Determine c, given that 3*c**4/4 + 39*c**3/4 + 36*c**2 + 27*c = 0.
-6, -1, 0
Factor -2*k**4 - 182*k**3 - 6150*k**2 - 91250*k - 500000.
-2*(k + 16)*(k + 25)**3
Factor 10*m**2/7 + 33*m/7 + 26/7.
(m + 2)*(10*m + 13)/7
Find n, given that -n**3/2 + 150*n**2 - 22197*n/2 - 22801 = 0.
-2, 151
Determine f so that -36*f**4 + 13788*f**3 + 16*f**2 - 6128*f = 0.
-2/3, 0, 2/3, 383
Let -3*k**5/8 - 25*k**4/8 - 45*k**3/8 - 15*k**2/8 + 5*k/2 + 3/2 = 0. Calculate k.
-6, -1, 2/3
Factor 3*z**4 - 3051*z**3 + 774189*z**2 + 777243*z.
3*z*(z - 509)**2*(z + 1)
Factor 2*o**3 - 102*o**2 - 324*o.
2*o*(o - 54)*(o + 3)
What is d in -d**2 + 51*d = 0?
0, 51
Factor 2*j**4/19 - 4*j**3/19 - 238*j**2/19 + 1176*j/19.
2*j*(j - 7)**2*(j + 12)/19
Find i such that -i**3/3 + 8*i**2/3 + 19*i/3 + 10/3 = 0.
-1, 10
Solve -5*v**5 - 945*v**4 - 54960*v**3 - 978980*v**2 - 5766240*v - 4841280 = 0.
-82, -12, -1
Factor 22*b**2/5 - 94*b/5 + 24/5.
2*(b - 4)*(11*b - 3)/5
Factor y**3/3 + 184*y**2/3 + 9877*y/3 + 41334.
(y + 18)*(y + 83)**2/3
Factor 4*g**2/5 - 252*g/5 + 248/5.
4*(g - 62)*(g - 1)/5
Factor 2*m**2 - 6688*m + 5591168.
2*(m - 1672)**2
Factor -j**2 + 166*j - 6889.
-(j - 83)**2
Factor b**2/2 + 43*b + 85/2.
(b + 1)*(b + 85)/2
Factor 8*k**2/11 + 1822*k/11 - 456/11.
2*(k + 228)*(4*k - 1)/11
Factor -q**3/2 + 12*q**2 + 62*q - 168.
-(q - 28)*(q - 2)*(q + 6)/2
What is y in 5*y**3 + 190*y**2 - 395*y + 200 = 0?
-40, 1
Find m, given that -2*m**3/11 + 26*m**2/11 - 24*m/11 = 0.
0, 1, 12
Find t such that t**2/3 - 10*t/3 - 704/3 = 0.
-22, 32
Let -21*u**2 + 234*u - 33 = 0. What is u?
1/7, 11
Suppose -2*g**2/3 + 514*g/3 - 512/3 = 0. What is g?
1, 256
Find a such that -4*a**3 + 80*a**2 + 932*a - 1008 = 0.
-9, 1, 28
Suppose d**5/5 - 11*d**4/5 + 26*d**3/5 + 26*d**2/5 - 15*d - 63/5 = 0. Calculate d.
-1, 3, 7
Factor 2*g**2/5 - 396*g/5 + 394/5.
2*(g - 197)*(g - 1)/5
Factor 2*t**2/5 + 44*t + 1210.
2*(t + 55)**2/5
Factor l**3/7 + 125*l**2/7 + 604*l/7 + 480/7.
(l + 1)*(l + 4)*(l + 120)/7
Factor 4*w**3/3 - 28876*w**2/3 + 17376132*w - 17366508.
4*(w - 3609)**2*(w - 1)/3
Suppose -j**4 - 39*j**3 - 140*j**2 = 0. Calculate j.
-35, -4, 0
Suppose -2*k**2 + 84*k - 882 = 0. What is k?
21
Find s such that 2*s**5/9 - 4*s**4/9 - 112*s**3/3 - 512*s**2/9 + 7168*s/9 = 0.
-8, 0, 4, 14
Factor o**5/2 + 7*o**4/2 - 3*o**3/2 - 23*o**2/2 - 7*o.
o*(o - 2)*(o + 1)**2*(o + 7)/2
Let 3*r**4 + 15*r**3 - 393*r**2 - 1971*r + 5346 = 0. What is r?
-9, 2, 11
Factor -c**2/3 + 26*c/3 + 9.
-(c - 27)*(c + 1)/3
Factor k**4/4 + 15*k**3/4 + 7*k**2/2.
k**2*(k + 1)*(k + 14)/4
Suppose -c**5/6 + c**4/6 + c**3/6 - c**2/6 = 0. What is c?
-1, 0, 1
Factor -q**4/3 - 59*q**3/3 + q**2/3 + 59*q/3.
-q*(q - 1)*(q + 1)*(q + 59)/3
Determine k so that 3*k**5/2 - 51*k**4 + 639*k**3/2 + 1938*k**2 + 2166*k = 0.
