 0, 1
Determine v, given that 4*v**5 - 28*v**3 + 8*v**2 + 48*v - 32 = 0.
-2, 1, 2
Solve i**3/3 - 31*i**2/3 - 100*i/3 - 68/3 = 0 for i.
-2, -1, 34
Suppose 8*a**4/19 + 82*a**3/19 + 212*a**2/19 + 48*a/19 = 0. Calculate a.
-6, -4, -1/4, 0
Factor -2*x**3/7 + 72*x**2/7 + 74*x/7.
-2*x*(x - 37)*(x + 1)/7
Suppose 7*v**4/5 - 5479*v**3/5 + 1068594*v**2/5 + 1381408*v/5 + 307328/5 = 0. Calculate v.
-1, -2/7, 392
Factor 5*t**2 - 35*t - 2470.
5*(t - 26)*(t + 19)
Factor -2*p**2 - 46*p - 44.
-2*(p + 1)*(p + 22)
Factor -14*d**3/9 + 134*d**2/9 - 8*d.
-2*d*(d - 9)*(7*d - 4)/9
Solve -3*l**3/4 + 459*l**2/4 - 23409*l/4 + 397953/4 = 0.
51
Factor -3*g**2 - 108*g - 105.
-3*(g + 1)*(g + 35)
Factor -18*p**4 + 86*p**3 - 96*p**2.
-2*p**2*(p - 3)*(9*p - 16)
Determine c so that 5*c**3 - 855*c**2 + 1690*c = 0.
0, 2, 169
Solve 2*f**3 + 38*f**2 + 70*f + 34 = 0.
-17, -1
Find r such that -2*r**2/3 + 44*r - 726 = 0.
33
Suppose -3*s**3/2 - 79*s**2/2 - 101*s/2 - 25/2 = 0. What is s?
-25, -1, -1/3
Find f such that -3*f**4/2 - 12*f**3 + 117*f**2/2 + 87*f - 132 = 0.
-11, -2, 1, 4
Factor -5*q**3/3 - 1065*q**2 - 170665*q - 508805/3.
-5*(q + 1)*(q + 319)**2/3
Factor 2*a**2 + 2428*a - 2430.
2*(a - 1)*(a + 1215)
Factor -4*d**2 + 3680*d - 846400.
-4*(d - 460)**2
Factor -3*k**3/4 + 9*k**2/2 - 9*k + 6.
-3*(k - 2)**3/4
Factor r**4/2 + 16*r**3 + 117*r**2/2 + 71*r + 28.
(r + 1)**2*(r + 2)*(r + 28)/2
Find o, given that -o**5/3 + 35*o**4 - 1168*o**3/3 + 1644*o**2 - 8992*o/3 + 1984 = 0.
2, 4, 93
Factor p**2/4 + 25*p/2 + 625/4.
(p + 25)**2/4
Factor -2*h**2 + 976*h + 978.
-2*(h - 489)*(h + 1)
Factor 2*s**3/3 + 12*s**2 + 22*s/3 - 68.
2*(s - 2)*(s + 3)*(s + 17)/3
Factor 4*l**2/7 + 16*l/7 - 20/7.
4*(l - 1)*(l + 5)/7
Factor -2*o**2 - 84*o + 270.
-2*(o - 3)*(o + 45)
Find z, given that -z**4/4 + 15*z**3/4 - z**2/2 - 78*z = 0.
-4, 0, 6, 13
Factor -5*x**3 - 27645*x**2 - 38198475*x + 38226125.
-5*(x - 1)*(x + 2765)**2
Suppose -2*s**2/19 - 20*s/19 - 32/19 = 0. Calculate s.
-8, -2
Factor -4*k**2 + 224*k - 3136.
-4*(k - 28)**2
Solve -6500*a**3 - 6492*a**2 + 8*a = 0.
-1, 0, 2/1625
Find n, given that -3*n**3/4 + 9*n**2/4 + 48*n + 45 = 0.
-6, -1, 10
Find v such that 2*v**5/5 + 26*v**4/5 + 4*v**3 - 236*v**2/5 + 298*v/5 - 22 = 0.
-11, -5, 1
Let -r**3 - 4*r**2 - 3*r = 0. What is r?
-3, -1, 0
Factor -x**4/4 + x**3 + 29*x**2/4 + 6*x.
-x*(x - 8)*(x + 1)*(x + 3)/4
Solve 2*p**2/15 - 32*p/15 + 22/3 = 0.
5, 11
Determine q so that 4*q**4/3 - 374*q**3/9 + 2332*q**2/9 + 9146*q/9 + 5780/9 = 0.
-2, -5/6, 17
Determine y so that y**2 + 296*y + 588 = 0.
-294, -2
Solve -4*c**2 - 24*c - 20 = 0.
-5, -1
Let -v**3 - 14*v**2 - 11*v + 26 = 0. What is v?
-13, -2, 1
Suppose -g**2/2 - 10*g - 75/2 = 0. What is g?
-15, -5
Factor -27*p**4 - 153*p**3 + 240*p**2 - 84*p.
