o*(o - 1)*(o + 2)**2
Suppose n + 3*s = 6, 0 = -0*n + 2*n + 5*s - 12. Suppose 4*f - n = 6. Factor 0 + 0 + o**f - o**4.
-o**3*(o - 1)
Let p(j) be the third derivative of j**5/15 + 2*j**4/3 - 2*j**2 - 31*j. Factor p(w).
4*w*(w + 4)
Let x = 4/9 - 5/18. Let z(g) be the second derivative of 1/10*g**5 - x*g**6 + 0*g**4 + 0*g**3 + 0 + g + 0*g**2. Factor z(m).
-m**3*(5*m - 2)
Let u(v) = v**5 - v**4 + v**2 + v + 1. Let p(t) = -9*t**5 + 6*t**4 + 3*t**3 - 6*t**2 - 6*t - 6. Let o(a) = p(a) + 6*u(a). Factor o(m).
-3*m**3*(m - 1)*(m + 1)
Factor k**2 + 0 + 2/3*k.
k*(3*k + 2)/3
Let m be 1 + -1 + 13/39. Let w(n) be the second derivative of 2/15*n**6 - 2*n + 0 + 0*n**5 - m*n**4 + 1/3*n**3 + 0*n**2 - 1/21*n**7. Let w(z) = 0. What is z?
-1, 0, 1
Let a(t) be the second derivative of t**4/4 + t**3/5 + 2*t. Suppose a(l) = 0. What is l?
-2/5, 0
Suppose 5*j + 1 - 21 = 0. Let s(h) be the first derivative of -2 - 1/5*h**5 + 0*h - 1/4*h**j + 0*h**3 + 0*h**2. Suppose s(k) = 0. Calculate k.
-1, 0
Let g(c) = 4*c**3 + 16*c**2 + 20*c + 8. Let m(u) = u**3 + 4*u**2 + 5*u + 2. Let p(r) = 6*g(r) - 22*m(r). Find w such that p(w) = 0.
-2, -1
Suppose -2*j + 0 = -10. Let x(g) be the third derivative of -1/30*g**j + 0*g + 4/9*g**3 + 0 + 2/9*g**4 - 2*g**2 - 1/20*g**6. Factor x(y).
-2*(y - 1)*(3*y + 2)**2/3
Suppose 4*n - 8 = 4. Find c such that -1/3 + 17/6*c**2 + 1/6*c + 7/3*c**n = 0.
-1, -1/2, 2/7
Let g(p) = -7*p**3 + 3*p**2 + 4*p - 6. Let x(d) = -6*d**3 + 3*d**2 + 3*d - 5. Let u(m) = 5*g(m) - 6*x(m). Factor u(a).
a*(a - 2)*(a - 1)
Let f be 11*(-6)/(-165) - (-8)/(-45). Determine u so that 4/9*u**3 + f + 8/9*u + 10/9*u**2 = 0.
-1, -1/2
Suppose 8 + 8 = 4*c. Let i be 1*(3 - c)/(-1). Factor 6 - 6*o**2 + 2 + 3*o**4 - 4 - i.
3*(o - 1)**2*(o + 1)**2
Suppose -4*c = -0 + 12. Let z = 6 + c. Determine b so that -2*b**2 + 3*b + 4*b**2 + b**z - 2*b = 0.
-1, 0
Let f(s) be the first derivative of s**9/7560 + s**8/2100 + s**7/2100 + 5*s**3/3 - 2. Let o(n) be the third derivative of f(n). Factor o(h).
2*h**3*(h + 1)**2/5
Let v(a) be the second derivative of a**6/180 + a**5/15 + a**4/4 - a**3 + 7*a. Let t(j) be the second derivative of v(j). Factor t(m).
2*(m + 1)*(m + 3)
Let o(h) be the first derivative of -h**4/12 + h**3/9 + h**2/6 - h/3 - 3. Determine v so that o(v) = 0.
-1, 1
Let n = 8 + -6. Factor 5 - v**3 - 3*v + 3*v**n - 2 - 2.
-(v - 1)**3
Let w(x) be the third derivative of -x**7/315 + 7*x**6/540 - x**5/54 + x**4/108 - x**2. Determine j so that w(j) = 0.
0, 1/3, 1
Let s(y) = -3*y**2 - 162*y + 2. Let h be s(-54). Suppose -1/2 + 1/2*g**h + 1/2*g**3 - 1/2*g = 0. What is g?
-1, 1
Suppose 13*c = 12*c + 3. Factor -2/7*g**c + 0 + 6/7*g**2 - 4/7*g.
-2*g*(g - 2)*(g - 1)/7
Factor -18*c**5 - 145*c**2 + 25*c**4 + 20 + 20*c**5 - 20*c + 33*c**5 - 35*c**3 - 80*c**3.
