 3
Find v such that 2*v**4 - 3*v**3 + v**2 = 0.
0, 1/2, 1
Find z such that -2*z**3/5 + 72*z**2/5 - 178*z/5 - 132 = 0.
-2, 5, 33
Find a, given that 2*a**2/13 - 12*a + 154/13 = 0.
1, 77
Find u such that 4*u**2 - 696*u - 700 = 0.
-1, 175
Factor 2*n**5/5 + 4*n**4/5 - 24*n**3/5 + 28*n**2/5 - 2*n.
2*n*(n - 1)**3*(n + 5)/5
Factor u**5 + 7*u**4/2 + 3*u**3/2.
u**3*(u + 3)*(2*u + 1)/2
Find v such that 4*v**2 + 176*v + 1260 = 0.
-35, -9
Find k, given that 180*k**5 - 234*k**4 + 34*k**3 + 26*k**2 - 6*k = 0.
-1/3, 0, 3/10, 1/3, 1
Factor h**5 + 6*h**4 - 48*h**3 - 416*h**2 - 768*h.
h*(h - 8)*(h + 4)**2*(h + 6)
Find a such that a**4/3 - 154*a**3 + 920*a**2/3 = 0.
0, 2, 460
Factor -14*u**2/5 + 268*u + 384/5.
-2*(u - 96)*(7*u + 2)/5
Factor -4*f**4 - 76*f**3 - 280*f**2.
-4*f**2*(f + 5)*(f + 14)
Factor o**4/2 + 44*o**3 + 1152*o**2 + 4096*o - 131072.
(o - 8)*(o + 32)**3/2
Suppose -4*f**5/9 + 112*f**4/9 - 1048*f**3/9 + 3712*f**2/9 - 4708*f/9 + 1936/9 = 0. What is f?
1, 4, 11
Solve 5*x**2/3 + 535*x/3 - 1090/3 = 0.
-109, 2
Factor -15*p**3 + 10*p**2.
-5*p**2*(3*p - 2)
Factor -o**3 + 3*o - 2.
-(o - 1)**2*(o + 2)
What is n in -5*n**5/4 - 45*n**4/4 - 15*n**3 + 80*n**2 + 240*n + 180 = 0?
-6, -2, 3
Factor -5*t**5 - 800*t**4 - 2370*t**3 - 2360*t**2 - 785*t.
-5*t*(t + 1)**3*(t + 157)
Let -4*f**2/7 + 1236*f/7 - 176 = 0. Calculate f.
1, 308
Find t, given that -4*t**3/7 + 2064*t**2/7 + 592*t = 0.
-2, 0, 518
Factor o**3 - 557*o**2 - o + 557.
(o - 557)*(o - 1)*(o + 1)
Find m, given that -m**5/2 + 22*m**4 - 299*m**3 + 1256*m**2 - 3401*m/2 + 722 = 0.
1, 4, 19
Factor -l**4/2 - 51*l**3/2 - 94*l**2.
-l**2*(l + 4)*(l + 47)/2
Factor -2*d**3/5 + 56*d**2/5 - 442*d/5 + 676/5.
-2*(d - 13)**2*(d - 2)/5
Solve a**3/3 + 68*a**2/3 + 44*a = 0.
-66, -2, 0
Find u such that 2*u**3/7 - 2146*u**2/7 - 2*u/7 + 2146/7 = 0.
-1, 1, 1073
Factor -n**2/3 - 12*n + 255.
-(n - 15)*(n + 51)/3
Find a such that 5*a**3 + 880*a**2 + 6800*a + 13440 = 0.
-168, -4
Determine c so that -c**3/2 - 16*c**2 - 30*c = 0.
-30, -2, 0
Let 5*n**2 - 390*n + 4480 = 0. Calculate n.
14, 64
Find l such that -2*l**5/7 - 2*l**4/7 + 68*l**3/7 + 260*l**2/7 + 318*l/7 + 18 = 0.
