h such that h**5/6 - 73*h**4/2 + 1943*h**3 + 18149*h**2/3 + 12247*h/2 + 4107/2 = 0.
-1, 111
Factor 250563*t**2/4 - 867*t + 3.
3*(289*t - 2)**2/4
Determine p, given that -p**2/6 - 49*p/6 + 25/3 = 0.
-50, 1
Let -6*f**5 + 86*f**4 + 386*f**3 + 186*f**2 - 108*f = 0. What is f?
-3, -1, 0, 1/3, 18
Suppose -3*k**3 - 57*k**2 - 192*k - 180 = 0. What is k?
-15, -2
Factor u**2 + 10*u + 24.
(u + 4)*(u + 6)
Let 8*f**5 - 6*f**4 - 2*f**3 = 0. What is f?
-1/4, 0, 1
Factor 3*c**4 + 6*c**3 - 15*c**2 - 18*c.
3*c*(c - 2)*(c + 1)*(c + 3)
Factor -m**2/3 + 311*m/3 + 104.
-(m - 312)*(m + 1)/3
Factor -w**4/9 + 88*w**3/9 + 46*w**2/3 - 91256*w/9 - 1075369/9.
-(w - 61)**2*(w + 17)**2/9
Solve -2754*h**5 + 3195*h**4 - 283*h**3 - 518*h**2/3 + 12*h + 8/3 = 0 for h.
-1/6, -2/17, 2/9, 1
Factor -2*z**2/5 - 82*z/5 - 16.
-2*(z + 1)*(z + 40)/5
Solve 2*u**2/13 - 16*u/13 + 32/13 = 0.
4
Suppose 16*j**3/5 - 532*j**2/5 + 26*j + 66/5 = 0. Calculate j.
-1/4, 1/2, 33
Let -12*i**3 + 1088*i**2 + 1468*i + 368 = 0. What is i?
-1, -1/3, 92
Factor l**2/2 + 105*l/2 + 103.
(l + 2)*(l + 103)/2
Factor -8*y**3 - 20*y**2 - 8*y.
-4*y*(y + 2)*(2*y + 1)
Solve 2*a**5/15 - 2*a**4/5 - 2*a**3/15 + 14*a**2/15 - 8/15 = 0.
-1, 1, 2
Factor -2*a**3 - 358*a**2 + 4968*a - 4608.
-2*(a - 12)*(a - 1)*(a + 192)
Factor 16*j**3 + 12*j**2 - 484*j + 120.
4*(j - 5)*(j + 6)*(4*j - 1)
Factor 2*k**2 - 20*k.
2*k*(k - 10)
Factor -u**4/4 - 49*u**3/4 - 156*u**2 - 144*u.
-u*(u + 1)*(u + 24)**2/4
Suppose -a**4/3 + a**3 - a**2 + a/3 = 0. What is a?
0, 1
Suppose 9*v**4 - 69*v**3 - 29*v**2 + 41*v - 8 = 0. Calculate v.
-1, 1/3, 8
Solve 3*c**2 - 231*c - 474 = 0 for c.
-2, 79
Let -20*k**3 + 45*k**2 + 50*k - 15 = 0. Calculate k.
-1, 1/4, 3
Factor 4*z**3 - 44696*z**2 + 124858276*z.
4*z*(z - 5587)**2
Solve 3*w**2 - 51*w - 3150 = 0.
-25, 42
Factor -4*h**4 + 608*h**3 - 24224*h**2 + 80512*h + 262848.
-4*(h - 74)**2*(h - 6)*(h + 2)
Factor 27*i**3/4 - 441*i**2/2 + 579*i/4 - 24.
3*(i - 32)*(3*i - 1)**2/4
Suppose -3*z**4/8 - 15*z**3/4 + 33*z**2/8 = 0. What is z?
-11, 0, 1
Factor 2*o**5 - 4*o**4 - 26*o**3 - 20*o**2.
2*o**2*(o - 5)*(o + 1)*(o + 2)
Factor 364*a**2 - 372*a + 8.
4*(a - 1)*(91*a - 2)
Factor z**2/4 - 185*z/4.
z*(z - 185)/4
Suppose 2*v**4/3 - 13*v**3/3 + 29*v**2/3 - 9*v + 3 = 0. Calculate v.
1, 3/2, 3
Factor -f**4/4 + 3*f**3/4 + f**2.
-f**2*(f - 4)*(f + 1)/4
Solve -j**3/6 - 23*j**2/6 - 22*j - 30 = 0.
-15, -6, -2
Factor 2*c**2/3 + 136*c/3 - 192.
2*(c - 4)*(c + 72)/3
Find m such that 3*m**5/4 + 21*m**4/4 - 15*m**3/4 - 213*m**2/4 + 30*m + 75 = 0.
-5, -1, 2
Factor 5*b**2 + 405*b.
5*b*(b + 81)
What is n in -18*n**4/7 + 2760*n**3/7 - 107624*n**2/7 + 139840*n/7 - 46208/7 = 0?
2/3, 76
Suppose 2*f**2 - 500*f - 502 = 0. Calculate f.
