such that 16*p**3 - 5222*p**4 + 1484*p**2 - 2584*p - 576 + 2586*p**4 + 2616*p**4 = 0.
-9, -1/5, 2, 8
Let l(j) be the second derivative of -j**4/18 + 236*j**3/9 - 13924*j**2/3 - 837*j - 2. Suppose l(u) = 0. What is u?
118
Let q(c) = -12*c**3 + 38*c**2 - 54*c + 18. Let y(n) = -n**3 - 3*n**2 + n + 1. Let k(l) = 2*q(l) - 4*y(l). What is u in k(u) = 0?
2/5, 2
Suppose -2*s - 9*d - 16 = -11*d, 4*s = -d - 17. Let x be 2 - (9 + s)*(-2)/8. Determine n so that 1/2*n**5 + 9/4*n**2 + 7/2*n**x + 1/2*n + 0 + 9/4*n**4 = 0.
-2, -1, -1/2, 0
Let w = 3477 - 1890. Solve w*g**2 + 29*g - 16*g + 3*g**4 - 13*g - 138*g**3 = 0.
0, 23
Let i(g) be the first derivative of -8*g**5/25 - 19*g**4/5 - 28*g**3/5 + 214*g**2/5 - 52*g + 365. Suppose i(d) = 0. Calculate d.
-13/2, -5, 1
Let x = -4/22119 + -13824299/420261. Let m = 33 + x. Factor 0 + 0*z**2 + m*z - 2/19*z**3.
-2*z*(z - 1)*(z + 1)/19
Let s = 52704 - 52699. Solve 2*q**3 + 2/3*q**2 + 0 + 2/3*q**s + 0*q + 2*q**4 = 0.
-1, 0
Let w(g) be the first derivative of -g**6/21 + 4*g**5 - 175*g**4/2 + 1645. Factor w(y).
-2*y**3*(y - 35)**2/7
Let n = 17 - 12. Suppose -x + 6 + 4 = -n*y, 3*y - 2 = -x. Solve 589*z**3 - 2*z**2 + 0*z - 587*z**3 + 2*z**4 - 2*z**x + 0*z = 0 for z.
-1, 0, 1
Let f = 91/45 + -9/5. Let k = 14887/67599 - -15/7511. Factor 0 - 4/9*m**2 + k*m**3 + f*m.
2*m*(m - 1)**2/9
Let y(l) be the third derivative of -3*l**6/20 - 23*l**5/20 + 17*l**4/4 - 5*l**3/2 + 4*l**2 + 15*l - 4. Factor y(x).
-3*(x - 1)*(x + 5)*(6*x - 1)
Let s(w) be the first derivative of -125*w**3/3 + 4385*w**2/2 - 350*w + 3327. Factor s(u).
-5*(u - 35)*(25*u - 2)
Suppose 5*b - 18 = 2*t, 0 = -4*b + 2*t + 5 + 11. Suppose -3*v = -3*r - 3 - 15, 0 = v - b*r - 8. Factor 12/5 - 3/5*n**5 + 3*n**3 + 3/5*n**2 - 24/5*n - 3/5*n**v.
-3*(n - 1)**3*(n + 2)**2/5
Let x be -1 + -5*(-3)/5. Suppose x = p - 4. Factor p*f**3 + 61*f**5 + 12*f**4 + 62*f**5 - 12*f**2 - 120*f**5 - 9*f.
3*f*(f - 1)*(f + 1)**2*(f + 3)
Let w(f) = f**2 - 26*f + 29. Let n be w(25). Factor -38*j + n*j**3 - 5*j**3 - 2*j**2 + 37*j.
-j*(j + 1)**2
Let j(w) be the first derivative of -3*w**5/50 - 4*w**4/15 - 4*w**3/15 + 11*w + 22. Let a(d) be the first derivative of j(d). Factor a(u).
-2*u*(u + 2)*(3*u + 2)/5
Let f(y) = -988*y**2 + 970. Let r(c) = -c**3 + 989*c**2 + c - 962. Let m(g) = -3*f(g) - 2*r(g). Factor m(a).
2*(a - 1)*(a + 1)*(a + 493)
Let v be (0 + 1 + (-714)/18)*-6 + -2. Let c(g) be the first derivative of -1875/2*g**6 + 600*g**5 - v*g**3 + 40*g + 6 + 1175/4*g**4 - 30*g**2. Factor c(l).
-5*(3*l + 1)**2*(5*l - 2)**3
Suppose 0 = 5*w + 2*x + 12, -x - 2 = -1. Let o = 5 + w. What is c in 38 - 9*c**2 - 4*c**o + c**3 - 38 = 0?
-3, 0
Let g(o) = -22*o**2 - 391*o + 5195. Let x(z) = -3*z**2 - 51*z + 742. Let i(w) = -4*g(w) + 30*x(w). Factor i(a).
