
Let k(j) be the third derivative of 1/300*j**5 + 1/600*j**6 + 138*j**2 + 0 + 0*j - 1/30*j**3 - 1/120*j**4. Find q, given that k(q) = 0.
-1, 1
Let x(n) = -n**3 + 6*n**2 + 3*n - 13. Suppose -9*y + 4*y = -30. Let v be x(y). Factor -4*h**2 + 4 + v*h**2 - 8*h + 15 - 3.
(h - 4)**2
Let z(m) be the first derivative of -m**6/360 + 2*m**5/45 - 7*m**4/72 - 3*m**2 - 10*m + 156. Let l(i) be the second derivative of z(i). Factor l(p).
-p*(p - 7)*(p - 1)/3
Suppose 5*y + 14*z - 11*z = 12, 4*z - 16 = 4*y. Let f(p) be the third derivative of -1/4*p**4 + 0 + y*p - 1/20*p**5 - 13*p**2 + 0*p**3. Factor f(b).
-3*b*(b + 2)
Let v(b) be the third derivative of -49*b**6/240 + 8393*b**5/10 + 4797*b**4/4 + 2056*b**3/3 + 2*b**2 + 61*b - 6. Factor v(i).
-(i - 2056)*(7*i + 2)**2/2
Let y be -2*4/(-16) - (5 - 5)/8. Factor -1/6*v**2 + 3 - y*v.
-(v - 3)*(v + 6)/6
Factor -110*l - 39*l + 6*l**2 - 129*l - 109*l.
3*l*(2*l - 129)
Let k = -562 - -584. Suppose 19*t - k*t - 2*z = 4, -t = -4*z - 22. Factor 8*h**t + 2/3*h**4 + 20/3*h + 4*h**3 + 2.
2*(h + 1)**3*(h + 3)/3
Suppose -5*q - 127 + 77 = -2*c, -c - 5*q = 35. Let y(p) be the first derivative of -1/35*p**c - 2/7*p + 1/2*p**2 - 3/7*p**3 + 5/28*p**4 + 42. Factor y(k).
-(k - 2)*(k - 1)**3/7
Let f = -19663/2 - -10234. Let l = f - 398. Determine q so that -9/2 - l*q**4 - 15*q**3 - 33/2*q - 1/2*q**5 - 23*q**2 = 0.
-3, -1
Let b(k) = 3*k**3 - k**2 + 1. Let x be b(1). Let j(v) = -v**3 + 4*v**2 + 5*v - 7. Let u be j(1). Factor -4 - u - x - 5*q**2 + 3 - 10*q.
-5*(q + 1)**2
Let r = -1693599/2 - -846801. Factor 27*s**3 + 0 - r*s**4 + 132*s + 126*s**2.
-3*s*(s - 22)*(s + 2)**2/2
Let o(g) = 38*g + 51. Let w be o(-2). Let p = 28 + w. Determine d, given that p*d - 1/4*d**2 - 9 = 0.
6
Let p(y) be the first derivative of -y**6/30 + y**5/10 - 39*y - 53. Let b(v) be the first derivative of p(v). Let b(m) = 0. What is m?
0, 2
Let t = -75 + 96. Suppose 24*y = t*y + 12. Suppose -8*s**2 - 4*s - 3*s**y + 4*s**5 - 2*s**4 + 18*s**4 - 5*s**4 = 0. What is s?
-1, 0, 1
Let j be (-2)/(-9) + 460/(-45) + 13 + -1. Let x(c) be the third derivative of -1/3*c**4 + 0 + 8/15*c**5 + 0*c + 17*c**j - 7/60*c**6 + 0*c**3. Factor x(t).
-2*t*(t - 2)*(7*t - 2)
Let t = -546811/15 + 36478. Let o = t - 113/5. Let -2/3 - 2/3*p**5 - o*p**2 + 2*p**4 - 4/3*p**3 + 2*p = 0. Calculate p.
-1, 1
Find y, given that 12*y**2 - 11 + 36*y**3 - 1 - 93*y**3 + 3*y + 54*y**3 = 0.
-1, 1, 4
Let g = 1280 + 3424. Let d = -297 + 521. Factor -16402 + g*m**2 - d*m**3 + 136648 - 43904*m + 4*m**4 + 33418.
4*(m - 14)**4
Let j be ((-126)/((-30)/(-5)) - -15) + 340/55. Factor -2*g + j*g**2 + 48/11.
2*(g - 8)*(g - 3)/11
Let f(x) = -2*x**3 - 27*x**2 + 13*x - 10. Let c be f(-14). Factor 75*k**2 + 45*k + 5*k**c + 257 - 257 + 35*k**3.