5*(c - 2)*(c + 1)**3*(7*c - 2)
Let o(l) be the second derivative of 1/30*l**6 + 0*l**3 + 7*l + 0*l**5 - 1/12*l**4 + 0 + 0*l**2. Determine m so that o(m) = 0.
-1, 0, 1
Suppose 4*n + n - 25 = 0. Suppose 2*q = n*q - 18. Determine c so that q + c - 6 + 3*c**2 + 3*c**3 + c**4 = 0.
-1, 0
Let t = -1209 + 1211. What is f in 1/2*f**t + 1/2*f - 1/2 - 1/2*f**3 = 0?
-1, 1
Factor 0 + 5/4*b**3 + b - 1/4*b**4 - 2*b**2.
-b*(b - 2)**2*(b - 1)/4
Let b = -463/5 + 93. Let f(t) be the first derivative of b*t**4 - 2/15*t**6 + 1 + 2/5*t - 4/15*t**3 - 2/5*t**2 + 2/25*t**5. Determine i so that f(i) = 0.
-1, 1/2, 1
Factor 10/7*x + 8/7 + 2/7*x**2.
2*(x + 1)*(x + 4)/7
Let u = 42 + -42. Suppose -1/2*z + 0*z**2 + u + 1/2*z**3 = 0. Calculate z.
-1, 0, 1
Suppose 2*a - 5 + 1 = 0. What is o in 22/7*o + 20/7*o**a + 18/7*o**5 - 24/7*o**4 + 4/7 - 40/7*o**3 = 0?
-1, -1/3, 1, 2
Let f = -5 - -8. Let -8*l**4 - l**5 + 3*l - 8*l**2 - l**5 - 5*l - 6*l**f - 6*l**3 = 0. Calculate l.
-1, 0
Let t(n) be the first derivative of -n**4/12 - n**3/9 + n**2/6 + 4*n + 2. Let l(y) be the first derivative of t(y). Solve l(a) = 0.
-1, 1/3
Factor 2/19*r**2 + 6/19 + 2/19*r**3 - 10/19*r.
2*(r - 1)**2*(r + 3)/19
Factor 4*k**5 - 4*k**2 - 2*k - 2*k**5 + 0*k + 4*k**4.
2*k*(k - 1)*(k + 1)**3
Let r = -39 + 197/5. Suppose 4/5*l - 2/5*l**2 - r = 0. What is l?
1
Let r(x) be the third derivative of -1/20*x**5 - 3/8*x**4 + 0 - x**2 + 0*x - x**3. Factor r(n).
-3*(n + 1)*(n + 2)
Suppose 14 = -3*y + 4*j, -5 = -j - 0. Let u(r) be the second derivative of -1/6*r**4 + y*r + 2/3*r**3 - r**2 + 0. Factor u(g).
-2*(g - 1)**2
Suppose 2*a = -a - 3*r + 18, a + 6 = 2*r. Suppose 3*l**a - 3*l + 3*l**3 + 0*l - 3*l**4 + 0*l**4 = 0. Calculate l.
-1, 0, 1
Let x(g) be the second derivative of -2*g**6/15 - 6*g**5/5 - 13*g**4/3 - 8*g**3 - 8*g**2 - 9*g. Factor x(c).
-4*(c + 1)**2*(c + 2)**2
Let b(t) be the second derivative of t**7/315 + t**6/72 + t**5/60 + t**4/12 - t. Let r(w) be the third derivative of b(w). Factor r(z).
2*(z + 1)*(4*z + 1)
Suppose 29 = 5*a - 3*n, 2*a - 21 + 7 = 2*n. Factor -z**5 - 3*z**4 - z**a - z + 3*z**2 - 6*z**3 - 7*z**2.
-z*(z + 1)**4
Suppose d - z + 12 = 2*z, 5*d = -4*z + 35. Suppose j + t + 3 = 2*t, -4*t + 14 = -d*j. What is g in -4*g + 7*g - 2 - g**j + 3*g - 3*g = 0?
1, 2
Let l(b) be the third derivative of b**8/53760 + b**7/6720 - b**5/240 + 7*b**4/24 + 5*b**2. Let u(t) be the second derivative of l(t). Solve u(f) = 0 for f.
-2, 1
Let k be (-15)/(-28) + (-54)/189. What is m in -k*m - m**2 + 0 = 0?
-1/4, 0
Let y(s) be the second derivative of 0 + 0*s**3 + 1/48*s**4 + s**2 - 4*s - 1/120*s**5. Let k(t) be the first derivative of y(t). Factor k(b).
-b*(b - 1)/2
Let b = 83 - 81. Factor -3 - 3/2*n**b + 9/2*n.
