at is b in 15*b**4/2 + 287*b**3/2 + 563*b**2/2 + 325*b/2 + 17 = 0?
-17, -1, -2/15
Solve 2*i**4 - 70*i**3 + 792*i**2 - 2592*i - 3456 = 0 for i.
-1, 12
Factor x**2/2 + 7*x + 33/2.
(x + 3)*(x + 11)/2
Let 3*r**2/7 - 213*r - 4500/7 = 0. What is r?
-3, 500
Find z, given that 3*z**3 - 156*z**2 - 159*z = 0.
-1, 0, 53
Factor -2*u**3/7 - 178*u**2/7 - 2960*u/7 - 13800/7.
-2*(u + 10)**2*(u + 69)/7
Determine d, given that 20*d**5 + 1032*d**4 + 13104*d**3 - 5408*d**2 = 0.
-26, 0, 2/5
Factor -2*a**3 + 50*a**2 - 296*a + 408.
-2*(a - 17)*(a - 6)*(a - 2)
Factor 3*v**2/5 + 12*v/5 - 231/5.
3*(v - 7)*(v + 11)/5
Factor -16*s**5/5 - 29*s**4/5 - 2*s**3 + 3*s**2/5.
-s**2*(s + 1)**2*(16*s - 3)/5
Factor s**5/2 + 2*s**4 + s**3/2 - 5*s**2 - 2*s + 4.
(s - 1)**2*(s + 2)**3/2
Let -3*c**5/5 + 18*c**4/5 + 33*c**3/5 - 36*c**2 - 60*c = 0. Calculate c.
-2, 0, 5
Factor -p**5/9 + 2*p**4/3 - 11*p**3/9 + 2*p**2/9 + 4*p/3 - 8/9.
-(p - 2)**3*(p - 1)*(p + 1)/9
Factor -37*o**3 - 151*o**2 + 432*o + 36.
-(o - 2)*(o + 6)*(37*o + 3)
Let 16*g**3/9 + 308*g**2/9 + 1420*g/9 + 112/3 = 0. What is g?
-12, -7, -1/4
Suppose 2*y**3 + 28*y**2 - 30*y = 0. Calculate y.
-15, 0, 1
Find p, given that -40*p**3 - 45*p**2 - 5*p = 0.
-1, -1/8, 0
Factor -4096*p**2/7 + 2304*p/7 - 324/7.
-4*(32*p - 9)**2/7
Determine j, given that -3*j**2/4 + 75*j/2 - 1875/4 = 0.
25
Solve 2*i**4 + 10*i**3 - 56*i**2 - 64*i = 0 for i.
-8, -1, 0, 4
Factor -l**4 + 10*l**3 + l**2 - 10*l.
-l*(l - 10)*(l - 1)*(l + 1)
Factor 2*d**3/7 - 1958*d**2/7 + 68320*d + 68600.
2*(d - 490)**2*(d + 1)/7
Determine r, given that -r**3 + 2814*r**2 - 5625*r + 2812 = 0.
1, 2812
Let 2*m**4/13 + 40*m**3/13 + 8*m**2 - 960*m/13 + 1152/13 = 0. Calculate m.
-12, 2
Determine z, given that -4*z**5 - 4*z**4 + 24*z**3 + 16*z**2 - 32*z = 0.
-2, 0, 1, 2
Factor 6*l**3/7 + 330*l**2 + 223488*l/7 + 221184/7.
6*(l + 1)*(l + 192)**2/7
Let f**4 + 14*f**3 - 101*f**2 - 114*f = 0. What is f?
-19, -1, 0, 6
Solve -3*u**3/5 - 225*u**2 - 28125*u - 1171875 = 0 for u.
-125
Determine l, given that l**3 - 3*l - 2 = 0.
-1, 2
What is h in 4*h**4 - 8*h**3 - 12*h**2 + 32*h - 16 = 0?
