2
Let t(o) = 2*o**3 + 25*o**2 + 288*o + 3315. Let f be t(-12). Determine b, given that 0 - 2/5*b**2 - 8/15*b + 2/15*b**f = 0.
-1, 0, 4
Let m be (-5)/(-9)*(-53)/((-47700)/216). Let y(q) be the first derivative of -16/9*q**3 + 16/3*q**2 + 0*q - m*q**5 + 23 - 7/6*q**4. Find h, given that y(h) = 0.
-4, 0, 1
Let s(y) be the third derivative of -y**5/12 - 385*y**4/24 + 4*y**2 - 18. Factor s(f).
-5*f*(f + 77)
Suppose -3*r = -f - 3*f - 22, 3*r = -5*f - 14. Determine c so that 86*c**3 - 84*c**3 - 18 + r - 8*c + 4*c**2 = 0.
-2, 2
Let h(p) be the third derivative of -p**6/900 + p**5/300 + p**4/10 + 29*p**3/3 + 57*p**2. Let r(z) be the first derivative of h(z). Factor r(k).
-2*(k - 3)*(k + 2)/5
Let k(z) = -50*z**3 + 252*z**2 - 275*z + 12. Let g(s) = -2*s**3 + s**2 + s. Let x(o) = 14*g(o) + 2*k(o). Factor x(l).
-2*(l - 2)**2*(64*l - 3)
Factor 58*m**2 + 296*m + 5*m**2 + 348 + 437*m**3 - 436*m**3.
(m + 2)*(m + 3)*(m + 58)
Let u(h) be the second derivative of -h**8/1344 - 25*h**7/504 + 13*h**6/72 + 5*h**4/3 - h**3/3 - 50*h. Let d(s) be the third derivative of u(s). Factor d(n).
-5*n*(n - 1)*(n + 26)
Let k = -847981 - -847983. Find m, given that 8 + 3*m + 1/2*m**3 - 9/2*m**k = 0.
-1, 2, 8
Let m(l) = 6*l**3 - 38*l**2 - 94*l - 58. Let i(h) = 5*h**3 - 35*h**2 - 90*h - 60. Let b(y) = 7*i(y) - 6*m(y). Suppose b(j) = 0. Calculate j.
-12, -3, -2
Let i(u) be the third derivative of -u**6/48 + 131*u**5/24 - 1400*u**4/3 + 5120*u**3 - 24*u**2 + 21. Find h, given that i(h) = 0.
3, 64
Let y be -4 - ((-49)/(-2)*(-23)/46 - -2). Let s(o) be the first derivative of -y*o**4 + 3*o**5 + 5/3*o**6 - 10*o - 65/3*o**3 - 14 - 45/2*o**2. Factor s(n).
5*(n - 2)*(n + 1)**3*(2*n + 1)
Let w = 11165/4 + -2791. Let p(r) be the first derivative of 7/2*r**2 - 14 - w*r**4 + 4*r + 2/3*r**3. Determine b, given that p(b) = 0.
-1, 4
Let o(h) = h**4 + 2*h**2 + h + 1. Let y(c) = 5*c**4 + 2*c**3 - c**2 - 14*c + 4. Let f(m) = 4*o(m) - y(m). Solve f(j) = 0.
-3, -2, 0, 3
Solve -4*j - 336/23 - 2/23*j**2 = 0.
-42, -4
Let o(x) be the first derivative of 2*x + 15 + 3/2*x**2 + 5/12*x**4 - 7/6*x**3 - 1/20*x**5. Let n(f) be the first derivative of o(f). Factor n(d).
-(d - 3)*(d - 1)**2
Let i = 73761 - 368792/5. Determine j so that -1/5*j**2 + i*j + 6 = 0.
-2, 15
Let r(l) = l**4 + 20*l**3 - 23*l**2 + 15*l. Let o(b) = -b**4 - 13*b**3 + 12*b**2 - 8*b. Let q(s) = -7*o(s) - 4*r(s). Factor q(d).
d*(d + 2)**2*(3*d - 1)
Let v be 45 - 35 - 32/4. Let w(b) be the first derivative of -3/4*b**4 - 12*b + 0*b**v + 3*b**3 - 14. Factor w(a).
-3*(a - 2)**2*(a + 1)
Let s(v) = v**3 - 20*v**2 - 31*v - 12. Let i be -1 - 4/(4/4). Let f(y) = 3*y**3 - 42*y**2 - 63*y - 23. Let z(t) = i*s(t) + 2*f(t). Solve z(k) = 0.
-14, -1
Let o(b) be the first derivative of b**6/10 - 564*b**5/25 + 1119*b**4/20 - 186*b**3/5 - 1304. Factor o(x).
