
Factor 2*v**3 - 40*v**2 + 150*v.
2*v*(v - 15)*(v - 5)
Factor -3*p**3 + 1197*p**2 - 159201*p + 7057911.
-3*(p - 133)**3
Factor -2*u**4 + 44*u**3 + 104*u**2 - 176*u - 384.
-2*(u - 24)*(u - 2)*(u + 2)**2
Factor j**2 - 2145*j - 4294.
(j - 2147)*(j + 2)
Find d, given that 9*d**4/5 - 6*d**3/5 - 63*d**2/5 - 12*d/5 + 36/5 = 0.
-2, -1, 2/3, 3
Let 2*u**2/3 + 292*u + 31974 = 0. Calculate u.
-219
Factor -2*y**3 - 16*y**2 - 10*y + 28.
-2*(y - 1)*(y + 2)*(y + 7)
Suppose -a**4/7 + 8*a**3/7 - 23*a**2/7 + 4*a - 12/7 = 0. Calculate a.
1, 2, 3
Let 6*p**2/11 - 168*p/11 = 0. What is p?
0, 28
Factor 3*z**3 - 9*z**2.
3*z**2*(z - 3)
Factor 3*x**2 - 33*x - 78.
3*(x - 13)*(x + 2)
Let -7*j**4 + 26*j**3 + 92*j**2 + 24*j = 0. Calculate j.
-2, -2/7, 0, 6
Factor -u**3/7 - 192*u**2/7 - 381*u/7 - 190/7.
-(u + 1)**2*(u + 190)/7
Suppose 3*t**5/5 - 51*t**3/5 - 108*t**2/5 - 12*t = 0. Calculate t.
-2, -1, 0, 5
Determine c, given that -c**3/5 - 6*c**2/5 - 11*c/5 - 6/5 = 0.
-3, -2, -1
Find p such that 6*p**2/11 - 370*p/11 + 244/11 = 0.
2/3, 61
Factor a**3 - 96*a**2 + 3072*a - 32768.
(a - 32)**3
Factor 3*d**3/4 + 25*d**2/4 + 2*d.
d*(d + 8)*(3*d + 1)/4
Factor -3*i**3 + 129*i**2 - 1488*i + 5184.
-3*(i - 27)*(i - 8)**2
Suppose -i**3/8 - 29*i**2/8 + i/8 + 29/8 = 0. What is i?
-29, -1, 1
Factor -l**4/3 + 2*l**3 - 11*l**2/3 + 2*l.
-l*(l - 3)*(l - 2)*(l - 1)/3
Find u such that -u**2 - 1570*u - 616225 = 0.
-785
Factor -3*h**3/4 - 81*h**2 - 2916*h - 34992.
-3*(h + 36)**3/4
Suppose -33*c**5/2 + 303*c**4/2 - 549*c**3/2 + 321*c**2/2 - 21*c = 0. What is c?
0, 2/11, 1, 7
Factor -3*g**3 + 84*g**2 - 363*g + 414.
-3*(g - 23)*(g - 3)*(g - 2)
Let 10*k**4 + 1275*k**3 + 40315*k**2 - 21120*k - 20480 = 0. What is k?
-64, -1/2, 1
Solve k**4/3 + 2*k**3/3 - 3*k**2 - 2*k/3 + 8/3 = 0 for k.
-4, -1, 1, 2
Factor 3*k**3 - 75*k.
3*k*(k - 5)*(k + 5)
Factor -5*n**2/3 + 235*n/3 - 230/3.
-5*(n - 46)*(n - 1)/3
Find i, given that -6*i**4 - 1082*i**3 - 3548*i**2 - 1400*i + 2832 = 0.
-177, -2, 2/3
Find r, given that r**5/7 - 5*r**4/7 - r**3/7 + 29*r**2/7 - 12*r/7 - 36/7 = 0.
-2, -1, 2, 3
Factor 5*q**5 + 205*q**4 - 210*q**3.
5*q**3*(q - 1)*(q + 42)
What is x in x**2/5 + 23*x/5 + 22/5 = 0?
-22, -1
Factor 2*g**4 - 390*g**3 - 3222*g**2 - 5266*g - 2436.
2*(g - 203)*(g + 1)**2*(g + 6)
Factor -5*o**2 + 205*o + 900.
-5*(o - 45)*(o + 4)
Find q, given that -2*q**5 + 7*q**4 + 38*q**3 - 103*q**2 - 60*q = 0.
-4, -1/2, 0, 3, 5
Factor -v**5 - 7*v**4 - 18*v**3 - 20*v**2 - 8*v.
-v*(v + 1)*(v + 2)**3
Factor 2*z**2 + 7*z + 3.
(z + 3)*(2*z + 1)
Solve -539*r**4/2 - 535*r**3/2 + 543*r**2/2 + 535*r/2 - 2 = 0 for r.
-1, 4/539, 1
Solve -3*t**4/2 - 1152*t**3 - 2301*t**2/2 = 0.
-767, -1, 0
Factor o**3 + 6*o**2 - 9*o - 14.
(o - 2)*(o + 1)*(o + 7)
Factor -85*i**2/2 + 75*i/2 + 5.
