
Determine t, given that 5*t**3/4 + 113*t**2/4 - 83*t/2 + 12 = 0.
-24, 2/5, 1
Find y such that y**3/4 - 23*y**2/4 + 143*y/4 - 121/4 = 0.
1, 11
Solve -108*u**5 + 81*u**4 + 138*u**3 - 84*u**2 - 30*u + 3 = 0 for u.
-1, -1/3, 1/12, 1
Factor 7*i**3 + 75*i**2 - 204*i + 52.
(i - 2)*(i + 13)*(7*i - 2)
Factor 65*d**3 + 85*d**2 + 20*d.
5*d*(d + 1)*(13*d + 4)
Factor -a**2/4 + 13*a + 53/4.
-(a - 53)*(a + 1)/4
Solve -6*r**5 + 14*r**4 - 4*r**3 - 12*r**2 + 10*r - 2 = 0 for r.
-1, 1/3, 1
Factor -2*h**3 - 10*h**2 + 2*h + 10.
-2*(h - 1)*(h + 1)*(h + 5)
Solve d**4/6 - 5*d**3/3 - 14*d**2/3 + 20*d/3 + 16 = 0.
-2, 2, 12
Determine p so that 21*p**5/5 + 45*p**4 + 102*p**3/5 - 468*p**2/5 + 24*p = 0.
-10, -2, 0, 2/7, 1
Factor 4*a**2 + 23896*a.
4*a*(a + 5974)
What is y in 15*y**5 - 820*y**4 - 7740*y**3 - 8550*y**2 + 2765*y + 4410 = 0?
-7, -1, 2/3, 63
Factor -y**4/3 - 17*y**3/3 + 19*y**2/3 + 17*y/3 - 6.
-(y - 1)**2*(y + 1)*(y + 18)/3
Let -4*u**2 + 236*u + 240 = 0. What is u?
-1, 60
Determine r so that 2*r**4 - 34*r**3 + 32*r**2 = 0.
0, 1, 16
Factor 5*y**2/2 - 150*y - 640.
5*(y - 64)*(y + 4)/2
Let 3*z**4/5 + 12*z**3/5 - 9*z**2/5 - 42*z/5 - 24/5 = 0. What is z?
-4, -1, 2
Factor 3*s**2 - s/3.
s*(9*s - 1)/3
Factor 3*g**3 - 2196*g**2 + 535824*g - 43580352.
3*(g - 244)**3
Solve 4*a**4/3 - 8*a**3/3 - 4*a**2/3 + 8*a/3 = 0.
-1, 0, 1, 2
Factor n**3/11 + 45*n**2/11 - 250*n/11.
n*(n - 5)*(n + 50)/11
Factor -b**2/2 - 189*b - 35721/2.
-(b + 189)**2/2
Let -9250*y**3 - 1750*y**2 - 145*y/2 + 1 = 0. Calculate y.
-1/10, 2/185
Solve -3*a**5/2 + 153*a**4 - 3585*a**3 - 16062*a**2 - 41499*a/2 - 8427 = 0.
-2, -1, 53
Factor -2*i**4 + 68*i**3 + 218*i**2 + 148*i.
-2*i*(i - 37)*(i + 1)*(i + 2)
Determine n, given that -3*n**5/5 - 21*n**4/5 + 162*n**3/5 - 228*n**2/5 - 24*n + 288/5 = 0.
-12, -1, 2
Factor -3*q**4 + 45*q**3 - 150*q**2.
-3*q**2*(q - 10)*(q - 5)
Factor -o**2/6 + 34*o/3 - 578/3.
-(o - 34)**2/6
Suppose -8*k**4/5 - 188*k**3/5 + 294*k**2/5 - 149*k/5 + 5 = 0. What is k?
-25, 1/2
Suppose -t**3/2 + t**2/2 + 5*t/2 + 3/2 = 0. Calculate t.
