 n = 31/30 + -14/15. Let a = 3/20 + n. Let -1/4*w - 1/4*w**2 + a + 1/4*w**3 = 0. What is w?
-1, 1
Let 1/3*o**2 + 0 - o = 0. What is o?
0, 3
Let z be 21/(-49) - (-110)/126. Let b(c) be the first derivative of 4/9*c**3 + 2/9*c + z*c**2 + 1 + 2/9*c**4 + 2/45*c**5. Factor b(a).
2*(a + 1)**4/9
Let w(g) be the first derivative of g**5/20 + g**4/6 - g**3/6 - g**2 - 3*g + 1. Let y(h) be the first derivative of w(h). Determine f, given that y(f) = 0.
-2, -1, 1
Let w be 3 + (-6 - 9/3). Let c be ((-3)/2)/(3/w). Suppose -2*d + 2*d**2 - 4*d**3 + 0*d**2 + 4*d**3 + 2*d**c - 2 = 0. Calculate d.
-1, 1
Let o(q) be the third derivative of 4*q**2 - 1/120*q**5 + 0*q - 3/4*q**3 + 0 - 1/8*q**4. Determine h so that o(h) = 0.
-3
Determine m, given that -8/9*m - 4/9*m**5 - 4/9*m**2 + 4/9*m**4 + 0 + 4/3*m**3 = 0.
-1, 0, 1, 2
Let m(k) be the second derivative of 3*k**4/8 + k**3/6 - 20*k. Factor m(p).
p*(9*p + 2)/2
Factor -5*i**2 + 4/3*i**3 - 1/2 + 19/6*i.
(i - 3)*(2*i - 1)*(4*i - 1)/6
Let g(h) = 1. Let j(k) = -k**2 + 4*k - 5. Let d(u) = 6*g(u) + 3*j(u). Factor d(a).
-3*(a - 3)*(a - 1)
Let p(l) = l**3 + 2*l**2 - 5*l - 2. Let z be p(-3). Factor -8*i**z + 5*i**4 + 5*i**4.
2*i**4
Suppose -4*x + 5*i = -12, -3*i - 2 = -5*x + 13. Suppose -8 = -4*h + 4*s, -x*h = -3*s + 7*s - 41. Factor -c + 3*c - c + h*c**3 + 5*c**2 + 3*c**4.
c*(c + 1)**2*(3*c + 1)
Let c(v) be the second derivative of -7*v**5/40 + 19*v**4/24 + v**3/2 + 18*v. Factor c(i).
-i*(i - 3)*(7*i + 2)/2
Let a(f) be the second derivative of f**6/6 - 10*f**4/3 + 40*f**2 - 23*f. Factor a(h).
5*(h - 2)**2*(h + 2)**2
Let r(m) = -m**2 - m + 2. Let z(a) = 5*a**2 + 4*a - 9. Let y(o) = 18*r(o) + 4*z(o). Factor y(b).
2*b*(b - 1)
Let s(r) be the third derivative of -3*r**7/350 + 17*r**6/100 - 83*r**5/100 - 21*r**4/10 + 18*r**3/5 + 8*r**2. Determine x, given that s(x) = 0.
-1, 1/3, 6
Let u(x) be the first derivative of -x**3/2 - 9*x**2/4 - 5. Factor u(w).
-3*w*(w + 3)/2
Let k(z) = 3*z**2 + 8*z + 3. Let a(t) = -39*t**2 - 105*t - 39. Let s(d) = 2*a(d) + 27*k(d). Factor s(j).
3*(j + 1)**2
Let 1/8*p**4 - 1/4*p**2 + 0*p - 1/8*p**3 + 0 = 0. Calculate p.
-1, 0, 2
Let j be (-12)/(-18)*(-54)/(-4). Factor -2*l - 4 + j*l**2 + 4*l**3 - 5*l**2 + 0*l**3 - 2*l**3.
2*(l - 1)*(l + 1)*(l + 2)
Let x(v) be the third derivative of v**6/300 + v**5/150 - v**4/60 - v**3/15 - 7*v**2. Suppose x(p) = 0. What is p?
-1, 1
Factor 32/7*j**2 - 4/7 + 10/7*j + 18/7*j**3.
2*(j + 1)**2*(9*j - 2)/7
Let s(p) be the third derivative of 4*p**6/165 + 4*p**5/165 - 7*p**4/132 + p**3/33 - 9*p**2. What is u in s(u) = 0?
-1, 1/4
Determine l, given that -1/7*l**3 + 5/7*l**2 + 3/7 - l = 0.
1, 3
Let r(n) = -2*n**4 - 11*n**3 - 25*n**2 + 16*n + 32. Let p(b) = 2*b**4 + 10*b**3 + 24*b**2 - 16*b - 32. Let y(g) = -5*p(g) - 6*r(g). Factor y(k).