5*k*(k + 1)*(k + 3)**2
Let s(y) be the second derivative of 5*y**4/12 - 595*y**3/3 + 149*y. Factor s(u).
5*u*(u - 238)
Let g(v) = 8*v**3 - 348*v**2 + 1000*v - 664. Let w(j) = 7*j**3 - 346*j**2 + 998*j - 662. Let x(h) = 3*g(h) - 4*w(h). Solve x(f) = 0.
1, 2, 82
Let d(c) = 2*c**3 - 4401*c**2 - 2859*c - 472. Let n(h) = 3*h**3 - h**2 - 2*h + 5. Let k(o) = d(o) + 6*n(o). Factor k(u).
(u - 221)*(4*u + 1)*(5*u + 2)
Suppose -w - 6 = -9. Find i, given that 4*i + 2*i**2 + 26*i**w - 5*i**2 - 3*i**2 - 24*i**3 = 0.
0, 1, 2
Find o such that 544*o - 224 - 198*o**2 + 95*o**4 + 76*o**4 - 169*o**4 + 11*o**3 = 0.
-14, 1/2, 4
Let u(l) be the first derivative of l**6/15 + 3*l**5/10 - l**4/6 - l**3 + 21*l + 41. Let q(m) be the first derivative of u(m). Factor q(i).
2*i*(i - 1)*(i + 1)*(i + 3)
Suppose 3*b + 3*o + 6 = 0, -14*o + 17*o = b - 18. Factor -128*f + 55*f + 61*f + 5*f**b - 2*f**3.
3*f*(f - 2)*(f + 2)
Find f, given that -30/17*f**4 - 144/17*f - 648/17 + 478/17*f**2 - 2/17*f**5 - 54/17*f**3 = 0.
-9, -1, 2
Let r(f) be the first derivative of -f**5/5 - 10*f**4/3 - 8*f**3 + 144*f**2 - 99*f + 181. Let w(m) be the first derivative of r(m). Factor w(v).
-4*(v - 2)*(v + 6)**2
Let a(s) = -3*s + 158. Let z be a(52). Suppose -z*x + 22 = 18. Factor 2/3 - 1/6*n**3 + 2/3*n - 1/6*n**x.
-(n - 2)*(n + 1)*(n + 2)/6
Let x(t) = -101 + 6*t**3 - 79*t**2 - 2*t**3 + 27 + 111*t + 83*t. Let y(q) = 25*q**3 - 475*q**2 + 1165*q - 445. Let w(k) = 35*x(k) - 6*y(k). Factor w(p).
-5*(p - 4)**2*(2*p - 1)
Determine m so that 4/13*m - 6/13*m**4 + 0 + 6/13*m**2 - 2/13*m**3 - 2/13*m**5 = 0.
-2, -1, 0, 1
Let n = 27139/253 - 1911/23. Factor 164/11*b - 24/11 - n*b**2 - 49/11*b**3.
-(b + 6)*(7*b - 2)**2/11
Let x(j) be the second derivative of j**6/70 - 9*j**5/20 + 25*j**4/14 + 36*j**3/7 + 88*j - 2. Factor x(q).
3*q*(q - 18)*(q - 4)*(q + 1)/7
Let o(i) be the first derivative of 1/20*i**5 + 0*i**3 + 25/2*i**2 - 42 - 3/8*i**4 + 0*i. Let p(g) be the second derivative of o(g). Factor p(x).
3*x*(x - 3)
Let k be 1822/15487 - 77/(-68). Suppose -190 - 275*m - 65/4*m**3 + k*m**4 - 255/2*m**2 = 0. Calculate m.
-2, 19
Let p(k) be the first derivative of -3*k**4/4 + k**3 + 12*k**2 - 36*k - 4151. Determine v, given that p(v) = 0.
-3, 2
Let x(c) = 35*c**5 + 45*c**4 - 165*c**3 + 215*c**2 + 240*c. Let b(h) = -h**5 - h**4 + h**3 - 5*h**2 - h. Let u(f) = 30*b(f) + x(f). Let u(q) = 0. Calculate q.
-7, -1, 0, 2, 3
Let s = 15081/10 + -1508. Let c(i) be the third derivative of 8*i**2 + s*i**3 + 1/8*i**4 + 0*i + 0 + 2/25*i**5 + 1/50*i**6. Factor c(r).
3*(r + 1)*(2*r + 1)**2/5
Let p(k) = -k**2 - 23*k - 118. Let m be p(-8). Determine y so that -32 + m*y**4 + 32 - 4*y**3 = 0.
0, 2
Let w(x) = -2*x**3 + 46*x**2 + 155*x + 31. Let i be w(26). Let m(z) be the second derivative of z**4 - 1/5*z**i - 28*z + 0*z**3 + 0 + 0*z**2. Factor m(r).