-3*(n - 2)*(n - 1)/2
Let j(g) = -4*g - 23. Let d be j(-7). Let y(z) be the first derivative of 0*z**2 - 2 + 0*z - 4/35*z**d - 1/21*z**6 + 0*z**3 + 0*z**4. Factor y(h).
-2*h**4*(h + 2)/7
Let a be 2 + (3 - 9)/(-1). Let p be (3/(-4))/((-12)/a). Find v such that p*v**2 + 1/2 + 5/4*v = 0.
-2, -1/2
Let s = -46/3 - -16. Let g(a) be the first derivative of -s*a**3 - 1 - 2/3*a + 1/6*a**4 + a**2. Factor g(y).
2*(y - 1)**3/3
Let j(i) be the second derivative of i**4/24 - i**2/4 + 23*i. Suppose j(o) = 0. Calculate o.
-1, 1
Let z be (1/(-5))/(12/50). Let j = z + 7/6. Factor 0*n + j*n**2 + 0 - 1/3*n**3.
-n**2*(n - 1)/3
Let d(n) be the second derivative of -7*n + 1/6*n**4 + 0 - 1/27*n**6 + 4/27*n**3 - 4/9*n**2 - 7/90*n**5 + 1/63*n**7. Determine j so that d(j) = 0.
-1, 2/3, 1, 2
Let z(c) be the third derivative of 0*c + 4*c**2 + 1/24*c**4 + 1/120*c**5 + 1/12*c**3 + 0. Let z(m) = 0. Calculate m.
-1
Let w = 3/4 - 1/4. Factor -1/2 - w*g**2 + g.
-(g - 1)**2/2
Let o = 2 + 0. Suppose -3*m + o*f + 8 = 0, -4*m + f + 9 = -0. Suppose -5/2*r**3 - 5/4*r - 5/2*r**m - 1/4*r**5 - 5/4*r**4 - 1/4 = 0. Calculate r.
-1
Let j(a) = 12*a**4 + 64*a**3 + 40*a**2 - 64*a - 52. Let r(i) = 4*i**4 + 21*i**3 + 13*i**2 - 21*i - 17. Let l(u) = 5*j(u) - 16*r(u). Factor l(m).
-4*(m - 1)*(m + 1)**2*(m + 3)
Let n(a) be the third derivative of 3/40*a**5 + 0 + 4*a**2 + 1/120*a**6 + 2/3*a**3 + 0*a + 1/4*a**4. Let l(m) be the first derivative of n(m). Factor l(i).
3*(i + 1)*(i + 2)
Let i(f) be the third derivative of -f**7/1470 - f**6/420 + f**4/84 + f**3/42 + 31*f**2. Factor i(a).
-(a - 1)*(a + 1)**3/7
Let q(x) be the third derivative of -x**11/110880 - x**10/25200 - x**9/20160 - x**5/30 - 6*x**2. Let m(t) be the third derivative of q(t). Factor m(v).
-3*v**3*(v + 1)**2
Let k = 7/2 + -3. Let h(i) be the second derivative of -4/15*i**6 + 0 + 0*i**3 + k*i**5 - 1/6*i**4 + 0*i**2 + i. Solve h(z) = 0 for z.
0, 1/4, 1
Let p be (1 - 0) + (-7 - -10). Factor 8*q - 2*q**2 + p*q**2 - 6*q**2.
-4*q*(q - 2)
Let g(i) be the first derivative of -3*i**2/2 + 3*i + 2. Let j be g(-3). Let 1/4 + j*n**2 - 3*n - 16*n**3 = 0. What is n?
1/4
Let s be 1*(-17)/12 + 20/12. Factor s*t**4 + 0*t**3 + 0*t**2 + 0 + 0*t + 1/4*t**5.
t**4*(t + 1)/4
Let o(k) be the first derivative of -k**6 - 22*k**5/5 - 15*k**4/2 - 6*k**3 - 2*k**2 + 10. Solve o(p) = 0 for p.
-1, -2/3, 0
Factor 0 + 0*v**2 + 4/7*v**4 + 0*v + 8/7*v**3.
4*v**3*(v + 2)/7
Suppose -4*b = -2*b - 10. Solve 3*r**5 - 3*r**4 - r + 3*r**2 - b*r + 12*r - 9*r**3 = 0 for r.
-1, 0, 1, 2
Let g(c) be the second derivative of 0*c**2 + 3/20*c**5 + 0*c**3 + c + 1/4*c**4 + 0. Factor g(t).
3*t**2*(t + 1)
Let l(x) = -14*x**2 + 2*x + 8. Let b(u) = 5*u**2 - u - 3. Let r(t) = -8*b(t) - 3*l(t). Determine n, given that r(n) = 0.
-1, 0
Let k(f) = 2*f + 2. Let c be