t**4 - 1/540*t**6 + 5*t. Let n(p) be the second derivative of q(p). Factor n(i).
-2*(i + 4)**2/3
Let s(a) be the third derivative of a**8/2520 - 2*a**7/1575 + a**5/225 - a**4/180 - 94*a**2. Factor s(n).
2*n*(n - 1)**3*(n + 1)/15
Let k(x) be the second derivative of x**6/30 - 13*x**5/60 - 5*x**4/18 + 597*x. Factor k(d).
d**2*(d - 5)*(3*d + 2)/3
Let z(a) be the second derivative of -2*a**7/49 - 4*a**6/105 + 12*a**5/35 + 8*a**4/21 - 21*a - 8. Find l such that z(l) = 0.
-2, -2/3, 0, 2
Let z(w) be the second derivative of w**4/9 + 40*w**3 + 5400*w**2 + 60*w. Factor z(b).
4*(b + 90)**2/3
Factor -34*z - 120 + 74*z**2 - 69*z**2 + 24*z.
5*(z - 6)*(z + 4)
Let c be (11/(-22))/(2/(-12)). Factor -c*l - 10*l**2 + 0*l + 11*l**2 - 4*l**2.
-3*l*(l + 1)
Find h such that -2565*h**4 + 2589*h**4 + 4*h**5 + 0*h**3 - 20*h - 72*h**2 + 16*h**3 + 48 = 0.
-4, -3, -1, 1
Factor -5/4*f**2 + 0 - 3/4*f**3 - 1/2*f + 1/4*f**4 + 1/4*f**5.
f*(f - 2)*(f + 1)**3/4
Let g(i) be the first derivative of i**6/3 + 2*i**5/5 - 3*i**4/2 - 10*i**3/3 - 2*i**2 + 53. Factor g(a).
2*a*(a - 2)*(a + 1)**3
Factor -4/7*i**4 + 4/7*i**3 + 60/7*i + 0 + 68/7*i**2.
-4*i*(i - 5)*(i + 1)*(i + 3)/7
Let q(i) be the third derivative of 0*i - 1/90*i**6 + 0*i**4 + 2/315*i**7 - 1/1008*i**8 - 6*i**2 + 0*i**3 + 0*i**5 + 0. Factor q(k).
-k**3*(k - 2)**2/3
Let x = 270/517 + -16/47. Let s(h) = h**3 + 4*h**2 + 3*h. Let i be s(-2). Let 0*u - 4/11*u**i + x + 0*u**3 + 2/11*u**4 = 0. Calculate u.
-1, 1
Let i(u) = u**2 + u. Let r(g) = 5*g**2 + 8*g + 4. Suppose -47 = -d - 8. Let s be -3*(d/9 + -3). Let w(z) = s*i(z) + r(z). Solve w(x) = 0 for x.
-2
Let g be -1 - (12 + (7 - 3)). Let j(t) = t**3 + 18*t**2 + 17*t + 4. Let n be j(g). Factor -5/4*i + 1/2 + i**3 + 1/2*i**2 + 1/4*i**5 - i**n.
(i - 2)*(i - 1)**3*(i + 1)/4
Let y(i) be the second derivative of -5*i**4/12 + 10*i**3 - 50*i**2 + 161*i. Factor y(f).
-5*(f - 10)*(f - 2)
Let d(i) be the second derivative of 9*i**7/56 + 3*i**6/20 - 3*i**5/10 - 3*i**4/8 - i**3/8 + 2*i - 18. Find n, given that d(n) = 0.
-1, -1/3, 0, 1
Let a(g) be the first derivative of g**7/40 + g**6/60 - 7*g**5/40 - g**4/4 - 10*g**3/3 - 6. Let b(o) be the third derivative of a(o). Solve b(q) = 0 for q.
-1, -2/7, 1
Let y(u) be the first derivative of -u**4/8 + 7*u**3/6 - 7*u**2/2 + 4*u - 121. Factor y(k).
-(k - 4)*(k - 2)*(k - 1)/2
Let d(f) be the first derivative of f**9/10584 - f**8/2940 + f**7/2940 - 7*f**3/3 + 15. Let p(i) be the third derivative of d(i). Factor p(u).
2*u**3*(u - 1)**2/7
Let o = -62367/7 - -8913. Factor 36/7 + 4/7*l**2 - o*l.
4*(l - 3)**2/7
Let r(s) be the third derivative of s**9/60480 - s**8/20160 - s**7/5040 + s**6/720 - 23*s**5/60 - 6*s**2. Let a(v) be the third derivative of r(v). Factor a(m).