-4*r**2*(r - 3)
Factor 106*o**3 + 67*o**3 - 576 - 582*o**2 - 170*o**3 + 1155*o.
3*(o - 192)*(o - 1)**2
Suppose -8268/7*u**3 - 338/7*u**4 - 52434/7*u**2 - 2592/7 - 22896/7*u = 0. Calculate u.
-12, -3/13
Let g = 104 + -146. Let k = -40 - g. Factor 0*t**4 - 44*t**2 - k*t**3 + t**3 - t - 3*t**4 + 2*t**5 + 47*t**2.
t*(t - 1)**2*(t + 1)*(2*t - 1)
Let s = 253 + -264. Let m be (s - 72/(-9))/((-57)/2). Factor 0*j + m*j**2 + 6/19*j**4 + 0 + 2/19*j**5 + 6/19*j**3.
2*j**2*(j + 1)**3/19
Suppose -146*c**2 + 194*c**2 - 63 - c**4 - 137*c**3 - 80*c + 136*c**3 - 65 = 0. What is c?
-8, -1, 4
Let n(b) be the first derivative of -27/34*b**4 + 10*b - 16/17*b**2 - 19 - 24/17*b**3. Let i(q) be the first derivative of n(q). Solve i(u) = 0.
-4/9
Let a(c) = c**4 - c**3 + c**2 - 2*c + 1. Let t(h) = -10*h**4 - 246*h**3 + 2846*h**2 - 4920*h + 2330. Let d(x) = 6*a(x) + t(x). Factor d(k).
-4*(k - 8)*(k - 1)**2*(k + 73)
Let o(g) be the third derivative of -g**6/1020 + 58*g**5/255 - 3245*g**4/204 - 6962*g**3/51 + 3675*g**2 + 2. Factor o(n).
-2*(n - 59)**2*(n + 2)/17
Let l(b) = b**3 - b**2 - 1. Let j(g) = 22*g**2 - 79*g + 64. Let d(a) = -21*a**2 + 78*a - 63. Let m(c) = 5*d(c) + 6*j(c). Let x(f) = -3*l(f) + m(f). Factor x(s).
-3*(s - 6)*(s - 2)**2
Let d(f) be the third derivative of f**8/504 - 22*f**7/315 - 101*f**6/180 - 41*f**5/45 + 25*f**4/9 + 104*f**3/9 - 10*f**2 + 65*f. Find c such that d(c) = 0.
-2, -1, 1, 26
Suppose 33*n + 28*n = 74 + 170. Let v(f) be the first derivative of 1/12*f**6 + 0*f**2 + 0*f**3 + 0*f + 0*f**n - 21 + 1/10*f**5. Let v(a) = 0. What is a?
-1, 0
Find p, given that -75/4*p + 9/4*p**5 + 33/2*p**4 - 54*p**2 + 33/2*p**3 + 75/2 = 0.
-5, -10/3, -1, 1
Let o(c) = -99*c**2 + 10*c - 28. Let p be o(3). Let q = -301 - p. Find h such that 1533/4*h**3 + 1029/4*h**5 + 51/2*h**2 - 6 - 33*h + q*h**4 = 0.
-1, -2/7, 2/7
Let i(t) = -6*t - 36. Let v be i(-7). Suppose 7*p - v = 29. Factor 43*j**3 + 2 + 18*j - 31*j**3 - p - 27*j**2.
3*(j - 1)**2*(4*j - 1)
Let w(t) be the first derivative of -t**5/90 + 11*t**4/27 - 76*t**3/27 + 8*t**2 + 53*t + 199. Let o(h) be the first derivative of w(h). Factor o(z).
-2*(z - 18)*(z - 2)**2/9
Suppose l - 4 = 47. Let p = 103 - l. Suppose -33*q**4 - 21*q**2 + 52*q - p*q + 5*q**2 + 4*q**5 + 72*q**3 = 0. Calculate q.
0, 1/4, 4
Let g(p) be the first derivative of 4*p**7/21 + 2*p**6/3 + 4*p**5/5 + p**4/3 + 63*p - 83. Let x(r) be the first derivative of g(r). Solve x(c) = 0 for c.
-1, -1/2, 0
Let j(o) be the third derivative of -o**7/378 + 4*o**6/135 + o**5/54 + 50*o**3/3 + o**2 + 28. Let v(a) be the first derivative of j(a). Factor v(h).
-4*h*(h - 5)*(5*h + 1)/9
Suppose 0 = -90748*m + 90651*m. Factor 7/4*y + 1/8*y**2 + m.
y*(y + 14)/8
Let l