r 2*u**5/5 - 12*u**4/5 + 24*u**3/5 - 16*u**2/5.
2*u**2*(u - 2)**3/5
Determine b, given that 2*b**4/13 + 66*b**3/13 + 594*b**2/13 + 1998*b/13 + 2268/13 = 0.
-21, -6, -3
Factor -3*j**3 + 1161*j**2 + 2331*j + 1167.
-3*(j - 389)*(j + 1)**2
Solve t**5/6 + 7*t**4/6 + 8*t**3/3 + 4*t**2/3 - 8*t/3 - 8/3 = 0 for t.
-2, 1
Suppose -3*q**4/2 + 24*q**3 - 96*q**2 = 0. What is q?
0, 8
Factor -3*j**2/4 + 132*j - 5808.
-3*(j - 88)**2/4
Suppose -4*n**3 - 4*n**2 + 100*n + 100 = 0. Calculate n.
-5, -1, 5
Suppose a**4/4 + 5*a**3/4 - 3*a**2 - 19*a - 20 = 0. Calculate a.
-5, -2, 4
Factor -w**2/4 + 6*w + 81/4.
-(w - 27)*(w + 3)/4
Find h, given that -6*h**5 + 39*h**4 - 93*h**3 + 96*h**2 - 36*h = 0.
0, 1, 3/2, 2
Suppose z**5/2 - 4*z**4 - 23*z**3/2 + 141*z**2 - 234*z + 108 = 0. Calculate z.
-6, 1, 6
Determine r, given that r**3/3 - 6*r**2 + 11*r - 16/3 = 0.
1, 16
Factor 3*g**3/7 + 75*g**2/7 + 186*g/7 - 264/7.
3*(g - 1)*(g + 4)*(g + 22)/7
Let 8*b**4/13 - 98*b**3/13 - 320*b**2/13 - 154*b/13 + 60/13 = 0. Calculate b.
-2, -1, 1/4, 15
Factor 7*g**3 + 39*g**2 - 22*g - 24.
(g - 1)*(g + 6)*(7*g + 4)
Find g, given that 32*g**4/3 + 16*g**3 - 10*g**2 + 4*g/3 = 0.
-2, 0, 1/4
Factor -p**5/3 + 4*p**4/3 + 4*p**3 + 2*p**2/3 - 11*p/3 - 2.
-(p - 6)*(p - 1)*(p + 1)**3/3
Factor -l**4/5 + 21*l**3/5 - 74*l**2/5 - 384*l/5 - 288/5.
-(l - 12)**2*(l + 1)*(l + 2)/5
Solve 16*n**2 + 300*n - 76 = 0 for n.
-19, 1/4
Factor 4*j**2 - 164*j + 1152.
4*(j - 32)*(j - 9)
Factor o**3/6 - 61*o**2/3 - 512*o/3 - 1040/3.
(o - 130)*(o + 4)**2/6
Let -7*v**5 - 443*v**4 - 987*v**3 - 673*v**2 - 122*v = 0. What is v?
-61, -1, -2/7, 0
Find j such that 80*j**3 + 96120*j**2 - 48075*j + 6010 = 0.
-1202, 1/4
Let m**5/2 - 25*m**4/2 + 33*m**3 = 0. What is m?
0, 3, 22
Let -n**4/3 + 9*n**3 - 25*n**2 + 73*n/3 - 8 = 0. What is n?
1, 24
Find z, given that 5*z**2 - 85*z + 260 = 0.
4, 13
Determine p, given that -2*p**2 + 22*p = 0.
0, 11
Factor 2*n**2/9 + 106*n/9 - 112/3.
2*(n - 3)*(n + 56)/9
Factor v**4/7 + 23*v**3/7 - 3*v**2/7 - 71*v/7 - 46/7.
(v - 2)*(v + 1)**2*(v + 23)/7
Determine g, given that 29*g**4/2 + 267*g**3/4 + 375*g**2/4 + 38*g + 3 = 0.
-2, -1/2, -3/29
Factor -4*b**2 - 128*b - 624.
-4*(b + 6)*(b + 26)
Suppose -14*o**5/5 - 92*o**4/5 - 28*o**3 + 24*o**2 + 234*o/5 - 108/5 = 0. Calculate o.
-3, -2, 3/7, 1
Determine u so that -2*u**5/5 - 236*u**4/5 - 6722*u**3/5 + 2832*u**2 - 1440*u = 0.
-60, 0, 1
Factor -5*l**3 - 250*l**2 - 2860*l + 6760.
-5*(l - 2)*(l + 26)**2
Factor s**5/9 - 8*s**4/9 - 8*s**3 - 158*s**2/9 - 137*s/9 - 14/3.
(s - 14)*(s + 1)**3*(s + 3)/9
Factor -g**2/2 - 47*g + 95/2.
-(g - 1)*(g + 95)/2
Factor 5*y**3/2 + 41*y**2 - 74*y - 36.
(y - 2)*(y + 18)*(5*y + 2)/2
Suppose 2*n**4/11 + 2*n**3/11 = 0. What is n?
-1, 0
What is v in 11*v**3/5 + 181*v**2/5 + 34*v = 0?