-2, 0, 19
Suppose -2*o**5 + 96*o**4 - 1176*o**3 + 2972*o**2 - 2790*o + 900 = 0. What is o?
1, 15, 30
Solve -324*u**4 - 615456*u**3 - 292136416*u**2 + 129929600*u - 14440000 = 0.
-950, 2/9
Find k such that 5*k**5 - 10*k**4 - 5*k**3 + 10*k**2 = 0.
-1, 0, 1, 2
What is x in x**4/2 + 9*x**3 + 33*x**2/2 + 8*x = 0?
-16, -1, 0
Factor w**4/5 + 38*w**3/5 - 41*w**2/5 - 78*w/5.
w*(w - 2)*(w + 1)*(w + 39)/5
Find b such that 3*b**5 + 10*b**4 - 10*b**2 - 3*b = 0.
-3, -1, -1/3, 0, 1
Solve r**2 - 108*r + 107 = 0.
1, 107
Suppose v**2/2 - 438*v + 95922 = 0. Calculate v.
438
What is b in -5*b**5 + 85*b**4 + 1040*b**3 - 520*b**2 - 12720*b + 18000 = 0?
-6, 2, 25
Let -45*m**4 - 915*m**3 - 275*m**2 + 495*m - 100 = 0. Calculate m.
-20, -1, 1/3
Let -r**4/4 + 385*r**3/4 - 36861*r**2/4 - 38021*r/4 + 37249/2 = 0. Calculate r.
-2, 1, 193
Solve 5*h**2/2 - 85*h/2 - 95 = 0.
-2, 19
Factor -4*h**4 + 64*h**3 - 100*h**2 - 168*h.
-4*h*(h - 14)*(h - 3)*(h + 1)
Factor -b**4/6 + 43*b**3/3 + 178*b**2/3 + 60*b.
-b*(b - 90)*(b + 2)**2/6
Solve -5*o**5 + 70*o**4 - 125*o**3 + 60*o**2 = 0 for o.
0, 1, 12
Determine q, given that -3*q**4 + 69*q**3 - 1611*q**2/4 + 165*q + 2541 = 0.
-2, 11/2, 14
Solve 4*g**5 + 144*g**4 + 1908*g**3 + 11432*g**2 + 30720*g + 28800 = 0 for g.
-12, -5, -2
Determine v, given that -v**2/2 + 11*v/2 + 6 = 0.
-1, 12
Factor 3*h**4 - 54*h**3 + 111*h**2 + 1188*h + 1452.
3*(h - 11)**2*(h + 2)**2
Determine c so that 2*c**4/3 + 38*c**3 + 110*c**2/3 - 38*c - 112/3 = 0.
-56, -1, 1
Let 5*o**5 - 15*o**4 - 30*o**3 + 50*o**2 + 105*o + 45 = 0. What is o?
-1, 3
Let -p**3 - 12437*p**2 - 38663523*p + 38675961 = 0. What is p?
-6219, 1
Factor 2*y**3/11 + 14*y**2/11 - 98*y/11 - 10.
2*(y - 5)*(y + 1)*(y + 11)/11
Find b, given that 16*b**5 + 88*b**4 + 81*b**3 - 58*b**2 + 8*b = 0.
-4, -2, 0, 1/4
Find u, given that -35*u**5 + 815*u**4 + 1765*u**3 - 6835*u**2 + 5290*u - 1000 = 0.
-4, 2/7, 1, 25
Let 9*z**4/4 - 61*z**3/4 - 23*z**2/4 + 61*z/4 + 7/2 = 0. What is z?
-1, -2/9, 1, 7
Factor 2*d**2/13 - 392*d/13 + 19208/13.
2*(d - 98)**2/13
Determine f so that -1784286*f**3/13 - 489804*f**2/13 + 5656*f/13 - 16/13 = 0.
-2/7, 2/357
Solve 2*u**4/7 - 30*u**3/7 - 34*u**2/7 + 30*u/7 + 32/7 = 0.
-1, 1, 16
Factor 13*l**3/2 + 11*l**2/2 - 14*l + 2.
(l - 1)*(l + 2)*(13*l - 2)/2
Solve g**3/2 + 42*g**2 - 86*g = 0.
-86, 0, 2
Let 3*b**4 - 12*b**3 + 6*b**2 + 12*b - 9 = 0. What is b?
-1, 1, 3
Factor 2*c**2/3 + 56*c/3 - 192.
2*(c - 8)*(c + 36)/3
Solve 3*v**5/2 - 30*v**4 + 27*v**3/2 + 273*v**2 + 228*v = 0 for v.
-2, -1, 0, 4, 19
Find s such that -s**5 - 5*s**4 + 57*s**3 - 95*s**2 + 44*s = 0.
-11, 0, 1, 4
Factor -12*a**4/11 + 646*a**3/11 + 108*a**2/11.
-2*a**2*(a - 54)*(6*a + 1)/11
Factor 4*w**5 - 240*w**4 + 5484*w**3 - 58432*w**2 + 279552*w - 442368.