-5*(i - 1)*(17*i + 2)/2
Factor -j**4/2 + 143*j**3/2 - 279*j**2/2 - 423*j/2.
-j*(j - 141)*(j - 3)*(j + 1)/2
Factor -47*u**2/6 - 5*u.
-u*(47*u + 30)/6
Factor -m**2 + 61*m + 260.
-(m - 65)*(m + 4)
Find k, given that -k**2 - 15*k = 0.
-15, 0
Solve 3*g**4/2 + 3*g**3 - 27*g**2/2 - 27*g = 0 for g.
-3, -2, 0, 3
Find o, given that o**3 + 67*o**2 + 1320*o + 6300 = 0.
-30, -7
Let -5*n**4/3 + 440*n**3/3 - 9680*n**2/3 = 0. What is n?
0, 44
What is u in -2*u**5/19 + 14*u**4/19 - 28*u**3/19 + 4*u**2/19 + 30*u/19 - 18/19 = 0?
-1, 1, 3
Determine c so that 4*c**3 + 676*c**2 + 29548*c + 82668 = 0.
-83, -3
Find v such that -4*v**4 + 752*v**3 - 36812*v**2 + 137632*v - 101568 = 0.
1, 3, 92
Determine i so that 21*i**3 + 129*i**2 - 318*i - 48 = 0.
-8, -1/7, 2
Factor 3*d**4 - 21*d**3 - 3*d**2 + 21*d.
3*d*(d - 7)*(d - 1)*(d + 1)
Let 4*p**5/7 + 16*p**4/7 - 4*p**3 - 136*p**2/7 - 96*p/7 = 0. Calculate p.
-4, -2, -1, 0, 3
Factor o**3/5 + 2*o**2/5 - 11*o/5 - 12/5.
(o - 3)*(o + 1)*(o + 4)/5
Factor 4*d**2 + 88*d + 84.
4*(d + 1)*(d + 21)
Factor 2*o**3/5 - 50*o**2 - 768*o/5.
2*o*(o - 128)*(o + 3)/5
Determine h, given that -4*h**5 - 64*h**4 - 276*h**3 - 376*h**2 - 160*h = 0.
-10, -4, -1, 0
Factor r**4/4 + 5*r**3/2 - 19*r**2/4 - 19*r + 33.
(r - 2)**2*(r + 3)*(r + 11)/4
Determine r so that -2*r**2/13 - 1172*r/13 = 0.
-586, 0
Factor -q**3 + 152*q**2/3 - 1975*q/3 + 1250/3.
-(q - 25)**2*(3*q - 2)/3
Factor -388*h**5 + 740*h**4 - 316*h**3 - 36*h**2.
-4*h**2*(h - 1)**2*(97*h + 9)
Determine v, given that -4*v**3 + 2976*v**2 - 738048*v + 61011968 = 0.
248
What is a in 25*a**4/2 + 15*a**3/2 - 37*a**2 - 48*a - 16 = 0?
-1, -4/5, 2
Factor 2*p**3 + 2*p**2 - 172*p + 528.
2*(p - 6)*(p - 4)*(p + 11)
Find f such that -62*f**3 + 748*f**2 - 2280*f + 144 = 0.
2/31, 6
Factor 2*l**2/13 + 98*l/13.
2*l*(l + 49)/13
Find l, given that 8*l**3/21 - 442*l**2/21 - 2818*l/21 + 244/7 = 0.
-6, 1/4, 61
Let 2*t**4/9 + 2*t**3/3 - 4*t**2/9 - 8*t/3 - 16/9 = 0. Calculate t.
-2, -1, 2
Factor 3*i**3 + 1182*i**2 - 2373*i + 1188.
3*(i - 1)**2*(i + 396)
Factor -10*d**3 + 25*d**2 - 20*d + 5.
-5*(d - 1)**2*(2*d - 1)
Factor 2*x**3/3 - 14*x**2 - 482*x/3 + 174.
2*(x - 29)*(x - 1)*(x + 9)/3
Factor m**4/4 + 31*m**3/2 - 539*m**2/4 + 363*m - 315.
(m - 3)**2*(m - 2)*(m + 70)/4
Determine j, given that -j**5 - 7*j**4 - 11*j**3 + 7*j**2 + 12*j = 0.
-4, -3, -1, 0, 1
Determine i so that -4*i**3 + 56*i**2 - 64*i - 384 = 0.
-2, 4, 12
Find j such that -j**2/9 + 443*j/9 - 442/9 = 0.
1, 442
Determine a so that 4*a**4 - 2480*a**3 + 7416*a**2 - 7408*a + 2468 = 0.
1, 617
Factor 2*q**3/9 + 22*q**2/9 + 20*q/9 - 16.
2*(q - 2)*(q + 4)*(q + 9)/9
Let i**2/5 + 3*i + 26/5 = 0. Calculate i.
-13, -2
Factor -3*k**3 + 3*k**2 + 51*k + 45.
-3*(k - 5)*(k + 1)*(k + 3)
Factor 2*x**2 - 6*x - 108.
