
0, 1, 46
Suppose -39*p**2 - 75*p - 36 = 0. What is p?
-1, -12/13
Factor 3*o**2 - 3834*o + 1224963.
3*(o - 639)**2
Factor 5*v**2 - 535*v - 1090.
5*(v - 109)*(v + 2)
Let v**4 + 932*v**3 + 218086*v**2 + 433380*v + 216225 = 0. What is v?
-465, -1
Let v**2/4 - 33*v/2 + 1089/4 = 0. Calculate v.
33
Suppose -3*y**2 + 456*y = 0. What is y?
0, 152
Let -5*i**2/4 - 375*i/4 = 0. Calculate i.
-75, 0
Determine p so that 147*p**4 - 2667*p**3 - 2358*p**2 - 4764*p/7 - 456/7 = 0.
-2/7, 19
Factor -k**3/2 - 7*k**2/4 - k/2 + 3/4.
-(k + 1)*(k + 3)*(2*k - 1)/4
Find t such that -t**3/5 + 79*t**2/10 + 4*t = 0.
-1/2, 0, 40
Suppose 2*i**4 - 12*i**3 - 18*i**2 + 188*i - 240 = 0. Calculate i.
-4, 2, 3, 5
Factor 2*i**2/23 - 90*i/23 + 88/23.
2*(i - 44)*(i - 1)/23
Factor -2*o**5/9 - 128*o**4/9 - 724*o**3/3 - 3968*o**2/9 - 1922*o/9.
-2*o*(o + 1)**2*(o + 31)**2/9
Factor -l**5/2 + 10*l**4 - 66*l**3 + 160*l**2 - 128*l.
-l*(l - 8)**2*(l - 2)**2/2
What is u in -2*u**3/13 + 14*u/13 + 12/13 = 0?
-2, -1, 3
Factor 58*v**2/5 + 7072*v/5 - 488/5.
2*(v + 122)*(29*v - 2)/5
Factor -2*j**3/5 + 54*j**2/5 - 192*j/5 - 512.
-2*(j - 16)**2*(j + 5)/5
Factor 2*w**2/5 + 366*w/5 + 364/5.
2*(w + 1)*(w + 182)/5
Factor s**3/6 - 77*s**2/2 + 5929*s/2 - 456533/6.
(s - 77)**3/6
Solve 2*d**2/3 - 2*d = 0 for d.
0, 3
Solve -18*c**3 + 26844*c**2 - 35768*c + 11920 = 0 for c.
2/3, 1490
Factor 3*w**3 - 9*w + 6.
3*(w - 1)**2*(w + 2)
Find p such that -2*p**4 + 6*p**3 + 2*p**2 - 6*p = 0.
-1, 0, 1, 3
Find s, given that 2*s**5/11 - 32*s**4/11 + 50*s**3/11 + 84*s**2/11 = 0.
-1, 0, 3, 14
Find w such that -24*w**4/11 + 614*w**3/11 - 920*w**2/11 + 192*w/11 = 0.
0, 1/4, 4/3, 24
Factor 3*m**3/2 + 57*m**2/2 + 357*m/2 + 735/2.
3*(m + 5)*(m + 7)**2/2
Suppose 10*p**3 - 102*p**2 + 180*p - 32 = 0. Calculate p.
1/5, 2, 8
Factor -t**2/3 - 3204*t - 7699212.
-(t + 4806)**2/3
Solve -6*a**2/19 + 35692*a/19 + 11898/19 = 0.
-1/3, 5949
Factor -2*y**4/13 - 4*y**3/13 + 4*y/13 + 2/13.
-2*(y - 1)*(y + 1)**3/13
Solve -74*i**2/13 + 6*i - 4/13 = 0.
2/37, 1
Solve 3*v**5 + 39*v**4/4 - 3*v**3/4 - 39*v**2/4 - 9*v/4 = 0.
-3, -1, -1/4, 0, 1
Suppose 5*u**4 + 115*u**3 + 365*u**2 - 375*u - 1710 = 0. What is u?
-19, -3, 2
Suppose 4*k**2 - 2048*k + 262144 = 0. Calculate k.
256
Factor 2*v**3 - 116*v**2 - 122*v + 236.
2*(v - 59)*(v - 1)*(v + 2)
Let 4*r**2 - 576*r + 20736 = 0. What is r?
72
Solve -2*o**3/3 - 18*o**2 - 52*o/3 = 0.
-26, -1, 0
Suppose -d**5/3 + 77*d**4/3 + 158*d**3/3 + 2*d**2/3 - 157*d/3 - 79/3 = 0. What is d?
-1, 1, 79
Factor -4*m**3 - 111*m**2/4 + 135*m/4 - 2.
-(m - 1)*(m + 8)*(16*m - 1)/4
Factor 5*l**2 - 3210*l - 3215.
5*(l - 643)*(l + 1)
What is a in -4*a**3 - 24*a**2 + 4*a + 24 = 0?
-6, -1, 1
Let -b**3 - 18*b**2 - 105*b - 196 = 0. Calculate b.
