Let i be ((-3)/4 + (-13)/(-52))/(-1). Solve 5/2*o + 1 + 2*o**2 + i*o**3 = 0 for o.
-2, -1
Determine w, given that -5*w**2 - 9*w**2 - 252 - 5*w**2 + 21*w**2 - 78*w = 0.
-3, 42
Let g be 13*(-4)/(-84) - (-14)/(-49). Let o(l) be the second derivative of 0*l**2 + 0*l**3 + 7*l + g*l**4 - 2/15*l**6 + 0 + 1/5*l**5 - 2/21*l**7. Factor o(a).
-4*a**2*(a - 1)*(a + 1)**2
Let k(q) be the second derivative of -q**5/80 - 83*q. Factor k(b).
-b**3/4
Determine q, given that -33/5*q + 2 + 18/5*q**2 + q**3 = 0.
-5, 2/5, 1
Let z(b) = 10*b**2 + 38*b + 30. Let v(q) = -19*q**2 - 73*q - 59. Let f(y) = 6*v(y) + 11*z(y). Determine s, given that f(s) = 0.
-3, -2
Let n(a) = -2*a**3 - 22*a**2 + 21*a + 1. Let m be n(-12). Suppose 21*q = m*q. Solve 2/13*r**5 + q - 2/13*r**2 - 2/13*r**3 + 0*r + 2/13*r**4 = 0.
-1, 0, 1
Let b(a) be the second derivative of 5*a**7/42 - 4*a**6/3 + 25*a**5/4 - 95*a**4/6 + 70*a**3/3 - 20*a**2 - 561*a. Factor b(x).
5*(x - 2)**3*(x - 1)**2
Suppose 0 = 7*a - 493 - 634. Let h = 163 - a. Factor -9/4 - 1/4*o**h + 3/2*o.
-(o - 3)**2/4
Let x(n) = n**3 - 6*n**2 + n - 4. Let z be x(6). Factor 2*o**3 - 6*o**2 + 6*o**3 - 2*o**4 - 2*o**2 + 8 + z*o**2 - 8*o.
-2*(o - 2)**2*(o - 1)*(o + 1)
Let v(p) = 19*p**2 - 27*p + 14. Let q(a) = -18*a**2 + 27*a - 12. Let o(k) = 6*q(k) + 5*v(k). Factor o(x).
-(x - 2)*(13*x - 1)
Let p(d) = d**4 - 2*d**3 - 6*d**2 - 2*d + 5. Let x(w) = 3*w + 10. Let a be x(-4). Let r(m) = -m**4 - m**3 - m + 1. Let n(o) = a*r(o) + p(o). Factor n(u).
3*(u - 1)**2*(u + 1)**2
Let n(z) be the first derivative of z**5/5 + z**4 + z**3/3 - 3*z**2 + 203. Factor n(f).
f*(f - 1)*(f + 2)*(f + 3)
Suppose 0 = 12*n - 9 - 75. Factor -x**2 + 12*x**3 - 12*x + 11*x**3 - n*x**2 - 19*x**3.
4*x*(x - 3)*(x + 1)
Let a(o) be the first derivative of 0*o**3 + 1/135*o**6 + 10 + 0*o**5 + 1/9*o**2 + 3*o - 1/27*o**4. Let q(m) be the first derivative of a(m). Factor q(j).
2*(j - 1)**2*(j + 1)**2/9
Factor 21*q - 33 - 26*q**2 - 17*q**2 + 103*q**2 + 96*q.
3*(4*q - 1)*(5*q + 11)
Factor -17672 + 196*m - 672*m + 100*m - 2*m**2.
-2*(m + 94)**2
Let u(i) = -i**3 - 4*i**2 - 6*i - 2. Let o be u(-2). Factor w**o - 29*w**3 - 1 + 28*w**3 + 0*w**2 + w.
-(w - 1)**2*(w + 1)
Suppose 1/6*n**2 + 15/2 + 23/3*n = 0. What is n?
-45, -1
Let u = -26443/15 + 1763. Factor u*d - 4/15 + 2/15*d**2.
2*(d - 1)*(d + 2)/15
Let b = 39/88 - -93/88. Factor 3/2*g**2 + 1/2*g**3 + 1/2 + b*g.
(g + 1)**3/2
Let h(l) be the first derivative of l**4/2 + 62*l**3/5 - 38*l**2/5 + 22. Factor h(y).
2*y*(y + 19)*(5*y - 2)/5
Suppose 3*k - 1 = -1. Let p = -86/15 + 32/5. Factor -p*o**2 + k*o + 0.
-2*o**2/3
Let d(y) be the second derivative of 1/21*y**4 + 0 + 0*y**2 - 1/140*y**5 + 18*y - 2/21*y**3. Let d(a) = 0. Calculate a.
