14*s/3.
2*s*(s - 1)*(s + 7)/3
Factor -5*z**2/3 - 5*z/3 + 10/3.
-5*(z - 1)*(z + 2)/3
Factor 6*k**5/7 - 6*k**4/7 - 180*k**3/7.
6*k**3*(k - 6)*(k + 5)/7
Factor -5*f**3 - 420*f**2 - 11760*f - 109760.
-5*(f + 28)**3
Factor -t**2/3 - 17*t/3 - 70/3.
-(t + 7)*(t + 10)/3
Factor -p**4 + 301*p**3.
-p**3*(p - 301)
Find u, given that 4*u**4 + 20*u**3 + 36*u**2 + 28*u + 8 = 0.
-2, -1
Factor -4*l**3/3 + 14*l**2 - 50*l/3 - 12.
-2*(l - 9)*(l - 2)*(2*l + 1)/3
Suppose 8192*m**3/9 + 72192*m**2 + 1908576*m + 16819326 = 0. Calculate m.
-423/16
Factor 55*u**4 - 65*u**3 + 10*u**2.
5*u**2*(u - 1)*(11*u - 2)
Factor -4*n**2/3 - 724*n - 8624/3.
-4*(n + 4)*(n + 539)/3
Factor -33*h**3 - 138*h**2 - 156*h - 24.
-3*(h + 2)**2*(11*h + 2)
Solve -4*g**4 + 28*g**3 + 12*g**2 - 220*g - 200 = 0.
-2, -1, 5
Factor -t**2/5 + 157*t/5 + 318/5.
-(t - 159)*(t + 2)/5
Determine m so that m**5/3 + 4*m**4/3 - 16*m**2/3 - 16*m/3 = 0.
-2, 0, 2
Find f, given that 2*f**2/7 - 310*f/7 - 1600/7 = 0.
-5, 160
Factor 4*y**4/3 - 592*y**3/3 + 1172*y**2/3 - 584*y/3.
4*y*(y - 146)*(y - 1)**2/3
What is y in -y**5 + 21*y**4 - 18*y**3 - 40*y**2 = 0?
-1, 0, 2, 20
Factor -g**4 - 970*g**3 - 240973*g**2 - 2787780*g - 8259876.
-(g + 6)**2*(g + 479)**2
Factor 2*i**2/7 + 984*i/7 + 121032/7.
2*(i + 246)**2/7
What is h in -4*h**5/7 + 144*h**4/7 - 20*h**3 = 0?
0, 1, 35
Determine l, given that 4*l**3 + 12*l**2 - 52*l - 60 = 0.
-5, -1, 3
Factor 5*n**2 - 100*n + 95.
5*(n - 19)*(n - 1)
Factor 381*p**3/5 + 7614*p**2/5 + 7596*p - 120.
3*(p + 10)**2*(127*p - 2)/5
Factor -2*j**5/3 + 74*j**4/3 - 646*j**3/3 - 722*j**2/3.
-2*j**2*(j - 19)**2*(j + 1)/3
Determine l, given that -3*l**2 + 63*l - 60 = 0.
1, 20
Factor -2*a**5 - 28*a**4 + 408*a**3 - 1620*a**2 + 2538*a - 1296.
-2*(a - 3)**3*(a - 1)*(a + 24)
Factor -3*i**3/4 - 263*i**2/4 + 355*i/4 - 89/4.
-(i - 1)*(i + 89)*(3*i - 1)/4
Factor -2*w**3/5 + 74*w**2/5 - 72*w/5.
-2*w*(w - 36)*(w - 1)/5
Factor 4*b**2 - 108*b.
4*b*(b - 27)
Solve 3*j**4 + 6*j**3 - 81*j**2 - 324*j - 324 = 0 for j.
-3, -2, 6
Factor -4*k**3 + 4*k**2.
-4*k**2*(k - 1)
Find f, given that 3*f**3/2 - 97*f**2 + 1153*f/2 + 203 = 0.
-1/3, 7, 58
Determine s so that 4*s**3/5 + 11*s**2/5 + s - 2/5 = 0.
-2, -1, 1/4
Factor -a**4/5 + 2*a**3/5 + 23*a**2/5 - 24*a/5 - 144/5.
-(a - 4)**2*(a + 3)**2/5
What is w in 80*w**3 - 404*w**2/5 - 796*w/5 + 8/5 = 0?
-1, 1/100, 2
Solve 5*q**4 + 70*q**3 + 265*q**2 + 380*q + 180 = 0 for q.
-9, -2, -1
Factor -4*q**3/3 - 92*q**2/3.
-4*q**2*(q + 23)/3
Factor -4*g**3/9 + 4*g**2/9 + 104*g/9 + 32/3.
-4*(g - 6)*(g + 1)*(g + 4)/9
Solve -9*u**4 + 12*u**3 + 321*u**2 - 432*u + 108 = 0 for u.
-6, 1/3, 1, 6
Factor -2*z**4 - 6*z**3 - 4*z**2.
-2*z**2*(z + 1)*(z + 2)
Solve g**3/5 + 636*g**2/5 + 134832*g/5 + 9528128/5 = 0.
