st derivative of 31 + 0*i**2 - 8/3*i**3 + 1/6*i**6 + 0*i - 6/5*i**5 + 3*i**4. Determine m, given that r(m) = 0.
0, 2
Let b be (126/3360)/((-9)/(-2)). Let i(l) be the second derivative of 5*l + 0 + 1/12*l**2 - 1/72*l**4 + 1/36*l**3 - b*l**5. Find v, given that i(v) = 0.
-1, 1
Let h(a) be the third derivative of a**6/24 - 47*a**5/48 - 10*a**4/3 - 65*a**3/24 + a**2 - a. Factor h(u).
5*(u - 13)*(u + 1)*(4*u + 1)/4
Let t(z) be the third derivative of z**6/480 - z**5/80 - 3*z**4/32 - 5*z**3/24 + 182*z**2 - 2*z. Factor t(s).
(s - 5)*(s + 1)**2/4
Factor 9 - 21*w**2 + 5*w**3 - 3*w + 6*w**3 - 2*w**3 + 5*w**3 + w**3.
3*(w - 1)**2*(5*w + 3)
Let j be 2/(((-40)/(-12))/5). Let d = j - 1. Factor 6*k**3 + k**2 - 5*k**d + k**2 - 3*k**4.
-3*k**2*(k - 1)**2
Let g(d) be the first derivative of -d**4/20 - d**3/5 + 2*d**2/5 + 12*d/5 - 393. Factor g(k).
-(k - 2)*(k + 2)*(k + 3)/5
Let z(j) be the second derivative of -j**7/21 + 2*j**6/15 + j**5/10 - j**4/3 + 61*j. Solve z(a) = 0 for a.
-1, 0, 1, 2
Let q(t) be the second derivative of -2/15*t**3 + 0 - 8*t + 0*t**2 + 1/60*t**4. Solve q(n) = 0 for n.
0, 4
Let u be 999/2886 - (-4)/26. Let l(f) be the first derivative of 0*f - 12 - 2*f**3 - u*f**2. Determine c so that l(c) = 0.
-1/6, 0
Let x = -3997/2 - -1999. Let y(d) be the second derivative of 0 - x*d**3 + d**2 + d + 0*d**4 + 1/20*d**5. Let y(f) = 0. Calculate f.
-2, 1
Let z(p) be the first derivative of 2*p**3/21 - 17*p**2/7 + 12*p + 321. Determine y, given that z(y) = 0.
3, 14
Factor 22*x**3 + 5*x**4 - 4*x**3 + 25*x**2 + 14*x**3 + 10*x - 12*x**3.
5*x*(x + 1)**2*(x + 2)
Let r = -102247/21 + 4875. Let 2/21*p**2 + r + 32/21*p = 0. What is p?
-8
Let v(p) = -18*p**3 + 20*p**2 - 8*p. Let z(r) = 53*r**3 - 60*r**2 + 24*r. Let n(d) = -17*v(d) - 6*z(d). Suppose n(f) = 0. Calculate f.
0, 2/3, 1
Let y be -18*(-2)/15 - (10 + (-576)/60). Suppose f - 1/5*f**y - 4/5 = 0. Calculate f.
1, 4
Suppose -2*j**2 - 64 + j**2 - 40*j + 0*j**2 - 3*j**2 = 0. Calculate j.
-8, -2
Let d(j) be the second derivative of 0 - 11/15*j**3 + 7/15*j**4 - 3/25*j**5 + 3/5*j**2 - 1/75*j**6 - 22*j + 1/105*j**7. Let d(q) = 0. Calculate q.
-3, 1
Determine b so that -1/5*b**3 + 14*b**2 + 0 - 245*b = 0.
0, 35
Let p(d) be the second derivative of d**4/96 + 7*d**3/24 + 3*d**2/2 - 21*d + 1. Solve p(k) = 0 for k.
-12, -2
Let z(d) be the second derivative of d**5/4 - 115*d**4/12 + 100*d**3 + 360*d**2 + 37*d. Suppose z(x) = 0. What is x?
-1, 12
Factor -27/5*n - 3/5*n**3 - 18/5*n**2 - 12/5.
-3*(n + 1)**2*(n + 4)/5
Suppose 2*a**2 + a**5 - 8*a**3 + 0 + 10/3*a**4 + 5/3*a = 0. What is a?
-5, -1/3, 0, 1
Suppose -3*v = -2*n - 12, 4*n = -9*v + 4*v + 20. Find g such that 2*g**5 - 5*g**5 + 8*g**v + 0*g**5 - g**5 - 4*g**3 = 0.
0, 1
Let a = 47636/45591 - -6/2171. Let r = 2/7 + a. Factor -r*x + 2/3 + 2/3*x**2.