0, 2
Let u = 95117/1257 + -4/1257. Let g = 153/2 - u. Factor -3/2*y**2 + 2*y**3 + 0 + 1/3*y - g*y**4.
-y*(y - 1)**2*(5*y - 2)/6
Let q(t) be the first derivative of -t**5/40 + t**3/4 - 11*t**2/2 - 12. Let p(l) be the second derivative of q(l). What is h in p(h) = 0?
-1, 1
Let h(l) be the second derivative of 0*l**2 + 5/6*l**3 + 0 + 1/200*l**5 + 0*l**4 + 1/1800*l**6 + 6*l. Let s(y) be the second derivative of h(y). Factor s(w).
w*(w + 3)/5
Let s(d) be the second derivative of 3/4*d**4 + 0 - d - d**3 - 1/10*d**5 + 1/180*d**6 + 0*d**2. Let m(q) be the second derivative of s(q). Factor m(a).
2*(a - 3)**2
Let i = -21 + 23. Suppose -5*q + 95 = -5*u, i*q + 0*q - 3*u - 39 = 0. Solve -2*x**2 + 2*x**2 - q*x**2 - 24*x**3 + 10*x - 8*x**4 - 14*x = 0.
-2, -1/2, 0
Let s = 755 + -751. Let i(h) be the second derivative of 1/2*h**2 + 2*h + 0 + 1/12*h**s - 1/3*h**3. Factor i(c).
(c - 1)**2
Let c(s) = s**4 + s**3 - s**2 - s + 1. Let g(x) = -18*x**3 + 18*x**2 - 4. Let r = 4 - 0. Suppose 4 = 2*y - r. Let v(i) = y*c(i) + g(i). Solve v(w) = 0 for w.
0, 1/2, 1, 2
Factor 5*a**4 - 2*a**2 - 13*a**4 + 3*a**4 - a**2 - 20*a + 23*a**2 + 5*a**3.
-5*a*(a - 2)*(a - 1)*(a + 2)
Let -4/3*w**2 + 2/3*w**5 - 4/3 + 8/3*w**3 - 10/3*w + 8/3*w**4 = 0. What is w?
-2, -1, 1
Suppose -17 = 8*l - 7*l. Let o = -16 - l. Find h, given that 5*h - o - 4*h**2 + 39*h**3 - 38*h**3 - 1 = 0.
1, 2
Let q(m) be the first derivative of 4 + 0*m**2 - 3/10*m**5 + 0*m - m**3 + 9/8*m**4. Factor q(v).
-3*v**2*(v - 2)*(v - 1)/2
Suppose -37*w + 38*w + 15*w = 0. Suppose 112/3*q**3 + w - 98*q**4 - 343/6*q**5 + 8*q**2 - 8/3*q = 0. What is q?
-2, -2/7, 0, 2/7
Let b be 2/4 + 15/10. Suppose -6 + b*f**2 - 2*f**2 + 4*f + 2*f**2 = 0. What is f?
-3, 1
Factor 2 + 4*j + 5/2*j**2 + 1/2*j**3.
(j + 1)*(j + 2)**2/2
Let a(t) be the third derivative of -44*t**2 + 0 + 1/4*t**4 - 17/20*t**5 + 0*t + 0*t**3. Factor a(v).
-3*v*(17*v - 2)
Suppose -9*c + 30 = 12. Factor v**2 + 5*v + 3*v**c + 4 - v + 4*v.
4*(v + 1)**2
Let g(m) be the first derivative of -3 - 8/3*m**3 - 2*m**2 - m**4 + 0*m. Determine s so that g(s) = 0.
-1, 0
Let o(i) be the second derivative of 1/2*i**3 + 1/12*i**4 - 4*i + 0 + 0*i**2. What is u in o(u) = 0?
-3, 0
Let f(s) = -54*s**3 + 1840*s**2 - 20804*s + 78604. Let u(j) = 108*j**3 - 3679*j**2 + 41609*j - 157209. Let c(k) = -7*f(k) - 4*u(k). Factor c(l).
-2*(3*l - 34)**3
Solve 4/5 + 6*k + 38/5*k**2 + 12/5*k**3 = 0.
-2, -1, -1/6
Let l(z) be the third derivative of -z**5/4 - z**4/2 + 2*z**2 + 14*z. Determine b so that l(b) = 0.
-4/5, 0
Suppose 0 = -18*l + 17*l + 3. Let k(g) be the third derivative of 0*g + 0*g**l + 1/36*g**4 + 0 - 1/270*g**5 - 2*g**2. Suppose k(i) = 0. Calculate i.
0, 3
Suppose 18 = 2*p - 5*t, -3 = -2*t - 7. Suppose -21*m**3 - 5*m**4 + 8*m**p + 15*m**3 + 3*m**5 = 0. Calculate m.
