 derivative of -f**9/36288 - f**8/6048 + f**7/1008 - f**5/15 - 9*f**2. Let r(j) be the third derivative of n(j). Factor r(d).
-5*d*(d - 1)*(d + 3)/3
Let u be ((-5)/((-25)/(-2)))/((-2)/20). Factor 92*q**4 - 44*q**u - 3*q**2 - 45*q**4.
3*q**2*(q - 1)*(q + 1)
Let w(z) be the second derivative of 0 + 4/3*z**3 + 4/35*z**5 + 18*z - 1/105*z**6 - 23/42*z**4 - 12/7*z**2. Find u such that w(u) = 0.
1, 2, 3
Suppose -3*x + 2*x - b = -91, -x + 3*b = -103. Solve 4*h**4 + 19*h**3 + 43*h**3 - x*h**3 = 0 for h.
0, 8
Let -160/3 - 56/9*x + 4/9*x**2 = 0. What is x?
-6, 20
Let i(z) be the first derivative of 3/4*z**4 + 0*z**2 + 0*z**3 + 6/5*z**5 - 4 + 0*z + 1/2*z**6. What is c in i(c) = 0?
-1, 0
Let j(u) be the first derivative of 2*u**3/3 - 2*u - 17. Factor j(s).
2*(s - 1)*(s + 1)
Solve -5/6*s - 25/3*s**4 - 30*s**2 + 5 - 35*s**3 + 5/2*s**5 = 0 for s.
-1, 1/3, 6
Let y(a) be the first derivative of 0*a - 1 + 35/4*a**4 + 25/2*a**2 + a**5 + 55/3*a**3. Let y(n) = 0. Calculate n.
-5, -1, 0
Let i = -1102 + 15429/14. Let m(o) be the first derivative of 3/28*o**4 - 4/21*o**3 + 0*o + 8 + i*o**2. Factor m(w).
w*(w - 1)*(3*w - 1)/7
Let d(v) = -v**3 - 13*v**2 + 10*v - 56. Let c be d(-14). Let i(m) be the second derivative of 0 + 4/3*m**4 + 2/3*m**3 - 9*m - m**5 + c*m**2. Factor i(r).
-4*r*(r - 1)*(5*r + 1)
Let i(q) be the first derivative of -q**6/30 + 16*q**5/25 - 24*q**4/5 + 256*q**3/15 - 128*q**2/5 - 320. Suppose i(s) = 0. Calculate s.
0, 4
Let h = -1829 - -1832. Let z(b) be the first derivative of -h - 1/3*b**2 + 1/18*b**6 + 0*b - 1/5*b**5 + 1/3*b**3 + 1/12*b**4. Factor z(c).
c*(c - 2)*(c - 1)**2*(c + 1)/3
Let f = 2/245 + 239/735. Let i(d) be the second derivative of 3*d - 2*d**2 + f*d**4 + 1/3*d**3 - 1/10*d**5 + 0. Factor i(j).
-2*(j - 2)*(j - 1)*(j + 1)
Suppose -3*t = -3*l - 24, 3*t = l - 9 + 33. Factor -6*c**3 + t*c + c**4 - 4*c**2 - 78*c**5 + 39*c**5 + 40*c**5.
c*(c - 2)*(c - 1)*(c + 2)**2
Let n(o) be the second derivative of -o**8/33600 - o**7/12600 + o**6/360 - o**5/75 - 31*o**4/12 + 33*o. Let u(h) be the third derivative of n(h). Factor u(a).
-(a - 2)*(a - 1)*(a + 4)/5
Let w = -163/4 + 41. Suppose -16*n - 3418 = -3418. Factor -w*z**5 + n*z - 1/2*z**4 + 0 - 1/4*z**3 + 0*z**2.
-z**3*(z + 1)**2/4
Suppose -f = 5, r + 0*f = f + 18. Suppose 1 = -4*j + r. Let -6*z**4 - 6*z**j - 2*z**2 - 2*z**5 + 213*z - 213*z = 0. What is z?
-1, 0
Let j = -1755 - -26329/15. Let f(o) be the first derivative of -1/15*o**6 + 2/5*o + 2/25*o**5 - 11 - j*o**3 - 1/5*o**2 + 1/5*o**4. Find c such that f(c) = 0.
-1, 1
Let p(y) = -y**3 - y + 2. Let j = 12 - 12. Let b be p(j). Factor 2 + b*i**2 + 9*i**3 - 5*i**2 - 7*i + 3*i**2.
(i + 1)*(3*i - 2)*(3*i - 1)
Let c(p) be the third derivative of p**9/15120 + p**8/3360 + p**7/2520 - p**4/6 - 3*p**2. Let b(m) be the second derivative of c(m). Solve b(u) = 0.