-1, 251
Factor 2*h**2/11 - 156*h/11.
2*h*(h - 78)/11
Determine o, given that 22*o**2/23 - 1074*o/23 - 196/23 = 0.
-2/11, 49
Factor l**2 - 110*l + 3025.
(l - 55)**2
Solve 2*n**4/5 + 14*n**3 + 60*n**2 = 0.
-30, -5, 0
Determine l, given that -3*l**3/2 - 90*l**2 - 2457*l/2 - 1140 = 0.
-40, -19, -1
Factor -4*v**2/5 + 16*v/5 + 128/5.
-4*(v - 8)*(v + 4)/5
Factor 2*t**2/3 + 11224*t/3 + 15747272/3.
2*(t + 2806)**2/3
Find x such that 5*x**5 + 70*x**4 + 260*x**3 + 130*x**2 - 265*x - 200 = 0.
-8, -5, -1, 1
Suppose -4*u**5/5 + 4*u**4 - 24*u**3/5 = 0. What is u?
0, 2, 3
Factor 3*h**2 + 456*h + 17328.
3*(h + 76)**2
Find v such that -v**2/5 + 16*v/5 + 17/5 = 0.
-1, 17
Suppose 2*k**5/11 - 12*k**4/11 + 8*k**3/11 + 12*k**2/11 - 10*k/11 = 0. What is k?
-1, 0, 1, 5
What is d in 46*d**3 - 1292*d**2 - 4166*d + 372 = 0?
-3, 2/23, 31
Factor 3*i**3 + 4542*i**2 + 18132*i + 18120.
3*(i + 2)**2*(i + 1510)
Let 8*u**5 - 76*u**4 + 92*u**3 + 332*u**2 + 44*u - 112 = 0. What is u?
-1, 1/2, 4, 7
Factor -2*c**3/13 + 38*c**2/13 - 190*c/13 + 154/13.
-2*(c - 11)*(c - 7)*(c - 1)/13
Factor -y**2/4 - 49*y/4 + 25/2.
-(y - 1)*(y + 50)/4
Suppose 3*v**3 + 111*v**2 - 480*v + 492 = 0. Calculate v.
-41, 2
Determine y so that -2*y**2/3 - 2528*y/3 - 798848/3 = 0.
-632
Determine v, given that v**3/2 + 5*v**2 - 61*v/2 - 35 = 0.
-14, -1, 5
What is x in 5*x**3 + 6465*x**2 + 12915*x + 6455 = 0?
-1291, -1
Find m such that -30*m**5 + 86*m**4 + 616*m**3/5 + 248*m**2/5 + 32*m/5 = 0.
-2/5, -1/3, 0, 4
Factor 5*g**2/4 - 25*g/4 + 15/2.
5*(g - 3)*(g - 2)/4
Suppose 14*q**5 - 2916*q**4 + 203692*q**3 - 4857048*q**2 + 5970294*q - 1314036 = 0. What is q?
2/7, 1, 69
Determine g, given that -3*g**4 - 159*g**3 - 2325*g**2 - 5625*g = 0.
-25, -3, 0
Solve -4*w**3/7 - 372*w**2/7 + 108*w - 380/7 = 0.
-95, 1
Solve -4*s**4 + 56*s**3 - 16*s**2 - 1656*s + 1620 = 0.
-5, 1, 9
What is b in -2*b**3 - 16*b**2 - 26*b - 12 = 0?
-6, -1
Factor 8*a**4/11 + 6*a**3/11 - 36*a**2/11 + 2*a.
2*a*(a - 1)**2*(4*a + 11)/11
Suppose 2*v**3 + 88*v**2 + 328*v + 320 = 0. Calculate v.
-40, -2
Factor -2*l**2/5 - 7*l/5 + 4/5.
-(l + 4)*(2*l - 1)/5
Factor -2*i**3/11 + 24*i**2/11 + 2*i/11 - 24/11.
-2*(i - 12)*(i - 1)*(i + 1)/11
Factor -u**3/3 + 200*u**2/3 - 10000*u/3.
-u*(u - 100)**2/3
Find g such that 6*g**5 + 2136*g**4/5 + 396*g**3/5 - 2136*g**2/5 - 426*g/5 = 0.
-71, -1, -1/5, 0, 1
What is w in w**2/5 + 56*w/5 + 11 = 0?
-55, -1
Solve 33*z**5/4 - 31*z**4/4 - 83*z**3 - 71*z**2 - 4*z = 0.
-2, -1, -2/33, 0, 4
Factor 4*b**4 + 960*b**3 + 59488*b**2 + 226560*b + 222784.
4*(b + 2)**2*(b + 118)**2
Factor 2*k**3/7 - 2*k**2 - 10*k/7 + 150/7.
2*(k - 5)**2*(k + 3)/7
Determine h so that -7*h**2/4 - 17*h/4 + 3 = 0.
-3, 4/7
Factor 20*h**2 - 8416*h - 1684.
4*(h - 421)*(5*h + 1)
Factor 4*o**3 - 1536*o**2 - 4636*o - 3096.
4*(o - 387)*(o + 1)*(o + 2)
Factor p**2 - 8*p + 7.
