 3
Solve -5*p**5 - 40*p**4 + 50*p**3 + 40*p**2 - 45*p = 0 for p.
-9, -1, 0, 1
Find n such that 3*n**4 - 24*n**3 + 39*n**2 - 18*n = 0.
0, 1, 6
Factor 2*b**2/7 - 1572*b/7 + 308898/7.
2*(b - 393)**2/7
Let q**3/9 + 4*q**2/3 + 7*q/3 - 98/9 = 0. What is q?
-7, 2
Find q such that -5*q**5 - 230*q**4 + 720*q**3 - 730*q**2 + 245*q = 0.
-49, 0, 1
Suppose -3*b**3 + 5*b**2 - 2*b = 0. What is b?
0, 2/3, 1
Suppose 36*u**3/7 + 44*u**2/7 + 8*u/7 = 0. What is u?
-1, -2/9, 0
Factor 3*h**5 - 21*h**4 + 36*h**3 + 12*h**2 - 48*h.
3*h*(h - 4)*(h - 2)**2*(h + 1)
Factor 2*q**2/11 + 3164*q/11 - 3166/11.
2*(q - 1)*(q + 1583)/11
Suppose 35*h**5 - 495*h**4 + 2590*h**3 - 6030*h**2 + 5535*h - 675 = 0. What is h?
1/7, 3, 5
Factor v**4/7 - v**3/7 - 22*v**2/7 - 44*v/7 - 24/7.
(v - 6)*(v + 1)*(v + 2)**2/7
Find t such that 2*t**2/5 - 1198*t/5 + 1196/5 = 0.
1, 598
Let 42*y**4 + 212*y**3 + 6*y**2 - 20*y = 0. Calculate y.
-5, -1/3, 0, 2/7
Solve 15*l**3/7 - 198*l**2/7 + 219*l/7 - 36/7 = 0 for l.
1/5, 1, 12
Solve l**5 - 6*l**4 + 14*l**3 - 16*l**2 + 9*l - 2 = 0.
1, 2
Factor -80*u**4 - 360*u**3 + 195*u**2 - 25*u.
-5*u*(u + 5)*(4*u - 1)**2
Find o such that o**5/6 + 5*o**4/6 - o**3/2 - 17*o**2/6 - 5*o/3 = 0.
-5, -1, 0, 2
Solve -h**3/3 + 35*h**2 - 936*h + 2704/3 = 0.
1, 52
Factor s**3/4 + 22*s**2 - 471*s/4 - 279/2.
(s - 6)*(s + 1)*(s + 93)/4
Solve -2*u**3/9 + 4*u**2/3 + 80*u/9 = 0.
-4, 0, 10
Factor -3*d**2/4 + 417*d/4.
-3*d*(d - 139)/4
Factor -4*k**3 + 504*k**2 - 21168*k + 296352.
-4*(k - 42)**3
Factor -2*g**3/3 - 20*g**2/9 + 176*g/9.
-2*g*(g - 4)*(3*g + 22)/9
Factor -2*l**3 - 242*l**2 - 6944*l + 23064.
-2*(l - 3)*(l + 62)**2
Find g such that 4*g**2 + 16*g - 240 = 0.
-10, 6
Factor -b**5/4 - 4*b**4 + 9*b**3 - b**2/2 - 35*b/4 + 9/2.
-(b - 1)**3*(b + 1)*(b + 18)/4
Solve -5*g**2 + 2685*g = 0.
0, 537
Let -g**5 + 42*g**4 - 518*g**3 + 1636*g**2 - 1881*g + 722 = 0. Calculate g.
1, 2, 19
Suppose z**3/9 - 5*z**2/9 - 8*z/9 + 16/3 = 0. Calculate z.
-3, 4
Factor -s**4/2 - 52*s**3 - 1881*s**2 - 26136*s - 179685/2.
