.
-4, -2, 2, 4
Suppose -3*p**2 + 246*p + 1305 = 0. Calculate p.
-5, 87
Determine i, given that -2*i**2 - 34*i - 60 = 0.
-15, -2
Factor 20*v**2/7 - 12*v/7 - 8/7.
4*(v - 1)*(5*v + 2)/7
Determine y, given that 2*y**2/5 + 214*y/5 + 5684/5 = 0.
-58, -49
Factor 2*u**3/9 - 4*u**2/9.
2*u**2*(u - 2)/9
Solve 8*m**2 + 180*m + 252 = 0.
-21, -3/2
Determine z so that z**2 + 104*z + 103 = 0.
-103, -1
Factor w**4/7 - 48*w**3/7 + 622*w**2/7 - 1104*w/7 + 529/7.
(w - 23)**2*(w - 1)**2/7
Determine u, given that 3*u**3 + 250*u**2/7 - 612*u/7 + 8 = 0.
-14, 2/21, 2
Find z such that 20*z**3 - 32*z**2 - 112*z + 192 = 0.
-12/5, 2
Factor -p**3/4 + 127*p**2/4 + p/4 - 127/4.
-(p - 127)*(p - 1)*(p + 1)/4
Suppose 25*s**5 - 40*s**4 - 94*s**3 - 32*s**2 - 3*s = 0. What is s?
-1, -1/5, 0, 3
Determine j so that -5*j**3 - 840*j**2 - 47040*j - 878080 = 0.
-56
Find d, given that -d**4 + 10*d**3 + 103*d**2 - 388*d - 480 = 0.
-8, -1, 4, 15
Factor 3*o**3 - 33*o**2 + 54*o.
3*o*(o - 9)*(o - 2)
Determine h so that h**2/6 - 41*h/3 - 172/3 = 0.
-4, 86
Let -7*k**5/3 + 61*k**4/3 - 178*k**3/3 + 196*k**2/3 - 40*k/3 - 32/3 = 0. What is k?
-2/7, 1, 2, 4
Find t such that 2*t**5 - 14*t**4 - 188*t**3 - 136*t**2 + 336*t = 0.
-6, -2, 0, 1, 14
Find q such that -q**3/3 - 622*q**2 - 290163*q = 0.
-933, 0
Find b, given that 14*b**3/11 + 60*b**2/11 - 54*b/11 - 20/11 = 0.
-5, -2/7, 1
Factor -44*r**4 + 1300*r**3 - 13716*r**2 + 59292*r - 81648.
-4*(r - 9)**3*(11*r - 28)
Factor m**3/5 - 48*m**2/5 + 576*m/5.
m*(m - 24)**2/5
Determine r, given that 3*r**2 - 339*r - 342 = 0.
-1, 114
Factor v**2 - 102*v - 103.
(v - 103)*(v + 1)
Factor 4*a**3 + 604*a**2 + 2368*a + 2352.
4*(a + 2)**2*(a + 147)
What is i in i**3 - 76*i**2 + 1280*i + 6400 = 0?
-4, 40
Factor -5*g**3 + 20*g.
-5*g*(g - 2)*(g + 2)
Factor 3*x**3 - 24*x**2 + 39*x - 18.
3*(x - 6)*(x - 1)**2
Find d such that -d**2/5 + 198*d/5 - 117 = 0.
3, 195
Solve l**4/2 + 676*l**3 - 2707*l**2/2 + 677*l = 0 for l.
-1354, 0, 1
What is i in 2*i**2 + 152*i + 2888 = 0?
-38
Find y, given that -2*y**4/13 + 128*y**3/13 - 176*y**2 + 7680*y/13 - 7200/13 = 0.
2, 30
Factor -5*u**4 - 40*u**3 + 45*u**2 + 540*u - 540.
-5*(u - 3)*(u - 1)*(u + 6)**2
Solve -m**3/3 + 13*m**2/3 + 10*m = 0.
-2, 0, 15
Suppose 2*n**2/11 - 548*n = 0. Calculate n.
0, 3014
Factor -2*u**3/7 - 554*u**2/7.
-2*u**2*(u + 277)/7
Factor 4*p**2/3 - 628*p/3 + 208.
4*(p - 156)*(p - 1)/3
Find g, given that -8*g**2 + 188*g + 636 = 0.
-3, 53/2
Factor -2*u**2/7 + 492*u/7 + 2000/7.
-2*(u - 250)*(u + 4)/7
Let 2*k**2/7 + 26*k/7 = 0. What is k?
-13, 0
Factor 12*g**3 - 7293*g**2 + 5460*g + 1821.
3*(g - 607)*(g - 1)*(4*g + 1)
Factor 4*t**2 + 28*t.
4*t*(t + 7)
Let -2*k**4/13 - 12*k**3/13 - 22*k**2/13 - 12*k/13 = 0. Calculate k.
-3, -2, -1, 0
What is u in 3*u**4/5 - 3*u**3/5 - 3*u**2/5 + 3*u/5 = 0?
-1, 0, 1
Factor -2*n**4 + 86*n**3 - 166*n**2 + 82*n.
