*3
Suppose 2*p**2/5 - 18*p = 0. Calculate p.
0, 45
Factor -4*r**4/5 + 1072*r**3/5 - 91512*r**2/5 + 415152*r + 35391708/5.
-4*(r - 93)**3*(r + 11)/5
Suppose -3*f**2 - 3180*f - 842700 = 0. Calculate f.
-530
Factor 3*r**2 - 1128*r + 2244.
3*(r - 374)*(r - 2)
Solve 2*x**2/13 - 184*x/13 + 360/13 = 0.
2, 90
Factor -5*o**3/4 - 135*o**2/4 - 185*o/2 - 60.
-5*(o + 1)*(o + 2)*(o + 24)/4
Determine z, given that 2*z**2 - 390*z + 772 = 0.
2, 193
Suppose 32*c**5 - 112*c**4 + 8*c**3 + 396*c**2 - 540*c + 216 = 0. What is c?
-2, 1, 3/2
Let 3*i**2 + 15*i + 12 = 0. What is i?
-4, -1
Determine i, given that -3*i**4 + 51*i**3 - 33*i**2 - 231*i - 144 = 0.
-1, 3, 16
Solve -5*c**4/3 - 35*c**3/3 - 40*c**2/3 + 80*c/3 = 0.
-4, 0, 1
Factor -2*b**4 + 114*b**3 - 1566*b**2 - 1682*b.
-2*b*(b - 29)**2*(b + 1)
Suppose -4*f**5 + 72*f**4 - 132*f**3 + 64*f**2 = 0. Calculate f.
0, 1, 16
Factor h**3/3 - 86*h**2/3 + 785*h/3 - 1900/3.
(h - 76)*(h - 5)**2/3
Factor 2*m**3/11 + 96*m**2/11 + 360*m/11 - 21600/11.
2*(m - 12)*(m + 30)**2/11
Solve f**5/7 + 48*f**4/7 + 417*f**3/7 - 3734*f**2/7 + 1188*f - 5832/7 = 0.
-27, 2
Solve -3*z**4 - 238*z**3 + 172*z**2 + 952*z - 640 = 0 for z.
-80, -2, 2/3, 2
Factor 3*y**4 - 483*y**3 + 19680*y**2 - 19200*y.
3*y*(y - 80)**2*(y - 1)
Factor 7*f**3/4 - 95*f**2 + 5211*f/4 - 729/2.
(f - 27)**2*(7*f - 2)/4
Let -3*n**3 - 69*n**2 - 420*n - 588 = 0. What is n?
-14, -7, -2
Find d such that -d**4/7 - 26*d**3/7 - 184*d**2/7 - 42*d - 135/7 = 0.
-15, -9, -1
Solve -2*t**4 + 234*t**3/5 - 1002*t**2/5 - 4706*t/5 + 2028/5 = 0 for t.
-3, 2/5, 13
Factor 2*a**4 - 4*a**3 + 4*a - 2.
2*(a - 1)**3*(a + 1)
Factor s**5/4 + 23*s**4/2 + 529*s**3/4.
s**3*(s + 23)**2/4
What is n in 2*n**2/3 - 44*n - 134/3 = 0?
-1, 67
Factor 5*w**3 - 560*w**2.
5*w**2*(w - 112)
Suppose -3*k**2/4 + 162*k - 8748 = 0. What is k?
108
Factor -3*n**3 - 42*n**2 - 171*n - 216.
-3*(n + 3)**2*(n + 8)
Find t such that t**2/2 + 510*t + 1019/2 = 0.
-1019, -1
Factor -b**2 + 580*b.
-b*(b - 580)
What is a in 4*a**2 - 8*a - 32 = 0?
-2, 4
Factor 10*z**3/3 + 164*z**2/3 - 34*z.
2*z*(z + 17)*(5*z - 3)/3
Factor -6*r**3 - 663*r**2 + 333*r.
-3*r*(r + 111)*(2*r - 1)
Suppose -2*z**4 - 18*z**3 + 20*z**2 = 0. Calculate z.
-10, 0, 1
Determine z, given that 2*z**2/5 + 18*z/5 - 44/5 = 0.
-11, 2
Factor -2*w**4 - 4*w**3 + 24*w**2 + 36*w - 54.
-2*(w - 3)*(w - 1)*(w + 3)**2
Factor -y**3 + 32*y**2 + 33*y.
-y*(y - 33)*(y + 1)
Suppose 52*z**5 + 284*z**4 + 484*z**3 + 324*z**2 + 72*z = 0. What is z?
-3, -1, -6/13, 0
Factor -g**5/4 + 2*g**4 - 11*g**3/2 + 7*g**2 - 17*g/4 + 1.
-(g - 4)*(g - 1)**4/4
Factor -16*j**3 - 3084*j**2 - 5340*j + 1528.
-4*(j + 2)*(j + 191)*(4*j - 1)
Let 3*r**5 - 60*r**4 + 231*r**3 + 726*r**2 = 0. Calculate r.
-2, 0, 11
Factor -35*p**2 + 65*p + 10.
