 6. Let t be 8/(-60) + (-352)/60. Let d(g) = 17*g**3 + 61*g**2 + 227*g - 11. Let u(m) = t*d(m) - 11*y(m). Factor u(p).
-3*p*(p + 6)**2
Let -96*a**2 - 752*a**4 + 18*a - 358*a**3 + 548*a**4 - 21*a**5 - 11*a**5 = 0. Calculate a.
-3, -1/2, 0, 1/8
Let v be (-6 + 0)/2 - (-102 - -106) - -10. Let r(s) be the second derivative of 0 + 2/5*s**2 + 7/12*s**4 - 11*s + 4/5*s**v. Factor r(a).
(5*a + 2)*(7*a + 2)/5
Let j(b) be the first derivative of b**5/15 - b**4/2 + 4*b**3/9 + b**2 - 5*b/3 - 3644. Suppose j(m) = 0. What is m?
-1, 1, 5
Suppose 4*k - 18 = -5*u + 18, k = 2*u - 4. Let h(l) = -l + 6. Let c be h(k). Find a such that 10*a**4 - 2*a**4 + 418*a**3 - 436*a**3 + 4*a**c = 0.
0, 1/4, 2
Let z = -3289 - -3293. Let q(v) be the third derivative of 0 + 6*v**z - 8/3*v**3 + 0*v - 27/5*v**5 - 16*v**2. Solve q(r) = 0 for r.
2/9
Let g(a) be the first derivative of -2*a**5/5 + 39*a**4/2 - 716*a**3/3 - 480*a**2 + 1600*a + 1075. Factor g(z).
-2*(z - 20)**2*(z - 1)*(z + 2)
Suppose 0 = 67*w - 58*w - 225. Suppose -2*n - g + 5 = -6, 0 = 5*g - w. What is t in -4/3*t + 4/3*t**n + 0 - 10/3*t**4 + 10/3*t**2 = 0?
-1, 0, 2/5, 1
Let o(u) = -4*u - 2. Let l be o(-1). Let i(p) be the third derivative of 1/30*p**5 + 0*p + 1/150*p**6 + 1/30*p**4 + 0*p**3 + 0 + 13*p**l. Factor i(h).
2*h*(h + 2)*(2*h + 1)/5
Let g = 13956140/7 - 1993734. Solve -256/7*v + 8192/7 + g*v**2 = 0 for v.
64
Let n(i) be the second derivative of i**6/30 - 3*i**5/10 - 7*i**4/4 + 73*i**3/3 - 60*i**2 - 3278*i + 1. Let n(x) = 0. What is x?
-5, 1, 4, 6
Let j be 2*(-13717)/(-66) + 4/(-6). Let p = 831/2 - j. What is c in p*c + 3 - 1/2*c**2 = 0?
-2, 3
Let b be (-4767)/(-220) + 88/484. Let l = b + -211/10. Factor 0 + h**2 - 1/4*h**3 - l*h.
-h*(h - 3)*(h - 1)/4
Let k(p) be the second derivative of -1/40*p**5 + 1/48*p**4 - 32 + 1/336*p**7 + 1/16*p**3 - 1/8*p**2 - 2*p + 0*p**6. What is m in k(m) = 0?
-2, -1, 1
Let q(t) = t**2 + 4. Let o(x) = 2*x**2 - 84*x - 84. Let v be o(43). Let d(n) = 4*n**2 - n + 20. Let p(h) = v*d(h) - 10*q(h). Determine u so that p(u) = 0.
-1, 0
Let w(b) be the second derivative of 2*b**6/45 - 3*b**5/20 - 5*b**4/18 + b**3/6 + 2*b - 382. Factor w(p).
p*(p - 3)*(p + 1)*(4*p - 1)/3
Let y(r) = 26*r - 232. Let h be y(9). Suppose 105 = -3*c + 330. Factor 40 - c + 34 + o**h.
(o - 1)*(o + 1)
Let h(a) be the first derivative of -2*a**6/21 + 8*a**5/35 + 36*a**4/7 + 352*a**3/21 + 128*a**2/7 - 211. Let h(y) = 0. What is y?
-2, 0, 8
Let z(n) = 173*n**2 - 344*n**2 + n + 2*n**3 + 170*n**2. Let p(c) = -29*c**3 - 128*c**2 - 106*c + 24. Let d(m) = -p(m) + 2*z(m). Factor d(q).
3*(q + 2)**2*(11*q - 2)
Let b(u) be the third derivative of 31*u**6/300 + 41*u**5/50 + 89*u**4/60 - u**3/5 + 115*u**2 + 5*u. Let b(c) = 0. What is c?
-3, -1, 1/31
Determine l, given that -30 + 34*l**3 + 300*l**2 + 273*l**3 + 30 + 78*l**3 - 5*l**5 + 80*l**4 = 0.
