t**3 - 55065*t**2 + 208060*t - 204020 = 0.
2, 101
Determine n, given that -n**2 - 97*n - 372 = 0.
-93, -4
Suppose -2*n**2 + 1136*n + 1138 = 0. Calculate n.
-1, 569
Determine r so that -r**5/3 + 7*r**4/3 - 5*r**3/3 - 7*r**2/3 + 2*r = 0.
-1, 0, 1, 6
Factor 2*x**3/11 - 54*x**2/11 + 102*x/11 - 50/11.
2*(x - 25)*(x - 1)**2/11
Let 2*g**3 - 108*g**2 + 1426*g - 1320 = 0. What is g?
1, 20, 33
Factor -4*n**5 - 12*n**4 - 8*n**3.
-4*n**3*(n + 1)*(n + 2)
Factor 5*x**3 + 50*x**2 + 120*x.
5*x*(x + 4)*(x + 6)
Solve -3*t**3 + 21*t**2 + 63*t - 81 = 0.
-3, 1, 9
Determine u so that -2*u**2 + 56*u - 392 = 0.
14
Factor i**4/3 + 4*i**3 - i**2/3 - 4*i.
i*(i - 1)*(i + 1)*(i + 12)/3
Factor d**5/3 + 5*d**4/3 - 14*d**3/3 + 2*d**2/3 + 13*d/3 - 7/3.
(d - 1)**3*(d + 1)*(d + 7)/3
Find f such that 4*f**2/3 - 16*f - 112/3 = 0.
-2, 14
Factor -2*w**4 + 12*w**3 - 18*w**2 - 8*w + 24.
-2*(w - 3)*(w - 2)**2*(w + 1)
Factor -3*t**5 + 51*t**4.
-3*t**4*(t - 17)
Factor 5*c**3 - 135*c**2 - 5*c + 135.
5*(c - 27)*(c - 1)*(c + 1)
Determine b, given that -3*b**5 - 243*b**4 - 5274*b**3 - 14394*b**2 - 13923*b - 4563 = 0.
-39, -1
Determine z so that -z**4 - 9*z**3 - 25*z**2 - 27*z - 10 = 0.
-5, -2, -1
Factor -4*q**2/7 - 44*q - 304/7.
-4*(q + 1)*(q + 76)/7
What is d in 3*d**3 + 216*d**2 + 213*d = 0?
-71, -1, 0
Factor -4*f**3 - 1436*f**2 + 4*f + 1436.
-4*(f - 1)*(f + 1)*(f + 359)
Determine h so that -4*h**5 - 104*h**4 - 816*h**3 - 2016*h**2 = 0.
-14, -6, 0
Factor 3*r**2/2 - 345*r/2.
3*r*(r - 115)/2
Suppose -2*d**3/17 + 54*d**2/17 - 486*d/17 + 1458/17 = 0. Calculate d.
9
Solve -j**3 - 23*j**2 - 107*j - 85 = 0 for j.
-17, -5, -1
Determine d, given that 4*d**3 - 60*d**2 + 192*d + 256 = 0.
-1, 8
Let 12*s**2 + 375*s + 93 = 0. Calculate s.
-31, -1/4
Factor 6*v**5/5 + 52*v**4/5 - 18*v**3/5.
2*v**3*(v + 9)*(3*v - 1)/5
Determine r so that 32*r**4/3 - 176*r**3/3 + 274*r**2/3 - 106*r/3 + 4 = 0.
1/4, 2, 3
Find b such that b**3/3 - 4*b**2/3 - 17*b + 18 = 0.
-6, 1, 9
Determine a so that -32*a**3 - 130*a**2 - 136*a - 8 = 0.
-2, -1/16
Factor -4*c**2 + 92*c.
-4*c*(c - 23)
Solve -15*f**4 + 3*f**3 + 12*f**2 = 0 for f.
-4/5, 0, 1
Determine f so that 3*f**5 + 3*f**4 - 48*f**3 + 60*f**2 = 0.
-5, 0, 2
Factor 3*w**2/5 + 6*w/5.
3*w*(w + 2)/5
Factor x**2 - 66*x + 128.
(x - 64)*(x - 2)
Suppose -55*p**4 - 175*p**3 - 195*p**2 - 85*p - 10 = 0. Calculate p.
-1, -2/11
Factor -2*t**2/5 - 2*t.
-2*t*(t + 5)/5
Factor -14*z**3/11 - 20*z**2/11 - 6*z/11.
-2*z*(z + 1)*(7*z + 3)/11
Factor -r**3/5 - r**2/5 + 4*r/5 + 4/5.
-(r - 2)*(r + 1)*(r + 2)/5
Find o, given that -2*o**5/15 - 8*o**4/5 + 232*o**3/15 + 92*o**2/5 - 46*o/3 - 84/5 = 0.
-18, -1, 1, 7
What is z in -3*z**3/5 + 6*z**2/5 + 12*z/5 - 24/5 = 0?
-2, 2
Solve 2*y**4 + 266*y**3 - 6*y**2 - 802*y - 532 = 0.