(m - 1)**2*(m + 1)
Let m(t) be the second derivative of t**5/45 + t**4/18 - 4*t**3/9 + 9*t**2/2 + 14*t. Let u(k) be the first derivative of m(k). Factor u(s).
4*(s - 1)*(s + 2)/3
Let u(x) be the second derivative of -x**5/30 + 10*x**4/9 - 128*x**3/9 + 256*x**2/3 + 443*x. Factor u(d).
-2*(d - 8)**2*(d - 4)/3
Let x(k) be the third derivative of -k**7/280 - k**6/30 - 3*k**5/40 - 2*k**3 + 7*k**2. Let d(s) be the first derivative of x(s). Factor d(p).
-3*p*(p + 1)*(p + 3)
Determine x so that 32 + 22/3*x**2 - 80/3*x - 2/3*x**3 = 0.
3, 4
Let w = 45/8 - 389/72. Let a be 6/33 + 8/198. Let w*c**2 + 0 + a*c = 0. What is c?
-1, 0
Let s(w) be the first derivative of -2*w**3/33 - 3*w**2/11 - 4*w/11 - 68. Factor s(i).
-2*(i + 1)*(i + 2)/11
Let t(u) = 3*u**2 + 1. Let z be t(1). Let y be 0/(-4 + 20/z). Factor 2*i**2 + 105*i + 2*i**3 - 109*i + y + 0.
2*i*(i - 1)*(i + 2)
Let z(r) = -65*r**3 - 3*r**2 - 52*r - 54. Let c be z(-1). Suppose 3/4*y**3 - 48 + c*y - 51/4*y**2 = 0. Calculate y.
1, 8
Factor 4710*k**3 + 75/4*k**4 + 47628 + 293898*k**2 - 237384*k.
3*(k + 126)**2*(5*k - 2)**2/4
Let a(o) be the second derivative of o**6/60 - o**5/30 - o**2/2 - 4*o. Let q(t) be the first derivative of a(t). Suppose q(k) = 0. Calculate k.
0, 1
Let l = -400 + 2401/6. Let z(m) be the third derivative of -2/3*m**3 + 0*m + 1/15*m**5 + 0 + 7*m**2 - l*m**4 + 1/30*m**6. Factor z(b).
4*(b - 1)*(b + 1)**2
Let q(g) be the first derivative of -3*g**5/35 + 3*g**4/2 - 44*g**3/7 + 60*g**2/7 + 184. Factor q(y).
-3*y*(y - 10)*(y - 2)**2/7
Let q(o) be the third derivative of o**9/4536 + o**8/630 + o**7/420 + 5*o**3/3 - 6*o**2. Let i(t) be the first derivative of q(t). Factor i(f).
2*f**3*(f + 1)*(f + 3)/3
Let v(w) be the third derivative of -w**4/24 - 4*w**2. Let l(r) = r**3 - r**2 - 6*r + 1. Let f(a) = -l(a) + 5*v(a). Factor f(j).
-(j - 1)**2*(j + 1)
Let f(k) = -2*k**3 + 2. Let l(t) = 11*t**3 + 7*t - 18. Let v(y) = -6*f(y) - l(y). Factor v(a).
(a - 2)*(a - 1)*(a + 3)
Let x(d) be the third derivative of -5*d**4/24 + 9*d**3/2 - 20*d**2. Let r be x(5). Determine i, given that -3*i**r + 12/7*i**3 + 6/7*i + 3/7 = 0.
-1/4, 1
Let w(r) be the second derivative of r**7/63 + r**6/9 + 4*r**5/15 + 2*r**4/9 + 76*r. Solve w(d) = 0 for d.
-2, -1, 0
Suppose -18 = 2*q + 6. Let n = q - -15. Factor 0*x + 7*x**2 - n*x**3 + 2*x**2 - 6*x.
-3*x*(x - 2)*(x - 1)
Let l = -5 - -7. Factor 1 - 16*q - 14*q - 5 - 25*q**l - 1.
-5*(q + 1)*(5*q + 1)
Let m(n) = n**2 - 13*n + 7*n + 7*n + 2*n. Let s be m(-4). Factor -v**5 + 0*v + 2/3*v**3 + 0*v**2 + 1/3*v**s + 0.
-v**3*(v - 1)*(3*v + 2)/3
Let s(z) = 26*z**5 - 27*z**5 + 1 - z**4 - 3*z**2 + 3*z**2. Let c(n) = -8*n**5 - 6*n**4 + 6*n**3 - 4*n**2 + 6. Let p(u) = c(u) - 6*s(u). Let p(k) = 0. What is k?
-2, 0, 1
Find b such that -12*b**2 - 3*b**2 + 0*b**2 - 5*b**3 + 0*b**3 = 0.