(p - 7)*(p - 1)
Suppose -m**2/3 = 0. Calculate m.
0
Solve -4*p**2/7 + 76*p/7 - 192/7 = 0 for p.
3, 16
Factor -3*s**3/5 - 78*s**2/5 - 504*s/5.
-3*s*(s + 12)*(s + 14)/5
Factor 5*s**2 - 2910*s - 2915.
5*(s - 583)*(s + 1)
Factor v**2/6 - 304*v - 1825/6.
(v - 1825)*(v + 1)/6
Let -2*a**3 - 104*a**2 = 0. Calculate a.
-52, 0
Factor -4*r**4 + 8*r**3 + 16*r**2 - 32*r.
-4*r*(r - 2)**2*(r + 2)
Determine h, given that -h**3 - 35*h**2 + 493*h + 19343 = 0.
-29, 23
Solve -2*r**2/7 + 594*r/7 - 252 = 0.
3, 294
Factor -w**2 - 7*w + 18.
-(w - 2)*(w + 9)
Determine b so that -2*b**2/11 - 26*b/11 - 24/11 = 0.
-12, -1
What is o in -4*o**3 - 120*o**2 - 900*o - 2000 = 0?
-20, -5
Solve -s**5/5 + s**4/2 + s**3/10 - 7*s**2/10 + s/10 + 1/5 = 0 for s.
-1, -1/2, 1, 2
Suppose 2*u**3/5 - 228*u**2/5 + 6498*u/5 = 0. Calculate u.
0, 57
Let -i**2 - 37*i + 918 = 0. What is i?
-54, 17
Factor -i**2/4 - 533*i/4 - 133.
-(i + 1)*(i + 532)/4
Suppose b**3/3 - 31*b**2/3 + 56*b = 0. What is b?
0, 7, 24
Suppose -d**2/3 - 3082*d/3 - 2374681/3 = 0. Calculate d.
-1541
What is n in -2*n**4 + 90*n**3 + 2*n**2 - 90*n = 0?
-1, 0, 1, 45
Factor -3*d**2 + 180*d + 183.
-3*(d - 61)*(d + 1)
Factor 2*f**3 - 78*f**2 + 736*f.
2*f*(f - 23)*(f - 16)
Factor k**3 + 42*k**2 + 441*k.
k*(k + 21)**2
Factor -2*m**3 - 24*m**2 - 96*m - 128.
-2*(m + 4)**3
Factor -2*c**3/11 - 1568*c**2/11 - 1566*c/11.
-2*c*(c + 1)*(c + 783)/11
Let 2*b**4/15 - 4*b**3/3 + 58*b**2/15 - 64*b/15 + 8/5 = 0. Calculate b.
1, 2, 6
Solve -2*f**2 + 29632*f - 109756928 = 0.
7408
Let -v**3/3 - 2*v**2/3 = 0. What is v?
-2, 0
Let -203*t**3/3 - 148*t**2 - 93*t - 38/3 = 0. What is t?
-1, -38/203
Suppose -4*f**4 + 56*f**3 - 52*f**2 = 0. Calculate f.
0, 1, 13
Factor 3*x**3/5 - 183*x**2 - 12*x/5 + 732.
3*(x - 305)*(x - 2)*(x + 2)/5
Factor 2*s**3/19 - 22*s**2/19 + 20*s/19.
2*s*(s - 10)*(s - 1)/19
Factor 2*j**2 + 32*j - 322.
2*(j - 7)*(j + 23)
Solve -2*i**2/9 + 38*i/9 - 20 = 0 for i.
9, 10
Solve -2*k**2 - 630*k - 628 = 0.
-314, -1
Factor 4*x**3 + 36*x**2 + 92*x + 60.
4*(x + 1)*(x + 3)*(x + 5)
Determine w so that -w**2/3 + 890*w/3 - 198025/3 = 0.
445
Factor q**3/3 - 3*q**2 - 22*q/3.
q*(q - 11)*(q + 2)/3
Factor -3*u**2 - 174*u + 360.
-3*(u - 2)*(u + 60)
Determine s so that 5*s**3 - 295*s**2 + 850*s - 560 = 0.
1, 2, 56
Factor -c**4/2 + 3*c**3/2 + 5*c**2/2 - 3*c/2 - 2.
-(c - 4)*(c - 1)*(c + 1)**2/2
Factor t**3/6 - 8*t**2/3 + 85*t/6 - 25.
(t - 6)*(t - 5)**2/6
Factor -9*w**4 + 75*w**3 + 57*w**2 - 27*w.
-3*w*(w - 9)*(w + 1)*(3*w - 1)
Determine u so that 5*u**4 - 80*u**3 + 235*u**2 + 80*u - 240 = 0.
-1, 1, 4, 12
Factor 4*h**3 - 8*h**2 - 96*h.
4*h*(h - 6)*(h + 4)
Suppose a**5 + 54*a**4 + 725*a**3 - 216*a**2 - 2916*a = 0. Calculate a.
-27, -2, 0, 2
Factor 2*n**5 - 40*n**4 + 300*n**3 - 1000*n**2 + 125