-212
Suppose 3*k**5 - 66*k**4 + 420*k**3 - 600*k**2 = 0. What is k?
0, 2, 10
Suppose 2*r**4/3 - 192*r**3 - 580*r**2/3 + 192*r + 578/3 = 0. Calculate r.
-1, 1, 289
Let 405*c**4 + 180*c**3 - 385*c**2 - 180*c - 20 = 0. Calculate c.
-1, -2/9, 1
Let -z**5 + 3*z**4 + 2*z**3 - 12*z**2 + 8*z = 0. Calculate z.
-2, 0, 1, 2
Determine c, given that 3*c**5 - 144*c**4 - 1467*c**3 - 4044*c**2 - 3420*c = 0.
-5, -2, 0, 57
Find c such that 5*c**2 - 1405*c - 1410 = 0.
-1, 282
Factor 49005*t**4/4 + 48015*t**3/2 + 45065*t**2/4 - 485*t + 5.
5*(t + 1)**2*(99*t - 2)**2/4
Factor -o**4/3 - 51*o**3 - 1819*o**2 + 30257*o/3 - 12482.
-(o - 3)*(o - 2)*(o + 79)**2/3
Let 2*k**2 - 730*k = 0. Calculate k.
0, 365
Find u, given that -4*u**2/5 + 592*u - 2956/5 = 0.
1, 739
Factor a**5 + 10*a**4 - 36*a**3 - 158*a**2 - 173*a - 60.
(a - 5)*(a + 1)**3*(a + 12)
Factor -3*s**4 - 540*s**3 - 32400*s**2 - 648000*s.
-3*s*(s + 60)**3
Solve 22*k**5/3 - 136*k**4/3 + 74*k**3 + 52*k**2/3 - 280*k/3 + 16 = 0.
-1, 2/11, 2, 3
Factor 18*s**3/5 + 1556*s**2/5 - 174*s.
2*s*(s + 87)*(9*s - 5)/5
Suppose -4*y**4 - 32*y**3 + 12*y**2 + 88*y - 64 = 0. What is y?
-8, -2, 1
Determine j so that -3*j**5 - 111*j**4 - 1134*j**3 - 2976*j**2 + 4224*j = 0.
-22, -8, 0, 1
Let -2*v**4/3 - 28*v**3/3 - 88*v**2/3 - 80*v/3 = 0. Calculate v.
-10, -2, 0
Find u such that -25*u**3 - 40*u**2 - 15*u = 0.
-1, -3/5, 0
Factor -3*s**3/4 - 15*s**2/4 + 75*s/4 + 375/4.
-3*(s - 5)*(s + 5)**2/4
Let 4*q**3 - 24*q**2 + 12*q + 40 = 0. What is q?
-1, 2, 5
Let -4*h**3 + 1040*h**2 - 2064*h = 0. What is h?
0, 2, 258
Determine j so that j**3 - 796*j**2 - 1595*j - 798 = 0.
-1, 798
Find r, given that 18*r**3 - 80*r**2 + 32*r = 0.
0, 4/9, 4
What is q in -2*q**3/3 + 72*q - 288 = 0?
-12, 6
Determine q so that -2*q**2/5 - 78*q/5 + 220 = 0.
-50, 11
Factor -5*r**2 + 215*r - 410.
-5*(r - 41)*(r - 2)
Find t, given that -t**5/4 + t**4/2 + 19*t**3/4 - 17*t**2 + 15*t = 0.
-5, 0, 2, 3
Factor 35*s**3 + 300*s**2 + 780*s + 640.
5*(s + 2)**2*(7*s + 32)
Factor -4*w**3/9 - 28*w**2/3 + 20*w - 92/9.
-4*(w - 1)**2*(w + 23)/9
Solve -4*t**3 - 24*t**2 = 0 for t.
-6, 0
Factor 4*l**5 - 8*l**4 + 4*l**3.
4*l**3*(l - 1)**2
Suppose -3*r**5 - 12*r**4 + 36*r**3 + 96*r**2 - 192*r = 0. What is r?
-4, 0, 2
Let 4*u**3 - 1412*u**2 + 125312*u - 123904 = 0. Calculate u.
1, 176
Determine y so that -4*y**3/7 + 32*y**2/7 - 68*y/7 + 40/7 = 0.
1, 2, 5
Determine q, given that -q**4/5 - q**3/5 + 122*q**2/5 - 24*q = 0.
-12, 0, 1, 10
Factor 4*q**3 - 30972*q**2 + 79938732*q - 68773955764.
4*(q - 2581)**3
Solve 3*z**2 - 501*z + 498 = 0 for z.
1, 166
Factor 3*y**4 - 12*y**3 - 9*y**2 + 42*y - 24.
3*(y - 4)*(y - 1)**2*(y + 2)
Factor a**3 + 342*a**2 + 29580*a + 57800.
(a + 2)*(a + 170)**2
Determine z, given that 384*z**3/13 - 160*z**2/13 - 58*z/13 - 4/13 = 0.