2*(k - 1)*(k + 1)*(k + 4)**2
Let m(y) = 4*y**5 - y**4 - 4*y**3 + y**2 - 3*y + 3. Let g(s) = -s**5 + s**3 + s - 1. Let j(n) = -12*g(n) - 4*m(n). Find u, given that j(u) = 0.
-1, 0, 1
Let q = 1095757357/681420645 - 2/365373. Let m = q + -3/373. Factor -m*x + 0*x**2 + 0 + 2/5*x**4 + 6/5*x**3.
2*x*(x - 1)*(x + 2)**2/5
Suppose 2*j = -4*r - 70, -74 = 2*r + 2*r - 2*j. Let i be 2/(-6) - 6/r. Factor i*b + 4/11*b**5 + 6/11*b**4 + 0 + 2/11*b**3 + 0*b**2.
2*b**3*(b + 1)*(2*b + 1)/11
Determine w, given that 0 - 1/5*w + 9/10*w**2 = 0.
0, 2/9
Let f(o) = -2*o**3 - 5*o**2 - 3*o. Let u be f(-1). Let -3/4*g**2 + u*g + 3/2*g**3 - 3/4*g**4 + 0 = 0. Calculate g.
0, 1
Let g be ((-90)/(-12))/(65/26). Find w, given that 0 + 6*w - 30*w**2 + 75/2*w**g = 0.
0, 2/5
Let j(c) be the second derivative of c**4/90 + c**3/45 - 2*c**2/15 - 36*c. Factor j(t).
2*(t - 1)*(t + 2)/15
Let k(c) be the first derivative of -c**4/4 - c**3/2 + 3*c + 1. Let i(h) be the first derivative of k(h). Find q such that i(q) = 0.
-1, 0
What is o in 190*o + 75 + o**2 + 2*o**2 - 160*o = 0?
-5
Let v(o) = -o**2 + 11*o - 11. Let b be v(10). Let t be b - (3 + -2) - -4. Determine h so that -6 + 6*h**3 + t + 2*h - 4*h + 8*h**2 = 0.
-1, 2/3
Let g be 2 + (-2)/(-2) - 1. Let p = 0 + 2. Factor -1 - p*x**4 - 1 + 4*x**g + 0*x**2.
-2*(x - 1)**2*(x + 1)**2
Let m(o) = -o**4 - o**3 + 2*o**2 + 1. Let b(v) = -8*v**4 - 8*v**3 + 16*v**2 + 7. Let i(x) = 2*b(x) - 14*m(x). Let i(q) = 0. Calculate q.
-2, 0, 1
Factor -9/2 + 3/8*x**3 - 3*x + 3/8*x**2.
3*(x - 3)*(x + 2)**2/8
Let f(z) be the first derivative of z**6/30 + 3*z**5/25 + 3*z**4/20 + z**3/15 - 21. Solve f(w) = 0.
-1, 0
Let y = 15/17 - -571/85. Determine t, given that 8/5 - y*t**2 + 14/5*t**3 + 16/5*t = 0.
-2/7, 1, 2
Let h(d) = -3*d**4 - 2*d**2 + 2. Let p(b) be the third derivative of 8*b**7/105 + 11*b**5/60 - 11*b**3/6 - 2*b**2. Let s(r) = 11*h(r) + 2*p(r). Factor s(y).
-y**4
Let r(v) be the third derivative of v**5/240 + 5*v**4/96 + v**3/4 - 26*v**2. Let r(u) = 0. Calculate u.
-3, -2
Suppose 0*x - 2 = 4*m + 2*x, -2*x = 5*m. Let d(g) be the first derivative of -4 - 2*g + 5/2*g**m + 7/3*g**3. Determine a so that d(a) = 0.
-1, 2/7
Let g be (-4)/18 - (-168)/270. Factor 0*m - g + 2/5*m**2.
2*(m - 1)*(m + 1)/5
Let s(q) be the second derivative of q**6/6 + 3*q**5/2 + 5*q**4 + 25*q**3/3 + 15*q**2/2 + 17*q. Factor s(o).
5*(o + 1)**3*(o + 3)
Let t(j) be the third derivative of 0*j**3 + 3*j**2 + 0 + 1/420*j**6 + 1/84*j**4 - 1/105*j**5 + 0*j. Suppose t(q) = 0. What is q?
0, 1
Let s = 2 - 0. Let q(t) = -4*t**4 - 3*t**3 + 8*t**2 - t - 5. Let j(r) = 1 + 4*r**4 - r**4 - r**2 - 2*r**4. Let v(w) = s*q(w) + 10*j(w). Factor v(h).
2*h*(h - 1)**3
Let p(s) = 2*s - 8. Let b be p(4). Let j(z) be the third derivative of 4/9*z**3 + z**2 + b + 1/90*z**5 + 0*z - 1/9*z**4. Factor j(n).
