 given that 2*w**4 - 58*w**3 + 306*w**2 + 58*w - 308 = 0.
-1, 1, 7, 22
Factor f**3 - 169*f**2 - 341*f - 171.
(f - 171)*(f + 1)**2
Factor 2*b**3 + 8*b**2 - 70*b - 300.
2*(b - 6)*(b + 5)**2
Find w such that 3*w**3 - 561*w**2 + 25944*w + 26508 = 0.
-1, 94
Solve -3*l**5/2 - 12*l**4 - 18*l**3 + 48*l**2 + 96*l = 0 for l.
-4, -2, 0, 2
Factor -51*f**3/4 + 57*f**2/4 - 3*f/2.
-3*f*(f - 1)*(17*f - 2)/4
Suppose -6*d**3 - 2026*d**2 - 1346*d + 674 = 0. Calculate d.
-337, -1, 1/3
Solve 243*p**5 + 1809*p**4 + 4413*p**3 + 3891*p**2 + 1152*p + 108 = 0.
-3, -1, -2/9
Factor -z**3/3 + 181*z**2/3.
-z**2*(z - 181)/3
Let -5*u**5 - 35*u**4 - 55*u**3 - 25*u**2 = 0. What is u?
-5, -1, 0
Determine a, given that 15*a**5 + 159*a**4 - 6*a**3 - 924*a**2 + 360*a = 0.
-10, -3, 0, 2/5, 2
Solve 20*h**4 + 428*h**3 + 1608*h**2 + 1936*h + 544 = 0.
-17, -2, -2/5
Suppose 2*d**5/21 + 30*d**4/7 - 94*d**3/21 - 30*d**2/7 + 92*d/21 = 0. What is d?
-46, -1, 0, 1
Find a, given that 2*a**3/23 - 198*a**2/23 = 0.
0, 99
Let 3*o**4 + 69*o**3 + 546*o**2 + 1632*o + 1152 = 0. What is o?
-8, -6, -1
Solve -i**4 - 258*i**3 - 16897*i**2 - 33024*i - 16384 = 0.
-128, -1
Factor -1922*k**3/11 + 1798*k**2/11 + 122*k/11 + 2/11.
-2*(k - 1)*(31*k + 1)**2/11
Factor -d**2/6 + 143*d/6 - 47.
-(d - 141)*(d - 2)/6
Factor 8*o**2/9 + 6*o - 14/9.
2*(o + 7)*(4*o - 1)/9
Solve -4*d**3/3 + 116*d**2/3 - 260*d - 300 = 0 for d.
-1, 15
Factor -5*v**5 + 555*v**4 - 15675*v**3 + 15125*v**2.
-5*v**2*(v - 55)**2*(v - 1)
What is f in -28*f**4 + 36*f**3 + 48*f**2 - 16*f = 0?
-1, 0, 2/7, 2
Solve -4*o**3 + 16*o**2 + 4*o - 16 = 0.
-1, 1, 4
Suppose 49*u**3/6 + 574*u**2/3 - 334*u/3 + 16 = 0. Calculate u.
-24, 2/7
Determine i so that -2*i**2/21 - 8*i/7 - 22/21 = 0.
-11, -1
Factor 71*o**3 - 2*o**2 - 71*o + 2.
(o - 1)*(o + 1)*(71*o - 2)
Find t such that 3*t**2 + 18*t - 273 = 0.
-13, 7
Let -t**4/5 + 3*t**3 - 66*t**2/5 + 16*t = 0. Calculate t.
0, 2, 5, 8
Solve -2*o**3/13 + 88*o**2/13 = 0.
0, 44
Let t**3 + 82*t**2 - 340*t + 344 = 0. What is t?
-86, 2
Factor -m**5 - 168*m**4 - 9407*m**3 - 175448*m**2 + 9408*m + 175616.
-(m - 1)*(m + 1)*(m + 56)**3
Factor -s**5/5 - 17*s**4/5 - 69*s**3/5 - 23*s**2 - 86*s/5 - 24/5.
-(s + 1)**3*(s + 2)*(s + 12)/5
Determine a so that -3*a**2/4 + 475*a/2 + 317/4 = 0.
-1/3, 317
Factor 16*d**2 - 196*d + 48.
4*(d - 12)*(4*d - 1)
Factor -2*k**2 + 270*k - 792.
-2*(k - 132)*(k - 3)
Determine g so that -g**2 - 250*g + 251 = 0.
-251, 1
Find k such that 2*k**2 + 46*k + 84 = 0.
-21, -2
Factor -2*s**2/5 - 22*s/5 + 52/5.
-2*(s - 2)*(s + 13)/5
Factor -4*g**2/5 - 276*g/5 - 208.
-4*(g + 4)*(g + 65)/5
Factor -4*g**4 - 16*g**3 + 64*g + 64.
-4*(g - 2)*(g + 2)**3
Suppose -5*s**2 + 58280*s - 169827920 = 0. Calculate s.
5828
Factor -2*y**2/5 + 6*y/5 + 52.
