second derivative of -y**10/35280 + y**9/6615 - y**8/3920 + y**6/2520 - y**4/6 + y. Let h(s) be the third derivative of l(s). Factor h(i).
-2*i*(i - 1)**3*(3*i + 1)/7
Let j = -508 + 39625/78. Let k(i) be the third derivative of -1/1365*i**7 + 1/39*i**3 + 0 + j*i**4 + 0*i + 0*i**5 - i**2 - 1/390*i**6. Factor k(g).
-2*(g - 1)*(g + 1)**3/13
Let b(j) be the second derivative of j**5/60 + j**4/12 + j**3/6 + j**2/6 + 29*j. Factor b(m).
(m + 1)**3/3
Let a(q) be the first derivative of q**6/15 - 6*q**5/25 + 3*q**4/10 - 2*q**3/15 + 37. Factor a(d).
2*d**2*(d - 1)**3/5
Let g = 37 + -34. Let t(c) be the first derivative of 0*c + c**2 + 0*c**4 - 1/3*c**6 - 1 - 4/3*c**g + 4/5*c**5. Factor t(d).
-2*d*(d - 1)**3*(d + 1)
Let j = 7/12 + -1/4. Suppose 0*o**4 + 0 - j*o**5 + 2/3*o**3 - 1/3*o + 0*o**2 = 0. Calculate o.
-1, 0, 1
Let v(d) = 3*d**3 - d**2 - d + 1. Let s be v(1). Find y such that -5*y**s + 4*y**2 - 2*y**3 - 4*y + 3*y**2 + 6*y - 2 = 0.
-1, 1
Let i(a) be the second derivative of a**9/6048 + a**8/3360 - a**7/1680 - a**6/720 + a**3/6 - 2*a. Let t(j) be the second derivative of i(j). Factor t(d).
d**2*(d - 1)*(d + 1)**2/2
Suppose -q - 4*q + 15 = 0, -v + 17 = 5*q. Factor 2/7*b**3 + 2/7*b + 0 + 4/7*b**v.
2*b*(b + 1)**2/7
Suppose -9 - 9 = 3*l. Let u(w) = w**3 + 6*w**2 - w - 2. Let q be u(l). Let 5*a**q + 2*a**2 + 2*a**4 - a**4 - 2*a**5 - 6*a**3 = 0. Calculate a.
0, 1
Let r(u) be the first derivative of u**5/35 + u**4/14 - u**2/7 - u/7 + 3. Factor r(w).
(w - 1)*(w + 1)**3/7
Let n(r) be the first derivative of -r**5/35 + 3*r**4/28 + r**3/21 - 3*r**2/14 + 7. Factor n(l).
-l*(l - 3)*(l - 1)*(l + 1)/7
Factor -4 + 8/3*m**2 + 2/3*m**3 + 2/3*m.
2*(m - 1)*(m + 2)*(m + 3)/3
Let g(n) be the second derivative of n**4/4 + n**3/2 - 3*n**2 + 5*n. What is j in g(j) = 0?
-2, 1
Suppose 0 = 3*i - 4*w - 21, 0 = -10*i + 6*i + 5*w + 27. Factor -3/2*s**i + 1/2*s**5 + 0 + 0*s + s**2 + 0*s**4.
s**2*(s - 1)**2*(s + 2)/2
Let j(d) be the first derivative of 1/2*d**2 - 1/9*d**3 - 2/3*d + 2. Factor j(b).
-(b - 2)*(b - 1)/3
Let n(i) be the second derivative of -i**5/5 - 2*i**4/3 - i**3 + i. Let j(h) = h**3 + h**2 + h. Let z(k) = 6*j(k) + n(k). Find l, given that z(l) = 0.
0, 1
Suppose -8*q = -q. Let a(c) be the third derivative of 0*c + 1/90*c**5 + q*c**3 + 0 + 1/36*c**4 - 2*c**2. Factor a(u).
2*u*(u + 1)/3
Let b(s) = -s**3 + 24*s**2 - 23*s + 4. Let f be b(23). Factor 0 - 1/4*t**2 - 1/4*t**3 + 1/4*t**f + 1/4*t.
t*(t - 1)**2*(t + 1)/4
Let o(u) = -4*u**3 + 8*u**2 + 4*u + 2. Let h(g) = -4*g**3 + 9*g**2 + 3*g + 2. Let w(z) = 5*h(z) - 6*o(z). Factor w(k).
(k - 2)*(k + 1)*(4*k + 1)
Let s be (-39)/26*(-4)/3. Factor -3*i**3 + i + 0*i + s*i.
-3*i*(i - 1)*(i + 1)
Let s be 63/28*2/3. Factor s*h**2 + 3/4 + 9/4*h.