-1, 3
Determine r, given that -r**3 - 7*r**2 + r + 7 = 0.
-7, -1, 1
Solve 10*n**4/9 + 62*n**3/9 + 2*n**2/9 - 62*n/9 - 4/3 = 0 for n.
-6, -1, -1/5, 1
Determine g, given that -15*g**5 - 99*g**4 - 693*g**3/5 + 339*g**2/5 - 36*g/5 = 0.
-4, -3, 0, 1/5
Solve w**3 + 16*w**2 - 39*w - 54 = 0.
-18, -1, 3
Factor 3995*p**3 - 23960*p**2 + 35895*p + 90.
5*(p - 3)**2*(799*p + 2)
Determine t so that 2*t**3 - 524*t**2 + 34840*t - 67600 = 0.
2, 130
Factor -65*v**2 + 4690*v - 720.
-5*(v - 72)*(13*v - 2)
Factor -4489*o**3/4 - 4355*o**2/2 + 133*o - 2.
-(o + 2)*(67*o - 2)**2/4
Factor 5*z**5 - 5*z**4 - 5*z**3 + 5*z**2.
5*z**2*(z - 1)**2*(z + 1)
Factor l**4/4 - 7*l**3/4 + 3*l**2/2 + 8*l - 8.
(l - 4)**2*(l - 1)*(l + 2)/4
Factor q**4/5 + 187*q**3/5 + 11529*q**2/5 + 226233*q/5 - 500094/5.
(q - 2)*(q + 63)**3/5
Solve -16*a**4 + 864*a**3 + 12*a**2 - 652*a + 216 = 0 for a.
-1, 1/2, 54
Factor -l**4/4 - 55*l**3/2 - 3025*l**2/4.
-l**2*(l + 55)**2/4
What is m in 5*m**2/3 - 20*m/3 - 25/3 = 0?
-1, 5
Factor p**5/5 - 86*p**4/5 - 356*p**3/5 - 72*p**2.
p**2*(p - 90)*(p + 2)**2/5
Solve -4*m**3 + 3996*m**2 - 1330668*m + 147704148 = 0 for m.
333
Determine c, given that 5*c**3/3 + 75*c**2 - 335*c - 1225/3 = 0.
-49, -1, 5
Find i, given that i**2/3 + 47*i/3 - 16 = 0.
-48, 1
Determine q, given that q**3/4 - 5*q**2/2 + 31*q/4 - 15/2 = 0.
2, 3, 5
Suppose -4*i**5 + 46*i**4 + 76*i**3 + 26*i**2 = 0. What is i?
-1, -1/2, 0, 13
Factor 3*n**4/4 + 13*n**3/2 + 33*n**2/4 - 7*n/2.
n*(n + 2)*(n + 7)*(3*n - 1)/4
Determine d, given that -3*d**5 - 78*d**4 - 219*d**3 + 3756*d**2 - 6528*d + 3072 = 0.
-16, 1, 4
Factor 2*z**3/3 + 202*z**2 + 20402*z + 2060602/3.
2*(z + 101)**3/3
Suppose -3*m**2 + 48*m - 45 = 0. Calculate m.
1, 15
Solve 21*r**5 - 174*r**4 + 552*r**3 - 816*r**2 + 528*r - 96 = 0.
2/7, 2
Factor -21*i**3/2 + 69*i**2/2 + 96*i - 30.
-3*(i - 5)*(i + 2)*(7*i - 2)/2
Factor -3*g**2 + 21*g - 30.
-3*(g - 5)*(g - 2)
Factor c**4/5 - 2*c**3/5 - 3*c**2/5 + 4*c/5 + 4/5.
(c - 2)**2*(c + 1)**2/5
Find y such that -3*y**5 + 24*y**4 + 111*y**3 - 96*y**2 - 396*y = 0.
-3, -2, 0, 2, 11
Factor -5*j**4 + 275*j**3 + 285*j**2 - 275*j - 280.
