, 2
Factor -l**3/4 - 55*l**2/2 - 109*l/4.
-l*(l + 1)*(l + 109)/4
Factor 2*r**3 + 1248*r**2 + 259584*r + 17997824.
2*(r + 208)**3
Suppose n**4 - 102*n**3 + 576*n**2 + 32*n - 3072 = 0. What is n?
-2, 4, 96
Solve 3*n**3 - 624*n**2 + 1236*n = 0 for n.
0, 2, 206
Suppose -2*c**3/5 - 12*c**2/5 + 18*c + 20 = 0. What is c?
-10, -1, 5
Factor 3*x**3 + 45*x**2 - 99*x + 51.
3*(x - 1)**2*(x + 17)
Let -304*y**5/3 - 303*y**4 + 3*y**3 = 0. What is y?
-3, 0, 3/304
Find i, given that -4*i**2/3 - 1772*i/3 - 1768/3 = 0.
-442, -1
Factor 5*v**3 + 14*v**2 - 96*v/5 - 288/5.
(v - 2)*(5*v + 12)**2/5
Let -8*w**5/7 + 50*w**4 + 1984*w**3/7 + 3578*w**2/7 + 2344*w/7 + 56 = 0. Calculate w.
-2, -1, -1/4, 49
Determine c, given that -2*c**2/7 + 976*c/7 + 978/7 = 0.
-1, 489
Factor g**2/3 - 17*g - 52/3.
(g - 52)*(g + 1)/3
Solve 2*l**3/19 + 16*l**2/19 - 640*l/19 + 3072/19 = 0 for l.
-24, 8
Factor 91*o**2/2 - 71*o/2 - 10.
(o - 1)*(91*o + 20)/2
Suppose -3*w**5 + 60*w**4 - 45*w**3 - 240*w**2 + 228*w = 0. What is w?
-2, 0, 1, 2, 19
Suppose -12*k**5 - 249*k**4 - 1353*k**3 - 366*k**2 + 2580*k - 600 = 0. Calculate k.
-10, -2, 1/4, 1
Determine n, given that -2*n**4 - 26*n**3 - 24*n**2 = 0.
-12, -1, 0
Factor -m**5 - 34*m**4 - 369*m**3 - 1296*m**2.
-m**2*(m + 9)**2*(m + 16)
Suppose -162*h**2 + 126*h - 49/2 = 0. Calculate h.
7/18
Let 2*z**4 - 10*z**3 = 0. Calculate z.
0, 5
Factor 5*l**2 + 300*l + 580.
5*(l + 2)*(l + 58)
Factor 8*w**4 + 4*w**3 - 20*w**2 + 8*w.
4*w*(w - 1)*(w + 2)*(2*w - 1)
Determine y so that -50*y**5 + 65*y**4 + 85*y**3 - 30*y**2 = 0.
-1, 0, 3/10, 2
Factor 2*y**3/3 + 5*y**2/3 + 2*y/3.
y*(y + 2)*(2*y + 1)/3
Determine t so that -t**5/2 + 13*t**4/2 - 15*t**3 - 2*t**2 + 20*t = 0.
-1, 0, 2, 10
Factor -p**2/8 + p - 15/8.
-(p - 5)*(p - 3)/8
Factor -2*c**3/9 - 80*c**2/9 - 26*c/3.
-2*c*(c + 1)*(c + 39)/9
Find r such that -r**3 - 4011*r**2 = 0.
-4011, 0
Determine q, given that q**3 - 20*q**2 + 97*q - 78 = 0.
1, 6, 13
Solve -x**2 - 6*x - 8 = 0.
-4, -2
What is z in 34*z**2/3 - 142*z/3 + 8 = 0?
3/17, 4
Factor -6*r**2 - 87*r - 180.
-3*(r + 12)*(2*r + 5)
Factor -6*y**3 - 92*y**2 - 114*y - 28.
-2*(y + 1)*(y + 14)*(3*y + 1)
Find n such that 90*n**3 + 184*n**2 + 98*n + 4 = 0.
-1, -2/45
Factor 3*v**5 - 72*v**4/5 + 138*v**3/5 - 132*v**2/5 + 63*v/5 - 12/5.
3*(v - 1)**4*(5*v - 4)/5
Factor -25*q**2 - 65*q - 30.
-5*(q + 2)*(5*q + 3)
Determine l so that -5*l**3 - 30*l**2 + 5*l + 30 = 0.
-6, -1, 1
Factor -12*c**3 - 16*c**2 + 68*c + 24.
-4*(c - 2)*(c + 3)*(3*c + 1)
Solve -2*z**5 - 14*z**4 - 26*z**3 + 6*z**2 + 36*z = 0.
-3, -2, 0, 1
Find f, given that -24*f**5/5 - 62*f**4 + 722*f**3/5 - 418*f**2/5 + 6*f = 0.