-3, -1, 7
Let 7*a**4/4 - 15*a**3 + 36*a**2 - 16*a = 0. Calculate a.
0, 4/7, 4
Solve 2*p**3/11 - 24*p**2/11 + 2*p = 0.
0, 1, 11
Factor -4*f**3 - 12*f**2 + 16.
-4*(f - 1)*(f + 2)**2
Factor -w**3/6 - 211*w**2/6 - 404*w - 1194.
-(w + 6)**2*(w + 199)/6
Factor m**5 - 13*m**4 + 16*m**3 + 192*m**2.
m**2*(m - 8)**2*(m + 3)
Find a, given that 3*a**2 - 4443*a - 4446 = 0.
-1, 1482
Factor -2*o**2/9 + 628*o/9.
-2*o*(o - 314)/9
Suppose -27*q**4/8 + 21*q**3/8 + 69*q**2/2 + 69*q/2 + 6 = 0. Calculate q.
-2, -1, -2/9, 4
Factor 4*m**4 + 456*m**3 - 12*m**2 - 1360*m + 912.
4*(m - 1)**2*(m + 2)*(m + 114)
Let -60*x**5 + 124*x**4 + 60*x**3 - 140*x**2 + 16 = 0. Calculate x.
-1, -1/3, 2/5, 1, 2
Find o such that 100*o**5 + 370*o**4 + 386*o**3 + 50*o**2 - 102*o - 36 = 0.
-2, -1, -3/5, 1/2
Find p such that -3*p**3/4 - 81*p**2/4 + 171*p/4 - 87/4 = 0.
-29, 1
Factor h**5/2 - 5*h**4 - 18*h**3 - 19*h**2 - 13*h/2.
h*(h - 13)*(h + 1)**3/2
Suppose 2*v**4/21 + 338*v**3/21 - 1034*v**2/21 - 338*v/21 + 344/7 = 0. Calculate v.
-172, -1, 1, 3
Factor m**3/7 + 2*m**2 + 43*m/7 + 30/7.
(m + 1)*(m + 3)*(m + 10)/7
Factor -18*v**4 + 58*v**3 - 48*v**2 + 8*v.
-2*v*(v - 2)*(v - 1)*(9*v - 2)
Factor 27*g**2 + 249*g + 54.
3*(g + 9)*(9*g + 2)
Factor 5*m**2/3 - 10*m + 25/3.
5*(m - 5)*(m - 1)/3
Factor -a**3/3 + 7*a/3 - 2.
-(a - 2)*(a - 1)*(a + 3)/3
Factor 3*a**3/5 - 9*a**2/5 - 63*a - 195.
3*(a - 13)*(a + 5)**2/5
Let g**4 + 42*g**3/5 + 76*g**2/5 + 24*g/5 = 0. Calculate g.
-6, -2, -2/5, 0
Factor 2*h**4 - 86*h**3 - 996*h**2 - 3328*h - 3392.
2*(h - 53)*(h + 2)*(h + 4)**2
Suppose 2*f**2 - 184*f + 4232 = 0. What is f?
46
Suppose 5*b**4 - 85*b**3 + 255*b**2 + 85*b - 260 = 0. Calculate b.
-1, 1, 4, 13
Factor 5*h**2 + 2595*h - 2600.
5*(h - 1)*(h + 520)
Factor 15*x**3 - 110*x**2 + 145*x + 150.
5*(x - 5)*(x - 3)*(3*x + 2)
Find k, given that k**5 + 25*k**4 + 166*k**3 - 138*k**2 - 2727*k + 2673 = 0.
-11, -9, 1, 3
Factor -w**4/3 - 9*w**3 + 40*w**2 - 124*w/3.
-w*(w - 2)**2*(w + 31)/3
Factor 2*z**2/5 - 876*z/5 + 95922/5.