4*(w - 16)**3*(w - 9)*(w - 3)
Let g**2 + 4*g = 0. Calculate g.
-4, 0
Suppose -3*l**3 - 3*l**2 + 30*l - 24 = 0. Calculate l.
-4, 1, 2
Let l**5/4 - 15*l**4/4 + 63*l**3/4 - 81*l**2/4 = 0. Calculate l.
0, 3, 9
Find l, given that -2*l**5/3 + 116*l**4/3 - 760*l**3 + 15884*l**2/3 - 13718*l/3 = 0.
0, 1, 19
Factor o**5/6 + 4*o**4/3 + 7*o**3/2 + 7*o**2/3 - 10*o/3 - 4.
(o - 1)*(o + 2)**3*(o + 3)/6
Factor 34*c**4/5 + 1944*c**3 + 694122*c**2/5 - 81796*c/5.
2*c*(c + 143)**2*(17*c - 2)/5
Factor -4*m**5 + 124*m**4 - 120*m**3.
-4*m**3*(m - 30)*(m - 1)
Find p, given that -2*p**3/5 - 48*p**2/5 = 0.
-24, 0
Factor 2*f**2 + 32*f + 96.
2*(f + 4)*(f + 12)
Factor 5*o**4 - 1100*o**3 + 59390*o**2 + 122100*o + 61605.
5*(o - 111)**2*(o + 1)**2
Let -5*l**5 + 160*l**4 + 1080*l**3 + 2240*l**2 + 1520*l = 0. What is l?
-2, 0, 38
Factor -h**3 + 1980*h**2 - 1306800*h + 287496000.
-(h - 660)**3
Let 2*y**2/13 + 34*y/13 + 120/13 = 0. Calculate y.
-12, -5
Factor 3*f**4 + 33*f**3 - 54*f**2 - 216*f.
3*f*(f - 3)*(f + 2)*(f + 12)
Solve -2*p**2/9 - 68*p/9 - 578/9 = 0.
-17
Solve -1488*j**2 - 4954*j/5 + 4/5 = 0 for j.
-2/3, 1/1240
Factor 4*d**4 + 24*d**3 + 44*d**2 + 24*d.
4*d*(d + 1)*(d + 2)*(d + 3)
Let 10*f**3/3 - 14*f**2/3 + 4*f/3 = 0. Calculate f.
0, 2/5, 1
What is j in j**5/5 - 49*j**4/5 + 426*j**3/5 - 1458*j**2/5 + 2133*j/5 - 1053/5 = 0?
1, 3, 39
What is h in 2*h**3/13 - 16*h**2/13 + 10*h/13 + 28/13 = 0?
-1, 2, 7
Factor 4*f**4/5 + 16*f**3 + 556*f**2/5 + 1488*f/5 + 1008/5.
4*(f + 1)*(f + 6)**2*(f + 7)/5
Solve 5*l**2 + 138*l - 56 = 0.
-28, 2/5
What is i in 2*i**4 - 178*i**3 - 196*i**2 + 1416*i + 2160 = 0?
-2, 3, 90
Solve -15*s**5 - 50*s**4 - 15*s**3 + 60*s**2 + 20*s = 0.
-2, -1/3, 0, 1
Let -14*a**3 + 326*a**2 - 400*a + 88 = 0. Calculate a.
2/7, 1, 22
Determine x so that -5*x**3 - 885*x**2 + 3600*x - 3620 = 0.
-181, 2
What is d in d**5/5 + 23*d**4 - 237*d**3/5 - 351*d**2/5 = 0?
-117, -1, 0, 3
Suppose -5*w**3 - 55*w**2 + 370*w - 480 = 0. Calculate w.
-16, 2, 3
Suppose 3*f**2 + 84*f + 561 = 0. What is f?
-17, -11
Let 16*m**3/5 + 72*m**2 + 540*m + 1350 = 0. Calculate m.
-15/2
What is f in -2*f**2/9 + 26368*f/9 - 86908928/9 = 0?
6592
Factor -2*z**2/7 - 516*z/7 + 1040/7.
-2*(z - 2)*(z + 260)/7
Factor -4*i**2/5 + 48*i/5 - 128/5.
-4*(i - 8)*(i - 4)/5
Solve 2*x**2/3 - 26*x - 80/3 = 0 for x.
-1, 40
Factor 199*l**4 + 794*l**3 + 788*l**2 - 8*l.
l*(l + 2)**2*(199*l - 2)
Suppose 2*r**2 + 812*r + 82418 = 0. Calculate r.
-203
Determine t, given that -50*t**3 - 45*t**2 + 105*t - 10 = 0.
-2, 1/10, 1
Factor -f**2/2 - 97*f - 9409/2.
-(f + 97)**2/2
Suppose 9*q**5 + 186*q**4 + 748*q**3 - 2312*q**2 = 0. Calculate q.
-34/3, 0, 2
Find x such that -2*x**4/15 + 6*x**3/5 - 28*x**2/15 - 16*x/5 = 0.
-1, 0, 4, 6
Find r, given that 3*r**5/7 - 3*r**4/7 - 3*r**3/7 + 3*r**2/