3*(h + 1)*(2*h + 1)/4
Let c be (-5)/(-6) + -1 + 272/96. Factor 2/3*s**3 + 4/3 + c*s**2 + 10/3*s.
2*(s + 1)**2*(s + 2)/3
Let t(n) = n**2 + 2*n + 2. Let w be t(-2). Let u(h) = h**2 + h - 1. Let l(d) = -d. Let r(k) = w*l(k) + 2*u(k). Factor r(z).
2*(z - 1)*(z + 1)
Let l be 6/(-3) - 958/(-364). Let h = l + -9/26. What is x in -8/7*x + 8/7 + h*x**2 = 0?
2
Let t(g) be the second derivative of -g**8/6720 + g**6/720 + g**4/4 - g. Let k(f) be the third derivative of t(f). Solve k(u) = 0 for u.
-1, 0, 1
Let c = 104 + -104. Let c - 10/9*g**2 + 14/9*g**5 + 10/9*g**4 - 2*g**3 + 4/9*g = 0. What is g?
-1, 0, 2/7, 1
Suppose 0 = 3*f - 8 - 4. Let d(u) be the third derivative of 0*u + 1/24*u**4 + 1/180*u**5 + 1/9*u**3 + f*u**2 + 0. Factor d(l).
(l + 1)*(l + 2)/3
Let f be (8/(-7))/(102/(-357)). Factor 0 - 4/5*y**5 + 0*y**3 - 4/5*y**f + 0*y**2 + 0*y.
-4*y**4*(y + 1)/5
Let f be (2 - (-12)/(-6))/(3 - 2). Let k(r) = r - 6. Let q be k(6). Factor q + f*v - 2/3*v**2.
-2*v**2/3
Suppose 0*y + 4*n = 2*y - 224, 0 = -5*y - 4*n + 518. Let v = 322/3 - y. Let -4/3*k + v + 1/3*k**2 = 0. Calculate k.
2
Factor -3*z**3 - 24 + 24 - 3*z - 6*z**2.
-3*z*(z + 1)**2
Let w be 102/27 - (-4)/18. Let n(m) be the third derivative of 1/90*m**5 + 0 + 0*m - 1/36*m**w + 1/180*m**6 - m**2 - 1/9*m**3. Factor n(i).
2*(i - 1)*(i + 1)**2/3
Let q = 4/45 - -2/15. Let y be 2/(-4)*(-8)/6. Determine i so that -2/3*i**2 - 2/9 - q*i**3 - y*i = 0.
-1
Factor 12*n**2 - 3*n**4 + 4*n**3 - n**4 - 10*n**2 + 6*n**2.
-4*n**2*(n - 2)*(n + 1)
Suppose 0 = 64*c - 68*c + 8. Factor 0*n**c + 1/2*n**3 - 1/2*n + 0.
n*(n - 1)*(n + 1)/2
Let u = -7/11 - -43/33. Determine w so that 1/3*w - u + 1/3*w**2 = 0.
-2, 1
Let h(p) be the third derivative of -p**8/10080 + p**7/1260 - p**5/20 - 3*p**2. Let d(s) be the third derivative of h(s). Find l such that d(l) = 0.
0, 2
Solve 0*n + 3/2*n**4 + 0 - 3*n**2 + 3/2*n**3 = 0.
-2, 0, 1
Let n = -20 - -19. Let s be -2 - n - (-7)/4. Factor 1/4*y**5 + 0*y + 3/4*y**3 + 0 - 1/4*y**2 - s*y**4.
y**2*(y - 1)**3/4
Let a(n) be the third derivative of -n**5/360 - n**4/48 - n**3/18 - 61*n**2. Let a(p) = 0. Calculate p.
-2, -1
Let g(b) be the first derivative of -b**4/12 + b**2/2 - 6*b - 3. Let s(l) be the first derivative of g(l). Determine w, given that s(w) = 0.
-1, 1
Factor -3/2*g + 0 - 3/4*g**2.
-3*g*(g + 2)/4
Let b(n) be the first derivative of -n**6/75 - n**5/25 - n**4/30 + n + 2. Let x(o) be the first derivative of b(o). Factor x(v).
-2*v**2*(v + 1)**2/5
Let -15*z**2 - 6*z**3 + 5*z**2 + 4*z**3 - 6 - 14*z = 0. What is z?
-3, -1
Let u be 11/5 + (-4)/20. Factor 3*c + 0*c + c - 2*c**u.
-2*c*(c - 2)
Let o(t) be the third derivative of 1/6*t**3 + 1/8*t**4 + 0 + 9*t**2 + 0*t + 1/30*t**5. Factor o(z).
(z + 1)*(2*z + 1)
Determine c, given that -12*c - 6*c + c**2 + 16*c = 0.
