*r**4/4 - 20*r**3 - 50*r**2 - 2272*r. Factor b(n).
-(n + 1)*(n + 10)**2
Suppose 211 = 4*o - o + 4*q, -4*o - q = -290. Suppose -53 + o*f**2 + 84*f + 16*f**3 + 17 - 3*f**4 - 142*f**2 + 8*f**3 = 0. What is f?
1, 2, 3
Suppose -355*s + 618*s = 333*s. Factor 0 - 2/23*v**4 - 30/23*v**2 + s*v + 32/23*v**3.
-2*v**2*(v - 15)*(v - 1)/23
Find d such that -1280*d**2 + 32*d**3 - 1/5*d**4 + 0*d + 0 = 0.
0, 80
Let n(m) be the second derivative of m**6/75 + 9*m**5/50 + 7*m**4/30 - 3*m**3 + 28*m**2/5 + 2*m + 1158. Factor n(j).
2*(j - 1)**2*(j + 4)*(j + 7)/5
Suppose 12*c - 256 = 17*c + v, -5*v = 4*c + 188. Let x be (-532)/(-1729) - 62/c. Suppose -1/4*b**3 + 8 - x*b**2 + 0*b = 0. What is b?
-4, 2
Let u be 2/8 + 0/(-2). Let l = 200653/4 - 50162. Suppose a + u*a**2 - l = 0. What is a?
-5, 1
Let j(y) = -14*y**3 + 113*y**2 + 3*y - 84. Let n be j(8). Find r, given that -3/2*r**2 + 6*r**5 - 6*r**3 + 0*r + 0 + 3/2*r**n = 0.
-1, -1/4, 0, 1
Factor -104 - 29/2*h - 1/2*h**2.
-(h + 13)*(h + 16)/2
Determine s so that 49*s**2 + 83*s**2 - 18*s**2 - 7*s**2 - 5*s**2 + 1734*s + 9826 + 2*s**3 = 0.
-17
Determine i, given that 112/5*i**4 - 24/5*i + 0 - 32/5*i**5 - 82/5*i**2 + 86/5*i**3 = 0.
-1, -1/4, 0, 3/4, 4
Let f(g) be the third derivative of g**8/840 - 2*g**7/525 - 7*g**6/100 + 7*g**5/75 + 32*g**4/15 + 32*g**3/5 - 1742*g**2 - 2. Let f(c) = 0. Calculate c.
-3, -2, -1, 4
Suppose 172*h = 156*h - 25840. Let t be 4/18 - (h/171 - -3). What is n in -50/3 - t*n - 2/3*n**2 = 0?
-5
Suppose -58*l + 1027 = -61*l - n, 4*n = -3*l - 1012. Let i = -1031/3 - l. Let 2/3*o - 1 + i*o**2 = 0. What is o?
-3, 1
Let x = 45064/9 - 5007. Let r(q) be the first derivative of 13 + x*q**3 - 1/2*q**2 + 0*q. Suppose r(w) = 0. What is w?
0, 3
Let x(u) = -4*u**5 + 52*u**4 + 108*u**3 - 4*u**2 - 104*u - 42. Let s(g) = g**5 + g**4 - g - 2. Let n(z) = -6*s(z) - x(z). Let n(c) = 0. What is c?
-27, -1, 1
Suppose 4 = -3*x - 4*u, -10*u = -9*u + 1. Suppose 4*m + 3*n - 888 = 0, -m + n + 265 = 43. What is j in 24*j**2 + x - m*j + 4*j**3 + 32 + 270*j = 0?
-2
Factor 56/13*n - 2/13*n**2 + 120/13.
-2*(n - 30)*(n + 2)/13
Let g(y) be the first derivative of -5*y**3/3 - 1590*y**2 + 2360. Factor g(n).
-5*n*(n + 636)
Determine p so that 882/5 - 1317/5*p + 441/5*p**3 - 9/5*p**2 + 3/5*p**4 = 0.
-147, -2, 1
Let v(a) be the second derivative of -361*a**6/10 + 5301*a**5/10 - 8269*a**4/4 - 930*a**3 - 150*a**2 - 780*a. Factor v(c).
-3*(c - 5)**2*(19*c + 2)**2
Let d(n) be the first derivative of -n**4/36 + 4*n**3/9 - 2*n**2 - 154*n + 79. Let k(u) be the first derivative of d(u). Suppose k(g) = 0. What is g?
2, 6
Let h(p) be the first derivative of 0*p**4 + 0*p**3 - 12 - 16*p**2 + 1/60*p**5 + 0*p. Let z(j) be the second derivative of h(j). Factor z(k).
k**2
Let p = 268 + -263. Determine g so that -21 - 874*g**4 + 343*g**p - 140*g + 385*g + 619*g - 2547*g**2 - 87 + 3325*g**3 - 939*g**4 = 0.
