)**2/4
Factor -s**4/2 + 5*s**3 - 21*s**2/2 - 2*s + 14.
-(s - 7)*(s - 2)**2*(s + 1)/2
Suppose -s**5/6 + 47*s**4/6 - 191*s**3/2 + 2485*s**2/6 - 1519*s/3 = 0. What is s?
0, 2, 7, 31
Determine g so that -3*g**4/4 - 157*g**3/4 - 1919*g**2/4 + 3537*g/4 - 729/2 = 0.
-27, 2/3, 1
Determine m, given that -m**3/10 + 9*m**2/10 = 0.
0, 9
Suppose -20*q**5 - 185*q**4 - 325*q**3 + 410*q**2 + 120*q = 0. Calculate q.
-6, -4, -1/4, 0, 1
Solve l**2/5 + 16*l/5 - 17/5 = 0 for l.
-17, 1
Factor -4*y**5 - 20*y**4 - 16*y**3.
-4*y**3*(y + 1)*(y + 4)
Solve m**3/4 + 131*m**2/2 - 1599*m/4 + 603 = 0.
-268, 3
Factor -4*q**4 - 28*q**3 - 56*q**2 - 32*q.
-4*q*(q + 1)*(q + 2)*(q + 4)
Determine z so that -5*z**3 - 615*z**2 + 620*z = 0.
-124, 0, 1
Determine c so that -3*c**4/8 + 45*c**3/2 - 423*c**2/4 + 291*c/2 - 495/8 = 0.
1, 3, 55
Factor -2*f**2 - 444*f + 1350.
-2*(f - 3)*(f + 225)
Factor -2*p**2/3 + 4*p + 32/3.
-2*(p - 8)*(p + 2)/3
Determine n, given that n**3/4 - 19*n**2/4 - 21*n/2 = 0.
-2, 0, 21
Find u, given that 4*u**4/7 + 8*u**3 + 128*u**2/7 - 8*u - 132/7 = 0.
-11, -3, -1, 1
Factor 2*l**3/3 + 16*l**2/3 + 10*l.
2*l*(l + 3)*(l + 5)/3
Factor -4*f**3/5 + 1992*f**2/5 - 330672*f/5 + 18297184/5.
-4*(f - 166)**3/5
Suppose -30*j**3/7 - 741*j**2 + 75*j + 1038/7 = 0. What is j?
-173, -2/5, 1/2
Factor -27*x**3 - 4332*x**2 - 6213*x - 1908.
-3*(x + 1)*(x + 159)*(9*x + 4)
Solve 5*n**5 - 10*n**4 - 30*n**3 + 20*n**2 + 65*n + 30 = 0 for n.
-1, 2, 3
Solve 2*p**2 + 130*p - 268 = 0.
-67, 2
Determine k, given that 3*k**3 + 177*k**2 + 2697*k + 2523 = 0.
-29, -1
Factor 10*p**2/21 - 134*p/21 + 52/21.
2*(p - 13)*(5*p - 2)/21
Factor -2*o**2 - 27920*o - 97440800.
-2*(o + 6980)**2
Factor 52*f**3 - 476*f**2 + 488*f - 64.
4*(f - 8)*(f - 1)*(13*f - 2)
Factor -b**3 + 7*b**2 - 4*b - 12.
-(b - 6)*(b - 2)*(b + 1)
Determine q so that 5*q**3 + 30*q**2 + 25*q = 0.
-5, -1, 0
Suppose -3*s**4 + 18*s**2 + 24*s + 9 = 0. Calculate s.
-1, 3
Let 2*q**2/3 - 98*q + 292/3 = 0. What is q?
1, 146
Factor 2*q**4/9 - 16*q**3/3 + 10*q**2 - 44*q/9.
2*q*(q - 22)*(q - 1)**2/9
Factor -2*b**2 + 24*b + 26.
-2*(b - 13)*(b + 1)
Factor c**4/6 + 10*c**3/3 + 77*c**2/6 - 121*c/3.
c*(c - 2)*(c + 11)**2/6
Let -10*m**3/7 + 66*m**2/7 - 32*m/7 - 24/7 = 0. What is m?
-2/5, 1, 6
Factor -s**5 + 3*s**4 + 9*s**3 + 5*s**2.
-s**2*(s - 5)*(s + 1)**2
Find i such that i**2/6 - 7*i/2 + 19/3 = 0.
2, 19
Factor -v**4 + 144*v**3 - 141*v**2 - 286*v.
-v*(v - 143)*(v - 2)*(v + 1)
Factor -y**4/5 + 111*y**2/5 + 22*y.
-y*(y - 11)*(y + 1)*(y + 10)/5
Factor 2*k**2/7 - 318*k/7 - 2672/7.
2*(k - 167)*(k + 8)/7
Let -845*t**5 - 1625*t**4 - 960*t**3 - 180*t**2 = 0. What is t?
-1, -6/13, 0
Determine r, given that -4*r**3 + 320*r**2 + 996*r = 0.
-3, 0, 83
Factor -4*j**2/9 + 544*j/9 + 368/3.