-2, 1, 2
Factor 2*s**4/13 - 4*s**3/13 + 4*s/13 - 2/13.
2*(s - 1)**3*(s + 1)/13
Let 2*h**2/13 - 86*h/13 + 240/13 = 0. What is h?
3, 40
Factor -3*x**3/2 + 167*x**2 + 112*x.
-x*(x - 112)*(3*x + 2)/2
Find j such that -10*j**4/3 - 132*j**3 + 210*j**2 + 2272*j/3 - 328 = 0.
-41, -2, 2/5, 3
Factor 5*a**5 + 505*a**4 + 12495*a**3 - 13005*a**2.
5*a**2*(a - 1)*(a + 51)**2
Suppose 3*j**4 - 195*j**3 + 381*j**2 - 189*j = 0. Calculate j.
0, 1, 63
Factor 5*f**2/4 + 11*f/4 + 1/2.
(f + 2)*(5*f + 1)/4
Factor h**3/4 - 72*h**2 + 21021*h/4 - 20449/2.
(h - 143)**2*(h - 2)/4
Let -2*a**3/7 + 80*a**2/7 - 874*a/7 + 1444/7 = 0. What is a?
2, 19
Factor 4*a**2 + 56*a - 60.
4*(a - 1)*(a + 15)
Factor -2*x**4/13 - 288*x**3/13 - 1918*x**2/13.
-2*x**2*(x + 7)*(x + 137)/13
Factor -n**5 + 9*n**4 - 27*n**3 + 31*n**2 - 12*n.
-n*(n - 4)*(n - 3)*(n - 1)**2
Factor -2*w**2/11 - 126*w/11.
-2*w*(w + 63)/11
Determine i so that -5*i**2 - 90*i - 160 = 0.
-16, -2
Factor 4*z**4 - 12*z**3 - 148*z**2 - 132*z + 288.
4*(z - 8)*(z - 1)*(z + 3)**2
Let -t**4/5 - 14*t**3/5 - 13*t**2/5 = 0. What is t?
-13, -1, 0
Suppose -4*g**4 - 24*g**3 - 44*g**2 - 24*g = 0. What is g?
-3, -2, -1, 0
Solve 4*n**5/3 + 2*n**4/9 - 68*n**3/3 + 398*n**2/9 - 56*n/3 - 40/9 = 0.
-5, -1/6, 1, 2
Solve 8*v**4 + 20*v**3 + 4*v**2 - 20*v - 12 = 0.
-3/2, -1, 1
Determine z so that 3*z**3/7 + 15*z**2 + 564*z/7 - 96 = 0.
-28, -8, 1
Factor 3*u**4 + 36*u**3 + 36*u**2 - 240*u.
3*u*(u - 2)*(u + 4)*(u + 10)
Suppose -4*n**3/7 - 1622*n**2/7 - 4024*n/7 + 2418/7 = 0. Calculate n.
-403, -3, 1/2
Factor -w**4/6 - 469*w**3/2 - 219961*w**2/2 - 103161709*w/6.
-w*(w + 469)**3/6
Factor 2*z**3/11 + 10*z**2/11 - 34*z/11 - 42/11.
2*(z - 3)*(z + 1)*(z + 7)/11
Suppose 2*n**3/7 + 366*n**2/7 + 22326*n/7 + 453962/7 = 0. What is n?
-61
Determine g, given that 2*g**2 + 292*g/9 + 64/9 = 0.
-16, -2/9
What is l in -147*l**5 - 966*l**4 - 957*l**3 + 1146*l**2 + 804*l + 120 = 0?
-5, -2, -2/7, 1
Factor 4*j**3 + 2308*j**2/3 + 37120*j + 12288.
4*(j + 96)**2*(3*j + 1)/3
Find w, given that 2*w**3/15 - 4622*w**2/5 + 10681442*w/5 - 24684812462/15 = 0.