2*(x - 1)**2/3
Suppose -2*q - q = -3. Suppose -6*h = -13 + q. Solve 31*f**3 - 21*f**3 - 2*f**4 - 12*f**h - 8*f + 11 + 5 = 0 for f.
-1, 2
Let d(f) be the second derivative of -f**7/42 + f**6/3 - 37*f**5/20 + 5*f**4 - 6*f**3 - 3*f - 3. Factor d(b).
-b*(b - 3)**2*(b - 2)**2
Let t(h) be the first derivative of 3*h**5/10 + 33*h**4/8 + 5*h**3/2 - 141*h**2/4 + 45*h - 840. Let t(g) = 0. Calculate g.
-10, -3, 1
Let p = -11 - -13. Suppose 0 = 5*h - 4 - 6. Factor -2*t**5 + 23*t**h + 12*t**4 + 12*t**p - 23*t**3 - 19*t**2 - t**3.
-2*t**2*(t - 2)**3
Suppose -x - 1/6*x**2 + 0 = 0. Calculate x.
-6, 0
Let b be (-5)/42*(-4)/10*6. Find p such that 0 + b*p**2 + 2/7*p = 0.
-1, 0
Let t = -9577 + 9579. Let 20/3*g**2 - 16/3 + t*g**3 + 8/3*g = 0. Calculate g.
-2, 2/3
Let c(l) be the first derivative of l**8/336 + l**7/168 - l**6/36 - 23*l**3/3 + 13. Let s(q) be the third derivative of c(q). Factor s(m).
5*m**2*(m - 1)*(m + 2)
Let i = 63 + -59. Let y be (i + 35/(-5))*(-8)/108. Let y + 4/9*g + 2/9*g**2 = 0. What is g?
-1
Let i = 7046 - 7044. Factor 0 + 0*a - a**5 + 2/3*a**i - 4/3*a**4 + 1/3*a**3.
-a**2*(a + 1)**2*(3*a - 2)/3
Factor -3*r - 9/2 - 1/2*r**2.
-(r + 3)**2/2
Suppose 0 = 4*b + 12, 3*c + 0*c - 6 = 3*b. Let s be (12 - 9) + (-2 - c). Solve m**2 - 4 + m**3 + 5 - m - s + 0*m = 0.
-1, 1
Find h such that 0*h + 64/7*h**3 - 2/7*h**4 - 512/7*h**2 + 0 = 0.
0, 16
Let f(k) be the third derivative of k**9/6048 + k**8/1680 - k**6/360 - k**5/240 - 2*k**3 - 33*k**2. Let d(c) be the first derivative of f(c). Factor d(m).
m*(m - 1)*(m + 1)**3/2
Let z(b) be the third derivative of 5/2*b**3 + 0 + 15*b**2 + 5/6*b**4 + 0*b + 1/12*b**5. Determine o so that z(o) = 0.
-3, -1
Suppose -2*l = q + 7, -4*q + l + 11 = -6. Factor -19*h**2 - 14*h + 2*h - 6 + h**3 + q*h**3 - 17*h.
(h - 6)*(h + 1)*(4*h + 1)
Factor -10*w**2 + 3*w**2 + 5*w**2 - 2*w**2 - 100 + 40*w.
-4*(w - 5)**2
Let g(q) be the first derivative of -2*q**3/39 - 8*q**2/13 + 40*q/13 + 27. Factor g(k).
-2*(k - 2)*(k + 10)/13
Let h = -1725/4 - -12235/28. Suppose -26/7*d**4 + 0*d + h*d**5 + 0*d**2 + 4/7*d**3 + 0 = 0. What is d?
0, 1/4, 2/5
Let x(h) be the third derivative of -1/8*h**4 + 0*h + 8*h**2 + 0 - 1/7*h**3 + 1/70*h**6 + 1/28*h**5. Factor x(u).
3*(u - 1)*(u + 2)*(4*u + 1)/7
Suppose 60 = d + 3*d. Let a = 28 + d. Factor a - 43 - 3*r**2.
-3*r**2
Let f(y) be the second derivative of 1/12*y**3 + 0 - 6*y + 1/24*y**4 + 0*y**2. Find v, given that f(v) = 0.
-1, 0
Let j(q) be the second derivative of 7/10*q**6 + 183/20*q**5 + 0 - 205/2*q**3 + 75*q**2 + 87/4*q**4 + 29*q. Factor j(c).
3*(c - 1)*(c + 5)**2*(7*c - 2)
Let r(a) = a + 6. Let l be r(-3). Suppose 2*d - 16 = 4*c, -5*c = -d - 4*d + 25. Solve 2*s**3 - 2*s**5 + 3*s**5 - 3*s**l - s**d + s**4 = 0.