-3, -1, 0, 20
Let 87/4 - 173/8*j - 1/8*j**2 = 0. Calculate j.
-174, 1
Suppose -32*d = -29*d - 6. Let x(r) be the third derivative of 0 - 1/45*r**5 + 16*r**d + 0*r + 0*r**4 + 1/315*r**7 + 1/9*r**3 + 0*r**6. Factor x(b).
2*(b - 1)**2*(b + 1)**2/3
Let b = -136 - -138. Solve -2 - 3*n**b - 6*n + 0*n - 7*n**2 + 6*n**2 = 0 for n.
-1, -1/2
Let i be ((-6)/8)/((-6*(-16)/(-384))/((-304)/(-36))). Factor i*z - 74/3 - 2/3*z**2.
-2*(z - 37)*(z - 1)/3
Let k(g) be the second derivative of 1/30*g**6 + 0*g**2 - 1/252*g**7 + 37*g + 0 - 1/12*g**3 + 5/36*g**4 - 1/10*g**5. Factor k(j).
-j*(j - 3)*(j - 1)**3/6
Let z(d) = 0 + 6 - 10 - 2*d - 15 - 5*d. Let v be z(-3). Factor 1/5*l**v - 1/5 + 0*l.
(l - 1)*(l + 1)/5
Let g be -5 + ((-45)/5)/(3/(-5)). Suppose 5*k = -s + 18, 0 = -9*k + g*k - 4*s + 9. Factor 1/3*u + 0 + 1/2*u**2 + 1/6*u**k.
u*(u + 1)*(u + 2)/6
Let n(u) = -u**2 - 6323*u - 9884691. Let t(d) = d**2 + 6316*d + 9884700. Let k(h) = -4*n(h) - 5*t(h). Solve k(m) = 0.
-3144
Suppose 0 = k - 2*r, -5*r - 6 + 5 = -3*k. Let f be (-1)/(-4)*25*104/1105. Factor -f + 2/17*l**k + 8/17*l.
2*(l - 1)*(l + 5)/17
Let h be 2 + 8/(-6) + 20/15. Suppose h*j = 11*j - 54. Factor 7*w + j*w + 9*w**2 + 3*w**3 - 13*w.
3*w**2*(w + 3)
Let j = 1921114 + -9605558/5. Factor -14/3*p**3 - 32/15*p**4 + 0 - j*p**2 + 2/15*p**5 + 0*p.
2*p**2*(p - 18)*(p + 1)**2/15
Solve -17108 + 46*y**2 + 17148 + 85*y - 3*y**2 + 23*y**2 + 5*y**3 - 16*y**2 = 0 for y.
-8, -1
Let c = 37783560323/4460 + -16943291/2. Let o = c + 3/892. Suppose 9/5*n**5 - 36/5*n - 6*n**2 + 81/5*n**3 + o - 48/5*n**4 = 0. Calculate n.
-2/3, 1, 2
Let m(i) be the third derivative of i**5/150 - 41*i**4/30 - 17*i**3 - i**2 - 1470*i. Factor m(g).
2*(g - 85)*(g + 3)/5
Find o, given that -8/9*o**3 - 2/3*o**5 + 0 + 32/3*o - 152/9*o**2 + 34/9*o**4 = 0.
-2, 0, 2/3, 3, 4
Let y be -26 - 15/((-765)/1326). Factor -84/5*f + 4/5*f**2 + y.
4*f*(f - 21)/5
Determine l, given that -444*l - 38*l**2 - 41*l**2 + 168*l**2 - 42*l**2 - 43*l**2 - 448 = 0.
-1, 112
Let m be ((-7)/((-14)/4))/13. Let t = 30727 - 30725. Factor -m*a**t - 4/13*a - 2/13.
-2*(a + 1)**2/13
Let u = 18436 - 1788308/97. Let y = u + 436/291. Determine k so that 1/3*k**3 + 0 + y*k**2 + 4/3*k = 0.
-2, 0
Let 12*g + 1425*g**2 - 719*g**2 - 705*g**2 = 0. What is g?
-12, 0
Let i(v) = 2*v**2 - 5. Let a(c) = -8*c**2 + 272*c - 9233. Let h(n) = a(n) + 3*i(n). Factor h(x).
-2*(x - 68)**2
Factor -7*l**4 + 88123 - 76*l**3 + 27968*l - 49184 + 708*l**2 + 8*l**4 + 96485.
(l - 46)**2*(l + 8)**2
Let l(f) be the first derivative of f**4/54 - f**3/27 - 16*f + 106. Let n(z) be the first derivative of l(z). Factor n(w).
2*w*(w - 1)/9
Let f be (-748)/(-391) - (-4)/46. Factor 30*q + 25 - 185*q**2 + 96*q**f + 119*q**2 + 55*q.
