so that -3*b**4 - 150*b**3 - 1539*b**2 + 8748*b = 0.
-27, 0, 4
Suppose 45*k**2 - 1855*k + 410 = 0. Calculate k.
2/9, 41
Factor -2*w**2 - 44*w + 96.
-2*(w - 2)*(w + 24)
Suppose -4*m**3 + 14676*m**2 - 13468896*m + 13454224 = 0. What is m?
1, 1834
Factor -x**3/2 + 271*x**2/2 + 273*x.
-x*(x - 273)*(x + 2)/2
Factor g**2/3 - 11*g + 32/3.
(g - 32)*(g - 1)/3
Determine r so that 2*r**2/13 - 1062*r/13 - 164 = 0.
-2, 533
Let -169*j**4/2 - 819*j**3 - 1005*j**2/2 + 214*j - 18 = 0. What is j?
-9, -1, 2/13
Factor 5*q**3 - 50*q**2 + 135*q - 90.
5*(q - 6)*(q - 3)*(q - 1)
Solve -2*l**4 - 16*l**3 + 114*l**2 - 200*l + 104 = 0 for l.
-13, 1, 2
Factor 4*s**3 + 14292*s**2 + 12759180*s - 12773476.
4*(s - 1)*(s + 1787)**2
What is r in -r**2/10 - 48*r/5 + 333/2 = 0?
-111, 15
Factor -4*o**2 + 72*o - 320.
-4*(o - 10)*(o - 8)
Determine v, given that -2*v**3/5 + 28*v**2/5 - 26*v/5 = 0.
0, 1, 13
Factor 4*w**5/7 + 17*w**4/7 + 9*w**3/7 - 34*w**2/7 - 20*w/7 + 24/7.
(w - 1)*(w + 2)**3*(4*w - 3)/7
Factor 3*b**3 - 84*b**2 - 93*b + 174.
3*(b - 29)*(b - 1)*(b + 2)
Solve -2*g**3 - 24*g**2 - 58*g - 36 = 0.
-9, -2, -1
Factor 11*m**3 - 559*m**2 + 976*m + 196.
(m - 49)*(m - 2)*(11*m + 2)
Solve w**5 - 3*w**3 - 2*w**2 = 0 for w.
-1, 0, 2
Factor -r**3 - 2*r**2 - r.
-r*(r + 1)**2
Let -4*r**5/7 + 4*r**4/7 = 0. Calculate r.
0, 1
Factor y**5/5 + 39*y**4/5 + 111*y**3/5 + 109*y**2/5 + 36*y/5.
y*(y + 1)**3*(y + 36)/5
Let 18*k**3 + 34*k**2 - 4*k = 0. What is k?
-2, 0, 1/9
Solve -9*r**5 - 294*r**4 - 2817*r**3 - 2916*r**2 + 47952*r - 15552 = 0.
-12, 1/3, 3
Determine l so that 5*l**5 - 65*l**4 - 235*l**3 - 95*l**2 + 230*l + 160 = 0.
-2, -1, 1, 16
Factor 50*f**3 - 95*f**2 - 10*f.
5*f*(f - 2)*(10*f + 1)
Factor 11*x**2 + 217*x + 152.
(x + 19)*(11*x + 8)
Factor 245*g**3 + 12390*g**2 + 7020*g + 1000.
5*(g + 50)*(7*g + 2)**2
What is u in 4394*u**4 - 18590*u**3 + 4134*u**2 - 314*u + 8 = 0?
1/13, 4
Factor 5*d**4 + 15*d**3 + 15*d**2 + 5*d.
5*d*(d + 1)**3
Factor 3*l**3 - 5193*l**2 + 2249865*l - 2244675.
3*(l - 865)**2*(l - 1)
Factor k**5 + 28*k**4 + 165*k**3 - 450*k**2.
k**2*(k - 2)*(k + 15)**2
Let -2*t**2 - 24*t = 0. Calculate t.
-12, 0
Factor 3*t**3 - 117*t**2 - 243*t - 123.
3*(t - 41)*(t + 1)**2
What is x in -2*x**3/19 - 140*x**2/19 - 1726*x/19 + 212 = 0?
-53, -19, 2
Suppose -2*v**4/21 + 2*v**3/7 - 2*v**2/21 - 2*v/7 + 4/21 = 0. What is v?
-1, 1, 2
Factor -4*f**4 + 240*f**3 - 3832*f**2 + 6960*f - 3364.
-4*(f - 29)**2*(f - 1)**2
Factor -2*c**3/9 + 2*c**2/9 + 4*c/9.
-2*c*(c - 2)*(c + 1)/9
Factor w**3/3 + 4*w**2/3 + w/3 - 2.
(w - 1)*(w + 2)*(w + 3)/3
Factor u**3 - 135*u**2 + 2888*u + 3024.
(u - 108)*(u - 28)*(u + 1)
Let -v**4 + 8*v**3 + 25*v**2 - 44*v - 60 = 0. Calculate v.
-3, -1, 2, 10
Factor -j**5/4 - j**4/2 + 15*j**3/4.