2*(x - 9)*(x + 6)
What is f in 5*f**4 - 65*f**3 - 320*f**2 - 340*f = 0?
-2, 0, 17
Factor 2*g**2/11 + 14*g/11 - 60/11.
2*(g - 3)*(g + 10)/11
Factor 2*i**2/3 - 8*i/3 - 14.
2*(i - 7)*(i + 3)/3
Factor 18*a**3 + 112*a**2 + 24*a.
2*a*(a + 6)*(9*a + 2)
Factor 3*a**5 - 15*a**4 - 18*a**3.
3*a**3*(a - 6)*(a + 1)
Find n, given that -n**3/5 - 46*n**2/5 = 0.
-46, 0
Factor -m**4 + 7*m**2 + 6*m.
-m*(m - 3)*(m + 1)*(m + 2)
Solve 2*r**2 + 338*r - 684 = 0 for r.
-171, 2
Let 4*z**3 - 38*z**2 - 70*z + 44 = 0. Calculate z.
-2, 1/2, 11
Factor x**3 - 9*x**2 + 15*x - 7.
(x - 7)*(x - 1)**2
Suppose f**5 + 336*f**4 - 2040*f**3 + 4094*f**2 - 3417*f + 1026 = 0. What is f?
-342, 1, 3
Factor 2*t**5/7 + 250*t**4/7 - 762*t**3/7 + 766*t**2/7 - 256*t/7.
2*t*(t - 1)**3*(t + 128)/7
Determine a, given that 2*a**5/3 + 5*a**4/2 - 25*a**2/6 + a = 0.
-3, -2, 0, 1/4, 1
Let -25*m**3 + 305*m**2 - 960*m + 180 = 0. What is m?
1/5, 6
Determine b, given that -b**5 + 41*b**4 + 2*b**3 - 82*b**2 - b + 41 = 0.
-1, 1, 41
Find s such that -s**4/3 - 8*s**3/3 - 4*s**2 = 0.
-6, -2, 0
Factor 2*y**2 - 2854*y - 5716.
2*(y - 1429)*(y + 2)
Determine k, given that k**3 + 1091*k**2 + 2179*k + 1089 = 0.
-1089, -1
Solve o**5 + 10*o**4 + 21*o**3 = 0.
-7, -3, 0
Solve 2*z**5 - 466*z**4 + 26438*z**3 + 82130*z**2 + 83072*z + 27848 = 0.
-1, 118
Let -2*n**4/7 + 390*n**3/7 + 226*n**2 + 1986*n/7 + 796/7 = 0. Calculate n.
-2, -1, 199
Factor 39*q**3 + 75*q**2/2 - 159*q/2 + 3.
3*(q - 1)*(q + 2)*(26*q - 1)/2
Factor 3*v**3/7 + 39*v**2/7 - 99*v/7 - 135/7.
3*(v - 3)*(v + 1)*(v + 15)/7
Suppose -k**4 - 190*k**3 - 9025*k**2 = 0. What is k?
-95, 0
Factor 2*h**2/7 + 138*h/7 + 136/7.
2*(h + 1)*(h + 68)/7
What is f in -10*f**5 - 152*f**4/3 - 136*f**3/3 - 32*f**2/3 = 0?
-4, -2/3, -2/5, 0
Find m such that 5*m**2 + 41650*m + 86736125 = 0.
-4165
Let 3*a**3/2 - 6*a**2 = 0. What is a?
0, 4
What is d in 5*d**2 + 115*d + 210 = 0?
-21, -2
What is b in -4*b**3 + 16*b**2 - 12*b = 0?
0, 1, 3
Suppose -o**2 - 53*o = 0. What is o?
-53, 0
Factor -d**4/6 - 2*d**3 + 31*d**2/6 + 7*d.
-d*(d - 3)*(d + 1)*(d + 14)/6
Let 4*c**5 + 12*c**4 + 4*c**3 - 12*c**2 - 8*c = 0. Calculate c.
-2, -1, 0, 1
Solve q**2/3 - 1/3 = 0 for q.
-1, 1
Factor -v**2/3 + 226*v/3 - 1105/3.
-(v - 221)*(v - 5)/3
Find r, given that -4*r**3 + 4*r**2 + 32*r - 48 = 0.
-3, 2
Factor 2*m**3 - 52*m**2 + 210*m.
2*m*(m - 21)*(m - 5)
Factor -p**3/2 - 41*p**2/2 - 76*p - 74.
-(p + 2)**2*(p + 37)/2
Find d, given that 5*d**4 + 180*d**3 + 510*d**2 + 500*d + 165 = 0.
-33, -1
Find x such that -2*x**2 - 336*x - 334 = 0.
-167, -1
Factor w**3/4 + 6*w**2 + 11*w.
w*(w + 2)*(w + 22)/4
Suppose 4*r**2/5 - 2808*r/5 - 2812/5 = 0. Calculate r.
-1, 703
Factor 4*c**3/5 + 257*c**2/5 + 316*c/5 + 63/5.
(c + 1)*(c + 63)*(4*c + 1)/5
Find v such that 3*v**5/2 - 1503*v**4/2 - 