2*(z - 219)**2/5
Solve r**5 + 7*r**4 - 36*r**2 = 0.
-6, -3, 0, 2
Factor 5*o**2 + 36480*o + 66539520.
5*(o + 3648)**2
Suppose 6*q**2 - 3177*q - 1590 = 0. Calculate q.
-1/2, 530
What is w in -2*w**5 - 1562*w**4 - 302630*w**3 + 917282*w**2 - 920416*w + 307328 = 0?
-392, 1
Factor -3*i**3 + 267*i**2 + 1683*i + 2565.
-3*(i - 95)*(i + 3)**2
Factor -15*f**3 - 156*f**2 - 60*f.
-3*f*(f + 10)*(5*f + 2)
Suppose -3*k**5 + 15*k**4 + 63*k**3 - 255*k**2 - 300*k = 0. Calculate k.
-4, -1, 0, 5
Factor -2*q**2 + 42*q + 144.
-2*(q - 24)*(q + 3)
Factor -5*s**4 + 715*s**3 + 2175*s**2 + 2185*s + 730.
-5*(s - 146)*(s + 1)**3
Suppose 3*v**4 - 78*v**3 + 579*v**2 - 1692*v + 1728 = 0. What is v?
3, 4, 16
Factor g**4 + 28*g**3 + 122*g**2 + 164*g + 69.
(g + 1)**2*(g + 3)*(g + 23)
Factor -2*w**3/9 - 146*w**2/9 - 1340*w/9 + 496/3.
-2*(w - 1)*(w + 12)*(w + 62)/9
Factor -2*d**3/13 - 74*d**2/13 - 432*d/13 - 360/13.
-2*(d + 1)*(d + 6)*(d + 30)/13
Determine k so that -k**2/5 - 4*k/5 = 0.
-4, 0
Determine z, given that 3*z**3 - 342*z**2 + 10080*z - 18816 = 0.
2, 56
Factor -v**2 + 9.
-(v - 3)*(v + 3)
Factor y**4/4 + 2*y**3 + 2*y**2 - 8*y - 12.
(y - 2)*(y + 2)**2*(y + 6)/4
Solve -4*y**3 - 104*y**2 + 108*y = 0 for y.
-27, 0, 1
Determine o so that 2*o**2/5 + 8*o - 88/5 = 0.
-22, 2
Factor -2*z**5/9 - 32*z**4/9 - 28*z**3/3 - 80*z**2/9 - 26*z/9.
-2*z*(z + 1)**3*(z + 13)/9
Factor 3*w**2 + 3180*w + 3177.
3*(w + 1)*(w + 1059)
Find f such that 2*f**5 - 20*f**4 + 30*f**3 + 20*f**2 - 32*f = 0.
-1, 0, 1, 2, 8
Let -2*b**2 + 78*b - 216 = 0. What is b?
3, 36
Find w, given that w**4 - 5*w**3 - 12*w**2 + 44*w + 80 = 0.
-2, 4, 5
Factor 3*n**4 - 57*n**3 + 117*n**2 + 513*n - 1296.
3*(n - 16)*(n - 3)**2*(n + 3)
Factor h**2 - 568*h + 80656.
(h - 284)**2
Factor j**2 - 388*j - 1173.
(j - 391)*(j + 3)
Find p, given that 2*p**2/5 + 44*p/5 + 114/5 = 0.
-19, -3
Factor -5*u**3 + 505*u**2 - 1470*u.
-5*u*(u - 98)*(u - 3)
Solve 2*r**4/3 - 8*r**3/3 - 32*r**2/3 + 128*r/3 = 0.
-4, 0, 4
Determine c so that c**3/8 - 721*c**2/8 - 361*c/4 = 0.
-1, 0, 722
Factor 3*f**4 + 75*f**3 + 306*f**2 - 2604*f - 5880.
3*(f - 5)*(f + 2)*(f + 14)**2
Factor -g**3/5 - 71*g**2/5 - 398*g/5 - 104.