-7, -4
Factor -27*b**3 + 105741*b**2 - 140952*b + 46980.
-3*(b - 3915)*(3*b - 2)**2
Factor -4*l**2 - 17940*l.
-4*l*(l + 4485)
Let -2*u**4 - 3*u**3 + 2*u**2 = 0. Calculate u.
-2, 0, 1/2
Find m, given that 2*m**4/17 - 24*m**3/17 + 26*m**2/17 + 132*m/17 + 80/17 = 0.
-1, 4, 10
What is c in -3*c**4 - 26*c**3 - 16*c**2 = 0?
-8, -2/3, 0
Solve -5*h**4 - 145*h**3 - 975*h**2 + 1125*h = 0.
-15, 0, 1
Suppose -2*i**3 - 22*i**2 + 114*i - 90 = 0. What is i?
-15, 1, 3
What is v in -3*v**4 + 21*v**3 - 27*v**2 - 81*v + 162 = 0?
-2, 3
Find q such that 3*q**3/4 - 15*q**2/2 + 12*q = 0.
0, 2, 8
Let 2*q**4/9 - 20*q**3/3 - 14*q**2 - 64*q/9 = 0. Calculate q.
-1, 0, 32
Let -3*n**3 + 273*n**2 + 276*n = 0. What is n?
-1, 0, 92
Solve 3*n**2/4 - 210*n + 14700 = 0.
140
Factor r**4 - 3332*r**3 + 2772222*r**2 + 5554444*r + 2778889.
(r - 1667)**2*(r + 1)**2
Let o**4/3 - o**3 - 94*o**2/3 + 120*o = 0. Calculate o.
-10, 0, 4, 9
Determine q so that 2*q**2/11 + 494*q/11 - 996/11 = 0.
-249, 2
Let -4*a**3 + 20*a**2 - 28*a + 12 = 0. What is a?
1, 3
Factor 1455218*m**3/17 + 1462042*m**2/17 + 6832*m/17 + 8/17.
2*(m + 1)*(853*m + 2)**2/17
Find o such that -2*o**4/7 + 24*o**3/7 - 86*o**2/7 + 48*o/7 + 160/7 = 0.
-1, 4, 5
Determine s so that s**3/4 + s**2 - 5*s - 12 = 0.
-6, -2, 4
Factor 5*h**2 + 281*h.
h*(5*h + 281)
Suppose 4*g**5 + 288*g**4 + 6452*g**3 + 46504*g**2 + 130944*g + 123008 = 0. What is g?
-31, -4, -2
Factor g**2/2 - 259*g + 67081/2.
(g - 259)**2/2
Solve 4*h**2 + 332*h + 648 = 0 for h.
-81, -2
Suppose -2*w**2/19 + 24*w/19 - 72/19 = 0. What is w?
6
Solve -x**5/3 - 2*x**4 - 4*x**3 - 10*x**2/3 - x = 0.
-3, -1, 0
Factor 2*z**4 + 16*z**3 - 338*z**2 + 1424*z - 1824.
2*(z - 4)**2*(z - 3)*(z + 19)
Solve 4*c**2/5 - 236*c/5 - 256 = 0.
-5, 64
Suppose f**2/2 - 83*f/2 - 85 = 0. What is f?
-2, 85
Factor -g**3/5 - 392*g**2/5 + 1183*g/5 - 158.
-(g - 2)*(g - 1)*(g + 395)/5
Let u**3/3 - 190*u**2/3 + 377*u/3 - 188/3 = 0. What is u?
1, 188
What is f in 2*f**4/13 - 36*f**3/13 + 240*f**2/13 - 704*f/13 + 768/13 = 0?
4, 6
Factor -2*f**2 - 220*f.
-2*f*(f + 110)
Factor -6*d**2 - 2108*d + 1408.
-2*(d + 352)*(3*d - 2)
Solve -2*h**3/13 + 18*h**2/13 - 48*h/13 + 32/13 = 0.
1, 4
Suppose 3*w**5/7 + 39*w**4/7 - 15*w**3/7 - 195*w**2/7 + 12*w/7 + 156/7 = 0. What is w?
-13, -2, -1, 1, 2
Determine c so that 4*c**2 - 976*c + 59536 = 0.
122
Find v, given that v**4 + 4*v**3 + 6*v**2 + 4*v + 1 = 0.
-1
Factor -3*d**2/7 - 54*d/7 - 51/7.
-3*(d + 1)*(d + 17)/7
Determine d, given that -2*d**4/5 + 24*d**3 - 232*d**2/5 = 0.
0, 2, 58
Suppose 9*i**4/7 + 93*i**3/7 + 201*i**2/7 - 213*i/7 - 90/7 = 0. Calculate i.
-6, -5, -1/3, 1
Factor -n**4 - 15*n**3 - 63*n**2 - 85*n - 36.
-(n + 1)**2*(n + 4)*(n + 9)
Factor 5*p**2/2 - 530*p + 28090.
5*(p - 106)**2/2
Determine h so that -968*h**3/9 - 70070*h**2/9 + 25576*h/9 - 776/3 = 0.