-5*(j - 56)*(j - 1)*(j + 1)**2
Factor 4*z**2 + 8*z - 60.
4*(z - 3)*(z + 5)
Suppose 3*n**4 + 55*n**3 + 267*n**2 + 281*n + 66 = 0. Calculate n.
-11, -6, -1, -1/3
Find l, given that -4*l**3 - 96*l**2 - 720*l - 1600 = 0.
-10, -4
Factor -2*o**4/5 + 6*o**3/5 - 4*o**2/5.
-2*o**2*(o - 2)*(o - 1)/5
Determine l so that -2*l**5/11 + 38*l**4/11 - 188*l**3/11 - 12*l**2/11 + 702*l/11 + 486/11 = 0.
-1, 3, 9
Solve 2*k**2/9 + 20*k/3 = 0 for k.
-30, 0
Factor -r**2/3 - 436*r/3 - 145.
-(r + 1)*(r + 435)/3
Determine m so that 4*m**4 - 16*m**3 - 28*m**2 + 40*m = 0.
-2, 0, 1, 5
Factor r**3/2 - 81*r**2 - 651*r/8 - 163/8.
(r - 163)*(2*r + 1)**2/8
Factor q**4 - 17*q**3 + 62*q**2 + 80*q.
q*(q - 10)*(q - 8)*(q + 1)
Factor -146*l**2/15 + 136*l + 56/15.
-2*(l - 14)*(73*l + 2)/15
Determine k, given that -2*k**2/15 + 112*k/15 + 118/5 = 0.
-3, 59
Let -f**2 - 78*f + 79 = 0. What is f?
-79, 1
Let -2*v**3/5 + 48*v**2/5 - 54*v + 224/5 = 0. What is v?
1, 7, 16
Suppose 2*c**2/15 - 34*c/15 + 28/5 = 0. What is c?
3, 14
Factor 5*h**2 - 1215*h.
5*h*(h - 243)
Factor -3*w**4 + 282*w**3 - 1359*w**2 + 2148*w - 1068.
-3*(w - 89)*(w - 2)**2*(w - 1)
Factor 20*n**3 + 88*n**2 + 92*n + 24.
4*(n + 1)*(n + 3)*(5*n + 2)
Determine h so that 68*h**3/5 - 2*h**2 - 272*h/5 + 8 = 0.
-2, 5/34, 2
Factor -a**2/3 - 14*a/3 - 8.
-(a + 2)*(a + 12)/3
What is p in -p**2 + 31*p + 102 = 0?
-3, 34
Factor -m**4/3 + 4*m**3 + 32*m**2/3 - 16*m - 112/3.
-(m - 14)*(m - 2)*(m + 2)**2/3
Factor 26*a**2 - 4*a/5.
2*a*(65*a - 2)/5
Factor q**3/7 + 43*q**2/7 - 142*q/7 - 184/7.
(q - 4)*(q + 1)*(q + 46)/7
Factor 4*m**2 + 224*m - 228.
4*(m - 1)*(m + 57)
Factor -2*a**4 - 12*a**3 - 16*a**2.
-2*a**2*(a + 2)*(a + 4)
Suppose -2*k**5 - 34*k**4 - 62*k**3 - 30*k**2 = 0. Calculate k.
-15, -1, 0
Let 2*k**4 + 32*k**3 + 104*k**2 + 96*k = 0. What is k?
-12, -2, 0
Suppose 8*n**4 + 34*n**3 + 40*n**2 + 8*n = 0. What is n?
-2, -1/4, 0
Let -g**4 - 29*g**3/5 - 49*g**2/5 - 19*g/5 + 6/5 = 0. What is g?
-3, -2, -1, 1/5
Find n such that -5*n**5 - 425*n**4 + 5*n**3 + 425*n**2 = 0.
