ind w, given that 4*w**5 + 76*w**4 + 68*w**3 - 76*w**2 - 72*w = 0.
-18, -1, 0, 1
Find h such that h**4/4 + 213*h**3/4 + 2862*h**2 + 2809*h = 0.
-106, -1, 0
Factor 18*b**3/11 + 148*b**2/11 + 158*b/11 + 28/11.
2*(b + 1)*(b + 7)*(9*b + 2)/11
Factor -4*w**2/3 + 120*w + 364/3.
-4*(w - 91)*(w + 1)/3
Suppose -2*p**2/9 + 902*p/3 + 2708/9 = 0. Calculate p.
-1, 1354
Factor -33*y**3/5 + 489*y**2/5 + 18*y.
-3*y*(y - 15)*(11*y + 2)/5
Determine q, given that -3*q**2 + 1320*q = 0.
0, 440
Find x, given that -44*x**4 + 4360*x**3 - 352*x**2 - 4360*x + 396 = 0.
-1, 1/11, 1, 99
Solve -5*j**4/2 - 11*j**3/2 - 3*j**2/2 + 7*j/2 + 2 = 0 for j.
-1, 4/5
Find v such that 14*v**5 - 116*v**4 + 200*v**3 - 48*v**2 = 0.
0, 2/7, 2, 6
Find c such that -2*c**2 + 108*c - 1458 = 0.
27
Let -8*c**4/7 - 20*c**3/7 + 80*c**2/7 + 20*c + 48/7 = 0. What is c?
-4, -1, -1/2, 3
Let 25*p**2 + 615*p + 360 = 0. Calculate p.
-24, -3/5
What is t in -2*t**3 + 210*t**2 - 1356*t - 1568 = 0?
-1, 8, 98
Factor 54*o**2 - 120*o/7 + 8/7.
2*(9*o - 2)*(21*o - 2)/7
Solve -a**2/3 + 5*a/3 + 2 = 0 for a.
-1, 6
Let -t**4/8 + 137*t**3/4 - 18213*t**2/8 - 19043*t/2 - 19321/2 = 0. Calculate t.
-2, 139
Factor t**4/6 - 7*t**3/6 + 17*t**2/6 - 17*t/6 + 1.
(t - 3)*(t - 2)*(t - 1)**2/6
Determine b, given that 5*b**5/2 + 15*b**4 - 5*b**3/2 - 15*b**2 = 0.
-6, -1, 0, 1
Determine j, given that j**2/8 + 785*j/4 - 1571/8 = 0.
-1571, 1
Factor 14*l**2/17 + 16*l/17 - 30/17.
2*(l - 1)*(7*l + 15)/17
Factor 3*k**4 - 66*k**3 + 288*k**2.
3*k**2*(k - 16)*(k - 6)
Let -490*a**5 + 12355*a**4 + 23895*a**3 - 7165*a**2 - 3365*a - 270 = 0. What is a?
-2, -1/7, 1/2, 27
Factor 3*k**2 - 153*k + 1482.
3*(k - 38)*(k - 13)
Find y, given that 10*y**4 + 5*y**3 - 15*y**2 - 5*y + 5 = 0.
-1, 1/2, 1
Find i, given that 3*i**5/2 - 36*i**4 + 240*i**3 - 189*i**2 - 2211*i/2 + 1089 = 0.
-2, 1, 3, 11
Factor -w**4 - 3*w**3 + w**2 + 3*w.
-w*(w - 1)*(w + 1)*(w + 3)
Factor z**5 - 28*z**4 + 196*z**3.
z**3*(z - 14)**2
Find u such that 2*u**2/15 + 38*u/5 + 44/3 = 0.
-55, -2
Factor -j**4/5 - 26*j**3/5 + 3*j**2/5 + 76*j/5 - 52/5.
-(j - 1)**2*(j + 2)*(j + 26)/5
Let 3*u**5/2 + 481*u**4/2 + 20293*u**3/2 + 81123*u**2/2 + 39780*u + 9126 = 0. What is u?
-78, -3, -1, -1/3
Let 16*d**5 - 244*d**4 + 988*d**3 - 1576*d**2 + 976*d - 160 = 0. What is d?
1/4, 1, 2, 10
Factor 3*a**4/7 + 39*a**3/7 - 144*a**2/7.
3*a**2*(a - 3)*(a + 16)/7
Factor -2*h**4 + 86*h**3 + 366*h**2 + 466*h + 188.
-2*(h - 47)*(h + 1)**2*(h + 2)
Factor o**3/4 - 469*o**2/2 + 2807*o/4 - 935/2.
(o - 935)*(o - 2)*(o - 1)/4
Factor 4*c**5/7 + 4*c**4 + 40*c**3/7.
4*c**3*(c + 2)*(c + 5)/7
Suppose 3*x**5 + 41*x**4 + 149*x**3 + 223*x**2 + 148*x + 36 = 0. What is x?
-9, -2, -1, -2/3
Solve -k**2/2 - 233*k/2 - 116 = 0.
-232, -1
Solve 2*q**3/9 + 16*q**2/9 + 38*q/9 + 8/3 = 0.