-133, -1, 2
Factor -3*d**5 + 15*d**4 - 18*d**3.
-3*d**3*(d - 3)*(d - 2)
What is s in -5*s**3 + 215*s**2 - 1680*s - 14400 = 0?
-5, 24
Let -5*n**5 + 120*n**4 + 130*n**3 - 120*n**2 - 125*n = 0. What is n?
-1, 0, 1, 25
Solve -q**3/4 + 7*q**2/4 - 4*q + 3 = 0.
2, 3
Factor -4*b**2/3 + 36*b - 560/3.
-4*(b - 20)*(b - 7)/3
Factor 4*v**2 + 32*v + 48.
4*(v + 2)*(v + 6)
Determine s so that 3*s**2 - 714*s + 1416 = 0.
2, 236
What is v in -3*v**3 + 33*v**2 + 168*v + 180 = 0?
-2, 15
Factor -z**3/2 - 5*z**2 + 37*z/2 - 13.
-(z - 2)*(z - 1)*(z + 13)/2
Factor -k**3 - 3231*k**2 - 3479787*k - 1249243533.
-(k + 1077)**3
Factor -2*i**2 + 2028*i - 514098.
-2*(i - 507)**2
Determine g so that -12*g**4 - 592*g**3 - 7100*g**2 + 5000*g = 0.
-25, 0, 2/3
Factor 5*m**4 + 365*m**3.
5*m**3*(m + 73)
Factor q**2 + 16*q + 64.
(q + 8)**2
Factor 2*k**2 + 192*k - 194.
2*(k - 1)*(k + 97)
Suppose -10*l**5/17 + 564*l**4/17 - 774*l**3/17 + 220*l**2/17 = 0. What is l?
0, 2/5, 1, 55
Determine b so that 2*b**4/9 + 4534*b**3/9 + 2571910*b**2/9 + 2567378*b/9 = 0.
-1133, -1, 0
Suppose -r**5/4 + 163*r**4/4 - 7035*r**3/4 + 31837*r**2/4 - 6241*r = 0. Calculate r.
0, 1, 4, 79
Factor -o**2/6 - o/3 + 4/3.
-(o - 2)*(o + 4)/6
Let 2*v**2/19 + 196*v/19 + 4802/19 = 0. What is v?
-49
Suppose -2*k**4/3 + 10*k**3/3 + 16*k**2 + 8*k/3 - 64/3 = 0. Calculate k.
-2, 1, 8
Factor 2*n**4/3 - 8*n**3/3 - 38*n**2/3 - 28*n/3.
2*n*(n - 7)*(n + 1)*(n + 2)/3
Suppose -5*d**4 + 565*d**3 - 555*d**2 - 565*d + 560 = 0. Calculate d.
-1, 1, 112
Find w such that -3*w**3 - 333*w**2 - 9405*w - 9075 = 0.
-55, -1
Factor -3*w**4/2 + 135*w**3/2 - 936*w**2 + 2688*w + 18432.
-3*(w - 16)**3*(w + 3)/2
Factor 3*v**2 + 186*v - 189.
3*(v - 1)*(v + 63)
Solve -3*z**3 + 12*z**2 + 75*z - 84 = 0.
-4, 1, 7
Find n such that 8*n**4 - 6*n**3 - 18*n**2 - 4*n = 0.
-1, -1/4, 0, 2
Factor n**2/2.
n**2/2
Solve -2*a**4/3 - 2*a**3 + 42*a**2 - 170*a/3 - 100 = 0.
-10, -1, 3, 5
Factor -m**2/10 + 3*m/5 - 1/2.
-(m - 5)*(m - 1)/10
Find o such that -676*o**4/5 + 9256*o**3/5 + 13036*o**2/5 + 3344*o/5 + 48 = 0.
-1, -2/13, 15
Suppose 48*t**5/11 + 142*t**4/11 - 6*t**3/11 - 192*t**2/11 + 8*t/11 = 0. Calculate t.
-2, 0, 1/24, 1
Factor -4*o**4 - 1032*o**3 - 89760*o**2 - 2716600*o - 7369500.
-4*(o + 3)*(o + 85)**3
Suppose 1372*a**4 + 2156*a**3 + 924*a**2 + 148*a + 8 = 0. What is a?
-1, -2/7, -1/7
Solve -c**2 - 19*c + 120 = 0.
-24, 5
What is s in -5*s**2 + 20*s + 25 = 0?
-1, 5
Factor g**4/6 + 29*g**3/6 - 2*g**2 - 182*g/3 - 232/3.
(g - 4)*(g + 2)**2*(g + 29)/6
Find m such that -2*m**2 + 288*m - 10368 = 0.
72
Determine m, given that 2*m**3/7 + 4*m**2/7 - 18*m/7 - 36/7 = 0.
-3, -2, 3
Solve f**5 - 2*f**4/3 - 7*f**3 - 4*f**2/3 + 4*f = 0.
-2, -1, 0, 2/3, 3
Determine p, given that 39*p**3 + 183*p**2 + 144*p = 0.
-48/13, -1, 0
Factor 68*x**5/7 + 270*x**4/7 + 264*x**3/7 - 8*x**2/7.