-2*n*(n - 41)*(n - 1)**2
Determine x so that 2*x**3/7 + 390*x**2/7 + 1536*x/7 + 1528/7 = 0.
-191, -2
Factor -2*x**2 + 26*x + 28.
-2*(x - 14)*(x + 1)
Factor -4*x**3 - 192*x**2 + 604*x - 408.
-4*(x - 2)*(x - 1)*(x + 51)
Suppose -2*a**4/17 + 22*a**3/17 - 54*a**2/17 + 50*a/17 - 16/17 = 0. What is a?
1, 8
Factor 3*z**2/5 - 147*z + 732/5.
3*(z - 244)*(z - 1)/5
Let -4*k**3 - 352*k**2 + 1084*k - 728 = 0. Calculate k.
-91, 1, 2
Factor 3*q**4 + 303*q**3 - 3*q**2 - 303*q.
3*q*(q - 1)*(q + 1)*(q + 101)
Determine t so that 21*t**3/2 + 83*t**2/2 - 109*t/2 + 5/2 = 0.
-5, 1/21, 1
Factor 3*b**2 - 12.
3*(b - 2)*(b + 2)
What is t in 4*t**5 - 4*t**4 - 40*t**3 + 40*t**2 + 36*t - 36 = 0?
-3, -1, 1, 3
Find z such that 500*z**3 + 3080*z**2 + 2416*z/5 + 96/5 = 0.
-6, -2/25
Factor 4*o**5/7.
4*o**5/7
Find u such that -3*u**2 - 81*u - 78 = 0.
-26, -1
Factor 2*l**4 + 142*l**3 - 146*l**2 - 142*l + 144.
2*(l - 1)**2*(l + 1)*(l + 72)
Factor -2*o**3/13 + 464*o**2/13.
-2*o**2*(o - 232)/13
Find y such that -y**5/2 + 51*y**4/2 - 375*y**3/2 - 7207*y**2/2 - 6540*y - 3150 = 0.
-7, -1, 30
Factor -g**2/3 + 2*g + 40/3.
-(g - 10)*(g + 4)/3
Factor 99*f**3 + 57*f**2 + 5*f - 1.
(3*f + 1)**2*(11*f - 1)
Factor z**2 + 609*z - 1222.
(z - 2)*(z + 611)
What is v in 45*v**5 - 438*v**4 - 7796*v**3/5 + 16888*v**2 + 22912*v/5 + 1536/5 = 0?
-6, -2/15, 8
Let -2*h**2 - 412*h = 0. Calculate h.
-206, 0
Let -8*a**2 + 2886*a + 722 = 0. Calculate a.
-1/4, 361
Find h such that 2*h**2/17 + 2*h/17 - 12/17 = 0.
-3, 2
Find w such that 5*w**5/7 - 13*w**4/7 + 9*w**3/7 + w**2/7 - 2*w/7 = 0.
-2/5, 0, 1
Determine m, given that -316*m**3 - 20*m**2 = 0.
-5/79, 0
Let 5*y**3 + 90*y**2 + 540*y + 1080 = 0. What is y?
-6
Factor c**5 + 5*c**4 - 140*c**3 - 1440*c**2 - 4320*c - 3024.
(c - 14)*(c + 1)*(c + 6)**3
Factor -45*j**5 - 170*j**4 - 140*j**3 + 40*j**2.
-5*j**2*(j + 2)**2*(9*j - 2)
Factor 5*c**2 + 150*c + 405.
5*(c + 3)*(c + 27)
Factor -6*j**4/5 + 344*j**3/5 - 14444*j**2/15 - 9976*j/15 - 1682/15.
-2*(j - 29)**2*(3*j + 1)**2/15
Suppose -2*p**5 - 2*p**4 + 20*p**3 + 20*p**2 - 18*p - 18 = 0. What is p?
-3, -1, 1, 3
Solve -4*n**3/3 + 104*n**2 + 1140*n + 8800/3 = 0 for n.
-5, 88
Factor -2*m**3 + 232*m**2 - 8800*m + 108416.
-2*(m - 44)**2*(m - 28)
Solve 5*z**2 - 505*z + 990 = 0 for z.
2, 99
Suppose 5*o**4 - 20*o**3 + 25*o**2 - 10*o = 0. What is o?
0, 1, 2
Find i, given that 3*i**4/2 - 51*i**3 + 747*i**2/2 + 1134*i - 1458 = 0.
-3, 1, 18
Factor 4*m**3/5 + 36*m**2/5 - 4*m/5 - 36/5.
4*(m - 1)*(m + 1)*(m + 9)/5
Factor n**4 + 6*n**3 - 25*n**2 + 18*n.
n*(n - 2)*(n - 1)*(n + 9)
Factor 4*u**2/5 - 28*u/5 + 24/5.
4*(u - 6)*(u - 1)/5
What is g in 5*g**3/2 - 15*g**2/2 - 65*g/2 + 75/2 = 0?
-3, 1, 5
Find o, given that o**3 - 75*o**2 - 232*o - 156 = 0.