-15, 0, 1/12, 1
Factor 5*k**2 + 175*k + 1500.
5*(k + 15)*(k + 20)
Suppose -3*w**5 + 21*w**4 + 3*w**3 - 21*w**2 = 0. Calculate w.
-1, 0, 1, 7
Solve -3*p**5 + 21*p**4 - 39*p**3 + 3*p**2 + 42*p - 24 = 0.
-1, 1, 2, 4
Factor -3*s**4/2 + 9*s**3 - 33*s**2/2 + 9*s.
-3*s*(s - 3)*(s - 2)*(s - 1)/2
Let -2*m**4/11 - 36*m**3/11 - 96*m**2/11 - 92*m/11 - 30/11 = 0. Calculate m.
-15, -1
Factor -3*i**5 + 189*i**4 - 2880*i**3 - 3072*i**2.
-3*i**2*(i - 32)**2*(i + 1)
Factor -8*h**2/5 - 34*h/5 - 8/5.
-2*(h + 4)*(4*h + 1)/5
Suppose -3*h**2 - 1398*h = 0. Calculate h.
-466, 0
Solve 4*f**2 + 12*f - 112 = 0 for f.
-7, 4
Factor 2*f**2/9 - 616*f/9 + 47432/9.
2*(f - 154)**2/9
Factor -4*j**2 + 60*j + 64.
-4*(j - 16)*(j + 1)
Solve -2*c**5/11 - 24*c**4/11 - 60*c**3/11 - 56*c**2/11 - 18*c/11 = 0.
-9, -1, 0
Find u such that u**4 - 2*u**3 - 12*u**2 + 8*u + 32 = 0.
-2, 2, 4
Solve 2*k**4 + 123*k**3 + 1978*k**2 + 2580*k - 1800 = 0 for k.
-30, -2, 1/2
Factor -12*j**4/5 + 33*j**3/5 + 9*j**2/5.
-3*j**2*(j - 3)*(4*j + 1)/5
Factor 16*t**3/5 + 196*t**2/5 + 48*t/5.
4*t*(t + 12)*(4*t + 1)/5
Factor 2*x**3/15 - 56*x**2/5 + 1056*x/5 + 15488/15.
2*(x - 44)**2*(x + 4)/15
Factor 12*u**4 - 477*u**3 - 612*u**2 - 123*u.
3*u*(u - 41)*(u + 1)*(4*u + 1)
Solve 5*g**4 + 405*g**3 - 1310*g**2 - 4200*g = 0.
-84, -2, 0, 5
Find i such that -2*i**4/5 - 12*i**3/5 + 48*i**2/5 - 52*i/5 + 18/5 = 0.
-9, 1
Factor 2*b**2/11 + 62*b/11.
2*b*(b + 31)/11
Factor 2*j**2/3 - 64*j/3 - 22.
2*(j - 33)*(j + 1)/3
Factor -f**4/5 - 64*f**3/5 - 958*f**2/5 + 2112*f/5 - 1089/5.
-(f - 1)**2*(f + 33)**2/5
Solve -5*u**3 + 70*u**2 - 120*u = 0.
0, 2, 12
Find b such that -4*b**4/3 - 4*b**3 + 20*b**2/3 + 4*b - 16/3 = 0.
-4, -1, 1
Factor 3*i**3/5 - 6*i**2/5 - 192*i/5 + 384/5.
3*(i - 8)*(i - 2)*(i + 8)/5
Factor 5*z**5 - 25*z**4 + 40*z**3 - 20*z**2.
5*z**2*(z - 2)**2*(z - 1)
Factor t**2/4 + 125*t/4 - 231.
(t - 7)*(t + 132)/4
Suppose 16*n**4/7 + 150*n**3/7 + 374*n**2/7 + 120*n/7 = 0. Calculate n.
-5, -4, -3/8, 0
Factor -t**3/2 + 3*t/2 - 1.
-(t - 1)**2*(t + 2)/2
Find g, given that 3*g**3/7 + 12*g**2/7 - 3*g/7 - 12/7 = 0.
-4, -1, 1
Factor -2*a**2/5 - 104*a/5 - 1352/5.
-2*(a + 26)**2/5
Determine o so that 3*o**2/4 + 21*o/4 + 15/2 = 0.
-5, -2
Factor -4*o**2 - 328*o - 6724.
-4*(o + 41)**2
Determine x so that -28*x**4 + 1436*x**3 - 24600*x**2 + 142992*x - 38880 = 0.
2/7, 15, 18
Factor -14*f**3 + 242*f**2 + 464*f - 152.
-2*(f - 19)*(f + 2)*(7*f - 2)
Suppose i**2 + 127*i + 126 = 0. Calculate i.
-126, -1
Factor -5*v**4 + 8*v**3 + 11*v**2 - 14*v.