-4, -3, -1
Factor 34*l**3/3 + 38*l**2/3 + 4*l/3.
2*l*(l + 1)*(17*l + 2)/3
Suppose -28*u**5/3 + 22*u**4/3 + 38*u**3/3 - 4*u**2 = 0. What is u?
-1, 0, 2/7, 3/2
Factor u**3/2 - 4*u**2 + 11*u/2 + 10.
(u - 5)*(u - 4)*(u + 1)/2
Solve -2*r**3 - 20*r**2 - 14*r + 36 = 0.
-9, -2, 1
Let -3*a**3 - 45*a**2 + 216*a - 228 = 0. Calculate a.
-19, 2
Suppose d**4/2 + 29*d**3 + 897*d**2/2 + 812*d + 392 = 0. Calculate d.
-28, -1
Factor -g**5/5 - 8*g**4/5 - 13*g**3/5 - 6*g**2/5.
-g**2*(g + 1)**2*(g + 6)/5
What is x in -4*x**2 - 108*x - 288 = 0?
-24, -3
Factor k**3 - 3*k**2 - 54*k + 112.
(k - 8)*(k - 2)*(k + 7)
Determine w so that 4*w**4 + 28*w**3/3 - 104*w**2 + 176*w - 224/3 = 0.
-7, 2/3, 2
Find j, given that -6*j**5 + 2*j**4 + 186*j**3 - 242*j**2 + 60*j = 0.
-6, 0, 1/3, 1, 5
Solve 2*o**3/11 + 64*o**2/11 + 122*o/11 + 60/11 = 0 for o.
-30, -1
Solve -3*i**4/4 - 45*i**3/4 + 369*i**2/4 - 219*i/4 - 315/2 = 0 for i.
-21, -1, 2, 5
Factor -3*u**5 - 48*u**4 - 144*u**3 + 798*u**2 + 2499*u - 6174.
-3*(u - 3)*(u - 2)*(u + 7)**3
Find q, given that 2*q**5/3 - 4*q**4/3 - 2*q**3/3 + 4*q**2/3 = 0.
-1, 0, 1, 2
Factor -2*f**2/3 - 112*f/3 - 920/3.
-2*(f + 10)*(f + 46)/3
Suppose r**2/3 - 356*r/3 + 355/3 = 0. Calculate r.
1, 355
Find x such that -3*x**5 + 327*x**4 - 7674*x**3 - 68556*x**2 - 60552*x = 0.
-6, -1, 0, 58
Factor -2*z**4/11 + 1146*z**3/11 - 19686*z**2 + 13037150*z/11 + 86268684/11.
-2*(z - 193)**3*(z + 6)/11
Suppose -10*c**3/3 + 154*c**2/3 - 500*c/3 + 176/3 = 0. Calculate c.
2/5, 4, 11
Let -4*x**3 - 56*x**2 - 140*x + 200 = 0. Calculate x.
-10, -5, 1
Let 5*t**5 + 10*t**4 - 145*t**3 + 230*t**2 + 100*t - 280 = 0. Calculate t.
-7, -1, 2
Factor -q**5/10 + q**4/2 + 3*q**3/5 - 19*q**2/5 + 43*q/10 - 3/2.
-(q - 5)*(q - 1)**3*(q + 3)/10
Solve -4*w**5 - 28*w**4 - 68*w**3 - 68*w**2 - 24*w = 0.
-3, -2, -1, 0
Solve 5*r**5 - 15*r**4 - 35*r**3 + 35*r**2 + 90*r + 40 = 0 for r.
-1, 2, 4
Solve f**3/3 + 7*f**2/3 + 10*f/3 = 0 for f.
-5, -2, 0
Factor 2*x**2/17 - 342*x/17 - 344/17.
2*(x - 172)*(x + 1)/17
Let -3*p**3 + 129*p**2 - 918*p = 0. What is p?
0, 9, 34
Factor 6*b**2/5 - 37*b/5 + 6/5.
(b - 6)*(6*b - 1)/5
Factor 2*p**2/3 + 40*p + 600.
2*(p + 30)**2/3
Let 15*f**3/4 - 171*f**2/2 = 0. Calculate f.
0, 114/5
Factor 5*h**2/3 + 1415*h/3 - 1430.
5*(h - 3)*(h + 286)/3
Factor 3*a**2 - 582*a.
3*a*(a - 194)
Find h such that -3*h**2 + 1848*h + 3708 = 0.
-2, 618
Factor 4*l**3 + 8952*l**2 + 6678192*l + 1660643744.
4*(l + 746)**3
Factor 3*f**2/7 - 1326*f/7 - 1329/7.
3*(f - 443)*(f + 1)/7
Factor 2*t**2 - 4*t - 2046.
2*(t - 33)*(t + 31)
What is r in -4*r**2 + 236*r = 0?
0, 59
Determine c so that -98*c**4/5 - 252*c**3 - 2104*c**2/5 - 228*c - 198/5 = 0.
-11, -1, -3/7
Suppose 5*o**5 - 175*o**4 + 630*o**3 - 290*o**2 - 635*o + 465 = 0. What is o?
