 0, 1
Determine s, given that -s**2/4 + 217*s/4 - 265 = 0.
5, 212
Find h such that -h**4/5 - 12*h**3/5 - 38*h**2/5 - 12*h/5 + 63/5 = 0.
-7, -3, 1
Solve 2*n**4 - 70*n**3 - 8*n**2 + 280*n = 0.
-2, 0, 2, 35
Factor 2*g**5 - 60*g**4 + 216*g**3 - 208*g**2.
2*g**2*(g - 26)*(g - 2)**2
Determine u, given that -2*u**5/7 - 188*u**4/7 - 6866*u**3/7 - 121104*u**2/7 - 1026432*u/7 - 3345408/7 = 0.
-24, -11
Solve -g**3/7 + 9*g**2/7 + g/7 - 9/7 = 0.
-1, 1, 9
Factor u**2/11 + 2*u/11 + 1/11.
(u + 1)**2/11
Factor 2*s**2/7 + 18*s/7 - 44/7.
2*(s - 2)*(s + 11)/7
Solve -450*h**2/11 + 480*h/11 - 128/11 = 0 for h.
8/15
Factor -30*z**3 + 415*z**2 - 685*z + 300.
-5*(z - 12)*(z - 1)*(6*z - 5)
Factor 3*f**5/7 + 498*f**4/7 + 2907*f**3/7 + 4320*f**2/7.
3*f**2*(f + 3)**2*(f + 160)/7
Suppose -5*n**2 + 585*n + 1800 = 0. What is n?
-3, 120
Factor -5*d**3 + 5505*d**2 - 1512495*d - 1518005.
-5*(d - 551)**2*(d + 1)
Solve 3*p**2 + 1410*p + 165675 = 0.
-235
Factor 2*d**4 + 672*d**3 + 84672*d**2 + 4741632*d + 99574272.
2*(d + 84)**4
Solve 3*q**3/7 + 195*q**2/7 + 3069*q/7 - 3267/7 = 0.
-33, 1
Solve 5*m**5 + 790*m**4 - 795*m**3 = 0 for m.
-159, 0, 1
Factor g**2/7 - 213*g/7 - 430/7.
(g - 215)*(g + 2)/7
Let 5*h**4/3 - 35*h**3/3 + 85*h**2/3 - 85*h/3 + 10 = 0. What is h?
1, 2, 3
Suppose 3*s**4 - 3*s**3 - 30*s**2 + 12*s + 72 = 0. Calculate s.
-2, 2, 3
Suppose 3*k**3 + 186*k**2 - 1431*k + 1242 = 0. Calculate k.
-69, 1, 6
Determine z, given that 3*z**5/7 + 58*z**4/7 + 250*z**3/7 + 20*z**2/7 - 253*z/7 - 78/7 = 0.
-13, -6, -1, -1/3, 1
Solve -4*i**2 + 64*i - 256 = 0 for i.
8
Factor 3*h**5 + 18*h**4 + 24*h**3 - 48*h**2 - 144*h - 96.
3*(h - 2)*(h + 2)**4
Factor u**4/2 + 57*u**3/2 + 360*u**2 - 1350*u.
u*(u - 3)*(u + 30)**2/2
Find o, given that -3*o**3 - 405*o**2 = 0.
-135, 0
Factor 2*p**4 - 72*p**3 + 430*p**2 + 504*p.
2*p*(p - 28)*(p - 9)*(p + 1)
Find f, given that 4*f**3 + 12*f**2 - 132*f - 140 = 0.
-7, -1, 5
Factor 121*y**4 + 891*y**3 + 312*y**2 + 28*y.
y*(y + 7)*(11*y + 2)**2
Suppose 2*d**3/7 - 32*d**2/7 + 26*d/7 + 60/7 = 0. What is d?
-1, 2, 15
Let 5*n**3/3 + 8*n**2 + 37*n/3 + 6 = 0. Calculate n.
-2, -9/5, -1
Suppose 3*x**2/7 + 177*x/7 + 2610/7 = 0. Calculate x.
-30, -29
Factor h**3 - 57*h**2 - h + 57.
(h - 57)*(h - 1)*(h + 1)
Find u such that 2*u**3/3 - 64*u**2/3 + 38*u/3 + 248 = 0.
-3, 4, 31
What is j in 9*j**3 + 78*j**2 - 27*j = 0?
-9, 0, 1/3
Factor 2*q**4/9 + 40*q**3/9 + 254*q**2/9 + 56*q.
2*q*(q + 4)*(q + 7)*(q + 9)/9
Factor 2*t**2/5 + 996*t/5 + 124002/5.
2*(t + 249)**2/5
Let 3*b**4 - 57*b**3 + 315*b**2 - 147*b - 2058 = 0. What is b?
-2, 7
Factor -o**4/5 + 5*o**3 - 206*o**2/5 + 124*o - 120.
-(o - 10)**2*(o - 3)*(o - 2)/5
Factor -k**3 - 507*k**2 + k + 507.