3/7, 2
Let p(k) = -5*k + 142. Let b be p(30). Let c be 0*((44/b - -4) + 1). Factor 15/4*u**4 + 5/4*u**5 + 15/4*u**3 + 0 + c*u + 5/4*u**2.
5*u**2*(u + 1)**3/4
Let o(c) = 7*c + 108. Let k be o(-12). Suppose 58 = k*h + 10. What is i in -18/13*i - 30/13*i**3 + 46/13*i**h + 2/13 = 0?
1/5, 1/3, 1
Let a = 2243/26964 + 1/6741. Let o(w) be the second derivative of a*w**3 + 0 + 11*w - 1/72*w**4 - 1/6*w**2. Factor o(d).
-(d - 2)*(d - 1)/6
Let u = 308218/5 + -61632. Find g, given that u*g**2 + 68/5*g - 2*g**5 - 9*g**3 - 24/5 - 47/5*g**4 = 0.
-2, 3/10, 1
Let -3*m**2 + 1470 + 8*m**2 + 8564773*m - 8564498*m = 0. Calculate m.
-49, -6
Let o be (-123)/(-60) - (-18)/(-8)*(-30)/(-54). Factor 12/5*z - o*z**3 + 8/5*z**2 + 0.
-4*z*(z - 3)*(z + 1)/5
What is m in 425*m - 159 + 224*m**2 - 269*m**2 + 7*m**3 + 909 - 52*m**3 - 5*m**4 = 0?
-5, -2, 3
Let h(r) be the second derivative of -4/15*r**3 - 1/210*r**7 + 0*r**2 + 1/30*r**4 - 3*r - 13 + 9/100*r**5 - 1/75*r**6. Find z such that h(z) = 0.
-4, -1, 0, 1, 2
Let n(t) be the first derivative of -949/9*t**3 + 67 - 5/3*t**5 - 196/3*t + 55/2*t**4 - 154*t**2. Factor n(u).
-(u - 7)**2*(5*u + 2)**2/3
Let 397*k**2 - 3*k**5 - 603*k**2 - 30*k**4 - 40*k**4 + 366*k**2 - 192*k**3 = 0. Calculate k.
-20, -4, 0, 2/3
Factor 1080*g**3 - 4160*g**2 - 3840 - 47*g**4 - 135*g**4 + 5*g**5 + 57*g**4 + 7040*g.
5*(g - 12)*(g - 4)**3*(g - 1)
Let t(w) be the second derivative of -w**6/15 - 37*w**5/10 - 70*w**4 - 1408*w**3/3 - 1024*w**2 + w - 194. Factor t(f).
-2*(f + 1)*(f + 4)*(f + 16)**2
Let -26*t**3 - 779 - 301 + 31*t**3 + 17*t**2 - 107*t**2 - 675*t = 0. Calculate t.
-3, 24
Solve 404/5*t**4 - 6*t**5 - 874/5*t**3 + 676/5*t**2 + 0 - 176/5*t = 0 for t.
0, 2/3, 4/5, 1, 11
Let y(l) be the third derivative of -l**6/24 + 7*l**5/6 - 65*l**4/24 + 250*l**2. Factor y(x).
-5*x*(x - 13)*(x - 1)
Let f = 1259 - 870. Let v = f - 387. Factor -10/3 + 0*d**v - 5/3*d**3 + 5*d.
-5*(d - 1)**2*(d + 2)/3
Let l(i) be the second derivative of 7*i**6/50 + 393*i**5/100 + 149*i**4/10 - 48*i**3/5 - 454*i. Determine r, given that l(r) = 0.
-16, -3, 0, 2/7
Suppose -27 - 1 = -4*s - 5*b, 4 = -2*s + 2*b. Suppose 4*h - 16 - 4*h**4 - 20*h**3 + 0*h**4 + 12*h - 11*h**2 + 31*h**s + 4*h**5 = 0. Calculate h.
-2, -1, 1, 2
Let c(m) = m**3 + 6*m**2 + 14*m + 30. Let w be c(-4). Suppose 0 = -b + 2, b - 10 = 4*v - w*v. Factor 3*a**2 + 1/6*a**v - 4/3*a**3 - 8/3*a + 5/6.
(a - 5)*(a - 1)**3/6
Suppose -87 = -5*i - 4*u - 76, 0 = i + 5*u + 2. Suppose 7/3 - 13/3*g + 5/3*g**2 + 1/3*g**i = 0. What is g?
-7, 1
Let p be (42/(-15) + 0)/((-72629)/(-944) - 77). Let -2/5*d**2 - p*d - 6272/5 = 0. What is d?
-56
Let m(p) be the second derivative of p**4/12 - p**3/2 - 54*p**2 + p - 974. Factor m(k).