-170/11, -1, 0
Determine a, given that -a**4 - 380*a**3 + 3*a**2 + 1138*a - 760 = 0.
-380, -2, 1
Let -5*d**4/6 + 23*d**3/6 - 5*d**2 + 2*d/3 + 4/3 = 0. Calculate d.
-2/5, 1, 2
Let 3*o**3 - 60*o**2 + 336*o - 576 = 0. What is o?
4, 12
Solve 4*j**2 + 96*j = 0 for j.
-24, 0
Factor -2*u**3 - 2*u**2 + 28*u + 48.
-2*(u - 4)*(u + 2)*(u + 3)
Factor 5*i**2 + 4490*i - 4495.
5*(i - 1)*(i + 899)
Factor o**5 - 3*o**4 - o**3 + 3*o**2.
o**2*(o - 3)*(o - 1)*(o + 1)
Let -2*b**3/7 + 292*b**2/7 - 862*b/7 + 572/7 = 0. What is b?
1, 2, 143
Suppose 2*v**3/3 - 8*v**2 + 26*v - 56/3 = 0. Calculate v.
1, 4, 7
Factor -3*n**4 - 3*n**3 + 150*n**2 - 144*n.
-3*n*(n - 6)*(n - 1)*(n + 8)
Solve 4*w**2 - 544*w - 548 = 0.
-1, 137
Factor 34*p**2 + 240*p + 14.
2*(p + 7)*(17*p + 1)
Factor 2*l**2 - 9888*l + 12221568.
2*(l - 2472)**2
Factor -i**5 + 7*i**3 - 2*i**2 - 12*i + 8.
-(i - 2)*(i - 1)**2*(i + 2)**2
Factor 2*t**3/5 - 226*t**2/5 + 446*t/5 - 222/5.
2*(t - 111)*(t - 1)**2/5
Factor v**4/4 - v**3/2 - 3*v**2 + 9*v/2 + 27/4.
(v - 3)**2*(v + 1)*(v + 3)/4
Let -j**2/3 + 216*j = 0. What is j?
0, 648
Determine p so that 3*p**5/7 + 156*p**4/7 + 1110*p**3/7 + 2424*p**2/7 + 2127*p/7 + 660/7 = 0.
-44, -5, -1
Factor -3*b**4 - 12*b**3 + 96*b**2.
-3*b**2*(b - 4)*(b + 8)
Determine w, given that -2*w**5 + 56*w**4/3 - 50*w**3 + 44*w**2/3 + 64*w - 64/3 = 0.
-1, 1/3, 2, 4
Factor 3*j**3/4 + 189*j**2/2 - 192*j.
3*j*(j - 2)*(j + 128)/4
Factor -c**4/4 + c**3/2 + 3*c**2 - 10*c + 8.
-(c - 2)**3*(c + 4)/4
Solve 9*x**3 - 24*x**2 - 15*x + 18 = 0 for x.
-1, 2/3, 3
Suppose y**4 - 48*y**3 + 217*y**2 - 78*y - 344 = 0. What is y?
-1, 2, 4, 43
Solve -3*v**5 - 21*v**4 - 6*v**3 + 120*v**2 = 0 for v.
-5, -4, 0, 2
Let 5*n**5 - 110*n**4 - 195*n**3 + 8800*n**2 + 32000*n = 0. Calculate n.
-5, 0, 16
Factor 5*v**3 + 3090*v**2 + 636540*v + 43709080.
5*(v + 206)**3
Solve c**5/6 - 25*c**4/6 + 23*c**3/6 + 25*c**2/6 - 4*c = 0.
-1, 0, 1, 24
Factor -5*s**2/2 - 23*s/2 + 5.
-(s + 5)*(5*s - 2)/2
Solve 3*n**2/2 + 365*n/3 = 0.
-730/9, 0
Factor -s**2 - 194*s - 2013.
-(s + 11)*(s + 183)
Suppose -5*q**3 - 30*q**2 + 180*q - 200 = 0. What is q?
-10, 2
Determine n, given that -2*n**2/21 - 2*n/3 = 0.
-7, 0
Solve 3*u**3 - 42*u**2 - 3*u + 42 = 0 for u.
-1, 1, 14
Factor -t**3/2 + 86*t**2 - 3698*t.
-t*(t - 86)**2/2
Let -2*s**4 + 66*s**3 - 726*s**2 + 2662*s = 0. Calculate s.
0, 11
Factor 2*p**4 - 42*p**3 + 38*p**2 + 42*p - 40.
2*(p - 20)*(p - 1)**2*(p + 1)
Factor -4*f**4 - 324*f**3 - 6048*f**2 + 21168*f.
-4*f*(f - 3)*(f + 42)**2
Factor -k**2 - 31*k/7 + 20/7.
-(k + 5)*(7*k - 4)/7
Determine j so that j**2/5 + 16*j/5 + 39/5 = 0.
-13, -3
Determine q, given that 324*q**4/5 - 14112*q**3/5 + 26924*q**2 + 61936*q/5 + 1392 = 0.
-2/9, 15, 29
Find l, given that -12*l**5 - 213*l**4 - 918*l**3 - 1053*l**2 + 324*l = 0.