5*(2*q + 5)*(3*q + 1)
Let r(x) = 4*x**4 + 73*x**3 + 123*x**2 + 9*x + 9. Let i(y) = -y**4 - 20*y**3 - 31*y**2 - 2*y - 2. Let m(h) = -18*i(h) - 4*r(h). Suppose m(b) = 0. Calculate b.
-33, -1, 0
Let h be 10*(247/(-19) + (-324)/(-24)). Solve -16/9*o**2 - 2/3*o**h - 56/9*o**4 - 22/3*o**3 + 0 + 0*o = 0 for o.
-8, -1, -1/3, 0
Let o(l) = -l**3 + 8*l**2 + 2*l - 58. Let q be o(7). Determine y so that 6*y**4 + 13 - 21*y**3 - 8*y**2 + 56*y - q*y**3 + 55 - 36 = 0.
-1, -2/3, 2, 4
Suppose -43 = -6*t + 5. Let h be 12/(-2)*(3 + -2) + t. Factor 8/5*k + 12/5*k**h + 2/5*k**4 + 8/5*k**3 + 2/5.
2*(k + 1)**4/5
Suppose 0 = -3*g - 2*f + 2, -3*f - 23 = g - 19. Let j(v) be the first derivative of -9 + 5/3*v**3 - 5*v**g - 15*v. Suppose j(m) = 0. What is m?
-1, 3
Let l(b) be the third derivative of -7*b**6/240 + 493*b**5/40 - 473*b**4/12 + 35*b**3 - 1097*b**2. Factor l(q).
-(q - 210)*(q - 1)*(7*q - 2)/2
Let k(z) be the first derivative of -2*z**3/15 - z**2 + 60*z + 2225. Factor k(r).
-2*(r - 10)*(r + 15)/5
Let a(p) be the third derivative of p**4 - 98*p**2 + 0 - 1/15*p**5 + 0*p - 6*p**3. Factor a(o).
-4*(o - 3)**2
Let b be (-18)/(15 - -39) - (23/46 + 755/(-42)). Factor -122/7 + b*t + 2/7*t**2.
2*(t - 1)*(t + 61)/7
Suppose 5*p + 134 - 140 = -2*a, 0 = a + p - 3. Factor 1/2*t**4 - 28*t - 3/2*t**2 - 24 + a*t**3.
(t - 3)*(t + 1)*(t + 4)**2/2
Let h be 318/4 - 32/368*23. Factor 0*f - 425/2*f**4 + h*f**3 + 0 - 15/2*f**2 + 125/2*f**5.
5*f**2*(f - 3)*(5*f - 1)**2/2
Let c(b) = -81*b + 506. Let s be c(-21). Suppose 16*u**2 + s - 2207 - 4*u**4 = 0. Calculate u.
-2, 0, 2
Let i be (1482/39 + -38)/(-1). Let z = 7 + -5. Let 2/7*n**z + 6/7*n + i = 0. Calculate n.
-3, 0
Let j(x) be the second derivative of x**7/126 + 7*x**6/90 + x**5/4 + x**4/4 - 912*x. Factor j(c).
c**2*(c + 1)*(c + 3)**2/3
Suppose -1718 = -882*u + 23*u. Find a, given that -2/3*a**u - 20/3*a - 50/3 = 0.
-5
Let l(j) = -85*j**2 - 117*j - 3494. Let u(b) = 33*b**2 + 47*b + 1397. Let y(d) = -7*l(d) - 18*u(d). Suppose y(k) = 0. What is k?
-16, 43
Let b(s) = 2*s**3 + 3*s**2 - 5. Let g be b(-3). Let i be (-494)/(-8) + -5*(-8)/g. Find m, given that -1/2*m**2 + 11*m - i = 0.
11
Let t be ((-240)/136 - -2) + 2916/612. Factor -16/23*h**2 + 6/23*h + 0*h**4 - 2/23*h**t + 12/23*h**3 + 0.
-2*h*(h - 1)**3*(h + 3)/23
Suppose 4*v + 5*c - 12 = 0, 0*v - 3*v - 3*c = -6. Let s = 2 - v. Find a such that 6 - a + 12*a**2 - 17*a**2 - 4*a + s = 0.
-2, 1
Let v = -43454 + 43458. Determine h so that -1/2*h**v + 0*h + 0 + 0*h**2 + 7/2*h**3 = 0.
0, 7
Suppose 204*i = 199*i - 3*t + 37, 0 = 4*i + 4*t - 36. Find c such that 12*c - 30*c**2 + 51/2*c**4 - 15/2*c**i - 9*c**3 + 0 = 0.
-1, 0, 2/5, 2
Let r = 584/7 - 82. Suppose 652 = 314344*a - 314018*a. Factor r*g - 6/