the third derivative of 0*s - 4/105*s**7 + 0 + 1/168*s**8 - 2/15*s**5 + 1/12*s**4 + 1/10*s**6 + 0*s**3 + 3*s**2. Factor u(m).
2*m*(m - 1)**4
Let f(h) = h**3 - 9*h**2 + 2*h - 14. Let m be f(9). Let a(u) be the second derivative of 0 + 1/48*u**m + 1/80*u**5 + u - 1/12*u**3 + 0*u**2. Factor a(i).
i*(i - 1)*(i + 2)/4
Let m be 1*(-140)/6*8/(-15). Suppose -22/3*n**2 - 32/9*n**4 - m*n**3 + 56/9*n - 8/9 = 0. Calculate n.
-2, 1/4
Let s(i) be the third derivative of i**8/840 - i**6/100 + i**5/75 + 2*i**2. Factor s(y).
2*y**2*(y - 1)**2*(y + 2)/5
Let q(g) be the second derivative of -g**4/3 + 10*g**3/3 + 28*g**2 - 3*g - 11. Let q(r) = 0. Calculate r.
-2, 7
Let a(g) be the second derivative of -g**4/3 - 4*g**3/3 - 2*g**2 + 15*g - 1. Find t, given that a(t) = 0.
-1
Factor -4 - 22*y**2 + 16*y + 16*y**3 + 15*y**2 - 17*y**2 - 4*y**4.
-4*(y - 1)**4
Suppose 2*j = 2*r - 3*r + 8, 5*r + 20 = 5*j. Let v(t) be the third derivative of 0*t + 1/180*t**6 + 0*t**3 + 2*t**2 + 0*t**5 + 0*t**4 + r. Factor v(y).
2*y**3/3
Suppose 3*v + 2 + 4 = 0. Let b = v - -5. Factor a + 0*a + 3*a**b + 3*a**2 - 7*a + 0*a.
3*a*(a - 1)*(a + 2)
Let s(z) be the first derivative of z**6/9 - z**4/6 - 4. Suppose s(d) = 0. Calculate d.
-1, 0, 1
Let k(q) be the third derivative of -5*q**8/336 - q**7/14 + q**6/4 + 5*q**5/6 - 35*q**4/8 + 15*q**3/2 + 7*q**2. Solve k(n) = 0.
-3, 1
Suppose 3*a - 21 = -z, -4*a - 52 = -2*z - 0. Let o be (-1)/(-2) - 6/z. Factor k**3 + k - 3/2*k**2 - o - 1/4*k**4.
-(k - 1)**4/4
Let a(l) = -l + 2. Let i be a(1). Let j be i + -2 - (-18)/12. Let -v**2 - j*v**4 + 3/2*v**3 + 0*v + 0 = 0. Calculate v.
0, 1, 2
Let m(g) be the first derivative of 0*g + 1/2*g**2 + 2/5*g**5 + 2 - 1/4*g**4 - 2/3*g**3. Find z such that m(z) = 0.
-1, 0, 1/2, 1
Solve -1/3*s**4 - 40/3*s - 25/3 - 2*s**2 + 8/3*s**3 = 0 for s.
-1, 5
Let i(p) be the third derivative of 1/20*p**4 + p**2 - 1/150*p**5 + 0*p + 0 + 0*p**3. Suppose i(c) = 0. Calculate c.
0, 3
Factor -1/2*l**2 + 1/2 - 1/4*l + 1/4*l**3.
(l - 2)*(l - 1)*(l + 1)/4
Let s = -117 - -119. Factor -4/7*q + 6/7 - 2/7*q**s.
-2*(q - 1)*(q + 3)/7
Suppose -k + 3*n - 7 = 6, n + 5 = 5*k. Suppose r = k + 1. Factor -i + 2*i**4 - r*i**2 + i**5 + 0*i + i**2.
i*(i - 1)*(i + 1)**3
Let w = -6 - -4. Let q = w + 9/4. Factor 0 + 3/4*k**5 - q*k**3 + k**4 - 1/2*k**2 + 0*k.
k**2*(k + 1)**2*(3*k - 2)/4
Factor -4/3 + 10/3*h**3 - 6*h**2 - 2/3*h**4 + 14/3*h.
-2*(h - 2)*(h - 1)**3/3
Let d(k) be the first derivative of -k**3/3 - 11*k**2/5 - 8*k/5 + 13. Factor d(l).
-(l + 4)*(5*l + 2)/5
Suppose u + 2*u - 18 = 0. Let b be 21/(-45) + u/9. Factor -1/5*n + 1/5*n**2 + 1/5*n**3 - b.
(n - 1)*(n + 1)**2/5
Let u = -181/2 - -91. Suppose -2*s = -7*s. Solve s - u*d**2 + d = 0.
0, 2
Let x = 224 + -219. Determine t so that 9/2*t**2 - 13/4*t + 9/4*t**x + 1/2 - 5*t**4 + t**3 = 0.