-85, -1, 0, 1
Determine h, given that -4*h**5/3 - 16*h**4 - 35*h**3/3 + 100*h**2/3 + 3*h - 22/3 = 0.
-11, -2, -1/2, 1/2, 1
What is h in -3*h**4/8 + 159*h**3/8 + 2667*h**2/8 + 9849*h/8 = 0?
-7, 0, 67
Find q such that -2*q**3/13 - 88*q**2/13 = 0.
-44, 0
Determine v so that 9*v**3/4 - 3*v**2/2 - 15*v/4 + 3 = 0.
-4/3, 1
Suppose k**4/8 + 31*k**3/8 + 105*k**2/8 - 99*k/8 - 243/4 = 0. What is k?
-27, -3, 2
Factor -5*p**2/2 - 39*p/4 + 1.
-(p + 4)*(10*p - 1)/4
Solve -f**5/4 - 59*f**4/4 - 1071*f**3/4 - 3969*f**2/4 + 9261*f = 0 for f.
-21, 0, 4
Factor -7*l**3/3 + 1150*l**2/3 + 827*l/3 - 110.
-(l - 165)*(l + 1)*(7*l - 2)/3
What is y in -5*y**4/2 - 30*y**3 - 55*y**2/2 = 0?
-11, -1, 0
Suppose o**5/5 + o**4/5 - 3*o**3/5 - o**2 - 2*o/5 = 0. What is o?
-1, 0, 2
Factor l**4/6 - 157*l**3/3 + 415*l**2/2 - 776*l/3 + 310/3.
(l - 310)*(l - 2)*(l - 1)**2/6
Suppose q**2/2 + 40*q = 0. What is q?
-80, 0
Factor 2*n**3/9 - 310*n**2 + 144150*n - 22343250.
2*(n - 465)**3/9
Factor -j**3/11 - 12*j**2/11 - 27*j/11.
-j*(j + 3)*(j + 9)/11
Let -150*m**4 - 710*m**3 - 1208*m**2/3 + 440*m/3 - 32/3 = 0. What is m?
-4, -1, 2/15
Factor -f**2/3 + 272*f - 1628/3.
-(f - 814)*(f - 2)/3
Factor 3*z**3 - 75*z**2 - 339*z - 261.
3*(z - 29)*(z + 1)*(z + 3)
Suppose -4*y**4 + 40*y**3 - 124*y**2 + 120*y = 0. What is y?
0, 2, 3, 5
Solve -3*n**5/7 + 9*n**3/7 + 6*n**2/7 = 0.
-1, 0, 2
Solve 3*p**4 + 31*p**3/3 + 10*p**2 + 8*p/3 = 0.
-2, -1, -4/9, 0
Factor 2*u**2 + 23536*u + 69242912.
2*(u + 5884)**2
Factor 6*z**2/11 - 72*z/11.
6*z*(z - 12)/11
Factor 6*p**2/11 - 11058*p/11.
6*p*(p - 1843)/11
Determine c so that -c**2/5 + 17*c/5 - 66/5 = 0.
6, 11
Let -2*h**4 + 86*h**3 - 966*h**2 + 882*h = 0. Calculate h.
0, 1, 21
Let 2*g**5/9 - 2*g**4/3 - 22*g**3/3 - 106*g**2/9 - 16*g/3 = 0. What is g?
-3, -1, 0, 8
Factor 5*v**4 + 45*v**3 + 125*v**2 + 135*v + 50.
5*(v + 1)**2*(v + 2)*(v + 5)
Suppose 12*a**4 - 52*a**3 + 28*a**2 + 68*a - 24 = 0. Calculate a.
-1, 1/3, 2, 3
Determine l, given that -3*l**3/5 + 33*l**2/5 - 21*l + 15 = 0.
1, 5
Suppose -2*i**5 + 22*i**4/3 + 242*i**3/3 + 134*i**2 + 36*i = 0. Calculate i.
-3, 