2*(n - 2)**2/3
Solve -14*v**3 - 3*v - 4*v**3 + v**2 - v - 2*v**5 - 15*v**2 - 10*v**4 = 0 for v.
-2, -1, 0
Let q be 1 + (-4)/8*-4. Let d(u) be the first derivative of 1/10*u**5 - 1/3*u**q - 1/4*u**4 + 1/4*u**2 + 1/2*u + 1/12*u**6 + 1. Find n such that d(n) = 0.
-1, 1
Let 4/5*k**3 - 4/5*k**2 + 0 + 0*k - 4/5*k**5 + 4/5*k**4 = 0. What is k?
-1, 0, 1
Let j(h) be the third derivative of -1/105*h**7 - 7/50*h**5 - 17/300*h**6 - 11/60*h**4 - 2/15*h**3 + 0 + 0*h - 2*h**2. Determine s, given that j(s) = 0.
-1, -2/5
Let 2/5*n**3 + 6/5*n**2 + 0 + 4/5*n = 0. Calculate n.
-2, -1, 0
Let t(f) be the first derivative of 3*f**4/20 - f**3/5 + 10*f + 7. Let k(y) be the first derivative of t(y). Factor k(q).
3*q*(3*q - 2)/5
Let w be (-10)/6*88/(-110). Determine x so that w*x + 2/3 - 2*x**2 = 0.
-1/3, 1
Suppose m - 3 = a + 3, -5*m = 2*a + 5. Let d(c) be the first derivative of 0*c**2 - m - 2/9*c**3 + 2/3*c. Factor d(r).
-2*(r - 1)*(r + 1)/3
Let l(j) be the third derivative of j**8/112 + 2*j**7/35 + j**6/20 - j**5/5 - 3*j**4/8 + j**2. Let l(i) = 0. What is i?
-3, -1, 0, 1
Let a(c) be the second derivative of c**4/42 + 2*c**3/7 + 8*c**2/7 + 44*c. Factor a(w).
2*(w + 2)*(w + 4)/7
Factor 8 - j**2 + 5 - 22 + 5 + 5*j.
-(j - 4)*(j - 1)
Let x = 8 - 5. Let z = 7 - 5. Determine d, given that z*d - d**x - 3*d + 2*d = 0.
-1, 0, 1
Let r(i) = i**2 + 41*i - 130. Let h be r(-44). Find u, given that 2/9*u**5 + 0 - 4/9*u + 2/3*u**h + 2/9*u**3 - 2/3*u**4 = 0.
-1, 0, 1, 2
Let b(d) = -d**4 - d**3 + d**2 + d + 1. Let s(h) = -24*h**4 + 45*h**3 - 9*h**2 + 3*h + 3. Let l(o) = 3*b(o) - s(o). Factor l(m).
3*m**2*(m - 2)*(7*m - 2)
Factor 6/5*v**2 - 8/15 + 32/15*v.
2*(v + 2)*(9*v - 2)/15
Let x = -2 + -2. Let k be x/14*(-21)/9. Factor 4/3*p**2 - 2/3*p**5 + 4/3*p**3 - 2/3 - k*p - 2/3*p**4.
-2*(p - 1)**2*(p + 1)**3/3
Find g such that 2/5*g + 2/15*g**2 - 8/15 = 0.
-4, 1
Let p(b) = -b - 1. Let l be p(-3). Factor -46*q - 3*q**3 + 3*q**2 - 24*q**3 - 2*q + 12 + 60*q**l.
-3*(q - 1)*(3*q - 2)**2
Let d(w) be the first derivative of w**6/120 + w**5/30 + w**4/24 - 3*w**2/2 + 1. Let x(u) be the second derivative of d(u). Factor x(c).
c*(c + 1)**2
Let l(f) be the first derivative of 0*f - 1/8*f**4 + 1/3*f**3 + 1/60*f**5 - 2 + 3/2*f**2. Let o(z) be the second derivative of l(z). Solve o(b) = 0.
1, 2
Let p(i) = -i**2 + i + 2. Let v be p(0). Let n = -3 + 5. Factor 3*h - 2*h + 2*h**n - v*h - h**3.
-h*(h - 1)**2
Determine a, given that -8/11*a**3 + 0 - 2/11*a**4 - 4/11*a - 10/11*a**2 = 0.
-2, -1, 0
Let u(c) = 9*c + 6. Let r be u(-4). Let p be (5/r)/((-4)/6). Factor -p*w**2 - 1/4 + 1/2*w.
-(w - 1)**2/4
Suppose -4*i + 18*i = 28. Factor 2 + 2/9*f**i + 4/3*f.
2*(f + 3)**2/9
Let 0 + 3/2*f**2