-2*(y - 13)*(y + 10)/5
Determine j, given that -3*j**3 - 15*j**2 - 6*j + 24 = 0.
-4, -2, 1
Factor -l**4/4 - 23*l**3/2 - 429*l**2/4 + 575*l - 625.
-(l - 2)**2*(l + 25)**2/4
Factor 4*z**5/7 + 24*z**4/7 + 36*z**3/7 + 16*z**2/7.
4*z**2*(z + 1)**2*(z + 4)/7
Find i such that i**3 + 58*i**2 = 0.
-58, 0
What is s in 3*s**4 - 27*s**3 - 3*s**2 + 27*s = 0?
-1, 0, 1, 9
Determine j so that 242*j**2/3 + 3344*j + 34656 = 0.
-228/11
Solve 2*d**3/7 + 736*d**2/7 + 622*d + 3620/7 = 0 for d.
-362, -5, -1
Solve 2*f**4 - 20*f**3 - 50*f**2 + 20*f + 48 = 0 for f.
-2, -1, 1, 12
Let -k**3 - 1431*k**2 = 0. What is k?
-1431, 0
Find c, given that 16*c**2/3 - 44*c - 36 = 0.
-3/4, 9
Find d such that 2*d**5 + 18*d**4 - 2*d**3 - 122*d**2 + 168*d - 64 = 0.
-8, -4, 1
Factor -5*x**2 + 500*x - 12500.
-5*(x - 50)**2
Factor -34*u**3 - 169*u**2 + 209*u - 6.
-(u - 1)*(u + 6)*(34*u - 1)
Factor 2*a**2 - 4*a - 30.
2*(a - 5)*(a + 3)
Factor -o**3/2 + 15*o**2/2 + 143*o.
-o*(o - 26)*(o + 11)/2
Let -k**3/8 + 145*k**2/4 - 72*k = 0. Calculate k.
0, 2, 288
Factor 60*r**3 + 4388*r**2 + 580*r - 292.
4*(r + 73)*(3*r + 1)*(5*r - 1)
Determine n, given that n**3/2 - 5*n**2/2 - 3*n = 0.
-1, 0, 6
Factor 2*l**3 + 10*l**2 + 8*l.
2*l*(l + 1)*(l + 4)
Find q such that -5*q**2 - 5*q + 10 = 0.
-2, 1
Factor 3*u**2 + 21*u + 18.
3*(u + 1)*(u + 6)
Factor -5*k**3/2 + 164*k**2 + 66*k.
-k*(k - 66)*(5*k + 2)/2
Find j such that -j**2/2 + 52*j - 1352 = 0.
52
Find c, given that -5*c**3 - 15*c**2 + 320*c + 960 = 0.
-8, -3, 8
Factor 3*l**3 + 402*l**2 - 1647*l + 1242.
3*(l - 3)*(l - 1)*(l + 138)
Determine f, given that 2*f**5/17 + 8*f**4/17 - 8*f**3/17 - 4*f**2 - 90*f/17 - 36/17 = 0.
-3, -2, -1, 3
Determine y, given that -2*y**4 + 152*y**3 - 2568*y**2 - 12160*y - 12800 = 0.
-2, 40
What is u in 12*u**5/5 - 12*u**4 + 111*u**3/5 - 96*u**2/5 + 39*u/5 - 6/5 = 0?
1/2, 1, 2
Determine z so that -6*z**5/11 + 2*z**4/11 + 24*z**3/11 - 8*z**2/11 = 0.
-2, 0, 1/3, 2
Let d**5/5 + 31*d**4/5 + 177*d**3/5 + 209*d**2/5 - 178*d/5 - 48 = 0. Calculate d.
-24, -5, -2, -1, 1
Let -5*w**3 - 20*w**2 - 15*w = 0. Calculate w.
-3, -1, 0
Determine m so that m**2/10 + 699*m/10 - 70 = 0.
-700, 1
Factor 2*d**4/7 + 6*d**3/7 + 2*d**2/7 - 6*d/7 - 4/7.
2*(d - 1)*(d + 1)**2*(d + 2)/7
Solve -54*d**5 - 12636*d**4 - 726480*d**3 + 1486816*d**2 - 998752*d + 222784 = 0 for d.
-118, 2/3
Factor 3*x**2 + 225*x - 702.
3*(x - 3)*(x + 78)
What is s in s**3/5 + 58*s**2/5 + 156*s - 360 = 0?
-30, 2
Factor -2*f**2 - 24*f - 70.
-2*(f + 5)*(f + 7)
Suppose -h**3 - 759*h**2 - 144399*h - 143641 = 0. What is h?
-379, -1
Factor -2*q**2/3 + 2*q + 80/3.
-2*(q - 8)*(q + 5)/3
Let 4*h**3 - 80*h**2 + 68*h + 152 = 0. What is h?
-1, 2, 19
What is g in g**4 - 95*g**3 + 369*g**2 - 457*g + 182 = 0?
1, 2, 91
Determine v, given that -4*v**4 - 8*v**3 + 48*v**2 - 56*v + 20 = 0.