-1, 2/9, 1
Let 0 - 6/11*x - 112/11*x**3 + 32/11*x**4 + 50/11*x**2 = 0. What is x?
0, 1/4, 3
Factor 3/5*g**2 + 0*g - 3/5.
3*(g - 1)*(g + 1)/5
Suppose -5*w + j = -3*w - 1, 3*w - 4*j + 11 = 0. Determine g, given that 12/5*g - 12/5*g**w + 9/5*g**4 - g**2 - 4/5 = 0.
-1, 2/3, 1
Factor -6*y - 5*y + 5*y + 2*y**2 + 6*y**3 - 4 + 4*y**4 - 2*y**4.
2*(y - 1)*(y + 1)**2*(y + 2)
Let l(h) be the third derivative of -h**6/120 + h**5/60 + h**4/24 - h**3/6 - 2*h**2. Find o such that l(o) = 0.
-1, 1
Let c(z) be the second derivative of 0 + 0*z**2 - z + 1/27*z**3 - 1/90*z**5 + 1/54*z**4 - 1/135*z**6. Factor c(g).
-2*g*(g - 1)*(g + 1)**2/9
Suppose -2*x - 12 = -6*x. Suppose -7 = -x*f - 1. Factor -3 + 2*k + 3 + 0*k**2 - k**f.
-k*(k - 2)
Let k(y) be the second derivative of 2/15*y**6 + 0 - 3*y + 0*y**3 + 0*y**2 + 0*y**4 - 1/21*y**7 - 1/10*y**5. Factor k(j).
-2*j**3*(j - 1)**2
Let c(r) = -98*r**4 + 42*r**3 + 48*r**2 + 8*r + 6. Let j(x) = -98*x**4 + 42*x**3 + 48*x**2 + 8*x + 7. Let h(a) = 7*c(a) - 6*j(a). Factor h(b).
-2*b*(b - 1)*(7*b + 2)**2
Let o(x) be the third derivative of -1/20*x**4 + x**2 + 0*x - 1/100*x**5 - 1/10*x**3 + 0. Factor o(d).
-3*(d + 1)**2/5
Let f(p) be the first derivative of -2*p**3/3 - 2*p**2 - 2*p - 25. Factor f(s).
-2*(s + 1)**2
Suppose 0*f - f - 13 = 2*a, 5*f + a + 20 = 0. Let g be 2 - (-2)/f*-3. Factor -2*i + 3 + 3*i**3 - 3*i**2 - g*i**3 - 3.
-i*(i + 1)*(i + 2)
Let u be ((-12)/15)/(6/(-15)). Factor p**u + 2*p**3 - 4*p**3 + 4*p**3 - p**3 - p**5 - p**4.
-p**2*(p - 1)*(p + 1)**2
Let g(r) = -5*r**2 - 7. Suppose d + d - 23 = 3*b, -5*d = 2*b - 67. Let x(h) = 11*h**2 + 15. Let l(s) = d*g(s) + 6*x(s). Let l(j) = 0. What is j?
-1, 1
Let r = 410 - 410. Solve r + 1/2*q**2 - 1/4*q - 1/4*q**3 = 0 for q.
0, 1
Let s(d) be the first derivative of 3*d**6/5 - 114*d**5/25 + 59*d**4/5 - 184*d**3/15 + 24*d**2/5 - 29. Find j, given that s(j) = 0.
0, 2/3, 2, 3
Let o(w) be the third derivative of -w**5/60 - w**4/8 - w**3/3 - 8*w**2. Factor o(s).
-(s + 1)*(s + 2)
Let h be (-118)/8 + 1/(-4). Let g = -15 - h. Suppose 2/3*n**3 + 0*n + g + 0*n**2 = 0. Calculate n.
0
Let p be (-3 - 33/(-15))*-56. Let f = p + -373/10. Factor 0*j - 5/2*j**3 + 2 + f*j**4 - 15/2*j**2 + 9/2*j**5.
(j + 1)**3*(3*j - 2)**2/2
Factor 11*d**2 - 24*d - 6*d**3 - 24*d**2 + 9*d**4 + 3*d**5 - 21*d**2 - 2*d**2.
3*d*(d - 2)*(d + 1)*(d + 2)**2
Suppose 2*m = -14 + 4. Let n = m + 9. Find f such that 0*f**2 + 2/7*f - 4/7*f**3 + 0*f**n + 0 + 2/7*f**5 = 0.
-1, 0, 1
Let u be (-2 - 64/(-35))/(24/(-480)). Find f, given that -u*f - 3/7*f**2 - 48/7 = 0.
-4
Suppose 0*l - 10/13*l**3 - 8/13*l**2 - 2/13*l**4 + 0 = 0. What is l?