-1, 0
Let j(d) be the first derivative of -1 + 0*d + 0*d**2 - 4/3*d**3 - d**4. Factor j(z).
-4*z**2*(z + 1)
Let o = -60 + 65. What is f in 8*f**3 + 32*f**3 + o*f**2 - 22*f + 25*f**4 + 12*f = 0?
-1, 0, 2/5
Factor 4 + 5*h**2 + 10*h + 7 + 0*h**2 - 2 - 4*h**2.
(h + 1)*(h + 9)
Let z(l) = -3*l. Suppose -3*d + v + v - 3 = 0, v = -3. Let k(n) = n**2 + 2*n. Let u(w) = d*k(w) - 4*z(w). Suppose u(x) = 0. Calculate x.
0, 2
Suppose 27 = -2*j + 5*j. Find z such that -z**3 - 3*z**4 + 5*z**2 - 8*z + 7*z**3 + 7*z**2 + 2*z - j = 0.
-1, 1, 3
Let r(d) be the first derivative of 2*d**3/3 + 24*d**2 + 238*d - 266. Let r(g) = 0. Calculate g.
-17, -7
Let m = 2 - 20. Let w = m + 37/2. Factor -3/2*n**3 + 0 + 3/2*n**2 - 1/2*n + w*n**4.
n*(n - 1)**3/2
Factor 3*t**2 - 96*t + 440 + 139 + 189.
3*(t - 16)**2
Solve 0 + 5/3*p**5 + p + 22/3*p**2 + 26/3*p**4 + 40/3*p**3 = 0.
-3, -1, -1/5, 0
Let j(v) = 12*v**4 + 28*v**3 + 12*v**2 - 2. Let k(t) = -46*t**4 - 112*t**3 - 48*t**2 + 9. Let p(b) = -9*j(b) - 2*k(b). Factor p(i).
-4*i**2*(i + 1)*(4*i + 3)
Suppose -15*v**4 + 12*v**4 + 2*v**3 + 5*v**4 = 0. Calculate v.
-1, 0
Let x(u) be the second derivative of 8*u - 1/42*u**4 - 5/21*u**3 + 0 - 4/7*u**2. Determine q so that x(q) = 0.
-4, -1
Suppose 4*g - 8 = -0. Suppose 27*f**4 + 6*f**3 - 9*f - 2*f**5 + 8*f**g + f - 31*f**4 = 0. Calculate f.
-2, 0, 1
Let d = 0 - 1. Let l(w) = 21*w**3 - 13*w**2 + 2*w + 1. Let f(x) = -3*x + 22. Let b be f(7). Let z(a) = a**3 + 1. Let m(o) = b*z(o) + d*l(o). Factor m(g).
-g*(4*g - 1)*(5*g - 2)
Let q(h) be the third derivative of h**8/84 - 8*h**7/35 + 8*h**6/5 - 64*h**5/15 + 65*h**2. Factor q(o).
4*o**2*(o - 4)**3
Let g(b) be the first derivative of -b**5/80 + b**4/4 - 2*b**3 + 3*b**2/2 + 2*b + 17. Let j(z) be the second derivative of g(z). Solve j(d) = 0.
4
Suppose 280/9 + 2*s**4 - 202/9*s**2 - 2/9*s**5 + 2/9*s**3 - 32/3*s = 0. Calculate s.
-2, 1, 5, 7
Let q(k) be the third derivative of -k**8/1344 + 11*k**7/840 - 3*k**6/160 - 119*k**5/240 - 49*k**4/48 - 36*k**2. Determine f, given that q(f) = 0.
-2, -1, 0, 7
Suppose 0 = -3*x - 4*s + 19, 2*x + s = -3*s + 14. Solve -72*n**3 - 3203 + 108*n - 4*n**x + 10*n**4 + 22*n**4 + 3203 = 0 for n.
-1, 0, 3
Let d be (2 - 926/350) + 6/21. Let f = 249/275 + d. Factor -f*w + 4/11 + 2/11*w**2.
2*(w - 2)*(w - 1)/11
Let p(m) be the first derivative of m**5/20 + 11*m**4/8 + 5*m**3 - m**2 + 16. Let t(r) be the second derivative of p(r). Solve t(i) = 0 for i.
-10, -1
Suppose -204 = -25*a + 23*a. Let x be a/(-17)*(-2)/6. Factor 0*y - 4/9*y**x + 0*y**3 + 2/9 + 2/9*y**4.
2*(y - 1)**2*(y + 1)**2/9
Let z be (-14)/(-10)*(-1 - (-44)/28). Solve -6/5 + z*k + 2/5*k**2 = 0.
-3, 1
Let l(c) be the third derivative of -c**6/540 + c**5/135 + 2*c**4/27 - 66*c**2. Factor l(t).