-(s + 5)*(s + 33)**3/2
Find d such that d**3 - 2*d**2/3 - d/3 = 0.
-1/3, 0, 1
Factor 2*g**3/21 - 2*g**2/7 + 4*g/21.
2*g*(g - 2)*(g - 1)/21
Solve -3*z**2 - 54*z + 345 = 0.
-23, 5
Factor -2*o**3/9 + 70*o**2/9 - 134*o/9 + 22/3.
-2*(o - 33)*(o - 1)**2/9
Determine g so that 4*g**5 - 80*g**4 + 592*g**3 - 1920*g**2 + 2304*g = 0.
0, 4, 6
Find r such that -5*r**2 - 1650*r + 1655 = 0.
-331, 1
Determine j so that 20*j**4 - 95*j**3 - 1865*j**2 - 3580*j - 780 = 0.
-6, -2, -1/4, 13
Determine y so that -3*y**2/2 + 81*y/2 = 0.
0, 27
Factor 3*a**4 + 78*a**3 - 168*a**2.
3*a**2*(a - 2)*(a + 28)
Let 5*h**2 - 820*h + 33620 = 0. What is h?
82
Determine l so that -2*l**3 + 30*l**2 - 126*l + 162 = 0.
3, 9
Factor 2*i**3/3 - 4*i**2 + 10*i/3.
2*i*(i - 5)*(i - 1)/3
Factor g**3/7 + 6213*g**2/7 + 12867123*g/7 + 8882603911/7.
(g + 2071)**3/7
Determine c, given that 5*c**5 - 25*c**4 + 30*c**3 + 20*c**2 - 40*c = 0.
-1, 0, 2
Determine x, given that -9*x**3 + 867*x**2 - 1143*x + 285 = 0.
1/3, 1, 95
Factor 2*s**2 + 8*s - 42.
2*(s - 3)*(s + 7)
Factor k**5/4 + 9*k**4/4 + 7*k**3 + 9*k**2 + 4*k.
k*(k + 1)*(k + 2)**2*(k + 4)/4
Solve -3*c**2/4 + 2577*c/2 = 0 for c.
0, 1718
Find u such that 6*u**5 + 92*u**4 + 312*u**3 + 292*u**2 + 66*u = 0.
-11, -3, -1, -1/3, 0
Let 2*f**5/3 - 14*f**4/3 - 40*f**3/3 + 88*f**2 + 96*f = 0. Calculate f.
-4, -1, 0, 6
Factor -4*c**3 - 1948*c**2 - 1944*c.
-4*c*(c + 1)*(c + 486)
Factor 4*a**2 - 12*a + 8.
4*(a - 2)*(a - 1)
Factor d**3 + 154*d**2 + 153*d.
d*(d + 1)*(d + 153)
Let 3*a**2 + 411*a - 414 = 0. Calculate a.
-138, 1
Find s, given that -2*s**2 + 596*s + 598 = 0.
-1, 299
Suppose -4*w**4 + 256*w**3 + 260*w**2 = 0. Calculate w.
-1, 0, 65
Find t, given that -2*t**3/17 + 10*t**2/17 + 26*t/17 + 14/17 = 0.
-1, 7
What is h in 52*h**5 + 164*h**4 - 444*h**3 + 188*h**2 + 40*h = 0?
-5, -2/13, 0, 1
Find a such that 7*a**3/5 + 562*a**2/5 - 2192*a/5 - 672/5 = 0.
-84, -2/7, 4
Let -3*g**5 + 6*g**4 - 6*g**2 + 3*g = 0. What is g?
-1, 0, 1
Factor -j**4/3 + 5*j**3/3 + 2*j**2 - 32*j/3 - 32/3.
-(j - 4)**2*(j + 1)*(j + 2)/3
Factor 2*q**2/7 + 8*q/7 - 64/7.
2*(q - 4)*(q + 8)/7
Factor -2*h**2 - 70*h + 148.