-12, -3, 0, 1/4
Factor s**2/3 - 8*s + 48.
(s - 12)**2/3
Factor r**4 - 40*r**3 + 239*r**2 - 248*r - 528.
(r - 33)*(r - 4)**2*(r + 1)
Solve -34*d**5/7 + 474*d**4/7 - 1196*d**3/7 + 1084*d**2/7 - 306*d/7 - 22/7 = 0.
-1/17, 1, 11
Factor 3*t**2 - 3072*t + 786432.
3*(t - 512)**2
Factor z**2/4 - 169*z/2 - 339/4.
(z - 339)*(z + 1)/4
Factor -n**3/2 - 17*n**2/2 + 40*n - 42.
-(n - 2)**2*(n + 21)/2
Find v such that -5*v**3 - 5*v**2 + 290*v + 560 = 0.
-7, -2, 8
Let -2*n**2/9 + 2026*n/3 - 6076/9 = 0. Calculate n.
1, 3038
Factor -2*o**3 + 6*o**2 + 108*o.
-2*o*(o - 9)*(o + 6)
Factor -d**2/5 + 16*d - 320.
-(d - 40)**2/5
What is z in -z**2/4 + 8*z + 33/4 = 0?
-1, 33
Factor 2*g**4 - 76*g**3 + 930*g**2 - 3304*g - 4312.
2*(g - 14)**2*(g - 11)*(g + 1)
Factor y**2/6 - 84*y - 505/6.
(y - 505)*(y + 1)/6
Factor 5*z**5 + 185*z**4 + 350*z**3 - 10*z**2 - 355*z - 175.
5*(z - 1)*(z + 1)**3*(z + 35)
Factor 4*d**2 + 494*d + 61009/4.
(4*d + 247)**2/4
Solve -7*y**2 + 17*y - 6 = 0 for y.
3/7, 2
Factor -2*u**3/5 + 4*u**2 + 442*u/5 + 84.
-2*(u - 21)*(u + 1)*(u + 10)/5
Find v such that 4*v**3 - 4*v**2 - 24*v = 0.
-2, 0, 3
Factor -u**2/9 + 1664*u/9 - 692224/9.
-(u - 832)**2/9
Suppose -2*v**3/15 - 32*v**2/5 - 462*v/5 - 6292/15 = 0. Calculate v.
-26, -11
Solve -4*v**2 + 1700*v + 15624 = 0.
-9, 434
Factor -2*w**4 - 12*w**3 - 24*w**2 - 20*w - 6.
-2*(w + 1)**3*(w + 3)
Determine a so that 3*a**4 + 27*a**3 = 0.
-9, 0
Find y such that -4*y**3 + 76*y**2 - 360*y + 288 = 0.
1, 6, 12
Factor -2*h**2/19 + 10*h/19 + 100/19.
-2*(h - 10)*(h + 5)/19
Solve 5*p**3/3 - 14*p**2/3 - 167*p/3 + 140/3 = 0.
-5, 4/5, 7
Find w, given that -w**2/3 + 6*w - 27 = 0.
9
Find s such that 12*s**4 - 8*s**3 - 68*s**2 + 32*s + 80 = 0.
-2, -1, 5/3, 2
Factor -t**4/4 + 48*t**3 - 3072*t**2 + 65536*t.
-t*(t - 64)**3/4
Factor t**2/5 + 42*t/5 - 43/5.
(t - 1)*(t + 43)/5
Suppose 2*h**3/11 + 18*h**2/11 + 40*h/11 = 0. Calculate h.
-5, -4, 0
Factor l**3/6 - 517*l**2/6 + 11180*l - 11094.
(l - 258)**2*(l - 1)/6
Factor -5*s**2 + 3095*s + 9330.
-5*(s - 622)*(s + 3)
Factor -s**4 - 14*s**3 - 48*s**2 + 14*s + 49.
-(s - 1)*(s + 1)*(s + 7)**2
Factor -i**2/8 + 383*i/8.
-i*(i - 383)/8
Solve 5*g**5 - 150*g**4 - 845*g**3 - 1050*g**2 = 0.
-3, -2, 0, 35
Factor 2*n**2/3 + 62*n/3 + 156.
2*(n + 13)*(n + 18)/3
Find u, given that -6*u**5 - 2*u**4 + 4*u**3 = 0.
-1, 0, 2/3
Factor m**5/5 + 124*m**4/5 - 252*m**3/5.
m**3*(m - 2)*(m + 126)/5
Factor -o**3/5 + 16*o/5.
-o*(o - 4)*(o + 4)/5
Solve 18*o**4 - 93*o**3/2 + 45*o**2/2 - 3*o = 0 for o.
0, 1/4, 1/3, 2
Determine x, given that 4*x**4/3 - 304*x**3/3 + 8272*x**2/3 - 31616*x + 129792 = 0.
12, 26
Let y**3/3 - 25*y**2/3 - 84*y - 132 = 0. Calculate y.
-6, -2, 33
Let n**2/6 - 107*n/3 + 11449/6 = 0. Calculate n.
107
Factor -4*p**5 + 9