2*x**2*(x + 2)**2*(34*x - 1)/7
Solve 4*p**2 + 160*p + 1456 = 0 for p.
-26, -14
Find h such that 3*h**2/7 - 30*h/7 = 0.
0, 10
Factor 2*v**3 - 24*v**2 + 58*v + 84.
2*(v - 7)*(v - 6)*(v + 1)
Solve -245*x**3 - 1365*x**2 - 720*x - 100 = 0.
-5, -2/7
Suppose a**5 - 7*a**4 + 9*a**3 + 27*a**2 - 54*a = 0. Calculate a.
-2, 0, 3
Factor o**3/2 - 29*o**2/2 - 440*o - 2450.
(o - 49)*(o + 10)**2/2
Suppose 2*v**3/15 - 14*v**2/15 + 16*v/15 + 32/15 = 0. Calculate v.
-1, 4
Factor -3*r**3 - 21*r**2.
-3*r**2*(r + 7)
Suppose -3*d**2 - 5463*d - 5460 = 0. Calculate d.
-1820, -1
Suppose 2*p**4 + 58*p**3 - 254*p**2 + 326*p - 132 = 0. Calculate p.
-33, 1, 2
Factor r**4/4 - 48*r**3 + 3072*r**2 - 65536*r.
r*(r - 64)**3/4
Solve 3*a**3/2 + 19*a**2/2 - 34*a + 18 = 0.
-9, 2/3, 2
Factor 4*n**2/5 + 1456*n/5 - 1476.
4*(n - 5)*(n + 369)/5
Factor 6*d**2 + 165*d - 84.
3*(d + 28)*(2*d - 1)
Suppose 3*y**4 + 37*y**3 + 31*y**2 - 137*y + 66 = 0. Calculate y.
-11, -3, 2/3, 1
Factor 2*t**4/7 - 2*t**3/7.
2*t**3*(t - 1)/7
Suppose 3*v**2 - 66*v = 0. What is v?
0, 22
Factor f**5 - 9*f**4 + 23*f**3 - 3*f**2 - 36*f.
f*(f - 4)*(f - 3)**2*(f + 1)
Factor -4*h**4 + 88*h**3 - 432*h**2 + 800*h - 512.
-4*(h - 16)*(h - 2)**3
Factor -d**3 + d.
-d*(d - 1)*(d + 1)
Factor 5*g**4 + 145*g**3 + 400*g**2 + 260*g.
5*g*(g + 1)*(g + 2)*(g + 26)
Suppose -4*n**4/7 + 16*n**3 + 684*n**2/7 - 792*n/7 = 0. Calculate n.
-6, 0, 1, 33
Suppose -4*u**3 - 568*u**2 - 1124*u - 560 = 0. Calculate u.
-140, -1
What is l in 2*l**3 - 56*l**2 + 256*l + 2048 = 0?
-4, 16
Factor f**3/6 - f**2/6 - 8*f/3 + 8/3.
(f - 4)*(f - 1)*(f + 4)/6
Solve 3*r**2 + 354*r + 10443 = 0 for r.
-59
Factor i**2/3 + 32*i/3 + 20.
(i + 2)*(i + 30)/3
Factor -z**2/11 - 268*z/11.
-z*(z + 268)/11
Determine g, given that -2*g**2/13 - 50*g = 0.
-325, 0
Let i**3 + 51*i**2 + 554*i + 504 = 0. Calculate i.
-36, -14, -1
Find v such that -2*v**5 + 16*v**4/3 - 2*v**3/3 - 16*v**2/3 + 8*v/3 = 0.
-1, 0, 2/3, 1, 2
Factor 172*h**3/9 - 4*h**2/9.
4*h**2*(43*h - 1)/9
Find p, given that -338*p**2 + 364*p - 98 = 0.
7/13
Factor -x**4/2 + 9*x**3/2 - 29*x**2/2 + 39*x/2 - 9.
-(x - 3)**2*(x - 2)*(x - 1)/2
Let 5*i**3/2 + 71*i**2 + 603*i/2 - 207 = 0. What is i?
-23, -6, 3/5
Determine j so that j**4 + 24*j**3/5 + 3*j**2 - 4*j/5 = 0.
-4, -1, 0, 1/5
Solve 36*y**2 - 1396*y - 312 = 0.
-2/9, 39
Let 3*c**5/4 + 159*c**4/4 + 147*c**3/4 - 471*c**2/4 - 75*c/2 + 78 = 0. What is c?
-52, -2, -1, 1
Factor x**2 + 82*x + 1681.
(x + 41)**2
Factor -49*q**3 - 224*q**2 - 116*q - 16.
-(q + 4)*(7*q + 2)**2
Let -g**4/2 + 5*g**3 - 29*g**2/2 + 16*g - 6 = 0. What is g?
1, 2, 6
Determine w, given that 1805*w**2 - 74480*w + 768320 = 0.
392/19
Factor 5*f**3 + 905*f**2/4 + 1105*f/4 + 55.
5*(f + 1)*(f + 44)*(4*f + 1)/4
Solv