-2, -1, 78
Factor 14*h**3/9 - 10028*h**2/9 + 1797160*h/9 - 512656/9.
2*(h - 358)**2*(7*h - 2)/9
Determine g, given that 4*g**4 - 4*g**3 - 36*g**2 + 36*g = 0.
-3, 0, 1, 3
Let u**4 - 5*u**3 + 3*u**2 + 5*u - 4 = 0. Calculate u.
-1, 1, 4
Factor -3*o**3/8 - 259*o**2/4 + 695*o/8 - 87/4.
-(o - 1)*(o + 174)*(3*o - 1)/8
Suppose 5*z**2 + 50*z + 125 = 0. Calculate z.
-5
Factor 2*p**3/3 + 114*p**2 + 5040*p + 14112.
2*(p + 3)*(p + 84)**2/3
Factor 5*q**4 - 30*q**3 + 25*q**2 + 120*q - 180.
5*(q - 3)**2*(q - 2)*(q + 2)
Suppose -2*z**5/7 - 32*z**4/7 + 86*z**3 - 1984*z**2/7 - 600*z/7 + 288 = 0. What is z?
-28, -1, 1, 6
Let -w**4/4 + 25*w**3/4 - 22*w**2 + 21*w = 0. Calculate w.
0, 2, 21
Determine u so that u**5 + 52*u**4 - u**3 - 52*u**2 = 0.
-52, -1, 0, 1
Factor -v**3 - 4*v**2 + 25*v + 28.
-(v - 4)*(v + 1)*(v + 7)
What is d in 5*d**2 + 45*d - 260 = 0?
-13, 4
Factor 270*w**3 - 4035*w**2 - 235*w + 150.
5*(w - 15)*(6*w - 1)*(9*w + 2)
Factor -5*r**2 + 30*r + 35.
-5*(r - 7)*(r + 1)
Factor 216*m**3 - 639*m**2 + 456*m - 84.
3*(m - 2)*(3*m - 2)*(24*m - 7)
Let 4*o**4/3 + 944*o**3/3 + 1847*o**2 + 4835*o/3 + 1150/3 = 0. What is o?
-230, -5, -1/2
Let 5*g**3/4 - 70*g**2 + 980*g = 0. What is g?
0, 28
Factor 10*w**2/11 + 246*w/11 - 100/11.
2*(w + 25)*(5*w - 2)/11
Solve 3*r**2/2 + 3*r/2 - 18 = 0 for r.
-4, 3
Factor -2*k**5 + 26*k**4 - 60*k**3.
-2*k**3*(k - 10)*(k - 3)
Factor -17*a**5 + 49*a**4/3 + 2*a**3/3.
-a**3*(a - 1)*(51*a + 2)/3
Factor k**2 - 28*k.
k*(k - 28)
Factor -u**2/6 - 805*u/3 - 648025/6.
-(u + 805)**2/6
Find x, given that -5*x**3/4 + 5*x**2/4 + 30*x + 45 = 0.
-3, -2, 6
Suppose -2*c**4 + 10*c**3 + 6*c**2 - 34*c + 20 = 0. What is c?
-2, 1, 5
Factor -2*p**2 - 130*p/7 + 316/7.
-2*(p - 2)*(7*p + 79)/7
Factor 2*w**5/5 + 58*w**4/5 + 326*w**3/5 - 1346*w**2/5 + 1472*w/5 - 512/5.
2*(w - 1)**3*(w + 16)**2/5
Find z, given that -48*z**5 - 216*z**4 - 291*z**3 - 108*z**2 - 12*z = 0.
-2, -1/4, 0
Let 2*y**2/7 + 958*y/7 + 3800/7 = 0. What is y?
-475, -4
Factor -3*m**3/8 - 21*m**2/8 - 33*m/8 - 15/8.
-3*(m + 1)**2*(m + 5)/8
Suppose -4*k**2 - 1400*k = 0. Calculate k.
-350, 0
Factor u**3/4 + 97*u**2/4 + 191*u/4 + 95/4.
(u + 1)**2*(u + 95)/4
Suppose -27075*k**3/2 + 27645*k**2 - 1146*k + 12 = 0. Calculate k.
2/95, 2
Find i, given that -i**5 + 10*i**4 + 71*i**3 + 60*i**2 = 0.
-4, -1, 0, 15
Determine s, given that -s**2/8 - 17*s/4 - 289/8 = 0.
-17
Suppose g**2/8 + 313*g/8 + 39 = 0. Calculate g.
-312, -1
Suppose -2*o**2/13 - 90*o/13 = 0. Calculate o.
-45, 0
Factor 3*v**4 + 105*v**3 + 384*v**2 + 372*v.
3*v*(v + 2)**2*(v + 31)
Determine f so that -8*f**5/5 + 88*f**4/5 - 138*f**3/5 - 572*f**2/5 - 338*f/5 = 0.
-1, 0, 13/2
Factor 3*w**4 - 6*w**3 - 36*w**2 - 42*w - 15.
3*(w - 5)*(w + 1)**