-5, 1
Solve -2*f**4/3 - 16*f**3/3 - 34*f**2/3 - 20*f/3 = 0 for f.
-5, -2, -1, 0
Factor -2*j**2/17 + 122*j/17 + 660/17.
-2*(j - 66)*(j + 5)/17
Determine d, given that 3*d**2 + 1824*d - 5499 = 0.
-611, 3
What is a in a**4/4 - 163*a**3/2 + 26569*a**2/4 = 0?
0, 163
Factor -g**4 + 35*g**3 - 34*g**2.
-g**2*(g - 34)*(g - 1)
Find v, given that 2*v**2 - 22*v + 36 = 0.
2, 9
Suppose 2*s**4/3 - 2*s**3 - 8*s**2/3 = 0. Calculate s.
-1, 0, 4
Let -4*a**5/7 - 8*a**4 - 208*a**3/7 - 32*a**2/7 + 128*a + 1024/7 = 0. What is a?
-8, -4, -2, 2
Factor 4*x**2/9 + 70*x/9 - 38/3.
2*(x + 19)*(2*x - 3)/9
Solve -3*i**2 - 84*i - 588 = 0 for i.
-14
Let 5*f**2 - 190*f - 840 = 0. Calculate f.
-4, 42
What is q in -2*q**2/5 + 16*q/5 - 32/5 = 0?
4
Factor -2*g**3/15 + 494*g**2/15 - 5950*g/3 - 6250.
-2*(g - 125)**2*(g + 3)/15
Factor p**4 - 41*p**3 + 440*p**2 - 400*p.
p*(p - 20)**2*(p - 1)
Factor -4*b**5 + 36*b**4 - 60*b**3 + 28*b**2.
-4*b**2*(b - 7)*(b - 1)**2
Factor 2*g**5 + 8*g**4 + 6*g**3.
2*g**3*(g + 1)*(g + 3)
Factor s**5/4 + s**4/2 - s**3/4 - s**2/2.
s**2*(s - 1)*(s + 1)*(s + 2)/4
Factor -2*w**5 + 18*w**4 + 122*w**3 + 238*w**2 + 192*w + 56.
-2*(w - 14)*(w + 1)**3*(w + 2)
Find l, given that -4*l**4 + 4460*l**3 + 4468*l**2 - 4460*l - 4464 = 0.
-1, 1, 1116
Factor 20*k**3 - 412*k**2 + 1192*k + 544.
4*(k - 17)*(k - 4)*(5*k + 2)
Determine x, given that x**5/3 - 4*x**4/3 - 17*x**3/3 + 32*x**2/3 + 124*x/3 + 80/3 = 0.
-2, -1, 4, 5
Let -3*d**5 + 1275*d**4 - 182712*d**3 + 9119040*d**2 - 41865600*d + 32928000 = 0. Calculate d.
1, 4, 140
Let -2*z**5 + 56*z**4 + 6*z**3 - 172*z**2 + 112*z = 0. What is z?
-2, 0, 1, 28
Determine k so that -k**3/3 - 9*k**2 - 50*k/3 = 0.
-25, -2, 0
Factor -2*j**2/7 - 40*j/7 + 6.
-2*(j - 1)*(j + 21)/7
Suppose 2*n**4/7 + 356*n**3/7 + 16194*n**2/7 + 31328*n/7 + 15488/7 = 0. Calculate n.
-88, -1
Solve 3*s**3 - 21*s - 18 = 0 for s.
-2, -1, 3
Factor 3*b**3 + 27*b**2 + 72*b + 60.
3*(b + 2)**2*(b + 5)
Factor 4*z**2 - 448*z + 12544.
4*(z - 56)**2
What is m in -2*m**3/11 - 42*m**2/11 + 4*m = 0?
-22, 0, 1
Factor p**3 + 27*p**2 + 26*p.
p*(p + 1)*(p + 26)
Solve 292*g**3/5 - 3508*g**2/5 - 3748*g/5 + 52/5 = 0.
-1, 1/73, 13
Factor -p**3/4 - 9*p**2/4 + p/4 + 9/4.
-(p - 1)*(p + 1)*(p + 9)/4
Factor -2*a**3 + 78*a**2 - 864*a + 1944.
-2*(a - 18)**2*(a - 3)
Factor -j**2/2 - 19*j - 36.
-(j + 2)*(j + 36)/2
Let 4*t**2/5 - 152*t/5 - 172 = 0. Calculate t.
-5, 43
Factor -4*g**3/9 + 40*g**2/3 - 68*g - 4624/9.
-4*(g - 17)**2*(g + 4)/9
Let 2*d**2/13 + 20*d/13 - 238/13 = 0. Calculate d.
-17, 7
Factor -2*y**2/5 + 14*y.
-2*y*(y - 35)/5
Factor -5*t**4 + 25*t**3 + 30*t**2.
-5*t**2*(t - 6)*(t + 1)
Factor -2*z**4/7 + 6*z**3 + 138*z**2/7 + 142*z/7 + 48/7.
-2*(z - 24)*(z + 1)**3/7
Factor 2*b**4/9 + 574*b**3/9 + 41470*b**2