he second derivative of -x**6/60 - x**5/40 - 6*x. Factor p(t).
-t**3*(t + 1)/2
Let x(a) be the first derivative of a**6/15 - 6*a**5/25 + 3*a**4/10 - 2*a**3/15 + 4. Suppose x(m) = 0. Calculate m.
0, 1
Let c = -17 + 67/4. Let s = c - -11/12. Suppose s*u**5 + 2*u - 4/3*u**2 - 8/3*u**3 + 0*u**4 + 4/3 = 0. Calculate u.
-1, 1, 2
Suppose -c = 1 - 3. Let r be -4*(3/c + -2). Factor -4*t**r + 2*t**2 - t + t**3 + t**2 + 1.
(t - 1)**2*(t + 1)
Let i(o) be the first derivative of o**4/18 - 4*o**3/27 + o**2/9 + 29. Factor i(c).
2*c*(c - 1)**2/9
Let a be (1/15)/(((-24)/9)/(-4)). Let v(j) be the second derivative of -4*j + 0 + 2/15*j**3 - a*j**4 + 0*j**5 + 0*j**2 + 1/75*j**6. Factor v(z).
2*z*(z - 1)**2*(z + 2)/5
Let k(l) be the second derivative of l**10/40320 + l**4/4 + 3*l. Let q(v) be the third derivative of k(v). Find a such that q(a) = 0.
0
Let g(j) be the second derivative of 0*j**3 - 4*j + 1/10*j**4 + 0*j**5 - 3/10*j**2 - 1/50*j**6 + 0. Solve g(n) = 0 for n.
-1, 1
Let w(t) be the third derivative of -t**9/302400 + t**5/60 + 3*t**2. Let c(o) be the third derivative of w(o). Factor c(s).
-s**3/5
Let f(g) = -g**3 - 8*g**2 - 7*g + 2. Let r be f(-7). Suppose -r = -4*x + 10. Factor 0*i**3 - 3*i**3 - 1 + i**4 + 0*i**x - 2*i + 5*i**3.
(i - 1)*(i + 1)**3
Let p = 28 + -26. Factor 10/3*o**p + 16/3*o + 8/3 + 2/3*o**3.
2*(o + 1)*(o + 2)**2/3
Let h = -84 - -20. Let y be -4 + 2 - h/6. Find m, given that -224/3*m**3 - y*m + 40*m**2 + 128/3*m**4 + 2/3 = 0.
1/4, 1
Let u(q) be the second derivative of -q**6/120 + q**5/20 - 2*q**3/3 + q**2 + 3*q. Let m(v) be the first derivative of u(v). Factor m(t).
-(t - 2)**2*(t + 1)
Let j be (-30)/(-7) - (-2)/(-7). Let m be -1 + 5/(15/9). Factor 5*x - m*x**2 - 2*x - x + j.
-2*(x - 2)*(x + 1)
Let a(b) be the second derivative of b**4/66 + 2*b**3/33 - 3*b**2/11 - 56*b. What is n in a(n) = 0?
-3, 1
Suppose -4*t - 10 = -6*t. Factor 8*n**2 + 16*n**3 - 14 - 4*n**t - 11*n - n + 6.
-4*(n - 2)*(n - 1)*(n + 1)**3
Let o(p) be the first derivative of p**5/3 - 5*p**4/4 - 5*p**3/9 + 5*p**2/2 + 21. Solve o(q) = 0.
-1, 0, 1, 3
Let b(f) = 18*f**4 - 65*f**3 + 42*f**2 + 5*f. Let h(q) = -3*q**4 + 11*q**3 - 7*q**2 - q. Let c(t) = -6*b(t) - 34*h(t). Let c(o) = 0. What is o?
0, 2/3, 1
Let n(f) = -f**2 - 3 - 2 + 7*f**2 - 4*f. Let b(p) = -9 - 5*p**2 + 5 + 8 + 3*p. Let x(c) = -5*b(c) - 4*n(c). Factor x(t).
t*(t + 1)
Let x(f) be the first derivative of f**5/240 - f**4/96 - f**2/2 + 1. Let n(r) be the second derivative of x(r). Find g, given that n(g) = 0.
0, 1
Suppose -6 = -5*x + 14. Solve -3*d + 6*d - 3*d**3 + x*d**3 + 1 + 3*d**2 = 0 for d.
-1
Let p(q) = -q**2 + 10*q + 10. Let i be p(11). Let s be 38/9 - (i + 5). Factor 0 + 2/9*t**5 - 2/9*t**3 + 0*t + 2/9*t**2 - s*t**4.
2*t**2*(t - 1)**2*(t + 1)/9
Suppose -5*c - p = -12, 4 = -2*c + 3*p + 2. Factor -o**2 - o**2 - 4*o + c*o.