2311
Suppose -3*q**3 - 855*q**2 - 81225*q - 2572125 = 0. What is q?
-95
Factor 2*g**4 - 16*g**2 + 32.
2*(g - 2)**2*(g + 2)**2
Factor -5*t**4 + 55*t**3 - 55*t**2 - 295*t - 180.
-5*(t - 9)*(t - 4)*(t + 1)**2
Factor -y**4/7 - 18*y**3/7 + 19*y**2/7.
-y**2*(y - 1)*(y + 19)/7
Solve 4*s**5/5 + 2*s**4 - 12*s**3/5 - 8*s**2 - 16*s/5 = 0.
-2, -1/2, 0, 2
Factor -14*n**3 + 24*n**2 - 6*n - 4.
-2*(n - 1)**2*(7*n + 2)
Factor -4*u**4 + 4*u**3 + 4*u**2 - 4*u.
-4*u*(u - 1)**2*(u + 1)
What is x in 2*x**2 + 276*x + 9522 = 0?
-69
Factor 2*s**5 + 6*s**4 + 4*s**3.
2*s**3*(s + 1)*(s + 2)
Let 2*u**4/5 - 38*u**3/5 + 36*u**2/5 = 0. What is u?
0, 1, 18
What is u in -98*u**3/5 + 126*u**2 + 384*u/5 + 56/5 = 0?
-2/7, 7
Factor f**2/5 + 59*f/5 + 828/5.
(f + 23)*(f + 36)/5
Solve -2*b**3 - 76*b**2 + 646*b + 720 = 0 for b.
-45, -1, 8
Find m such that -m**5 + 7*m**4 - 5*m**3 - 7*m**2 + 6*m = 0.
-1, 0, 1, 6
Solve 3*a**4 - 438*a**3 - 9*a**2 + 1308*a + 876 = 0.
-1, 2, 146
What is m in 5*m**3 + 40*m**2 - 155*m + 110 = 0?
-11, 1, 2
Let 2*m**3/13 - 278*m**2/13 + 6608*m/13 - 43512/13 = 0. What is m?
14, 111
Find c such that -3*c**2/7 + 150*c/7 - 21 = 0.
1, 49
Factor -8*y**4 - 19*y**3 - 6*y**2.
-y**2*(y + 2)*(8*y + 3)
Factor -2*p**2/17 - 2116*p/17 + 2118/17.
-2*(p - 1)*(p + 1059)/17
Factor -r**4/4 - 13*r**3 + 27*r**2/2 + 13*r - 53/4.
-(r - 1)**2*(r + 1)*(r + 53)/4
Solve -2*a**4 - 30*a**3 - 26*a**2 + 30*a + 28 = 0 for a.
-14, -1, 1
Let 4*o**5/9 + 16*o**4/3 + 68*o**3/3 + 352*o**2/9 + 64*o/3 = 0. What is o?
-4, -3, -1, 0
Factor -q**2/6 + 8*q/3 - 32/3.
-(q - 8)**2/6
Factor 4*u**2 + 32*u + 48.
4*(u + 2)*(u + 6)
Let -t**4/5 + 2*t**3/5 + 12*t**2/5 - 18*t/5 - 27/5 = 0. What is t?
-3, -1, 3
Factor 6*r**3 - 94*r**2 - 244*r - 144.
2*(r - 18)*(r + 1)*(3*r + 4)
Suppose -8*k**5/7 + 788*k**4/7 - 384*k**3/7 - 788*k**2/7 + 56*k = 0. What is k?
-1, 0, 1/2, 1, 98
Factor q**2 - 15*q + 54.
(q - 9)*(q - 6)
Let 5*y**4 - 1440*y**3 = 0. Calculate y.
0, 288
Factor -2*r**2/13 + 44*r/13 - 80/13.
-2*(r - 20)*(r - 2)/13
Suppose 5*w**2 + 1015*w + 1010 = 0. What is w?