-(g + 2)*(g + 4)*(g + 65)/5
Factor -2*r**2/7 + 34*r + 240/7.
-2*(r - 120)*(r + 1)/7
Factor 165*f**2/2 + 507*f/2 + 18.
3*(f + 3)*(55*f + 4)/2
Suppose -3*c**2 + 1218*c - 2424 = 0. Calculate c.
2, 404
Let -2*c**2 + 82*c - 420 = 0. Calculate c.
6, 35
Suppose -3*g**4/2 + 3*g**3/2 + 15*g**2/2 + 9*g/2 = 0. Calculate g.
-1, 0, 3
Factor -w**2 - 30*w + 31.
-(w - 1)*(w + 31)
Solve -4*a**2/5 + 84*a/5 - 152/5 = 0 for a.
2, 19
Factor -2*v**3/17 + 4*v**2/17 + 10*v/17 - 12/17.
-2*(v - 3)*(v - 1)*(v + 2)/17
Factor -3*h**5 - 45*h**4 - 222*h**3 - 492*h**2 - 504*h - 192.
-3*(h + 1)*(h + 2)**3*(h + 8)
Factor 4*p**4 + 12*p**3 - 4*p**2 - 12*p.
4*p*(p - 1)*(p + 1)*(p + 3)
Factor 3*f**2 - 22008*f + 40362672.
3*(f - 3668)**2
Factor 2*h**5 - 6*h**4 - 12*h**3 + 52*h**2 - 54*h + 18.
2*(h - 3)*(h - 1)**3*(h + 3)
Factor -q**2/5 + 33*q/5.
-q*(q - 33)/5
Find u such that 2*u**3/11 + 18*u**2 + 1488*u/11 + 2912/11 = 0.
-91, -4
Factor -3*u**2/4 - 1509*u/4.
-3*u*(u + 503)/4
Factor 5*s**3 + 5*s**2 - 60*s.
5*s*(s - 3)*(s + 4)
Factor 3*m**3 - 57*m**2 + 105*m - 51.
3*(m - 17)*(m - 1)**2
Factor 2*h**3 + 396*h**2 + 24192*h + 423360.
2*(h + 30)*(h + 84)**2
Factor -2*i**3 + 1310*i**2 - 1308*i.
-2*i*(i - 654)*(i - 1)
Solve 3*a**3 + 201*a**2 - 840*a + 852 = 0.
-71, 2
Find s, given that s**5/7 + s**4/7 - 2*s**3/7 = 0.
-2, 0, 1
Find o such that 5*o**5/4 - 75*o**4/4 - 5*o**3/4 + 75*o**2/4 = 0.
-1, 0, 1, 15
Factor 9*y**4 + 34*y**3 + 28*y**2 - 8*y.
y*(y + 2)**2*(9*y - 2)
Factor 3*q**2/2 - 39*q/2 + 18.
3*(q - 12)*(q - 1)/2
Suppose -3*c**3 - 18*c**2 + 216*c = 0. Calculate c.
-12, 0, 6
What is n in n**4/3 + 10*n**3/3 + 37*n**2/3 + 20*n + 12 = 0?
-3, -2
Factor -2*m**3 - 56*m**2 - 200*m - 192.
-2*(m + 2)**2*(m + 24)
Factor 2*t**5/7 - 16*t**4/7 - 12*t**3/7 + 80*t**2/7 + 122*t/7 + 48/7.
2*(t - 8)*(t - 3)*(t + 1)**3/7
Solve -2*w**2 + 18*w - 40 = 0.
4, 5
Solve -2*t**5/9 - 2*t**4/9 + 10*t**3/9 + 10*t**2/9 - 8*t/9 - 8/9 = 0 for t.
-2, -1, 1, 2
Factor 3*h**5 - 39*h**4 + 69*h**3 - 33*h**2.
3*h