-2, 0, 1
Let j(r) be the second derivative of r**4/16 - 3*r**3/8 - 27*r**2/4 + 18*r. Factor j(w).
3*(w - 6)*(w + 3)/4
Suppose 2*g = -3*o - 2*o - 27, -8 = 4*o + 5*g. Let b = o - -19. Factor -3*c**2 - c - b*c + 10*c.
-3*c*(c + 1)
Let k be (-1 - 3) + 3 + 3. Factor 9*q - 5*q - 18*q**2 + 16*q**3 - k*q**2.
4*q*(q - 1)*(4*q - 1)
Factor -15*a**4 - 6*a**3 - 35*a**5 + 61*a**5 + 0*a**3 - 35*a**5.
-3*a**3*(a + 1)*(3*a + 2)
Let b(h) be the first derivative of 2*h**3/39 - 18*h**2/13 - 38*h/13 + 34. Determine a, given that b(a) = 0.
-1, 19
Let i be 10278/56 + (-10)/40. Let j = i - 183. Factor 6/7 - j*q**2 - 4/7*q.
-2*(q - 1)*(q + 3)/7
Find f such that -6 - 2*f**2 - 46*f - 36 - 24 + 18 + 4*f**2 = 0.
-1, 24
Let c(x) be the third derivative of 1/315*x**7 + 1/90*x**5 + 0*x - 19*x**2 + 0*x**3 + 0 + 0*x**4 + 1/90*x**6. Factor c(m).
2*m**2*(m + 1)**2/3
Factor 18*j + 3*j**2 - 12*j**3 - 214*j**4 + 106*j**4 + 111*j**4.
3*j*(j - 3)*(j - 2)*(j + 1)
Let n(j) be the first derivative of -j**3/4 + 39*j**2/2 - 507*j - 59. Factor n(k).
-3*(k - 26)**2/4
Let z be (10 - (7 + 990/350))/(3/10). Suppose -z*s**2 + 8/7*s - 4/7 = 0. What is s?
1
Let c = -8173/75 + 109. Let j(x) be the third derivative of 1/150*x**6 - c*x**5 + 10*x**2 - 1/30*x**4 + 0*x + 0 + 4/15*x**3. Factor j(n).
4*(n - 2)*(n - 1)*(n + 1)/5
Let x(k) = k**3 - 6*k**2 + k + 6. Let f be x(5). Let s be (9 - -1)*f/(-35). Factor -w**2 + 11*w**4 - s*w**4 - 2*w**3 - 8*w**4.
-w**2*(w + 1)**2
Let h(y) be the first derivative of -1/3*y**3 - 4*y + 0*y**2 + 1/12*y**4 + 3/20*y**5 + 4. Let c(w) be the first derivative of h(w). Let c(o) = 0. Calculate o.
-1, 0, 2/3
Determine u, given that -1/5*u**3 - 12/5*u + 0 - 8/5*u**2 = 0.
-6, -2, 0
Let a(x) be the first derivative of -4*x**3/3 + 8*x**2 + 128*x + 139. Factor a(f).
-4*(f - 8)*(f + 4)
Let t(n) be the third derivative of n**5/330 - n**3/33 - 20*n**2. Find s such that t(s) = 0.
-1, 1
Let t(n) be the third derivative of -7*n**6/60 + 4*n**5/3 - 23*n**4/12 - 10*n**3/3 + 20*n**2. Factor t(l).
-2*(l - 5)*(l - 1)*(7*l + 2)
Let r(k) be the first derivative of 1/3*k**3 + 5/6*k**4 + 0*k**2 + 23/40*k**5 + 3 + 7/60*k**6 + 2*k. Let h(s) be the first derivative of r(s). Factor h(a).
a*(a + 1)*(a + 2)*(7*a + 2)/2
Factor 132/7 + 12/7*l**2 + 531/7*l.
3*(l + 44)*(4*l + 1)/7
Let w(s) = -8*s**5 + 41*s**4 - 32*s**3 - 9*s - 9. Let q(j) = -4*j**5 + 20*j**4 - 16*j**3 - 4*j - 4. Let n(z) = 9*q(z) - 4*w(z). Suppose n(u) = 0. Calculate u.
0, 2
Let m(y) = 118*y**2 - 99*y - 1. Let q(h) = -58*h**2 + 49*h + 1. Let d(v) = -4*m(v) - 9*q(v). Factor d(n).
5*(n - 1)*(10*n + 1)
Let h = -112 - -115. Let g(s) be the second derivative of 6*s + 0*s**2 + 3/8*s**h - 1/16*s**4 - 1/16*s**5 + 0 - 1/120*s**6. Factor g(z).
-z*(z - 1)*(z + 3)**2/4
Factor 2*f**4 - 278*f**3 - 439*f**2 - 4