-j**3*(j - 3)*(j + 5)/4
Factor -c**3/6 + 3*c**2/2 + c/6 - 3/2.
-(c - 9)*(c - 1)*(c + 1)/6
Factor -2*y**2/9 - 1240*y - 1729800.
-2*(y + 2790)**2/9
Find y such that 4*y**4/3 + 20*y**3/3 - 20*y**2 - 20*y/3 + 56/3 = 0.
-7, -1, 1, 2
Let -r**2/5 - 506*r - 320045 = 0. Calculate r.
-1265
Factor 2*o**5/3 - 2*o**4 + 4*o**3/3.
2*o**3*(o - 2)*(o - 1)/3
Determine o so that -8*o**5/21 - 38*o**4/21 + 34*o**3/21 + 14*o**2/3 - 106*o/21 + 20/21 = 0.
-5, -2, 1/4, 1
Solve 26*w**4 - 70*w**3 - 24*w**2 + 104*w + 32 = 0.
-1, -4/13, 2
Factor b**4/6 + 52*b**3 - 157*b**2 + 472*b/3 - 105/2.
(b - 1)**3*(b + 315)/6
Factor 2*v**4 - 6*v**3 - 10*v**2 + 6*v + 8.
2*(v - 4)*(v - 1)*(v + 1)**2
Let -2*t**3/17 - 36*t**2/17 + 42*t/17 + 76/17 = 0. What is t?
-19, -1, 2
Factor 5*x**2 + 640*x + 20480.
5*(x + 64)**2
Factor -3*r**3 + 311*r**2 - 8008*r - 2704.
-(r - 52)**2*(3*r + 1)
Solve 5*i**3 + 25*i**2 = 0.
-5, 0
Factor -3*a**3 + 1674*a**2 - 231840*a - 470400.
-3*(a - 280)**2*(a + 2)
Let -3*s**2 - 48*s - 45 = 0. What is s?
-15, -1
Let -4*f**5 - 68*f**4 + 84*f**3 + 212*f**2 - 80*f - 144 = 0. Calculate f.
-18, -1, 1, 2
Suppose z**2 + 34*z - 936 = 0. Calculate z.
-52, 18
Factor 4*i**3/9 + 16*i**2/9 - 112*i/9 + 128/9.
4*(i - 2)**2*(i + 8)/9
Factor -5*v**3 - 165*v**2 - 1440*v - 1280.
-5*(v + 1)*(v + 16)**2
Let -2*k**4/15 + 16*k**3/15 + 2*k**2/5 - 44*k/15 - 32/15 = 0. Calculate k.
-1, 2, 8
Factor q**4/6 - q**3/6 - 7*q**2/2 + 15*q/2.
q*(q - 3)**2*(q + 5)/6
Factor 5*b**2 + 40*b + 60.
5*(b + 2)*(b + 6)
Determine d so that 2*d**5/3 + 8*d**4/3 - 2*d**3/3 - 8*d**2/3 = 0.
-4, -1, 0, 1
Factor -w**4/2 - 3141*w**3/2 - 3288627*w**2/2 - 1147730823*w/2.
-w*(w + 1047)**3/2
Factor p**2/3 - 8*p + 44/3.
(p - 22)*(p - 2)/3
Find z such that -2*z**5 + 176*z**4 - 3314*z**3 - 24268*z**2 - 51512*z - 35344 = 0.
-2, 47
Find v, given that -v**2 - 66*v - 65 = 0.
-65, -1
Let -v**2/2 - 368*v + 737/2 = 0. Calculate v.
-737, 1
Suppose k**4 - 13*k**3 - 19*k**2 + 73*k - 42 = 0. Calculate k.
-3, 1, 14
Solve 3*u**2/5 - 78*u + 1143/5 = 0 for u.
3, 127
Solve -4*b**5 - 8*b**4 + 192*b**3 - 488*b**2 + 452*b - 144 = 0.
-9, 1, 4
Solve -98*g**4/11 - 560*g**3/11 - 1136*g**2/11 - 960*g/11 - 288/11 = 0 for g.
-2, -6/7
Factor 2*w**2/13 - 170*w/13 - 2772/13.
2*(w - 99)*(w + 14)/13
Factor -4*w**3/7 - 40*w**2/7 - 92*w/7 - 8.
-4*(w + 1)*(w + 2)*(w + 7)/7
Determine l so that l**2/5 + 1422*l/5 + 505521/5 = 0.
-711
Determine g, given that g**4 + 15*g**3 - 93*g**2 + 137*g - 60 = 0.
-20, 1, 3
Suppose 3*a**3/4 - 333*a**2/4 + 12321*a/4 - 151959/4 = 0. Calculate a.
37
Let -3*c**4 + 258*c**2 + 1080*c + 825 = 0. What is c?
-5, -1, 11
Determine q so that -4*q**3 - 152*q**2 + 2060*q - 4704 = 0.
-49, 3, 8
Determine y, given that -55*y**2 + 1530*y + 280 = 0.
-2/11, 28
Find l such that -6*l**5 + 26*l**4/3 + 280*l**3/3 - 416*l**2/3 + 128*l/3 = 0.
