 2)*(k + 1)/5
Let c(t) be the first derivative of -t**3 - 3*t**2 + 9*t - 17. Let c(l) = 0. Calculate l.
-3, 1
Let x(m) be the first derivative of -m**4/14 + 2*m**3/21 + 20. Factor x(n).
-2*n**2*(n - 1)/7
Suppose -2*n + 18 = 3*l - 6*n, 5*l - 5*n - 25 = 0. Factor u**l + u - 3*u + 4*u**2 - 4*u**2.
u*(u - 2)
Let w(n) be the second derivative of -7*n**5/90 + n**4/27 + 7*n**3/27 - 2*n**2/9 - 8*n. Factor w(j).
-2*(j - 1)*(j + 1)*(7*j - 2)/9
Let y(r) be the second derivative of -2*r**6/75 - r**5/25 + 2*r. Factor y(v).
-4*v**3*(v + 1)/5
Let c(x) = -x**3 - x**2 + x - 1. Let g(l) = -5*l**3 - 3*l**2 + 5*l - 3. Let t(m) = -3*c(m) + g(m). Suppose t(r) = 0. Calculate r.
-1, 0, 1
Suppose 4*r + 2 = f, r + 3 = 4*f - 5. Suppose f*k + 0*q - q - 6 = 0, -2 = -q. Determine a so that -2/5*a**3 + 2/5*a + 8/5*a**k - 8/5*a**2 + 0 = 0.
-1, 0, 1/4, 1
Let g = -11/34 + 39/68. Let g*w**4 - 1 + 2*w - 1/2*w**3 - 3/4*w**2 = 0. C