-2*(h - 2)*(h + 37)
Factor -c**3/4 + 5*c**2 - 47*c/4 - 17.
-(c - 17)*(c - 4)*(c + 1)/4
Let 5*u**5 - 5*u**4 - 30*u**3 + 20*u**2 + 40*u = 0. Calculate u.
-2, -1, 0, 2
Determine j, given that 2*j**5/7 - 226*j**4/7 + 446*j**3/7 - 222*j**2/7 = 0.
0, 1, 111
Factor 3*d**3 - 1491*d**2 + 187473*d - 549081.
3*(d - 247)**2*(d - 3)
Determine r, given that 4*r**3 + 12*r**2 + 8*r = 0.
-2, -1, 0
Suppose -3*o**3/5 + 18*o**2 - 243*o/5 = 0. What is o?
0, 3, 27
Factor -3*s**3 - 108*s**2.
-3*s**2*(s + 36)
Factor i**5/4 + i**4 - 7*i**3/4 - 5*i**2/2.
i**2*(i - 2)*(i + 1)*(i + 5)/4
Factor y**3/6 + 5*y**2/6 - 4*y/3 - 8.
(y - 3)*(y + 4)**2/6
Factor -2*h**4/9 - 70*h**3/9 - 704*h**2/9 - 512*h/3.
-2*h*(h + 3)*(h + 16)**2/9
Factor -3*p**4 - 18*p**3 + 45*p**2 - 24*p.
-3*p*(p - 1)**2*(p + 8)
What is f in 4*f**2/3 + 320*f + 19200 = 0?
-120
Factor b**2/2 - 7*b - 51/2.
(b - 17)*(b + 3)/2
Determine k so that -2*k**2 - 222*k - 220 = 0.
-110, -1
Solve 50*n**5 + 20*n**4 - 48*n**3 - 20*n**2 - 2*n = 0.
-1, -1/5, 0, 1
Solve 86*b**2/3 + 148*b/3 - 16 = 0 for b.
-2, 12/43
What is v in v**5/6 + v**4/2 - 9*v**3/2 + 13*v**2/6 + 7*v = 0?
-7, -1, 0, 2, 3
Factor -p**2 + 103*p + 104.
-(p - 104)*(p + 1)
Let -z**4/4 + 5*z**3/4 - 2*z**2 + z = 0. What is z?
0, 1, 2
Factor 5*s**3 + 60*s**2 + 45*s - 110.
5*(s - 1)*(s + 2)*(s + 11)
Factor -3*l**2 - 306*l + 309.
-3*(l - 1)*(l + 103)
Suppose 30*n**5/7 - 424*n**4/7 + 446*n**3/7 + 7508*n**2/7 + 8712*n/7 - 1296/7 = 0. Calculate n.
-2, 2/15, 9
Determine z so that -2*z**4 + 34*z**3 - 202*z**2 + 470*z - 300 = 0.
1, 5, 6
Solve -k**5/2 + 4*k**3 + 3*k**2 - 7*k/2 - 3 = 0 for k.
-2, -1, 1, 3
What is w in -4*w**3 - 728*w**2 - 4196*w + 4928 = 0?
-176, -7, 1
What is s in -14*s**5 - 4*s**4 + 42*s**3 - 16*s**2 - 8*s = 0?
-2, -2/7, 0, 1
Factor -4*p**2 - 156*p + 160.
-4*(p - 1)*(p + 40)
Suppose 3*h**4 - 12*h**3 - 3*h**2 + 48*h - 36 = 0. Calculate h.
-2, 1, 2, 3
Suppose 4*k**4/5 - 9976*k**3/5 + 1246000*k**2 - 12420128*k/5 = 0. Calculate k.
0, 2, 1246
Factor -2140*d**3 + 15*d**2.
-5*d**2*(428*d - 3)
Solve -228*b**2 + 236*b - 8 = 0.