-(k - 1)*(k + 1)*(k + 507)
What is h in 2*h**5/3 - 20*h**4/3 + 14*h**3 + 8*h**2/3 - 56*h/3 = 0?
-1, 0, 2, 7
Let -x**2/5 + 43*x/5 - 92 = 0. What is x?
20, 23
Let -c**4 - 40*c**3 - 261*c**2 - 146*c + 448 = 0. What is c?
-32, -7, -2, 1
Factor -4*a**2 + 42040*a - 110460100.
-4*(a - 5255)**2
Factor 2*o**4/3 - 2*o**3 - 4*o**2 + 16*o/3.
2*o*(o - 4)*(o - 1)*(o + 2)/3
Solve x**3/5 - 3*x**2/5 + 2*x/5 = 0.
0, 1, 2
Find i, given that 3*i**3/4 - 3*i**2/2 - 45*i/4 + 27 = 0.
-4, 3
Factor -4*k**4 - 67*k**3 + 251*k**2 - 180*k.
-k*(k - 1)*(k + 20)*(4*k - 9)
Factor -3*q**5 + 45*q**4 + 135*q**3 - 2025*q**2 - 9720*q - 11664.
-3*(q - 12)**2*(q + 3)**3
Factor g**2/2 - 20*g + 279/2.
(g - 31)*(g - 9)/2
What is h in -3*h**4 + 72*h**3 + 1050*h**2 + 3600*h + 2625 = 0?
-5, -1, 35
Factor -3*u**2/2 - 27*u - 108.
-3*(u + 6)*(u + 12)/2
Find g such that -185073116*g**3/7 - 3093144*g**2/7 - 17232*g/7 - 32/7 = 0.
-2/359
Factor l**3/2 - 19*l**2 - 41*l/2 + 39.
(l - 39)*(l - 1)*(l + 2)/2
Find r such that 10*r**3/11 - 226*r**2/11 + 928*r/11 + 408/11 = 0.
-2/5, 6, 17
Factor -f**2/10 + 8*f/5.
-f*(f - 16)/10
Factor -5*w**3 + 75*w**2.
-5*w**2*(w - 15)
Solve -3*v**2 + 2271*v + 2274 = 0 for v.
-1, 758
Determine w so that -484*w**4 - 3564*w**3 + 2624*w**2 + 1296*w + 128 = 0.
-8, -2/11, 1
Factor -6*i**3 + 856*i**2 - 2234*i - 840.
-2*(i - 140)*(i - 3)*(3*i + 1)
Factor -x**3/2 + 119*x**2 - 1397*x/2 + 580.
-(x - 232)*(x - 5)*(x - 1)/2
Suppose z**5 + 46*z**4 + 317*z**3 - 4768*z**2 + 13716*z - 11664 = 0. Calculate z.
-27, 2, 4
Find g, given that 3*g**2 - 150*g + 423 = 0.
3, 47
Factor -5*u**3 - 305*u**2 + 625*u - 315.
-5*(u - 1)**2*(u + 63)
Determine f, given that -5*f**4/2 + 45*f**3/2 - 105*f**2/2 + 95*f/2 - 15 = 0.
1, 6
Determine v, given that v**3/4 - 31*v**2/2 + 59*v - 58 = 0.
2, 58
Solve 2*o**4/15 + 58*o**3/5 + 1232*o**2/5 - 3872*o/15 = 0.
-44, 0, 1
Solve -3*v**5 - 96*v**4 - 765*v**3 + 96*v**2 + 768*v = 0 for v.
-16, -1, 0, 1
Determine a so that a**2 - 7*a + 12 = 0.
3, 4
Find a, given that -2*a**2 - 596*a - 1770 = 0.
-295, -3
Solve -15*n**4 + 35106*n**3 - 27392040*n**2 + 7129231200*n - 2847312000 = 0.
2/5, 780
Suppose -2*k**4 + 168*k**3 - 318*k**2 - 832*k + 984 = 0. Calculate k.
-2, 1, 3, 82
Solve 2*v**2/7 - 18/7 = 0 for v.
-3, 3
Determine o, given that o**5/4 + 6*o**4 + 117*o**3/4 + 83*o**2/2 + 18*o = 0.
-18, -4, -1, 0
Factor 76*z**4 + 220*z**3 + 128*z**2 - 16*z.
4*z*(z + 1)*(z + 2)*(19*z - 2)
Factor -i**3/4 + 47*i**2/2 - 90*i.
-i*(i - 90)*(i - 4)/4
Suppose 273529*i**2/2 - 6276*i + 72 = 0. What is i?
12/523
Factor -3*n**2 - 270*n - 6075.
-3*(n + 45)**2
Factor -4*d**4/5 + 3*d**3/5 + 9*d**2/5 + 2*d/5.
-d*(d - 2)*(d + 1)*(4*d + 1)/5
Factor -3*y**3/5 - 3*y**2/5.
-3*y**2*(y + 1)/5
Determine u, given that -2*u**3 + 18*u**2 - 16*u = 0.
0, 1, 8
Find y such that 2*y**2/5 - 258*y/5 + 1476/5 = 0.