-4, 0, 4/9, 1, 4
Suppose -2*g**5/5 + 2*g**4/5 + 14*g**3/5 - 2*g**2/5 - 12*g/5 = 0. Calculate g.
-2, -1, 0, 1, 3
Factor 5*i**2 + 225*i - 2430.
5*(i - 9)*(i + 54)
Factor -35*v**3 + 11135*v**2 - 886425*v + 126405.
-5*(v - 159)**2*(7*v - 1)
Suppose -k**2/7 + 620*k/7 - 1851/7 = 0. What is k?
3, 617
Find j such that -2*j**4/7 + 20*j**3/7 - 74*j**2/7 + 120*j/7 - 72/7 = 0.
2, 3
Determine t, given that 4*t**2 + 76*t = 0.
-19, 0
What is o in -o**5/3 + 26*o**4/3 + 59*o**3/3 - 76*o**2/3 - 220*o/3 - 112/3 = 0?
-2, -1, 2, 28
Factor -2*l**4 - 39*l**3 - 18*l**2 + 19*l.
-l*(l + 1)*(l + 19)*(2*l - 1)
Factor -25*z**2/4 + 265*z/2 - 2809/4.
-(5*z - 53)**2/4
Let 4*u**5/3 - 4*u**4 - 4*u**3/3 + 44*u**2/3 - 16*u + 16/3 = 0. What is u?
-2, 1, 2
Suppose -12*m**4 - 141*m**3 + 7161*m**2 - 42471*m - 35937 = 0. What is m?
-33, -3/4, 11
Suppose 3*t**4/4 - 6*t**3 - 3*t**2/2 + 54*t - 189/4 = 0. What is t?
-3, 1, 3, 7
Suppose 128*i**2 - 12*i = 0. What is i?
0, 3/32
Factor 3*c**2 + 2946*c + 723243.
3*(c + 491)**2
Suppose -3*x**5 - 3*x**4 + 51*x**3 - 45*x**2 = 0. Calculate x.
-5, 0, 1, 3
Factor 2*b**3/3 + 4*b**2/3.
2*b**2*(b + 2)/3
Factor 4*f**2/5 + 8632*f/5 - 8636/5.
4*(f - 1)*(f + 2159)/5
Factor 162*v**4 - 252*v**3 - 136*v**2 - 16*v.
2*v*(v - 2)*(9*v + 2)**2
Solve -3*c**2 - 42*c - 72 = 0.
-12, -2
Factor m**4/4 + 3*m**3/2 + m**2 - 3*m/2 - 5/4.
(m - 1)*(m + 1)**2*(m + 5)/4
Factor -2*s**2 + 68*s + 144.
-2*(s - 36)*(s + 2)
Find h, given that -4*h**2 + 820*h + 824 = 0.
-1, 206
Factor 3*x**5 - 18*x**4 + 12*x**3 + 18*x**2 - 15*x.
3*x*(x - 5)*(x - 1)**2*(x + 1)
Determine f, given that 4*f**4 + 104*f**3 + 716*f**2 + 1864*f + 1632 = 0.
-17, -4, -3, -2
Let -s**2/2 + 4804*s - 11539208 = 0. Calculate s.
4804
Find s such that s**5/3 + 11*s**4/3 - 13*s**3/3 - 11*s**2/3 + 4*s = 0.
-12, -1, 0, 1
Factor a**5/5 - 23*a**4/5 + 143*a**3/5 - 121*a**2/5.
a**2*(a - 11)**2*(a - 1)/5
Factor -3*a**2 + 123*a + 540.
-3*(a - 45)*(a + 4)
Factor 2*g**3/7 - 150*g**2/7 - 152*g/7.
2*g*(g - 76)*(g + 1)/7
Factor 5*v**5/2 - 470*v**4 + 21130*v**3 + 90240*v**2 + 92160*v.
5*v*(v - 96)**2*(v + 2)**2/2
Find d, given that 3*d**5/2 + 6*d**4 - 15*d**3/2 = 0.
-5, 0, 1
Factor 5*w**4 - 75*w**3 + 70*w**2.
5*w**2*(w - 14)*(w - 1)
Solve -5*u**4 + 25*u**3 - 25*u**2 - 25*u + 30 = 0.
-1, 1, 2, 3
Find t, given that -t**5/9 + 10*t**4/9 - 13*t**3/3 + 74*t**2/9 - 68*t/9 + 8/3 = 0.
1, 2, 3
Find x such that -2*x**3/13 + 18*x**2/13 - 46*x/13 + 30/13 = 0.
1, 3, 5
Factor 2*d**2 - 2456*d + 753992.
2*(d - 614)**2
Suppose r**4/4 + 7*r**3/4 + 11*r**2/4 + 5*r/4 = 0. What is r?
-5, -1, 0
Find o, given that -25*o**4 - 60*o**3 - 35*o**2 = 0.
-7/5, -1, 0
Factor 3*a**2 - 9*a + 6.
3*(a - 2)*(a - 1)
Find m, given that 3*m**2/2 - 3*m - 36 = 0.
-4, 6
Factor -g**3/3 - 8*