-1, 0, 1
Let -6/7 + 5/7*f**2 + 5/7*f**3 - 5/7*f + 1/7*f**4 = 0. Calculate f.
-3, -2, -1, 1
Let p(k) be the third derivative of k**5/240 - k**4/48 - k**3/8 + 2*k**2 + 23. What is o in p(o) = 0?
-1, 3
Let j(t) = -t**3 + 7*t**2 + 24*t - 53. Let w(n) = -8*n - n**2 - 11*n + 7*n - 2*n**2 + 27. Let a(r) = 3*j(r) + 5*w(r). Suppose a(m) = 0. Calculate m.
-2, 2
Let r be -27 + 26 + -2 - (-18)/4. Factor -r*p + 15/4*p**2 + 0.
3*p*(5*p - 2)/4
Let c(m) be the second derivative of 2/45*m**3 + 0 + 0*m**2 - 4*m - 1/90*m**4. Factor c(a).
-2*a*(a - 2)/15
Let h(g) be the second derivative of -g**7/560 + g**6/240 + g**5/80 - g**4/16 + 11*g**3/6 + 23*g. Let q(r) be the second derivative of h(r). Factor q(t).
-3*(t - 1)**2*(t + 1)/2
Let i(c) = c**3 - c**2 + c. Let d(r) = -1 + 1 + 3 - 25*r**2 + 3*r**3 + 24*r**2 - 3*r. Let o(b) = -3*d(b) + 6*i(b). Determine t, given that o(t) = 0.
-3, 1
Let y be ((27/6)/(-3))/(255/(-136)). Factor -2/5*u**4 + 16/5*u + 0 + 8/5*u**2 - y*u**3.
-2*u*(u - 2)*(u + 2)**2/5
Let o(u) be the third derivative of 0*u - 7/8*u**4 - 1/40*u**6 + 0 - 16*u**2 + 3/2*u**3 + 1/4*u**5. Factor o(r).
-3*(r - 3)*(r - 1)**2
Let w = -8/161 + 362/805. Let 2/5*d**2 - w*d - 4/5 = 0. What is d?
-1, 2
Let a = 63 - 52. Determine o so that 12*o**2 + 42*o**3 - 9*o**4 - 5*o**4 - a*o + 11*o**4 - 13*o - 9*o**5 = 0.
-2, -1, 0, 2/3, 2
Solve 53 + 12 + 92*o**2 + 20*o - 43*o**2 - 44*o**2 + 50*o = 0 for o.
-13, -1
Let o = 210 + -206. Let s(b) be the first derivative of 20/3*b - 8 + 1/3*b**5 - 5/3*b**3 - 5/6*b**o + 10/3*b**2. Factor s(f).
5*(f - 2)**2*(f + 1)**2/3
Find q such that -26/3*q**2 + 4*q + 0 - 2/3*q**4 + 16/3*q**3 = 0.
0, 1, 6
Let v(a) be the second derivative of -1/78*a**4 - 1/13*a**2 + 0 - 13*a - 2/39*a**3. Factor v(k).
-2*(k + 1)**2/13
Let t(m) be the third derivative of -m**6/720 - m**5/10 - 9*m**4/4 + 81*m**2. Factor t(u).
-u*(u + 18)**2/6
Suppose 0 = -2*n + 3 + 3. Factor -3105 + 2*h**n + 3105.
2*h**3
Let p be 4/10*3/36. Let w(a) be the second derivative of 0 + 1/90*a**6 - 4*a + 0*a**3 + 0*a**2 + 1/36*a**4 - p*a**5. Factor w(f).
f**2*(f - 1)**2/3
Let m(o) be the first derivative of 25*o**3/3 + 45*o**2/2 - 90*o - 367. Suppose m(s) = 0. What is s?
-3, 6/5
Let m(j) be the first derivative of -j**4 - 44*j**3/3 - 60*j**2 - 792. Factor m(u).
-4*u*(u + 5)*(u + 6)
Let b = 3/46 - -65/414. Let i(s) = -142*s + 284. Let a be i(2). Suppose -2/3*u**3 + 0*u + b*u**2 + a + 2/3*u**4 - 2/9*u**5 = 0. Calculate u.
0, 1
Let s(y) = 7*y**4 - 6*y**2 + 8*y - 5. Let a(t) = -12*t**4 + t**3 + 10*t**2 - 17*t + 11. Let j(w) = -4*a(w) - 7*s(w). Determine i so that j(i) = 0.
-3, 1
Let u(k) be the third derivative of 0*k**4 + 0*k + 4*k**2 - 1/90*k**6 - 1/15*k**5 + 0 + 0*k**3. Find h, given that u(h) = 0.
-3, 0
Let x = 398/9 + -158