-3*p*(p + 7)*(3*p - 2)**2
Factor -99*j**2/7 + 2*j/7.
-j*(99*j - 2)/7
Factor 4*b**2 - 1620*b.
4*b*(b - 405)
Factor 3*j**2 + 435*j - 438.
3*(j - 1)*(j + 146)
Factor -y**4/4 + 27*y**3/4 + 172*y**2.
-y**2*(y - 43)*(y + 16)/4
Determine l so that l**2/8 + 25*l/4 + 301/8 = 0.
-43, -7
Factor -15*l**2 + 2390*l + 1600.
-5*(l - 160)*(3*l + 2)
Suppose 2*t**3/5 - 10*t = 0. Calculate t.
-5, 0, 5
Factor 2*g**3/3 + 616*g**2/3 + 47432*g/3.
2*g*(g + 154)**2/3
Solve -2*j**5/3 + 2*j**4/3 + 10*j**3/3 - 10*j**2/3 - 8*j/3 + 8/3 = 0 for j.
-2, -1, 1, 2
Find s, given that 35*s**5 - 2565*s**4 + 625*s**3 + 7625*s**2 + 2940*s - 1460 = 0.
-1, 2/7, 2, 73
Solve w**4/3 - 5*w**3/3 = 0 for w.
0, 5
Factor k**3 + 158*k**2 - 644*k + 648.
(k - 2)**2*(k + 162)
Find j, given that 4*j**4 - 100*j**3 + 764*j**2 - 1484*j - 2352 = 0.
-1, 7, 12
Factor -22*j**2/5 + 304*j/5 + 56/5.
-2*(j - 14)*(11*j + 2)/5
Determine y so that 8*y**4/7 + 20*y**3/7 - 8*y**2 - 32*y/7 = 0.
-4, -1/2, 0, 2
What is u in u**5/3 - 29*u**3 - 190*u**2/3 + 212*u - 120 = 0?
-6, 1, 10
Suppose 32*y**5 + 612*y**4 + 1196*y**3 + 684*y**2 + 68*y = 0. What is y?
-17, -1, -1/8, 0
Factor -5*q**5 + 100*q**4 + 1380*q**3 + 3490*q**2 + 3265*q + 1050.
-5*(q - 30)*(q + 1)**3*(q + 7)
Find k such that -k**2/3 - 18*k - 243 = 0.
-27
Factor y**2/3 - 14*y/3 - 32/3.
(y - 16)*(y + 2)/3
Solve 2*f**2 - 292*f + 10658 = 0.
73
Determine z so that 2*z**2 + 54*z + 52 = 0.
-26, -1
Find k, given that k**2/2 + 4228*k + 8937992 = 0.
-4228
Determine f, given that 4*f**3/7 + 4*f**2/7 - 4*f/7 - 4/7 = 0.
-1, 1
Factor 25*u**5/2 + 135*u**4 + 102*u**3 + 20*u**2.
u**2*(u + 10)*(5*u + 2)**2/2
Let 35*n**2 - 71*n + 2 = 0. What is n?
1/35, 2
Solve -i**4/3 - 10*i**3/3 - 4*i**2 + 30*i + 63 = 0.
-7, -3, 3
Factor h**2/5 - 12*h/5 - 28/5.
(h - 14)*(h + 2)/5
Factor -y**4/9 - 16*y**3/3 + 104*y**2/9 + 64*y/3 - 400/9.
-(y - 2)**2*(y + 2)*(y + 50)/9
Solve g**4 + 12*g**3 + 20*g**2 = 0 for g.
-10, -2, 0
Determine n so that 3*n**2 + 348*n + 345 = 0.
-115, -1
Factor -2*m**2/15 - 122*m/3 - 4172/15.
-2*(m + 7)*(m + 298)/15
Find y, given that 5*y**4 - 60*y**3 - 315*y**2 - 110*y + 480 = 0.
-3, -2, 1, 16
Factor 2*u**2 - 484*u + 29282.
2*(u - 121)**2
Solve 4*l**3/7 - 48*l**2/7 + 144*l/7 - 128/7 = 0 for l.
2, 8
Factor -5*l**4 - 25*l**3 + 35*l**2 + 25*l - 30.
-5*(l - 1)**2*(l + 1)*(l + 6)
Solve -r**3/7 + 5*r**2/7 - 2*r/7 - 8/7 = 0 for r.
-1, 2, 4
Factor k**5/4 - k**3/4.
k**3*(k - 1)*(k + 1)/4
Solve j**4 + 199*j**3 + 591*j**2 + 589*j + 196 = 0 for j.
-196, -1
Let 3*d**4 + 1461*d**3 - 4401*d**2 + 4407*d - 1470 = 0. Calculate d.
-490, 1
Factor -3*i**5 + 18*i**4 + 30*i**3 - 48*i**2 - 99*i - 42.
-3*(i - 7)*(i - 2)*(i + 1)**3
Factor -3*z**3 - 123*z**2 - 237*z - 117.
-3*(z + 1)**2*(z + 39)
Let a**2/6 - 545*a/3 + 363/2 = 0. What is a?