0, 2
Let z(u) be the third derivative of 25*u**8/336 - 3*u**7/7 + 11*u**6/12 - 2*u**5/3 - 5*u**4/8 + 5*u**3/3 + 6*u**2. Find s such that z(s) = 0.
-2/5, 1
Let j(o) = -o**5 - o**4 + o**2 + o. Suppose 0 = 6*u - 6. Let d(b) = -21*b**5 - 12*b**4 - 3*b**3 + 18*b**2 + 18*b. Let m(i) = u*d(i) - 18*j(i). Factor m(n).
-3*n**3*(n - 1)**2
Let g(n) be the third derivative of -1/120*n**5 + 0 + 0*n - 1/6*n**3 + 4*n**2 + 1/16*n**4. Factor g(m).
-(m - 2)*(m - 1)/2
Let s(m) = -4*m**2 - 6*m + 3. Let q(u) = -5*u**2 - 7*u + 4. Let j(k) = -3*q(k) + 4*s(k). Determine i, given that j(i) = 0.
-3, 0
Determine z so that -4 + 44*z**2 + 0*z + 88*z**3 + 36*z**2 - 8*z - 80*z**5 - 76*z**4 = 0.
-1, -1/5, 1/4, 1
Suppose -62*z**3 - 50/9*z**5 + 8/3 + 290/9*z**4 + 470/9*z**2 - 176/9*z = 0. What is z?
2/5, 1, 3
Let l(t) be the first derivative of 0*t - 2*t**2 + 2/3*t**3 - 1. Factor l(n).
2*n*(n - 2)
Let j(r) be the third derivative of -r**7/4620 - r**6/990 - r**5/660 - r**3/6 - 3*r**2. Let h(o) be the first derivative of j(o). Suppose h(f) = 0. What is f?
-1, 0
Determine z, given that -z**5 + 2*z**5 + 186*z**2 - 186*z**2 = 0.
0
Suppose 0 = -2*j - 0*j. Let x(z) be the third derivative of -1/60*z**5 + 0*z**3 + 2*z**2 + j + 0*z + 0*z**4. What is s in x(s) = 0?
0
Let v be (3*-17)/(3/(-4)). Let f = -190/3 + v. Factor 4/3*d + f*d**2 + 0.
2*d*(7*d + 2)/3
Let z(i) be the second derivative of i**7/105 - i**6/75 - i**5/50 + i**4/30 - 6*i. Suppose z(c) = 0. Calculate c.
-1, 0, 1
Suppose 5*p = 9*p. Suppose p*z - 5*z + 10 = 0. Factor -2*x + 3 + 1/3*x**z.
(x - 3)**2/3
Let r(x) be the first derivative of -5*x**8/336 - x**7/30 - x**6/60 - 3*x**2/2 + 4. Let b(k) be the second derivative of r(k). Let b(t) = 0. Calculate t.
-1, -2/5, 0
Suppose -6 = 5*k - 4*k. Let l(u) = u**3 + u**2 - u. Let w(j) = -8*j**3 + 2. Let h(c) = k*l(c) - w(c). Factor h(r).
2*(r - 1)**3
Let a(p) = 2*p**3 - 6*p**2 + 8*p. Let m(d) = d + 3. Let i be m(-4). Let o(h) = h + 1. Let f(y) = i*a(y) + 2*o(y). Factor f(g).
-2*(g - 1)**3
Let -3*r**5 - 36*r**3 - r**5 + 18*r**2 + 10*r**2 - 8*r + 20*r**4 = 0. Calculate r.
0, 1, 2
Find c such that 12 - 3*c**2 - c**2 + 10 - 6 = 0.
-2, 2
Factor -5*a**5 + 6*a**2 - 97*a**3 - 13*a**5 + 55*a**3 + 50*a**4 + 2*a + 2*a.
-2*a*(a - 1)**3*(9*a + 2)
Let u(w) = 3*w**5 - 3*w**3 + 2*w**2 + 2. Let o(c) = c**3 + c + 3. Let b be o(0). Let x(j) = -j**5 + j**3 - j**2 - 1. Let q(n) = b*u(n) + 6*x(n). Factor q(v).
3*v**3*(v - 1)*(v + 1)
Suppose 6*i = 3*i + 18. Let m be 12/i - (-6)/(-4). Determine r so that m - 1/2*r**2 + 0*r = 0.
-1, 1
Let v(y) be the second derivative of y**4/78 - y**3/39 - 2*y**2/13 - 6*y. Solve v(r) = 0 for r.
-1, 2
Let a be -2 + -1 + (2 - -8). Factor -3*d + 4*d - 9*d**2 + 2*d**4 + 14*d**2 - a*d**2 - d**5.
-d*(d - 1)**3*(d + 1)
Fact