-2*o*(o + 1)
Let g(a) = -23*a**4 + 39*a**3 + 41*a**2 - 39*a - 1. Let t(v) = -3*v**4 + 5*v**3 + 5*v**2 - 5*v. Let w(z) = 6*g(z) - 51*t(z). Factor w(r).
3*(r - 1)**2*(r + 1)*(5*r - 2)
Let h = 5 - 5. Let l = 3 + h. Factor p**2 - 4*p**4 + p**2 + 5*p**4 + 3*p**l.
p**2*(p + 1)*(p + 2)
Let n(y) be the third derivative of y**5/100 + y**4/10 - y**3/2 + 15*y**2. Let n(h) = 0. Calculate h.
-5, 1
Let m(f) = -f**3 - 7*f**2 + f + 7. Let r be m(-7). Suppose -3*k + 5*q = -21, -3*k + q - 3*q = r. Determine o, given that 243*o**3 + 36*o - 8/3 - 162*o**k = 0.
2/9
Let t(l) be the first derivative of -2 + 0*l**3 + 1/18*l**4 + 0*l - 1/2*l**2 + 1/10*l**5. Let w(r) be the second derivative of t(r). Factor w(h).
2*h*(9*h + 2)/3
Let h be 2*-1 + 0 - -7. Suppose -5 - 3 = -4*y, h*y = 5*g. Factor -2*z**2 + 4*z**g - 26*z**3 + 10*z**3 + 0*z**2 + 10*z**4 + 4*z.
2*z*(z - 1)**2*(5*z + 2)
Suppose 4*s + 7 = 31. Suppose 0 = 2*j + 2*y - 6, -2*y + 0 - s = -4*j. Factor -h**2 - h - 2 + j.
-h*(h + 1)
Suppose -14*u = -10*u - 8. Factor u*l**3 + 2*l - 8*l**2 - 21 + 21 + 4*l.
2*l*(l - 3)*(l - 1)
Let h(o) be the first derivative of 2*o**5/15 - o**4/12 - 2*o**3/9 + o**2/6 + 4. Suppose h(n) = 0. What is n?
-1, 0, 1/2, 1
Let q(u) be the third derivative of 0*u + 0 - 32/63*u**8 + 0*u**7 + 8/9*u**5 + 5*u**2 + 1/9*u**3 + 5/12*u**4 + 8/9*u**6. Factor q(w).
-2*(w - 1)*(4*w + 1)**4/3
Let n(d) be the first derivative of -d**5/100 - 5*d - 7. Let a(i) be the first derivative of n(i). Factor a(w).
-w**3/5
Let o be -1 - ((-2 - 1) + 2). Factor -3*n - 3*n**5 + 3*n**4 + 3 + o*n**4 - 4*n**2 + 6*n**3 + 2*n**2 - 4*n**2.
-3*(n - 1)**3*(n + 1)**2
Let i(r) be the first derivative of r**8/7560 - r**7/1890 + r**6/1620 - 3*r**3 - 10. Let f(a) be the third derivative of i(a). Let f(m) = 0. Calculate m.
0, 1
Suppose -5*c = 4*o - 0 + 4, 0 = -c + 3*o + 3. Let t = 2 + c. Factor y**2 - 4*y**4 + 2*y + 5*y**2 - t*y**4 - 2*y**3.
-2*y*(y - 1)*(y + 1)*(3*y + 1)
Suppose 2*y + 15 = -3*q, -y + 14 = -3*q - 1. Let j(d) be the second derivative of -3*d**2 - 2/5*d**6 + 3/2*d**4 + d - 7/2*d**3 + y + 21/20*d**5. Solve j(l) = 0.
-1, -1/4, 1, 2
Let b(t) be the first derivative of t**3/2 - 3*t**2/4 - 3*t - 7. Factor b(g).
3*(g - 2)*(g + 1)/2
Suppose l = 2, 4*l - 5 = 3*q - 4*q. Let j be (-2 - (0 + 2))*q. Factor -d**2 + d**3 - 4 + j*d - 4 - 5*d**2.
(d - 2)**3
Let 886*y**3 - 1634*y**3 - 320*y - 245*y**5 - 2080*y**2 + 1820*y**4 - 2072*y**3 = 0. Calculate y.
-2/7, 0, 4
Let k = 399 - 1987/5. Suppose 0*g**2 + 0*g - 4/5*g**5 + 0 + k*g**4 - 4/5*g**3 = 0. Calculate g.
0, 1
Determine f, given that -4/7*f + 6/7 - 2/7*f**2 = 0.
-3, 1
Let c(n) be the first derivative of -n**6/66 - n**5/11 - 9*n**4/44 - 7*n**3/33 - n**2/11 + 6. Factor c(o).