1, 1089
Factor -a**3/4 - a**2 - 5*a/4 - 1/2.
-(a + 1)**2*(a + 2)/4
What is b in -2*b**5 - 28*b**4 + 868*b**3 - 5416*b**2 + 10654*b - 6076 = 0?
-31, 1, 2, 7
Suppose 12*n**4 - 101*n**3 - 70*n**2 + 61*n + 18 = 0. Calculate n.
-1, -1/4, 2/3, 9
Let s**5 - 10*s**4 + 29*s**3 - 32*s**2 + 12*s = 0. Calculate s.
0, 1, 2, 6
Find l such that -l**5/6 + l**4/2 + 27*l**3/2 + 99*l**2/2 + 54*l = 0.
-3, 0, 12
Factor 3*j**5/7 + 6*j**4 + 216*j**3/7 + 480*j**2/7 + 384*j/7.
3*j*(j + 2)*(j + 4)**3/7
Factor 2*z**3/7 - 68*z**2/7 + 66*z/7.
2*z*(z - 33)*(z - 1)/7
What is w in -w**3/9 + 3*w**2 - 56*w/3 - 196/9 = 0?
-1, 14
Solve 6*t**5/13 - 32*t**4 + 9656*t**3/13 - 75900*t**2/13 + 17986*t/13 + 48668/13 = 0 for t.
-2/3, 1, 23
Solve 3*i**3 - 12*i**2 + 9*i = 0 for i.
0, 1, 3
Let 4*w**3 - 112*w**2 + 108*w = 0. Calculate w.
0, 1, 27
Solve -5*y**3 + 43*y**2 + 68*y + 20 = 0.
-1, -2/5, 10
Factor 4*y**2/3 + 656*y/3 + 26896/3.
4*(y + 82)**2/3
Suppose 2*w**3/3 - 2*w**2/3 - 32*w/3 - 40/3 = 0. What is w?
-2, 5
Suppose -6*y**2/5 - 608*y/5 - 160 = 0. Calculate y.
-100, -4/3
Solve 3*p**5/4 - 69*p**4/4 + 87*p**3 + 177*p**2 - 360*p - 432 = 0.
-2, -1, 2, 12
Factor 4*q**4 + 96*q**3 - 312*q**2 + 320*q - 108.
4*(q - 1)**3*(q + 27)
Determine i, given that -2*i**5/15 - 16*i**4/15 - 16*i**3/5 - 68*i**2/15 - 46*i/15 - 4/5 = 0.
-3, -2, -1
Suppose -3*x**4/4 + 4875*x**3/2 = 0. Calculate x.
0, 3250
Determine l, given that 4*l**3 + 24*l**2 - 64*l = 0.
-8, 0, 2
Factor 2*p**3/13 - 6*p**2/13 - 308*p/13.
2*p*(p - 14)*(p + 11)/13
Determine p, given that -3*p**3/4 - 123*p**2/4 + 831*p/4 - 705/4 = 0.
-47, 1, 5
Suppose -2*m**3 - 30*m**2 - 54*m - 26 = 0. What is m?
-13, -1
Let -4*z**2 + 656*z - 26896 = 0. What is z?
82
Factor -23*h**2 + h/6.
-h*(138*h - 1)/6
Suppose k**4/5 + 13*k**3/5 - 19*k**2/5 - 277*k/5 - 78 = 0. What is k?
-13, -3, -2, 5
Let -10*z**3 + 1981*z**2 - 98208*z + 9801 = 0. What is z?
1/10, 99
Find g such that 4*g**3/7 - 328*g**2/7 + 6724*g/7 = 0.
0, 41
Factor 3*o**5/8.
3*o**5/8
Factor -2*p**3/13 + 266*p**2/13 - 1032*p/13.
-2*p*(p - 129)*(p - 4)/13
Factor 5*c**4 + 20*c**3 - 55*c**2 + 30*c.
5*c*(c - 1)**2*(c + 6)
Determine y so that -y**3/6 - 14*y**2/3 - 55*y/2 + 75 = 0.
-15, 2
Factor 5*a**5/4 - 23*a**4 + 114*a**3 + 161*a**2/2 - 5341*a/4 + 1029/2.
(a - 7)**3*(a + 3)*(5*a - 2)/4
Determine w, given that -25*w**4 + 2190*w**3 + 3105*w**2 + 890*w = 0.
-1, -2/5, 0, 89
Factor 2*m**2 - 40*m + 72.
2*(m - 18)*(m - 2)
Let x**3 + 3810*x**2 + 4838700*x + 2048383000 = 0. What is x?
-1270
Determine b, given that 4*b**4 - 368*b**3 + 6120*b**2 - 11152*b + 5396 = 0.
1, 19, 71
Suppose -4*b**2/3 + 136*b/3 - 256/3 = 0. Calculate b.
2, 32
Factor 2*b**2/3 + 334*b/3.
2*b*(b + 167)/3
What is r in 2*r**2/13 + 14*r/13 + 24/13 = 0?
-4, -3
Let 8*l**5 + 36*l**4 + 24*l**3 - 44*l**2 - 