2/57, 1
Determine r, given that 50*r**3/7 + 46*r**2/7 - 4*r/7 = 0.
-1, 0, 2/25
Solve 5*v**4/6 + 3*v**3/2 - 7*v**2/6 - 3*v/2 + 1/3 = 0.
-2, -1, 1/5, 1
Factor z**3/6 - 8*z**2/3 + 13*z/2.
z*(z - 13)*(z - 3)/6
Factor -3*p**5 - 57*p**4 - 102*p**3.
-3*p**3*(p + 2)*(p + 17)
Find h such that 3*h**3 - 51*h**2 + 93*h - 45 = 0.
1, 15
Factor 4*c**5 + 159*c**4 + 2360*c**3 + 15400*c**2 + 36000*c - 10000.
(c + 10)**4*(4*c - 1)
Factor -2*z**2 - 144*z - 670.
-2*(z + 5)*(z + 67)
Factor j**4/6 - 7*j**3/6 + j**2 + 14*j/3 - 20/3.
(j - 5)*(j - 2)**2*(j + 2)/6
Find m, given that 5*m**4 - 185*m**3 + 160*m**2 + 740*m - 720 = 0.
-2, 1, 2, 36
Determine q, given that 6348*q**4 - 11684*q**3 + 6120*q**2 - 816*q + 32 = 0.
2/23, 2/3, 1
Solve 4*l**5 - 64*l**4 + 388*l**3 - 1112*l**2 + 1520*l - 800 = 0 for l.
2, 5
Factor -4*s**3/11 + 133*s**2/11 - 1054*s/11 - 867/11.
-(s - 17)**2*(4*s + 3)/11
Let 3*j**4/4 - 57*j**3/4 + 48*j**2 - 45*j = 0. What is j?
0, 2, 15
Suppose 3*v**5 - 46*v**4 + 54*v**3 + 32*v**2 - 57*v + 14 = 0. Calculate v.
-1, 1/3, 1, 14
Factor 4*t**3 - 17*t**2 + 16*t - 3.
(t - 3)*(t - 1)*(4*t - 1)
Factor f**3 - f**2 - 169*f + 169.
(f - 13)*(f - 1)*(f + 13)
Factor -5*d**5 + 15*d**3 - 10*d**2.
-5*d**2*(d - 1)**2*(d + 2)
What is a in 3*a**2 - 4146*a + 1432443 = 0?
691
Determine b, given that -b**5/5 - 8*b**4/5 + 13*b**3/5 + 116*b**2/5 + 96*b/5 = 0.
-8, -3, -1, 0, 4
Factor -4*t**2/7 + 136*t/7 - 132/7.
-4*(t - 33)*(t - 1)/7
Solve 2*b**5/15 + 52*b**4/15 + 338*b**3/15 = 0 for b.
-13, 0
Factor g**2/4 - 7*g/4 - 2.
(g - 8)*(g + 1)/4
Factor 4*c**3 - 23508*c**2 + 46052172*c - 30072068316.
4*(c - 1959)**3
Let -2*v**4/5 + 4*v**3/5 + 14*v**2/5 - 8*v + 24/5 = 0. What is v?
-3, 1, 2
Factor 4*g**3 - 172*g**2 - 176*g.
4*g*(g - 44)*(g + 1)
Find v, given that 2*v**2 - 744*v - 746 = 0.
-1, 373
Let -21*n**3 + 69*n**2 - 60*n + 12 = 0. Calculate n.
2/7, 1, 2
Find q such that -2*q**2 - 2*q + 4 = 0.
-2, 1
Factor 4*v**4 - 34*v**3 + 86*v**2 - 86*v + 30.
2*(v - 5)*(v - 1)**2*(2*v - 3)
Factor -z**2/8 + 43*z/4 + 45.
-(z - 90)*(z + 4)/8
Find p such that -2*p**5/9 - 14*p**4/3 - 178*p