-4, -1, 0
Let v be (-2 - -4)*3/2. Suppose 5*n - 2*c = v*n + 14, -5*c = 25. Factor -19/2*y**3 - n - 8*y - 7/2*y**4 - 25/2*y**2 - 1/2*y**5.
-(y + 1)**3*(y + 2)**2/2
Let b(w) be the second derivative of w**9/3024 - w**8/840 + w**6/180 - w**5/120 + w**3/3 - 2*w. Let u(l) be the second derivative of b(l). Factor u(x).
x*(x - 1)**3*(x + 1)
Let k(m) = m + 13. Let z be k(-11). Factor -4 - z*q**2 + 4 - 2*q**3 + 2*q + 2*q**4.
2*q*(q - 1)**2*(q + 1)
Determine g, given that 2/9*g**4 - 4/9*g**3 + 0 + 4/9*g - 2/9*g**2 = 0.
-1, 0, 1, 2
Let x(j) be the third derivative of -j**7/1260 + j**6/360 - j**5/360 + 29*j**2. Factor x(b).
-b**2*(b - 1)**2/6
Let m(h) = h**4 - h**2 - h - 1. Suppose -5*v + 1 + 9 = 0. Let y(z) = -17*z**4 - 4*z**3 + 11*z**2 + 2. Let g(l) = v*m(l) + y(l). Factor g(x).
-x*(x + 1)*(3*x - 1)*(5*x - 2)
Factor -735/2*o**2 - 105/2*o**3 - 5/2*o**4 - 1715/2*o + 0.
-5*o*(o + 7)**3/2
Suppose 2/11*s - 2/11*s**2 + 0 = 0. What is s?
0, 1
Let m(b) be the third derivative of b**7/840 - b**6/240 + b**5/240 - 8*b**2. Factor m(c).
c**2*(c - 1)**2/4
Let v(d) = -2*d**2 - 8*d - 1. Let t = 8 - 3. Let i(c) = -c**2 - 7*c - 2. Let n(p) = t*i(p) - 4*v(p). Solve n(g) = 0 for g.
-1, 2
Let m(g) = g**3 + 17*g**2 + 30*g + 2. Let i be m(-15). Let r = -245/143 - -27/13. Solve 14/11*p - r - 6/11*p**i = 0 for p.
1/3, 2
Let u(m) be the first derivative of 8*m**3/27 + 14*m**2/9 + 20*m/9 + 35. Factor u(c).
4*(c + 1)*(2*c + 5)/9
Let b(v) = -v**3 + 3*v**2 + v + 2. Let d(l) = l**2 + 1. Let u(t) = b(t) - 2*d(t). Let c(k) = 7*k**3 + 7*k**2 + 19*k + 16. Let z(a) = c(a) + 5*u(a). Factor z(o).
2*(o + 2)**3
Let o(q) = -q**2 + 4*q + 2. Let m be o(2). Let n(b) be the third derivative of 0*b + 1/3*b**3 + 0 - 1/30*b**5 - b**2 - 1/60*b**m + 1/12*b**4. Factor n(c).
-2*(c - 1)*(c + 1)**2
Let i(o) = -6*o**2 - 56*o - 18. Let z be i(-9). Factor z*t**2 + 0 - 2/5*t**3 + 0*t.
-2*t**3/5
Let v be (12/48)/((-1)/(-2)). Factor -v*o**2 + 0*o + 1/2.
-(o - 1)*(o + 1)/2
Factor 2*q**3 + 2 - 3 + 5 - 6*q + 0.
2*(q - 1)**2*(q + 2)
Suppose -3*f - 6 = 5*j - 2*f, -3*j + 4*f - 22 = 0. Let r = j + 20. Factor 2*t + 4*t**5 + r*t**3 - 19*t**4 - 6*t**2 - 4*t**2 + 5*t**4.
2*t*(t - 1)**3*(2*t - 1)
Suppose 4*l + l - 15 = 0. Factor -3*j + 4 - l*j + 0*j + 2*j**2.
2*(j - 2)*(j - 1)
Suppose 25*f + 35 = 32*f. Factor -2/7 - 20/7*s**3 - 10/7*s - 20/7*s**2 - 2/7*s**f - 10/7*s**4.
-2*(s + 1)**5/7
Let s be (-20)/36*(-2)/10. Let u(d) be the first derivative of -1/12*d**4 - 2 + 0*d**2 + 0*d - s*d**3. Let u(y) = 0. Calculate y.
-1, 0
Let v(o) be the third derivative of o**8/10080 - o**7/2520 - o**5/60 + o**2. Let f(w) be the third derivative of v(w). Factor f(m).
2*m*(m - 1)
Let z(j) be the second derivative of -j**5/40 + j**4/6 + j**3/4 - 9*j**2/2 - 15*j. Suppose z(b) = 0. What is b?
-2, 3
Let z(u) = 5 - u**2 + 2*u - 3 + 5*u**2 - 5. Let q(d) = 11*d**2 + 5*d - 8. Let t(j)