-1/8, 2/3
Factor -4*n**5 - 16*n**4 + 48*n**3 - 8*n**2 - 44*n + 24.
-4*(n - 1)**3*(n + 1)*(n + 6)
Suppose 34*h**2 - 3096*h + 182 = 0. What is h?
1/17, 91
Factor z**4 - 35*z**3 + 459*z**2 - 2673*z + 5832.
(z - 9)**3*(z - 8)
Determine c, given that c**5/3 + c**4/3 - 2*c**3/3 - 2*c**2/3 + c/3 + 1/3 = 0.
-1, 1
Determine c, given that -100*c**4 + 1620*c**3 - 3856*c**2 - 3888*c - 832 = 0.
-2/5, 4, 13
Let 2*f**2 + 122*f - 520 = 0. What is f?
-65, 4
Factor -2*s**2 - 4048*s + 4050.
-2*(s - 1)*(s + 2025)
Let -4*i**5 + 16*i**4 + 156*i**3 - 376*i**2 - 1280*i + 2688 = 0. Calculate i.
-4, 2, 3, 7
Determine m so that -3*m**3/2 + 312*m**2 - 31815*m/2 - 33075 = 0.
-2, 105
Solve 3*y**3 + 45*y**2 + 108*y = 0 for y.
-12, -3, 0
Factor -w**5/2 - 15*w**4/2 + 45*w**3/2 + 675*w**2/2 - 1620*w + 1944.
-(w - 3)**3*(w + 12)**2/2
Factor 2*x**3 + 266*x**2 - 2*x - 266.
2*(x - 1)*(x + 1)*(x + 133)
Factor 60*z**4 - 8*z**3.
4*z**3*(15*z - 2)
Factor 121*b**3/3 + 1100*b**2/3 + 364*b + 96.
(b + 8)*(11*b + 6)**2/3
Factor -2*y**2 - 116*y.
-2*y*(y + 58)
Let 2*w**2/5 - 288*w/5 + 10368/5 = 0. Calculate w.
72
Determine s so that s**5/7 + 12*s**4/7 - 6*s**3 + 44*s**2/7 - 15*s/7 = 0.
-15, 0, 1
Determine k so that -22*k**3 - 436*k**2/5 - 424*k/5 + 16/5 = 0.
-2, 2/55
What is w in 2*w**2/9 + 2*w/3 + 4/9 = 0?
-2, -1
Find i such that -i**2/4 - 1187*i/4 - 1185/2 = 0.
-1185, -2
Factor -5*j**2 + 830*j + 835.
-5*(j - 167)*(j + 1)
Let 42*w**4/5 - 208*w**3/5 + 326*w**2/5 - 152*w/5 - 8/5 = 0. What is w?
-1/21, 1, 2
Let h**4 - 3*h**3 - 33*h**2 + 35*h = 0. What is h?
-5, 0, 1, 7
Suppose 3*j**5 + 18*j**4 + 21*j**3 - 54*j**2 - 132*j - 72 = 0. What is j?
-3, -2, -1, 2
Let g**2 - 226*g + 12769 = 0. Calculate g.
113
Suppose -p**2/3 - 382*p/3 - 760/3 = 0. Calculate p.
-380, -2
Factor i**4/2 - 95*i**3 + 749*i**2/2 - 466*i + 186.
(i - 186)*(i - 2)*(i - 1)**2/2
Factor 2*h**2 - 2*h.
2*h*(h - 1)
Factor 3*z**3 - 18*z**2 - 75*z - 54.
3*(z - 9)*(z + 1)*(z + 2)
Factor -t**3/3 - 86*t**2/3.
-t**2*(t + 86)/3
Factor 2*j**3/9 - 20*j**2 + 1408*j/3 - 7744/9.
2*(j - 44)**2*(j - 2)/9
Factor -4802*h**2/9 - 3136*h/9 - 512/9.
-2*(49*h + 16)**2/9
Determine s so that 2*s**4 - 66*s**3 - 68*s**2 = 0.
-1, 0, 34
Suppose -27*o**5 + 129*o**4 + 138*o**3 - 516*o**2 - 120*o = 0. What is o?
-2, -2/9, 0, 2, 5
What is o in -o**4/12 + 38*o**3/3 - 371*o**2/6 + 86*o - 147/4 = 0?
1, 3, 147
Factor 2*v**4 - 18*v**3.
2*v**3*(v - 9)
Factor 2*g**5/5 - 142*g**4/5 - 588*g**3/5 - 892*g**2/5 - 598*g/5 - 30.
2*(g - 75)*(g + 1)**4/5
Suppose v**5 + 8*v**4 + 16*v**3 = 0. What is v?
-4, 0
Factor 3*c**4/8 - 33*c**3/8 - 27*c**2 + 135*c/2.
3*c*(c - 15)*(c - 2)*(c + 6)/8
Suppose -12*c**5 - 160*c**4 + 704*c**3 - 744*c**2 + 76*c + 136 = 0. Calculate c.
-17, -1/3, 1, 2
Factor 2*c**3/3 + 962*c**2 + 462722*c + 222569282/3.
2