-3, 0
Let i(u) be the first derivative of -8/15*u**5 - 1/6*u**4 + 0*u + 21 + 0*u**3 + 0*u**2. Factor i(o).
-2*o**3*(4*o + 1)/3
Let t(q) be the second derivative of 8*q**6/5 + 42*q**5/5 + 33*q**4/4 - 14*q**3 + 6*q**2 + q + 117. Factor t(k).
3*(k + 2)**2*(4*k - 1)**2
Let f = 16399 + -16397. Factor -12/5*p - 2 - 2/5*p**f.
-2*(p + 1)*(p + 5)/5
Let k(z) = z**4 - 3*z**3 - 3*z**2 + z - 2. Let q(a) = a**4 - a**3 - 2*a**2 - 1. Let o(n) = 5*k(n) - 10*q(n). Factor o(y).
-5*y*(y - 1)*(y + 1)**2
Let f = -18094 - -36193/2. What is i in -1/2*i**3 - 1 + f*i - 3/2*i**2 + 1/2*i**4 = 0?
-2, 1
Let p(n) = -n**4 - n**3 - n**2 + n - 1. Suppose -5*u = 4*u - 54. Let g(k) = 7*k**4 + 12*k**3 + 11*k**2 - 6*k + 6. Let z(i) = u*p(i) + g(i). Factor z(m).
m**2*(m + 1)*(m + 5)
Suppose -8*d + 235 + 493 = 0. Let 16*g**2 + 4*g**3 - 173 + 82 + 12*g + d = 0. Calculate g.
-3, -1, 0
Let b(q) be the third derivative of -q**7/1470 + 3*q**6/280 - q**5/21 + q**4/14 - 173*q**2. Find f such that b(f) = 0.
0, 1, 2, 6
Let u = 808 - 808. Determine h, given that 1/2*h**2 + h + u - 1/2*h**3 = 0.
-1, 0, 2
Let p = 35 - 29. Let t(m) be the first derivative of 16/5*m**5 + 8/3*m**3 - 1 - 5*m**4 + 0*m**2 - 2/3*m**p + 0*m. Factor t(s).
-4*s**2*(s - 2)*(s - 1)**2
Let c(x) be the second derivative of x**7/504 + x**6/144 - 19*x**4/12 - 6*x. Let y(w) be the third derivative of c(w). Factor y(m).
5*m*(m + 1)
Let h(q) be the third derivative of -q**9/60480 - q**8/6720 + q**6/180 + 13*q**5/60 - 18*q**2. Let i(m) be the third derivative of h(m). Factor i(a).
-(a - 1)*(a + 2)**2
Let a(b) be the second derivative of b**5/10 + 5*b**4/6 + 8*b**3/3 + 4*b**2 - 61*b. Factor a(w).
2*(w + 1)*(w + 2)**2
Let s(l) = -51*l + 0 + 13 + 54*l + 16. Let y be s(-9). Find j such that -22/13*j**3 + 0 - 4/13*j - y*j**2 = 0.
-1, -2/11, 0
Let p(t) be the first derivative of t**6/21 - 2*t**5/5 + 9*t**4/7 - 40*t**3/21 + 8*t**2/7 + 516. Let p(g) = 0. Calculate g.
0, 1, 2
Factor -28/5*t + 7/5*t**2 - 12/5 + t**3.
(t - 2)*(t + 3)*(5*t + 2)/5
Let 2 + 3/2*q + 1/4*q**2 = 0. Calculate q.
-4, -2
Let i(t) = -2*t**3 + 5*t**2 + 2*t + 2. Let r be i(0). Determine w so that 6/5*w - 2*w**r + 2/5*w**3 + 18/5 = 0.
-1, 3
Let k(x) = 0*x - x**3 - 2 - 5*x - 4*x**2 - x**2. Let t be k(-4). Factor 0*q**2 + q**t - 4*q - 3 + 1 + 6.
(q - 2)**2
Solve 144*m**2 + 5083*m**4 - 39*m**3 - 2552*m**4 - 2534*m**4 = 0 for m.
-16, 0, 3
Let y = 486/5 - 4369/45. Factor -y*p + 1/9*p**2 - 2/9.
(p - 2)*(p + 1)/9
Let m(a) be the third derivative of -a**5/40 - 11*a**4/16 - 9*a**3/2 - 852*a**2. Factor m(i).
-3*(i + 2)*(i + 9)/2
Factor 48*u**3 - 48*u + 1156*u**4 - 1160*u**4 + 0*u**2 + 4*u**2.
-4*u*(u - 12)*(u - 1)*(u + 1)
Let u(t) be the first derivative of -t**5/105 + 2*t**4/21 + 5*t**2/2 - 13. 