-4*(j - 138)*(j + 2)/9
Determine c so that 87*c**2/5 - 123*c/5 + 36/5 = 0.
12/29, 1
What is a in -a**4/4 - 3*a**3/4 - a**2/2 = 0?
-2, -1, 0
Let -2*x**2 + 58*x + 60 = 0. What is x?
-1, 30
Factor -2*h**3/3 - 28*h**2/3 - 50*h/3 - 8.
-2*(h + 1)**2*(h + 12)/3
Suppose 19*s**3/2 + 129*s**2/2 - 90*s + 16 = 0. What is s?
-8, 4/19, 1
Solve 2*d**2 - 22912*d + 65619968 = 0 for d.
5728
Factor q**3 - 286*q**2 + 20449*q.
q*(q - 143)**2
Factor -5*d**2 + 270*d - 3645.
-5*(d - 27)**2
Solve -3*k**5/4 + 3*k**4/2 + 9*k**3/4 - 6*k**2 + 3*k = 0 for k.
-2, 0, 1, 2
Let y**2/2 - 11*y/2 + 5 = 0. Calculate y.
1, 10
What is a in -12*a**5 + 38*a**4 - 30*a**3 + 4*a**2 = 0?
0, 1/6, 1, 2
Factor -f**2/2 + 1063*f/2 + 532.
-(f - 1064)*(f + 1)/2
What is x in 7*x**2 + 527*x + 150 = 0?
-75, -2/7
Factor p**2/3 - 766*p + 440067.
(p - 1149)**2/3
Factor -x**4 + 122*x**3 - 241*x**2 + 120*x.
-x*(x - 120)*(x - 1)**2
Let -3*n**5 - 6*n**4 + 153*n**3 - 2268*n + 3888 = 0. Calculate n.
-6, 3, 4
Let 3*p**2 + 537*p + 534 = 0. Calculate p.
-178, -1
Factor a**3/8 - 3*a**2/4 + 3*a/8 + 5/4.
(a - 5)*(a - 2)*(a + 1)/8
Factor 3*m**3/4 + 93*m**2/4 - 195*m/4 + 99/4.
3*(m - 1)**2*(m + 33)/4
Factor 4*z**3 - 44*z**2 + 128*z - 112.
4*(z - 7)*(z - 2)**2
Find o such that -2*o**3/11 + 28*o**2/11 - 70*o/11 + 4 = 0.
1, 2, 11
Factor -k**5/3 - k**4 + 10*k**3/3 - 2*k**2/3 - 3*k + 5/3.
-(k - 1)**3*(k + 1)*(k + 5)/3
Factor 4*c**3/3 - 220*c**2/3 + 1044*c - 972.
4*(c - 27)**2*(c - 1)/3
Determine g, given that -320*g**4 - 240*g**3 + 75*g**2 - 5*g = 0.
-1, 0, 1/8
Factor g**3/6 - 4*g**2 - 31*g/6 + 25.
(g - 25)*(g - 2)*(g + 3)/6
Let -5*r**4 + 762*r**3 - 29929*r**2 + 68100*r - 22500 = 0. Calculate r.
2/5, 2, 75
Factor 20*b**4 - 5*b**3 - 60*b**2 - 25*b + 10.
5*(b - 2)*(b + 1)**2*(4*b - 1)
Let -2*s**2/7 - 32*s - 654/7 = 0. Calculate s.
-109, -3
Suppose -4*c**4/7 + 180*c**3/7 - 500*c**2/7 - 180*c/7 + 72 = 0. Calculate c.
-1, 1, 3, 42
Factor p**3/2 + 69*p**2/2 + 612*p + 578.
(p + 1)*(p + 34)**2/2
Factor 39*w**3/8 - 51*w**2 + 999*w/8 - 189/4.
3*(w - 7)*(w - 3)*(13*w - 6)/8
Let 4*b**2 - 4196*b = 0. What is b?
0, 1049
Determine v, given that -2*v**2/19 - 86*v/19 + 276/19 = 0.
-46, 3
Factor -2*l**3 - 114*l**2 + 1026*l - 910.
-2*(l - 7)*(l - 1)*(l + 65)
Factor -k**4/9 - 2*k**3/9 + k**2/9 + 2*k/9.
-k*(k - 1)*(k + 1)*(k + 2)/9
Let 4*c**5 - 32*c**3 - 24*c**2 + 28*c + 24 = 0. What is c?
-2, -1, 1, 3
Suppose -4*h**5 - 80*h**4 - 580*h**3 - 1880*h**2 - 2800*h - 1568 = 0. Calculate h.
-7, -2
Factor 3*b**4/2 - 3*b**3/2 - 15*b**2 - 12*b.
3*b*(b - 4)*(b + 1)*(b + 2)/2
Factor -2*j**5 + 310*j**4 - 17300*j**3 + 407020*j**2 - 3556490*j + 10174654.
-2*(j - 47)**3*(j - 7)**2
Suppose 2*w**5/15 - 16*w**4/15 + 8*w**3/5 + 4*w**2/15 - 26*w/15 + 4/5 = 0. What is w?
-1, 1, 6
Determine f, given that f**2/7 + 101*f/7 - 60 = 0.