-2*t*(t - 4)*(t + 2)/9
Suppose 0 = -3*a + 7 - 1. Let p = -426 - -426. Suppose p*o + 0 - 2/5*o**3 + 4/5*o**a = 0. What is o?
0, 2
Let m(w) = -w - 2. Let r be -6 - ((-9)/(-3) + 1). Let y be m(r). Factor -31*i**2 + 33*i**2 - 7*i + y + 15*i.
2*(i + 2)**2
Suppose -3*s - s - 16 = 0. Let i = 0 - s. Factor -i*g + 2*g**2 + 0*g**2 - 1 + 3.
2*(g - 1)**2
Let r(w) be the first derivative of w**6/2 + 12*w**5/5 - 9*w**4/2 - 32*w**3 - 105*w**2/2 - 36*w - 179. Suppose r(q) = 0. What is q?
-4, -1, 3
Let l(f) be the first derivative of -9/4*f**5 - 35/4*f**3 + 125/16*f**4 + 5/2*f + 15/8*f**2 + 16. Determine j so that l(j) = 0.
-2/9, 1
Suppose 0 = 2*v, 2*b + 2*b - 40 = 4*v. Factor 5*u + 30 + b*u + 10*u**2 + 20*u - 5*u**2.
5*(u + 1)*(u + 6)
Let d(m) be the first derivative of -m**5/35 + 3*m**4/14 - 5*m**3/21 - 289. Factor d(x).
-x**2*(x - 5)*(x - 1)/7
Determine r so that 96 + 30*r**2 + 8*r**3 - 9/2*r**4 - 112*r + 1/2*r**5 = 0.
-3, 2, 4
Let q(v) be the second derivative of v**4/54 - 2*v**3/9 + 5*v**2/9 + 436*v. Determine t, given that q(t) = 0.
1, 5
Suppose -5*x + 9 + 21 = 0. Let l(c) be the third derivative of -7/300*c**x - 8/15*c**3 - 1/3*c**4 - 3*c**2 + 13/75*c**5 + 0 + 0*c. Suppose l(a) = 0. What is a?
-2/7, 2
Let s = -1335/8 - -12079/72. Let -s*b**3 - 4/9*b**2 - 2/9*b**4 + 2/3 + 8/9*b = 0. Calculate b.
-3, -1, 1
Let z be 33/(-55) + (-36)/450 + 706/450. Factor -4/3*o**2 + z*o**3 + 2/9*o**4 - 8/9*o + 10/9.
2*(o - 1)**2*(o + 1)*(o + 5)/9
Let v = 181889/1092 - 1166/7. Let s = v - -631/1092. Find q, given that 0 + 2/7*q**2 - s*q**3 + 2/7*q = 0.
-1/2, 0, 1
Let d(m) be the first derivative of -25/3*m**3 + 0*m + 14 + m**5 - 15/4*m**4 - 5*m**2 + 5/6*m**6. Find y such that d(y) = 0.
-1, 0, 2
Factor -115*q**3 + 39*q**3 - 45 + 51*q**3 + 105*q - 35*q**2.
-5*(q - 1)*(q + 3)*(5*q - 3)
Let q(k) be the second derivative of 0 - 2/27*k**3 - 2/3*k**2 - 3*k + 1/9*k**4 + 1/45*k**5. Factor q(m).
4*(m - 1)*(m + 1)*(m + 3)/9
Let q(d) be the second derivative of 1/126*d**7 + 0*d**4 + 0*d**2 + 1/18*d**3 - 1/30*d**5 + 0*d**6 + 0 - 2*d. Factor q(w).
w*(w - 1)**2*(w + 1)**2/3
Solve -20*q**4 - 55*q + 4*q**5 + q**5 - 12*q**5 + 60*q**3 + 2*q**5 + 30 - 10*q**2 = 0.
-6, -1, 1
Let c(f) be the first derivative of f**6/7 - 12*f**5/7 + 39*f**4/14 + 120*f**3/7 + 108*f**2/7 + 792. Let c(t) = 0. Calculate t.
-1, 0, 6
Let d(n) be the first derivative of 3*n**5/5 + 27*n**4/4 + 15*n**3 - 75*n**2/2 - 1. Factor d(k).
3*k*(k - 1)*(k + 5)**2
What is n in 50 + 21/2*n**2 - 60*n - 1/2*n**3 = 0?
1, 10
Let t(j) be the first derivative of -j**6/255 - j**5/170 + 8*j - 13. Let m(z) be the first derivative of t(z). Factor m(w).
-2*w**3*(w + 1)/17
Let u = 23 - 18. Suppose -5*z - u = -4*k, k - 3*z + 4 = -0*z. 