-5*(p - 2)*(7*p + 1)
Solve -2*j**4/3 + 86*j**3/3 - 82*j**2 + 242*j/3 - 80/3 = 0 for j.
1, 40
Factor -k**5/3 + 10*k**4/3 + 23*k**3/3 + 4*k**2.
-k**2*(k - 12)*(k + 1)**2/3
Solve -2*h**5/13 - 2*h**4 + 2*h**3/13 + 2*h**2 = 0 for h.
-13, -1, 0, 1
Factor 2*o**4/9 - 2*o**3 + 4*o**2/3 + 32*o/9.
2*o*(o - 8)*(o - 2)*(o + 1)/9
Suppose -3*y**4 + 42*y**3 - 156*y**2 - 72*y + 864 = 0. Calculate y.
-2, 4, 6
Determine d so that d**2/3 - 11*d/3 + 10/3 = 0.
1, 10
Factor 2*o**2/3 + 44*o/3 + 38.
2*(o + 3)*(o + 19)/3
Let -t**2 + 12222*t - 37344321 = 0. Calculate t.
6111
Factor -2*m**4/7 - 12*m**3/7 - 10*m**2/7.
-2*m**2*(m + 1)*(m + 5)/7
Factor j**3 + 43*j**2 + 159*j + 117.
(j + 1)*(j + 3)*(j + 39)
Let u**3/6 + 25*u**2/2 + 69*u = 0. What is u?
-69, -6, 0
Factor -2*b**2 - 22*b + 52.
-2*(b - 2)*(b + 13)
Find g, given that 3*g**4 + 66*g**3 - 141*g**2 + 72*g = 0.
-24, 0, 1
Find f such that -2*f**2/17 + 2/17 = 0.
-1, 1
Factor u**5/5 - 12*u**4/5 - 28*u**3/5 - 2*u**2/5 + 27*u/5 + 14/5.
(u - 14)*(u - 1)*(u + 1)**3/5
Factor -2*h**3/17 + 10*h**2 + 18*h/17 - 90.
-2*(h - 85)*(h - 3)*(h + 3)/17
What is y in 3*y**3 - 13*y**2 + 16*y - 4 = 0?
1/3, 2
Factor -2*s**3/3 - 274*s**2/3 - 8960*s/3 + 9800.
-2*(s - 3)*(s + 70)**2/3
Factor g**5 + 5*g**4 - 21*g**3 - 85*g**2 + 100*g.
g*(g - 4)*(g - 1)*(g + 5)**2
Solve -3*m**5 - 87*m**4 - 369*m**3 - 201*m**2 + 372*m + 288 = 0 for m.
-24, -4, -1, 1
Factor -q**4/4 + q**3/4 + q**2 - q.
-q*(q - 2)*(q - 1)*(q + 2)/4
What is c in c**5/6 - 11*c**4/2 + 16*c**3/3 = 0?
0, 1, 32
Factor 5*m**3 - 6120*m**2 + 1872720*m.
5*m*(m - 612)**2
Determine t so that -t**2/8 + 7*t/4 - 3 = 0.
2, 12
Find t such that -t**3/2 - 507*t**2 - 171366*t - 19307236 = 0.
-338
Factor -d**2 + 862*d.
-d*(d - 862)
Factor -z**2 + 11346*z - 32182929.
-(z - 5673)**2
Factor 4*a**4 + 32*a**3 + 72*a**2 + 64*a + 20.
4*(a + 1)**3*(a + 5)
Determine b, given that -5*b**3 - 360*b**2 - 2905*b - 4410 = 0.
-63, -7, -2
Solve -9*y**4/5 + 123*y**3/5 - 417*y**2/5 + 333*y/5 + 162/5 = 0 for y.
-1/3, 2, 3, 9
Factor 75*j**2 + 40*j + 5.
5*(3*j + 1)*(5*j + 1)
Factor -4*i**3 + 83*i**2 - 419*i - 110.
-(i - 11)*(i - 10)*(4*i + 1)
Find s such that -4*s**4/3 - 28*s**3/3 - 20*s**2/3 + 28*s/3 + 8 = 0.
-6, -1, 1
Solve 5*m**2 + 460*m + 10580 = 0 for m.
-46
Determine v so that -2*v**4/13 + 22*v**3/13 + 80*v**2/13 + 56*v/13 = 0.
-2, -1, 0, 14
Determine v, given that 2*v**3 + 50*v**2 - 2*v - 50 = 0.
-25, -1, 1
Let s**4 - 12*s**3 + 256*s = 0. Calculate s.
-4, 0, 8
Find w such that w**4/11 + 5*w**3/11 - 47*w**2/11 + 39*w/11 + 90/11 = 0.
-10, -1, 3
Solve 4*l**3 - 196*l**2 - 1284*l - 1980 = 0.
-3, 55
Solve -2*i**2 - 18*i - 16 = 0.
-8, -1
Factor -2*x**3/3 + 4*x**2/3 + 22*x/3 - 8.
-2*(x - 4)*(x - 1)*(x + 3)/3
Determine d, given that -d**2 + 475*d + 476 = 0.