3*x**2*(x - 186)*(x - 1)**2/5
Let g(q) be the first derivative of q**5/80 + q**4/6 + 2*q**3/3 + 15*q + 18. Let f(m) be the first derivative of g(m). Factor f(t).
t*(t + 4)**2/4
Let t = 4497 - 4493. Let q(f) be the first derivative of 3/10*f**2 - 3 + 4/15*f**3 + 0*f + 1/20*f**t. Factor q(o).
o*(o + 1)*(o + 3)/5
Let b(l) = 5*l**2 - 2*l - 72. Let a(d) = -d**2 + 4*d. Let z(c) = -4*a(c) - b(c). Determine k so that z(k) = 0.
-18, 4
Let x(c) = -c**2 - 63*c - 852. Let r be x(-43). Let z(w) be the second derivative of 0*w**2 - 7/40*w**5 + r*w + 1/12*w**4 + 0*w**3 + 0. Factor z(o).
-o**2*(7*o - 2)/2
Let w = 3145 + -3145. Let o(d) be the third derivative of -1/3*d**4 - 1/30*d**5 + 0 - 4/3*d**3 - 5*d**2 + w*d. Factor o(h).
-2*(h + 2)**2
Let a(y) be the third derivative of -13*y**6/60 - 53*y**5/15 - 107*y**4/12 - 14*y**3/3 + 520*y**2. Suppose a(o) = 0. Calculate o.
-7, -1, -2/13
Let g(m) be the third derivative of 104*m**2 - 1/150*m**5 - 2/5*m**3 + 0*m + 1/12*m**4 + 0. Factor g(k).
-2*(k - 3)*(k - 2)/5
Let j(n) = n**2 - 2*n + 8. Let g(b) = 34*b**2 - 884*b - 500. Let x(m) = -g(m) + 38*j(m). Factor x(w).
4*(w + 1)*(w + 201)
Let r(k) be the first derivative of 27/17*k**2 + 11 + 0*k**3 - 108/17*k - 1/34*k**4. Factor r(f).
-2*(f - 3)**2*(f + 6)/17
Let -110*l - 5*l**4 + 583*l**3 - 1199*l**3 - 1 + 5*l**2 + 726*l**3 + 1 = 0. What is l?
-1, 0, 1, 22
Let a(q) be the first derivative of -35 + 1/18*q**3 + 13/6*q**2 + 169/6*q. Let a(o) = 0. What is o?
-13
Let l(j) be the first derivative of j**4/2 - 72*j**3 - 550. Factor l(f).
2*f**2*(f - 108)
Suppose -4/7*k**4 + 52/7*k**2 + 0 + 4*k + 20/7*k**3 = 0. What is k?
-1, 0, 7
Let i = -7951 - -7956. Let i*q + 435/2*q**4 + 225/4*q**5 + 4 - 58*q**2 - 179/4*q**3 = 0. What is q?
-4, -1/3, 2/5
Let r = -2187 - -2191. Let y(v) be the second derivative of 2/3*v**r + 0*v**2 + 8/15*v**6 + 0*v**3 - 2/21*v**7 - v**5 + 0 + 21*v. Factor y(k).
-4*k**2*(k - 2)*(k - 1)**2
Let u = -25236 + 25239. Let i(r) be the first derivative of 7/10*r**2 + 0*r + 1/15*r**u + 38. Find k such that i(k) = 0.
-7, 0
Let f(h) be the second derivative of 1/4*h**4 - 25*h**3 + 134*h + 1875/2*h**2 + 0. Find n such that f(n) = 0.
25
Let v(y) be the first derivative of -y**6/1020 - y**5/255 + 2*y**4/51 + 34*y**2 + 37. Let j(b) be the second derivative of v(b). Factor j(c).
-2*c*(c - 2)*(c + 4)/17
Factor 9/2*i**2 + 27/4*i - 15/4*i**3 - 3/2.
-3*(i - 2)*(i + 1)*(5*i - 1)/4
Factor -296*k**5 - 88*k**3 + 635*k**5 - 140*k - 47*k**3 - 10*k**4 - 334*k**5 - 260*k**2.
5*k*(k - 7)*(k + 1)*(k + 2)**2
Find c, given that -216/7*c + 36/7*c**2 - 2/7*c**4 + 8/7*c**3 + 270/7 = 0.
-5, 3
Let x(y) = -y**4 - 9*y**3 + y**2 + 33*y - 24. Let o(c) = -3*c**4 - 26*c**3 + 2*c**2 + 100*c - 73. Let l(s) = -4*o(s) + 14*x(s). Factor l(r).