-o*(o + 1)**3*(o + 2)/11
Let g(s) be the first derivative of 0*s**2 + 1 + 2*s + 1/6*s**3 + 1/12*s**4. Let l(r) be the first derivative of g(r). Factor l(i).
i*(i + 1)
Let s(k) be the third derivative of -k**5/90 + k**4/36 - 4*k**2. Factor s(a).
-2*a*(a - 1)/3
Suppose -2*i**2 - 4*i**2 + 27 + 1024*i - 1048*i + 3*i**2 = 0. Calculate i.
-9, 1
Suppose -3*g - 12 = -6*g. Let u(h) be the first derivative of -8/3*h + 2 + 14/3*h**2 - 38/9*h**3 + 1/18*h**6 + 25/12*h**g - 8/15*h**5. Factor u(n).
(n - 2)**3*(n - 1)**2/3
Suppose 0 = -n, -4*x + 5 = -3*n - 15. Suppose 3*d**3 + 5*d**4 + 0*d + 9*d**2 + 1 - x*d + d**2 - 13*d**3 - d**5 = 0. What is d?
1
Let b(n) be the first derivative of -n**6/57 + 2*n**5/95 + n**4/38 - 2*n**3/57 + 10. Factor b(t).
-2*t**2*(t - 1)**2*(t + 1)/19
Let j be 6/(-3) - 0 - -3. Suppose 3*m - j = 5. Factor 2*r**4 - 7*r + 4*r**4 + r - 4*r**m - 2 + 2*r**5 + 4*r**3.
2*(r - 1)*(r + 1)**4
Let y(b) be the third derivative of b**5/12 + 5*b**4/24 - 5*b**3/3 - 6*b**2. Factor y(z).
5*(z - 1)*(z + 2)
Let t = 23 + -65/3. Solve -3*g**4 + 1/3 + 8/3*g**2 - 2*g + 2/3*g**3 + t*g**5 = 0 for g.
-1, 1/4, 1
Factor 0 - 5/3*u**2 - 20/3*u.
-5*u*(u + 4)/3
Let t(g) be the first derivative of g**7/420 - g**6/90 - 2*g**3/3 - 2. Let q(l) be the third derivative of t(l). Factor q(c).
2*c**2*(c - 2)
Suppose 4*v = 5*c - 8, -3*v + 0 = 3*c - 21. What is q in -1/5*q - 1/5*q**c + 1/5*q**2 + 0 + 1/5*q**3 = 0?
-1, 0, 1
Suppose 8 = 7*c - 3*c. Let b(j) be the second derivative of -3*j - j**3 - 1/2*j**c + 0 - 1/5*j**5 - 3/4*j**4. Suppose b(g) = 0. What is g?
-1, -1/4
Let b(j) be the second derivative of -j**5/20 - 11*j**4/4 - 121*j**3/2 - 1331*j**2/2 + 63*j. Determine m, given that b(m) = 0.
-11
Suppose -1 - 8*m + 3 + m**2 + 9*m + 2*m = 0. What is m?
-2, -1
Suppose -k + 4*k = 2*d + 7, -2*k = -d - 5. Let t be 18/(-54) + 1/3. Factor -2/9*w**2 + 2/9*w**k + t + 0*w.
2*w**2*(w - 1)/9
Let x(f) be the third derivative of 1/120*f**5 + 0 + 1/120*f**6 + 1/420*f**7 + 0*f + 0*f**3 + 0*f**4 + 3*f**2. Factor x(a).
a**2*(a + 1)**2/2
Let j(o) = 12*o**2 + 12*o - 23. Let h(m) = 11*m**2 + 11*m - 24. Let r(s) = 7*h(s) - 6*j(s). Factor r(v).
5*(v - 2)*(v + 3)
Let h be 0/(-2) - 0/(-2). Let t(n) be the second derivative of 1/9*n**3 - 7/36*n**4 + 1/15*n**5 + h + 1/6*n**2 - 2*n. Factor t(l).
(l - 1)**2*(4*l + 1)/3
Let h be (1/(-3))/((-280)/63). Let m(a) be the third derivative of -2*a**2 + h*a**4 + 1/100*a**5 + 1/5*a**3 + 0*a + 0. Solve m(p) = 0 for p.
-2, -1
Let o(a) = 5*a**2 - 44*a + 147. Let v(d) = -81*d**2 + 705*d - 2352. Let f(n) = -33*o(n) - 2*v(n). Suppose f(r) = 0. Calculate r.
7
Let g = -128/25 - -3484/75. Let d = -862/21 + g. Factor d*w + 0 - 2/7*w**2.
-2*w*(w - 1)/7
Let d(c) = 4*c**3 - 25*c**2 + 27*c - 16. L