-2*(a - 37)*(a + 20)
Find p, given that -3/8*p**3 + 45/2 + 99/8*p**2 - 69/2*p = 0.
1, 2, 30
Suppose -159 = 75*n - 78*n. Solve -n - 19 + 0*z**2 + 9*z**2 - 122*z + 0*z**2 + 20*z = 0 for z.
-2/3, 12
Let k(f) be the third derivative of f**8/2520 + 59*f**7/1575 + 61*f**6/90 + 1111*f**5/225 + 569*f**4/36 + 235*f**3/9 - 552*f**2. Solve k(l) = 0.
-47, -5, -1
Let z(p) be the first derivative of -25 + 1/9*p**3 + 1/3*p**4 + 0*p + 1/15*p**5 - p**2. Factor z(s).
s*(s - 1)*(s + 2)*(s + 3)/3
Let h = 231879 + -463753/2. Factor -60*l - h*l**3 + 50 + 45/2*l**2.
-5*(l - 5)*(l - 2)**2/2
Suppose -8*r + 18*r - n - 2 = 0, -n - 2 = r. Let p(f) be the second derivative of r - 1/3*f**4 - 1/15*f**5 - 19*f - 2/3*f**3 - 2/3*f**2. Solve p(v) = 0.
-1
Let b(v) be the second derivative of v**8/1344 + v**7/420 - v**5/120 - v**4/96 + 31*v**2 - 50*v. Let f(g) be the first derivative of b(g). Solve f(t) = 0.
-1, 0, 1
Suppose 3*t - g = -2*t + 15, 3*t = 5*g + 31. Factor -2*z**t + 137 - 267 + 134 - 2*z.
-2*(z - 1)*(z + 2)
Let s(r) = -r**3 - r**2 - r. Let m = -7 + 6. Let z(d) = 78*d**3 - 43*d**3 - 32*d**3 + 6*d**2 + 14*d**2 - 60*d. Let b(x) = m*z(x) - 4*s(x). Solve b(a) = 0.
0, 8
Factor 46/5 + 1/5*j**2 + 5*j.
(j + 2)*(j + 23)/5
Let r = -568 - -573. Let 5*o**r + 55*o - 79*o**4 - 27*o**2 - 60*o**3 + 129*o**4 - 23*o**2 = 0. Calculate o.
-11, -1, 0, 1
Let f(c) be the third derivative of 0*c + 0 + 0*c**3 + 62*c**2 + 1/8*c**4 - 1/20*c**5 - 1/40*c**6 + 1/70*c**7. Factor f(x).
3*x*(x - 1)**2*(x + 1)
Let j = -41 - -379/9. Let u(o) = -o - 11. Let d be u(-13). Solve j*k - 8/9 - 2/9*k**d = 0 for k.
1, 4
Let q(y) be the second derivative of y**4/12 + 131*y**3/6 - 411*y**2 + 8*y + 317. Determine r, given that q(r) = 0.
-137, 6
Let f = 61004/3 - 20767. Let i = -431 - f. Factor 4/3*m - i*m**2 + 4/3*m**4 + 0 - 4/3*m**3.
4*m*(m - 1)**2*(m + 1)/3
Suppose 2390 - 255*h - 646 - h**2 - 330*h + 153*h = 0. What is h?
-436, 4
Let w(c) = -3*c**3 - 44*c**2 + 37*c + 334. Let z be w(-15). Suppose 1/6*y**2 + 8/3 + 1/6*y**4 - y**3 + z*y = 0. Calculate y.
-1, 4
Suppose -16*m + 753 = -15. Let t = 12 - 9. Factor -588*y**2 + 4 + 498*y**2 + 50*y**t + m*y - 6 - 6.
2*(y - 1)*(5*y - 2)**2
Let p = -217 + 219. Factor 7*i - p*i - 9*i + i**2 + 3.
(i - 3)*(i - 1)
Let f = -3241393/15 + 216093. Find q such that f*q**3 - 1102736/15 + 13448/5*q - 164/5*q**2 = 0.
82
Let u(y) be the third derivative of -y**6/1800 - 7*y**5/300 - 49*y**4/120 - 23*y**3/2 + 4*y**2. Let a(q) be the first derivative of u(q). Factor a(t).
-(t + 7)**2/5
Let b(h) be the third derivative of -42*h**2 - 1/15*h**5 + 3/4*h**3 - 1 - 1/420*h**7 - 1/8*h**4 + 0*h + 1/40*h**6. Factor b(z).
-(z - 3)**2*(z - 1)*(z + 1)/2
Let n(a) be the first derivative of a**3/3 - 81*a**2/2 + 80*a + 1060. Suppose n(d) = 0. What is d?