-1, 476
Factor w**4/2 - 3*w**3 + 4*w**2.
w**2*(w - 4)*(w - 2)/2
Let l**2 - 94*l + 2208 = 0. What is l?
46, 48
What is h in -h**3/2 - 13*h**2/2 + h/2 + 13/2 = 0?
-13, -1, 1
Factor 2*g**4 + 186*g**3 + 4582*g**2 + 11430*g - 16200.
2*(g - 1)*(g + 4)*(g + 45)**2
Solve -3*s**3/7 + 27*s**2/7 - 60*s/7 + 36/7 = 0.
1, 2, 6
Factor 2*x**4 - 16*x**3 + 26*x**2 - 12*x.
2*x*(x - 6)*(x - 1)**2
What is k in 8*k**5 - 42*k**4 + 60*k**3 - 8*k**2 - 36*k + 18 = 0?
-3/4, 1, 3
Factor 66*n**3 + 3*n**2.
3*n**2*(22*n + 1)
Determine s so that -2*s**4 + 40*s**3 - 136*s**2 + 128*s = 0.
0, 2, 16
Let -2*a**3/7 - 5904*a**2/7 - 4357152*a/7 = 0. What is a?
-1476, 0
Solve 4*a**4/3 - 736*a**3/3 + 35260*a**2/3 - 42000*a - 54000 = 0 for a.
-1, 5, 90
Suppose 177*j**4 - 6*j**3 - 177*j**2 + 6*j = 0. What is j?
-1, 0, 2/59, 1
Let i**2/4 + 37*i + 1369 = 0. Calculate i.
-74
Determine k, given that -2*k**5 - 12*k**4 + 2*k**3 + 12*k**2 = 0.
-6, -1, 0, 1
Find c such that -4*c**5/13 + 10*c**4/13 + 22*c**3 + 140*c**2/13 = 0.
-7, -1/2, 0, 10
Factor 5*p**4 + 25*p**3 - 35*p**2 - 25*p + 30.
5*(p - 1)**2*(p + 1)*(p + 6)
Determine j so that 2*j**2/13 - 36*j/13 - 38/13 = 0.
-1, 19
Factor y**3 - 11*y**2 - 40*y - 28.
(y - 14)*(y + 1)*(y + 2)
Factor -2*k**2/15 - 4*k/15 + 2.
-2*(k - 3)*(k + 5)/15
Suppose -2*u**2/3 - 6*u - 40/3 = 0. What is u?
-5, -4
Determine y so that 82*y**2 + 562*y - 84 = 0.
-7, 6/41
Determine q so that -q**4/2 + 265*q**3/2 + 1071*q**2/2 + 1343*q/2 + 269 = 0.
-2, -1, 269
Suppose p**2/4 - 265*p/4 + 66 = 0. Calculate p.
1, 264
Let 5*h**2 + 1930*h + 9525 = 0. Calculate h.
-381, -5
Determine h, given that 3*h**3 + 6*h**2 + 3*h = 0.
-1, 0
Solve -2*d**3/3 - 184*d**2/3 - 1942*d/3 - 1760/3 = 0.
-80, -11, -1
Suppose -4*w**2/15 - 10*w/3 - 8/5 = 0. What is w?
-12, -1/2
Suppose -3*l**5/5 + 14*l**4/5 - l**3/5 - 26*l**2/5 - 8*l/5 = 0. Calculate l.
-1, -1/3, 0, 2, 4
Factor 3*b**3 + 13*b**2 - 11*b - 5.
(b - 1)*(b + 5)*(3*b + 1)
Factor 73167*s**4/4 - 189225*s**3/2 - 86652*s**2 - 24672*s - 2304.
3*(s - 6)*(29*s + 8)**3/4
Factor -5*i**2 + 70*i + 360.
-5*(i - 18)*(i + 4)
Solve -3*m**3 + 129*m**2 + 267*m + 135 = 0.
-1, 45
Suppose -10*k**5 - 35*k**4/2 - 15*k**3/4 + 5*k**2 + 5*k/4 = 0. What is k?
-1, -1/4, 0, 1/2
Factor -2*i**2/5 + 104*i - 518/5.
-2*(i - 259)*(i - 1)/5
Factor 2*w**4/13 - 4*w**3/13 - 2*w**2/13 + 4*w/13.
2*w*(w - 2)*(w - 1)*(w + 1)/13
Let -5*i**3/2 + 25*i**2 - 95*i/2 - 75 = 0. What is i?
-1, 5, 6
Find b such that 256*b**5 - 1344*b**4 + 304*b**3 + 84*b**2 - 20*b = 0.
-1/4, 0, 1/4, 5
Factor 1715*s**5 + 9800*s**4 + 18585*s**3 + 15860*s**2 + 6320*s + 960.
5*(s + 1)*(s + 3)*(7*s + 4)**3
Let 26*j**2 - 248*j - 120 = 0. What is j?
-6/13, 10
Factor 3*i**4 - 12*i**3 + 15*i**2 - 6*i.
3*i*(i - 2)*(i - 1)**2
Solve 4*x**4 - 24*x**3 - 92*x**2 + 240*x - 128 = 0.
-4, 1, 8