-105, 4
Factor 2*o**2/7 + 28152*o/7 + 99066888/7.
2*(o + 7038)**2/7
Factor -4*q**3/3 + 17*q**2/3 + 44*q/3 - 4.
-(q - 6)*(q + 2)*(4*q - 1)/3
Let v**2/4 - v/4 - 1/2 = 0. What is v?
-1, 2
Suppose -2*c**5/7 - 26*c**4/7 - 86*c**3/7 - 30*c**2/7 + 144*c/7 = 0. Calculate c.
-8, -3, 0, 1
Let -2*f**4 - 14*f**3 - 32*f**2 - 24*f = 0. Calculate f.
-3, -2, 0
Determine f, given that 6*f**3/11 - 48*f**2/11 = 0.
0, 8
Let -14*x**5/3 - 10*x**4/3 + 32*x**3/3 - 8*x**2/3 = 0. What is x?
-2, 0, 2/7, 1
Let 245*c**5/2 + 1155*c**4 - 7995*c**3/2 - 2420*c**2 + 2250*c - 360 = 0. Calculate c.
-12, -1, 2/7, 3
Determine i, given that i**2 - 23*i + 22 = 0.
1, 22
Factor 3*l**2 - 33*l + 90.
3*(l - 6)*(l - 5)
Factor -b**2 - 119*b + 120.
-(b - 1)*(b + 120)
Factor -3*j**3 + 55*j**2 - 106*j - 96.
-(j - 16)*(j - 3)*(3*j + 2)
Suppose 5*s**4 + 90*s**3 + 355*s**2 - 450*s = 0. Calculate s.
-10, -9, 0, 1
Factor 14*b**3/9 - 94*b**2/9 + 112*b/9 + 40/9.
2*(b - 5)*(b - 2)*(7*b + 2)/9
Factor n**3 + 46*n**2 - 4*n - 184.
(n - 2)*(n + 2)*(n + 46)
Suppose -u**5/5 - 22*u**4/5 + 72*u**3/5 - 74*u**2/5 + 5*u = 0. What is u?
-25, 0, 1
Let d**2 - 2*d - 48 = 0. What is d?
-6, 8
Factor -6*m**3/7 - 6*m**2/7 + 36*m/7.
-6*m*(m - 2)*(m + 3)/7
Suppose -147*h**2 - 1890*h - 6075 = 0. Calculate h.
-45/7
Suppose -2*b**5 + 10*b**4 + 6*b**3 - 58*b**2 - 4*b + 48 = 0. What is b?
-2, -1, 1, 3, 4
Factor 4*p**2 + 2128*p + 283024.
4*(p + 266)**2
Factor -z**2/6 + 1127*z/6 + 1129/3.
-(z - 1129)*(z + 2)/6
Find y, given that -y**4 + y**3 + 10*y**2 - 4*y - 24 = 0.
-2, 2, 3
Solve -3*g**3 - 13626*g**2 - 20629764*g - 10411154232 = 0 for g.
-1514
Find t, given that -4*t**4 + 68*t**3 - 92*t**2 - 404*t - 240 = 0.
-1, 4, 15
Factor 2*j**2/9 + 92*j/3.
2*j*(j + 138)/9
Factor -3*v**4 - 60*v**3 - 222*v**2 + 924*v + 1089.
-3*(v - 3)*(v + 1)*(v + 11)**2
Let -3*v**5 + 9*v**4/5 + 21*v**3/5 - 9*v**2/5 - 6*v/5 = 0. What is v?
-1, -2/5, 0, 1
Suppose -75*z**4 - 1140*z**3 - 4962*z**2 - 4788*z - 1323 = 0. Calculate z.
-7, -3/5
Let 2*y**4/15 - 26*y**3/15 - 2*y**2/5 + 82*y/15 - 52/15 = 0. Calculate y.
-2, 1, 13
Suppose p**4 + 5*p**3 + 13*p**2/4 - 15*p/2 + 9/4 = 0. Calculate p.
-3, 1/2
Factor 2*v**2 - 3502*v - 3504.
2*(v - 1752)*(v + 1)
Factor 20*z**3 + 36*z**2 - 96*z - 176.
4*(z + 2)**2*(5*z - 11)
Determine n so that 4*n**5/7 + 492*n**4/7 + 484*n**3/7 - 492*n**2/7 - 488*n/7 = 0.
-122, -1, 0, 1
Factor j**3 - 3*j**2 + 2*j.
j*(j - 2)*(j - 1)
What is z in -z**3 + 121*z**2 = 0?
0, 121
Factor -t**4/4 - 34*t**3 - 1518*t**2 - 21160*t + 48668.
-(t - 2)*(t + 46)**3/4
Factor 441*x**4/4 + 840*x**3 + 2062*x**2 + 1760*x + 484.
(3*x + 2)**2*(7*x + 22)**2/4
Determine a so that -2*a**5/3 - 4*a**4 + 6*a**3 + 100*a**2/3 - 24*a - 48 = 0.
-6, -3, -1, 2
Let -182*j**4/9 - 176*j**3/3 - 542*j**2/9 - 76*j/3 