6, 123
Let -2*w**5 - 39*w**4 - 296*w**3 - 1083*w**2 - 1880*w - 1200 = 0. Calculate w.
-5, -4, -3/2
Determine u, given that -u**4/4 + 11*u**3 + 139*u**2/4 + 47*u/2 = 0.
-2, -1, 0, 47
Factor -5*o**3 - 60*o**2 - 100*o.
-5*o*(o + 2)*(o + 10)
Suppose 5*v**5 - 2010*v**4 + 204000*v**3 - 400000*v**2 = 0. Calculate v.
0, 2, 200
Find g such that 2*g**4 - 157*g**3/2 - 121*g**2/2 + 20*g = 0.
-1, 0, 1/4, 40
Determine u, given that -2*u**3 + 1620*u**2 + 2*u - 1620 = 0.
-1, 1, 810
Solve f**3 - 14*f**2 + 11*f + 26 = 0.
-1, 2, 13
Factor -4*s**5/5 - 4*s**4 - 24*s**3/5 + 16*s**2/5 + 32*s/5.
-4*s*(s - 1)*(s + 2)**3/5
Determine z so that 6*z**4 + 3795*z**3 + 5679*z**2 - 3*z - 1893 = 0.
-631, -1, 1/2
Let -35*m**2 - 6515*m - 930 = 0. What is m?
-186, -1/7
Solve 2*h**4/9 - 16*h**3/9 + 32*h**2/9 = 0.
0, 4
Find a such that a**2 - 37*a - 38 = 0.
-1, 38
Factor -t**3/3 - 5*t**2/3 + 22*t/3 + 56/3.
-(t - 4)*(t + 2)*(t + 7)/3
Factor 1250*p**2/23 - 23200*p/23 + 107648/23.
2*(25*p - 232)**2/23
Solve 2*u**2/9 - 172*u + 33282 = 0.
387
Factor -q**3 - 2112*q**2 - 1113021*q + 2234498.
-(q - 2)*(q + 1057)**2
Determine u, given that 3*u**5 + 69*u**4 + 429*u**3 + 363*u**2 = 0.
-11, -1, 0
Suppose -5*h**3 + 85*h**2 - 155*h + 75 = 0. Calculate h.
1, 15
Let -2*v**4/3 + 106*v**3/3 - 104*v**2/3 = 0. What is v?
0, 1, 52
Factor 4*l**4 + 20*l**3 - 24*l**2.
4*l**2*(l - 1)*(l + 6)
Factor j**2/3 + 7*j - 232/3.
(j - 8)*(j + 29)/3
Factor 3*v**2 - 63*v + 312.
3*(v - 13)*(v - 8)
Factor 3*r**3/7 - 639*r**2/7 - 1944*r/7.
3*r*(r - 216)*(r + 3)/7
Solve -4*f**5 - 4*f**4 + 36*f**3 - 44*f**2 + 16*f = 0 for f.
-4, 0, 1
Factor a**5 - 81*a**4 + 1599*a**3 + 1681*a**2.
a**2*(a - 41)**2*(a + 1)
Determine g, given that -6*g**2/11 - 1224*g/11 - 1218/11 = 0.
-203, -1
Determine z, given that 2*z**5/7 + 20*z**4/7 + 62*z**3/7 + 60*z**2/7 = 0.
-5, -3, -2, 0
Let -4*g**3 + 52*g**2 - 136*g - 192 = 0. Calculate g.
-1, 6, 8
Determine f, given that f**5 - 66*f**4 + 1017*f**3 + 2516*f**2 - 3468*f = 0.
-3, 0, 1, 34
Factor -2*m**2/23 + 2216*m/23.
-2*m*(m - 1108)/23
Solve -m**4 + 25*m**3/3 - 65*m**2/3 + 55*m/3 - 4 = 0.
1/3, 1, 3, 4
Determine o, given that -2*o**3 - 36*o**2 + 42*o + 76 = 0.
-19, -1, 2
Factor -7*i**2/6 + 6*i + 6.
-(i - 6)*(7*i + 6)/6
What is j in -32*j**2/7 - 130*j/7 - 8/7 = 0?
-4, -1/16
Factor -2*p**2/13 + 1732*p/13 - 374978/13.
-2*(p - 433)**2/13
Find o, given that -4*o**3 - 100*o**2 = 0.
-25, 0
Factor 2*t**3/19 - 208*t**2/19 - 2*t/19 + 208/19.
2*(t - 104)*(t - 1)*(t + 1)/19
Solve 9*o**5 - 228*o**4 + 1152*o**3 - 2178*o**2 + 1767*o - 522 = 0 for o.
1, 3, 58/3
Solve 4*q**4 - 17*q**3 + 22*q**2 - 9*q = 0.
0, 1, 9/4
Factor w**2 + 75*w + 74.
(w + 1)*(w + 74)
Factor -2*d**5/5 + 16*d**4/5 + 7*d**3/2 + 9*d**2/10.
-d**2*(d - 9)*(2*d + 1)**2/10
Factor 10*v**5 + 24*v**4 + 18*v**3 +