-2*(r - 1)**2*(r + 2)*(r + 11)
Let b(n) = -2*n**2 - 51*n + 236. Let x be b(4). Let k(s) be the third derivative of 0 - 7*s**2 + x*s**4 + 0*s - 1/20*s**5 + 1/2*s**3. Factor k(z).
-3*(z - 1)*(z + 1)
Let l = -7421/7 + 1061. Let c(y) be the first derivative of -l*y**2 - 2/35*y**5 + 0*y**4 + 0*y + 2/3*y**3 + 9. Factor c(u).
-2*u*(u - 2)*(u - 1)*(u + 3)/7
Suppose 2*r**2 + 4*r + 1/7*r**5 - 24/7 - 4/7*r**4 - 15/7*r**3 = 0. Calculate r.
-2, 1, 6
Let p(z) be the third derivative of z**8/30240 + z**7/756 - 19*z**4/12 - z**3/2 + 2*z**2 - 6*z. Let o(l) be the second derivative of p(l). Factor o(k).
2*k**2*(k + 15)/9
Factor -1184/7 + 2/7*v**2 + 84*v.
2*(v - 2)*(v + 296)/7
Let p(b) be the third derivative of b**5/60 - 3*b**4/2 - 751*b**2. Factor p(r).
r*(r - 36)
Let h = 230060/7 + -32927. Let w = h - -1723/28. Find z, given that 0*z + 0 - 1/8*z**3 + w*z**2 = 0.
0, 2
Suppose -145 = -50*q + 55. Let p(w) be the third derivative of 1/140*w**5 + 18/7*w**3 + 3/14*w**4 - q*w**2 + 0 + 0*w. Factor p(s).
3*(s + 6)**2/7
Let d = -121445/2 + 1093021/18. Suppose -28/9*o - 20/9*o**2 - d = 0. Calculate o.
-1, -2/5
Let z(f) be the first derivative of -f**5/5 - 5*f**4/2 + 12*f**3 - 19*f**2 + 13*f + 2027. Suppose z(k) = 0. Calculate k.
-13, 1
Let l(x) be the second derivative of x**6/360 + x**5/60 - 2*x**3/9 + 27*x**2 + 4*x - 10. Let p(g) be the first derivative of l(g). Solve p(a) = 0.
-2, 1
Let b be (-30)/27*(-114)/76. Let a(l) be the third derivative of 1/6*l**5 - b*l**3 - 1/8*l**6 + 0*l + 18*l**2 + 0 + 5/8*l**4. Factor a(p).
-5*(p - 1)*(p + 1)*(3*p - 2)
Let b be ((-3)/(-7))/((-4194)/(-4893)). Factor -1/2*p**2 - b*p**3 + 6 + 4*p.
-(p - 3)*(p + 2)**2/2
Suppose -2139 = -205*m - 291*m - 651. Determine k, given that -2*k**2 - 3/2*k + 0 - 1/2*k**m = 0.
-3, -1, 0
Suppose -5*v + 5*m - 1 = 3*m, -10 = -v - 3*m. Let p be 3/21 - v/7. Factor 0 - 1/5*k**5 + 2/5*k**3 + 0*k**4 + p*k**2 - 1/5*k.
-k*(k - 1)**2*(k + 1)**2/5
Let 830*t**3 + 412*t**4 - 42*t**5 + 611*t**2 - 195*t**2 + 20*t**5 + 20*t**5 = 0. Calculate t.
-1, 0, 208
Let i(f) be the second derivative of -242*f**6/15 + 528*f**5/5 - 60*f**4 + 32*f**3/3 - 17*f + 2. Factor i(m).
-4*m*(m - 4)*(11*m - 2)**2
Let q = -117 + 118. Let c(b) = -b**4 - b**3 + b**2 - b + 1. Let s(v) = -22*v**2 + 0 + 10*v + 5 + 2*v**2. Let p(d) = q*s(d) - 5*c(d). Factor p(a).
5*a*(a - 1)**2*(a + 3)
Let f(i) be the third derivative of 8/3*i**4 + 1/6*i**6 - 3 - 8/3*i**3 + 0*i + 19/15*i**5 + 17*i**2. Factor f(a).
4*(a + 2)**2*(5*a - 1)
Suppose q - 16 - 6 = 0. Suppose q = -11*i + 66. Factor -94*u**3 - 4*u**i - 10*u + 16 - 3*u**2 - 6*u - 9*u**2 + 110*u**3.
-4*(u - 2)**2*(u - 1)*(u + 1)
Let h(i) = 49*i**2 - 378*i + 800. Let u(k) = -107*k**2 + 754*k - 1600. L