-291/4, 2/11
Suppose 4*b**4/7 - 44*b**3/7 - 32*b**2 - 240*b/7 = 0. What is b?
-2, 0, 15
Factor 4*w**2 + 1328*w - 1332.
4*(w - 1)*(w + 333)
Suppose 3*w**4/7 - 78*w**3/7 - 171*w**2/7 + 78*w/7 + 24 = 0. Calculate w.
-2, -1, 1, 28
Factor 2*h**2 - 38*h - 40.
2*(h - 20)*(h + 1)
Factor 4*c**5 + 20*c**4 + 4*c**3 - 84*c**2 - 72*c.
4*c*(c - 2)*(c + 1)*(c + 3)**2
Factor 215*x**3 + 1715*x**2 + 1465*x - 35.
5*(x + 1)*(x + 7)*(43*x - 1)
Let -16*d**3/3 - 60*d**2 + 1588*d/3 + 136 = 0. What is d?
-17, -1/4, 6
Factor -2*u**3/3 + 68*u**2/3 - 130*u/3 + 64/3.
-2*(u - 32)*(u - 1)**2/3
Suppose 32*l**4 + 1764*l**3 + 4438*l**2 + 1446*l - 1260 = 0. Calculate l.
-105/2, -2, -1, 3/8
Find b such that b**3/4 + 271*b**2/4 - 554*b + 1116 = 0.
-279, 4
Determine d so that -2*d**2/9 - 104*d/9 + 106/9 = 0.
-53, 1
Solve -3*b**5 + 3966*b**4 - 1746354*b**3 + 255540096*b**2 + 260799021*b - 514596726 = 0 for b.
-2, 1, 441
Suppose 4*a**2 - 8*a - 32 = 0. What is a?
-2, 4
Let -8*l**2/9 - 26*l/9 - 2/3 = 0. What is l?
-3, -1/4
Factor -5*w**2 + 30*w + 80.
-5*(w - 8)*(w + 2)
Find s, given that 12*s**4 + 81*s**3 + 186*s**2 + 171*s + 54 = 0.
-3, -2, -1, -3/4
Factor 42*t**2 - 76*t - 16.
2*(t - 2)*(21*t + 4)
Factor -3*b**4 - 63*b**3 - 468*b**2 - 1488*b - 1728.
-3*(b + 4)**3*(b + 9)
Let -c**2/2 - 13*c/2 + 34 = 0. What is c?
-17, 4
Determine i, given that -i**2/5 - 24*i/5 - 23/5 = 0.
-23, -1
Suppose -s**4 - 6*s**3 - 4*s**2 + 6*s + 5 = 0. What is s?
-5, -1, 1
Factor -200*z**4 - 19460*z**3 - 5826*z**2 - 2911*z/5 - 97/5.
-(z + 97)*(10*z + 1)**3/5
Factor 36*o**3 - 7928*o**2 + 1760*o.
4*o*(o - 220)*(9*o - 2)
Determine o so that -10*o**5 + 5*o**4 + 60*o**3 - 110*o**2 + 70*o - 15 = 0.
-3, 1/2, 1
Factor 2*f**3 + 2512*f**2 + 788768*f.
2*f*(f + 628)**2
What is r in -2*r**4 - 18*r**3 - 14*r**2 + 18*r + 16 = 0?
-8, -1, 1
What is w in -2*w**4/9 - 14*w**3/9 + 218*w**2/9 - 370*w/9 - 200/3 = 0?
-15, -1, 4, 5
Factor 5*h**3/2 - 40*h**2 - 190*h - 200.
5*(h - 20)*(h + 2)**2/2
Find f, given that -5*f**4 + 50*f**3 - 85*f**2 + 40*f = 0.
0, 1, 8
Factor 4*o**3 + 556*o**2 + 18460*o - 60492.
4*(o - 3)*(o + 71)**2
What is d in 4*d**3 - 44*d**2 + 96*d = 0?
0, 3, 8
Suppose 3*k**5/7 - 3*k**4/7 - 9*k**3 + 21*k**2 + 24*k/7 - 180/7 = 0. Calculate k.
-5, -1, 2, 3
Factor -6*j**3 + 155*j**2.
-j**2*(6*j - 155)
What is i in i**3 - 5*i**2 + 7*i - 3 = 0?
1, 3
Find p, given that -4*p**5/5 + 16*p**3/5 - 8*p**2/5 - 12*p/5 + 8/5 = 0.
-2, -1, 1
Factor 3*x**3/4 - 12*x**2 - 165*x/4 - 57/2.
3*(x - 19)*(x + 1)*(x + 2)/4
Factor g**4 - 37*g**3 + 102*g**2.
g**2*(g - 34)*(g - 3)
Factor -5*q**2 + 15*q.
-5*q*(q - 3)
Let -2*a**5 + 6*a**4 - 2*a**3 - 6*a**2 + 4*a = 0. What is a?
-1, 0, 1, 2
Factor -7*q**3/4 + 627*q**2 - 3215*q/4 + 357/2.
-(q - 357)*(q - 1)*(7*q - 2)/4
Find m, giv