(k - 12)*(k + 9)
Suppose -5*r - 9 = -3*h, 8*r - 6*r - 3*h + 9 = 0. Suppose r = -8*o + 7*o + 3. Determine l, given that 12*l**3 - 328*l**2 + 6*l + 3*l**3 + 0*l**o + 307*l**2 = 0.
0, 2/5, 1
What is g in 1/8*g**3 - 34 + 27/8*g**2 - 123/4*g = 0?
-34, -1, 8
Let -56*h**2 + 5800 + 95*h + 25*h**2 + 568*h + 36*h**2 - 33*h = 0. Calculate h.
-116, -10
Suppose 1218 + 1177 = -26*v + 3622 - 1149. Let 28/5*b**v + 44/5*b**4 - 8/5*b**5 + 0*b - 24/5*b**2 + 0 = 0. Calculate b.
-1, 0, 1/2, 6
Solve -148124*p + 7*p**4 - 14*p**3 - 16*p**2 + 148124*p - 10*p**4 = 0.
-8/3, -2, 0
Let k be (14/(-4))/1 + (-9)/18. Let d be (-1 + 15/(-9))/(k/6). Suppose c - 4*c - d + 0*c + c**2 = 0. Calculate c.
-1, 4
Suppose -2*b + 37 = 31. Suppose 2*l - l + b*q - 13 = 0, -q + 3 = 0. Factor -15*f**3 - 3*f**4 - 3*f**2 + 12*f**3 + 3*f + 6*f**l.
3*f*(f - 1)**2*(f + 1)
Let k = -386518 + 386522. Factor -54*d**2 + 78/7*d**3 - 6/7*d**k - 648/7 + 810/7*d.
-6*(d - 4)*(d - 3)**3/7
Suppose -915*m + 938 + 1064 = 172. Let 32/9*q - 286/9*q**m - 4*q**3 + 18*q**4 + 128/9 = 0. What is q?
-8/9, 1
Let z = -31699/1604 - -5/401. Let g = z - -403/20. Find t, given that -7/5*t - g*t**2 + 1/5*t**3 - 4/5 = 0.
-1, 4
Suppose -15*a - 5*o = -18*a + 26, 3*a - 3*o - 30 = 0. Solve -a*v**3 - 12*v**3 - 97*v**2 + 75*v**2 - 2*v**4 = 0.
-11, -1, 0
Suppose 39*x + 26*x = 2600. Let z(n) = -n + 42. Let y be z(x). Factor 0*h - 1/3*h**y + 1/3.
-(h - 1)*(h + 1)/3
Let p = 5229/9265 - -66/1853. Factor 6/5*u + p*u**2 - 9/5.
3*(u - 1)*(u + 3)/5
Let j(y) be the first derivative of -y**9/12096 - y**8/1680 + 4*y**3 - 66. Let q(v) be the third derivative of j(v). Factor q(t).
-t**4*(t + 4)/4
Factor 30*a + 18*a**2 - 13*a**3 - a**3 + 24*a**3 + 14*a**2 - 8*a**3.
2*a*(a + 1)*(a + 15)
Let w(d) be the second derivative of -3*d**5/40 + d**4/2 + 5*d**3/4 + 2*d + 182. Factor w(q).
-3*q*(q - 5)*(q + 1)/2
Let k be 1 - (-7)/(7/4) - 2. Factor 4*u**2 + 15*u**k + 5*u**4 + 180*u - 88*u - 29*u**2 - 5*u**5 - 82*u.
-5*u*(u - 1)**3*(u + 2)
Let r = -10 - -101. Let p = r + -91. Factor -j**5 + 0*j**5 + 20*j**3 - 4*j**2 + 4*j**4 - 14*j**3 - 5*j + p*j**5.
-j*(j - 5)*(j - 1)*(j + 1)**2
Let v = 403 - 421. Let c(w) = w**2 - 24*w + 9. Let x(f) = -2*f - 1. Let l(t) = v*x(t) - 2*c(t). Find h, given that l(h) = 0.
0, 42
Suppose 0 = 11*f - 959 - 8457. Determine r so that -16*r**4 - 243*r + 152*r**2 + f*r**2 - 87*r**4 - 4*r**5 - 664*r**3 + 1811*r - 5*r**4 = 0.
-14, -1, 0, 2
Let q = -28 - -44. Suppose 8*t + 11*t**3 + 2*t**3 - 4*t**2 + q - 15*t**3 = 0. What is t?
-2, 2
Let i(p) = 115*p**2 - 2395*p - 15. Let w(u) = -31*u**2 + 599*u + 4. Let y(r) = 4*i(r) + 15*w(r). What is g in y(g) = 0?
-119, 0
Suppose 2*w + 4*r = 54, 5*w - 83 = -0*r + 3*r. Suppose -21*f + w