1, 80
Let n be (619/5)/(-10 + (-202)/(-20)). Let m = n - 6162/5. Factor -36/5*r + 0 - 4/5*r**4 - m*r**3 - 12*r**2.
-4*r*(r + 1)*(r + 3)**2/5
Let t(b) be the third derivative of -b**5/20 + 1465*b**4/4 - 2146225*b**3/2 - 1063*b**2 + 3. Factor t(c).
-3*(c - 1465)**2
Let m be (46 - 47)*(6 + -6). Factor -2/5*o**4 + 1/5*o**3 + m*o**2 + 0*o + 0.
-o**3*(2*o - 1)/5
Let r be 33/3 - (-9 + (-632)/(-32)). Let 81 - 9*f + r*f**2 = 0. Calculate f.
18
Let -8*t - 1/4*t**3 - 8 - 5/2*t**2 = 0. What is t?
-4, -2
Let p(w) be the second derivative of 93*w + 10*w**2 + 1 - 3*w**3 - 1/6*w**4. Find s such that p(s) = 0.
-10, 1
Let g(t) be the third derivative of 0 + 25/4*t**4 - 125/4*t**5 - 1/2*t**3 + 0*t - 223*t**2. What is b in g(b) = 0?
1/25
Let m = -6369 - -6376. Let d(o) be the third derivative of -3/140*o**m - 27/4*o**3 - 27/4*o**4 + 0 - 9/4*o**5 + 14*o**2 + 0*o - 7/20*o**6. Factor d(u).
-3*(u + 3)**3*(3*u + 1)/2
Factor -996 - 580*y**3 - 152*y**2 + 1150*y - 575*y**3 - 591*y**3 + 1744*y**3.
-2*(y - 6)*(y - 1)*(y + 83)
Let y(r) = 4*r**4 + 124*r**3 + 558*r**2 + 874*r + 388. Let q(m) = 24*m**4 + 738*m**3 + 3349*m**2 + 5245*m + 2330. Let k(z) = 6*q(z) - 35*y(z). Factor k(s).
4*(s + 1)**2*(s + 10)**2
Let i(j) be the second derivative of -j**4/84 + 5*j**3/21 - 9*j**2/14 - 1798*j. Factor i(u).
-(u - 9)*(u - 1)/7
Let l(b) be the second derivative of 0*b**3 - 1/10*b**6 + 31*b + 0 + 0*b**5 + 2*b**4 - 24*b**2. Factor l(z).
-3*(z - 2)**2*(z + 2)**2
Factor -17*d**2 + 79 - 39*d**2 + 65 + 16*d**2 + 108*d + 6*d**3 - 10*d**3.
-4*(d - 3)*(d + 1)*(d + 12)
Let h = 4547 - 4543. Let d(o) be the first derivative of -1/16*o**2 + 0*o - 1/40*o**5 + 1/32*o**h + 18 + 1/24*o**3. Factor d(u).
-u*(u - 1)**2*(u + 1)/8
Let n(l) = 2*l**3 - 11*l**2 + 2*l + 17. Let i be n(5). Suppose -7 - 41 - 3*k**i + 0*k**2 + 30*k = 0. Calculate k.
2, 8
Let x(g) = -3*g - 18. Let t be x(8). Let b(z) = 2*z**3 + 83*z**2 - 41*z + 44. Let r be b(t). Let 2/5 + 0*h**r - 1/5*h**3 + 3/5*h = 0. What is h?
-1, 2
Solve 318 - 145*r + 5477*r**2 + 54*r - 5474*r**2 - 74*r = 0 for r.
2, 53
Let b = -114 + 114. Factor -2 + b + 117*g**2 + 16*g - 97*g**2 - 2.
4*(g + 1)*(5*g - 1)
Let t(w) = -10*w**3 - 12*w**2 + 2*w + 48. Let q(h) = 12*h**3 + 13*h**2 - 2*h - 58. Let g(n) = -4*q(n) - 5*t(n). Factor g(x).
2*(x - 1)*(x + 1)*(x + 4)
Let k(q) be the third derivative of 1/3*q**4 - 1/10*q**6 + 1/3*q**5 + 0*q**3 + 0*q + 0 - 14*q**2. Factor k(j).
-4*j*(j - 2)*(3*j + 1)
Let k(l) be the first derivative of 3*l**4/28 - 39*l**2/2 + 270*l/7 + 1340. Determine i so that k(i) = 0.
-10, 1, 9
Let a(n) be the first derivative of 45/2*n**3 + 1215/4*n**2 + 40 + 3645/2*n + 5/8*n**4. What is h in a(h) = 0?
-9
Let s(t) be the third derivative of 82*t**2 + 0*t**3 - 1/210*t**8 + 0 + 2/25*t**5 - 