-1, 1, 3, 31
Suppose 3*k**4/7 + 12*k**3 + 705*k**2/7 + 1368*k/7 - 2160/7 = 0. Calculate k.
-12, -5, 1
What is q in -2*q**3 + 7156*q**2 - 6401042*q = 0?
0, 1789
Let -9*s**2/7 - 15*s/7 - 6/7 = 0. Calculate s.
-1, -2/3
Suppose 2*h**2 - 2064*h + 532512 = 0. Calculate h.
516
Factor -w**2/5 + 21*w + 106/5.
-(w - 106)*(w + 1)/5
Factor -4*b**4 + 72*b**3 - 432*b**2 + 952*b - 588.
-4*(b - 7)**2*(b - 3)*(b - 1)
Find q, given that q**3/6 + 7*q**2/6 + q = 0.
-6, -1, 0
Suppose 5*l**2/6 - 15625*l/3 + 48828125/6 = 0. Calculate l.
3125
Factor -3*f**4 - 12*f**3.
-3*f**3*(f + 4)
Factor h**3/4 - 7*h**2/4 + 9.
(h - 6)*(h - 3)*(h + 2)/4
Let 4*s**5 + 92*s**4 + 556*s**3 + 116*s**2 - 2288*s - 1936 = 0. What is s?
-11, -2, -1, 2
Suppose -3*u**2/2 + 27*u - 48 = 0. Calculate u.
2, 16
Suppose -44*h**3 + 92*h**2 + 32*h - 80 = 0. Calculate h.
-10/11, 1, 2
Solve 45*f**5 + 2832*f**4 - 3060*f**3 + 768*f**2 = 0 for f.
-64, 0, 2/5, 2/3
Find k such that 2*k**4 + 26*k**3 + 96*k**2 + 72*k = 0.
-6, -1, 0
Solve -3*w**4 + 18*w**3 - 15*w**2 = 0.
0, 1, 5
Factor 2*i**2 - 72.
2*(i - 6)*(i + 6)
Let -12*h**5 + 548*h**4 - 884*h**3 + 172*h**2 + 176*h = 0. Calculate h.
-1/3, 0, 1, 44
Factor 2*z**2 + 3308*z/7 + 944/7.
2*(z + 236)*(7*z + 2)/7
Factor 132098*f**2 - 28784*f + 1568.
2*(257*f - 28)**2
Suppose -3*n**2 - 951*n - 1890 = 0. What is n?
-315, -2
Factor s**5/6 - s**4/2 - 5*s**3/3 + 26*s**2/3 - 12*s + 16/3.
(s - 2)**3*(s - 1)*(s + 4)/6
Determine y so that -y**5/4 - 11*y**4/8 + y**3 + 11*y**2/8 - 3*y/4 = 0.
-6, -1, 0, 1/2, 1
Factor 4*l**2 - 816*l + 41616.
4*(l - 102)**2
What is o in -3*o**3/2 + 19*o**2/2 - 3*o = 0?
0, 1/3, 6
Factor 4*g**4/3 - 40*g**3 - 176*g**2 - 544*g/3.
4*g*(g - 34)*(g + 2)**2/3
Factor -2*w**5/11 + 26*w**4/11 - 46*w**3/11 + 2*w**2.
-2*w**2*(w - 11)*(w - 1)**2/11
What is r in r**3 - 113*r**2 + 440*r - 436 = 0?
2, 109
Factor -3*a**2/7 - 3*a/7 + 6/7.
-3*(a - 1)*(a + 2)/7
Solve -36*w**5/7 + 204*w**4/7 - 28*w**3 - 220*w**2/7 + 184*w/7 - 32/7 = 0 for w.
-1, 1/3, 2, 4
Factor 202*k**3/3 + 136*k**2 + 8*k/3.
2*k*(k + 2)*(101*k + 2)/3
Factor 6*z**2/5 - 542*z/5 + 36.
2*(z - 90)*(3*z - 1)/5
Factor 3*d**3/11 - 707*d**2/11 + 1172*d/11 - 468/11.
(d - 234)*(d - 1)*(3*d - 2)/11
Solve 2*a**4/5 - 394*a**3/5 + 19206*a**2/5 + 19602*a/5 = 0.
-1, 0, 99
Factor -12*j**5/7 + 38*j**4/7 - 6*j**3 + 18*j**2/7 - 2*j/7.
-2*j*(j - 1)**3*(6*j - 1)/7
What is b in b**5/4 + 24*b**4 + 189*b**3/4 + 47*b**2/2 = 0?
-94, -1, 0
Solve 5*z**2 + 110*z + 605 = 0.
-11
Suppose r**3/2 + 3*r**2/2 - 54*r - 110 = 0. Calculate r.
-11, -2, 10
Factor 2*v**4 + 24*v**3 - 118*v**2 + 156*v - 64.
2*(v - 2)*(v - 1)**2*(v + 16)
What is t in -5*t**4 + 1015*t**3 - 50990*t**2 - 54060*t + 104040 = 0?
-2, 1, 102
Factor 40*p**2/3 - 235*p.
5*p*(8*p - 141)/3
Let -10*h**3/7 - 438*h**2/7