-202, -1
Factor -t**5/2 + 177*t**4/2.
-t**4*(t - 177)/2
Factor -2*p**3/17 + 38*p**2/17 - 96*p/17.
-2*p*(p - 16)*(p - 3)/17
Factor -32*n**2/3 + 148*n/3 + 20.
-4*(n - 5)*(8*n + 3)/3
Find q, given that -q**5/3 - 11*q**4/3 - 40*q**3/3 - 16*q**2 = 0.
-4, -3, 0
Factor 160*s**4/3 - 10744*s**3/3 + 80634*s**2 - 3714949*s/6 + 704969/3.
(4*s - 89)**3*(5*s - 2)/6
Determine h, given that 2*h**2/15 - 176*h/15 + 58/5 = 0.
1, 87
Factor -2*s**5 - 44*s**4.
-2*s**4*(s + 22)
Factor 2*m**4/9 + 2*m**3/9 - 16*m**2/9 - 8*m/3.
2*m*(m - 3)*(m + 2)**2/9
Suppose b**5/2 - 5*b**4 + 33*b**3/2 - 20*b**2 + 8*b = 0. What is b?
0, 1, 4
Suppose -b**2 - 69*b - 68 = 0. Calculate b.
-68, -1
Let -2*g**2 - 544*g - 36992 = 0. Calculate g.
-136
Determine p, given that -9*p**4 - 57*p**3 + 152*p**2 + 268*p + 96 = 0.
-8, -2/3, 3
Determine w so that 5*w**2 + 475*w - 10830 = 0.
-114, 19
Factor 242*k**4 - 2794*k**3 + 1470*k**2 - 198*k.
2*k*(k - 11)*(11*k - 3)**2
Factor 44*w**2/7 + 94*w - 30/7.
2*(w + 15)*(22*w - 1)/7
Solve -4*i**4 - 12*i**3 = 0.
-3, 0
Find r, given that -2*r**4/7 + 2*r**3/7 + 2*r**2/7 - 2*r/7 = 0.
-1, 0, 1
Factor q**3 - 5*q**2 - 6*q.
q*(q - 6)*(q + 1)
Factor 5*n**4/4 - 2*n**3 - 19*n**2/4 - 3*n/2.
n*(n - 3)*(n + 1)*(5*n + 2)/4
What is g in -20*g**5 + 380*g**4 - 345*g**3 - 280*g**2 + 175*g + 90 = 0?
-1/2, 1, 18
Factor -84*n**3 - 8*n**2.
-4*n**2*(21*n + 2)
Factor 4*t**5 - 112*t**4 + 496*t**3 - 856*t**2 + 652*t - 184.
4*(t - 23)*(t - 2)*(t - 1)**3
Factor 3*z**3 + 534*z**2 + 3609*z + 3078.
3*(z + 1)*(z + 6)*(z + 171)
Solve -o**5/6 - 25*o**4/6 - 75*o**3/2 - 875*o**2/6 - 625*o/3 = 0 for o.
-10, -5, 0
What is q in -5*q**5 + 25*q**4 + 15*q**3 - 65*q**2 - 50*q = 0?
-1, 0, 2, 5
Suppose 2*i**5 + 8*i**4 + 2*i**3 - 28*i**2 - 40*i - 16 = 0. Calculate i.
-2, -1, 2
Factor -8*q**3/5 - 78*q**2/5 + 4*q.
-2*q*(q + 10)*(4*q - 1)/5
Determine t, given that 2*t**4/7 + 2068*t**3/7 + 534578*t**2/7 = 0.
-517, 0
Factor 2*o**2/3 - 22*o/3 + 20/3.
2*(o - 10)*(o - 1)/3
Let q**3 - 55*q**2 - 113*q - 57 = 0. What is q?
-1, 57
Suppose 2*o**4/7 - 2*o**3/7 - 18*o**2/7 + 18*o