-v*(v - 2)*(v - 1)*(5*v + 7)
Factor 3*m**2 + 27006*m + 60777003.
3*(m + 4501)**2
Factor -4*c**4 - 12*c**3 + 48*c**2 + 208*c + 192.
-4*(c - 4)*(c + 2)**2*(c + 3)
Factor o**4/3 - 125*o**3/3 + 3968*o**2/3 - 3844*o/3.
o*(o - 62)**2*(o - 1)/3
Suppose -2*n**2/3 - 368*n/3 - 16928/3 = 0. Calculate n.
-92
Factor -k**4/3 + 22*k**3/3 + 4*k**2 - 280*k/3 + 352/3.
-(k - 22)*(k - 2)**2*(k + 4)/3
Factor -y**3/4 - y**2/2 + y/4 + 1/2.
-(y - 1)*(y + 1)*(y + 2)/4
Factor -v**3 + 19*v**2 - 50*v + 32.
-(v - 16)*(v - 2)*(v - 1)
Factor -3*h**5 + 18*h**3 - 24*h**2 + 9*h.
-3*h*(h - 1)**3*(h + 3)
Factor -9*n**2/4 + 103*n + 23.
-(n - 46)*(9*n + 2)/4
Factor -s**2/7 + 634*s/7 - 100489/7.
-(s - 317)**2/7
Factor 2*c**3/5 - 92*c**2/5 + 342*c/5 - 252/5.
2*(c - 42)*(c - 3)*(c - 1)/5
What is c in -c**2/3 - 10*c/3 + 13 = 0?
-13, 3
Suppose -2*s**4 + 8*s**3 + 22*s**2 + 12*s = 0. What is s?
-1, 0, 6
Find s, given that 5*s**4 + 80*s**3 - 15*s**2 - 230*s + 160 = 0.
-16, -2, 1
Factor 2*k**3/5 - 2*k**2/3 - 4*k/15.
2*k*(k - 2)*(3*k + 1)/15
Solve 2*y**2/11 - 36*y/11 + 160/11 = 0 for y.
8, 10
Factor -2*c**5/5 + 278*c**4/5 - 822*c**3/5 + 818*c**2/5 - 272*c/5.
-2*c*(c - 136)*(c - 1)**3/5
Suppose 2*y**4/11 - 388*y**3/11 + 1528*y**2/11 - 1520*y/11 = 0. What is y?
0, 2, 190
Factor 2*m**5/7 + 4*m**4/7 - 6*m**3/7 - 8*m**2/7 + 8*m/7.
2*m*(m - 1)**2*(m + 2)**2/7
Factor r**2/8 + 1223*r/4 - 2447/8.
(r - 1)*(r + 2447)/8
Solve 2*o**4/9 + 4*o**3 - 2*o**2/9 - 4*o = 0 for o.
-18, -1, 0, 1
Let -2*t**2/9 + 490*t/9 - 488/9 = 0. Calculate t.
1, 244
Let -3*b**5 - 9*b**4 + 15*b**3 + 9*b**2 - 12*b = 0. Calculate b.
-4, -1, 0, 1
Suppose 3*c**2 - 1017*c + 1014 = 0. What is c?
1, 338
Factor 8*n**2 - 14*n - 60.
2*(n + 2)*(4*n - 15)
Factor 2*i**3 - 96*i**2 + 360*i + 21600.
2*(i - 30)**2*(i + 12)
Determine c so that -c**4 + 9852*c**3 - 36398214*c**2 + 59765867388*c - 36800832844161 = 0.
2463
Factor 2*t**2 + 3278*t - 6564.
2*(t - 2)*(t + 1641)
Factor 3*x**4 - 27*x**3 - 108*x**2 - 12*x + 144.
3*(x - 12)*(x - 1)*(x + 2)**2
Find j such that -6*j**2/5 + 882*j/5 = 0.
0, 147
Suppose 2*b**4/13 + 24*b**3/13 + 60*b**2/13 + 56*b/13 + 18/13 = 0. What is b?
-9, -1
Solve 5*p**4 - 5*p**3 - 5*p**2 + 5*p = 0.
-1, 0, 1
Suppose -q**3/2 - 179*q**2/2 - 7347*q/2 + 60543/2 = 0. What is q?
-93, 7
Determine k so that 2*k**3 + 18*k**2 - 68*k + 48 = 0.
-12, 1, 2
Factor 3*y**4 + 6*y**3 - 57*y**2 - 60*y.
3*y*(y - 4)*(y + 1)*(y + 5)
Find q, given that q**3/2 + 46*q**2 + 1058*q = 0.
-46, 0
Factor 3*b**3 - 9*b**2 - 8640*b + 187392.
3*(b - 32)**2*(b + 61)
Suppose -2*c**3/5 + 136*c**2/5 + 174*c + 1332/5 = 0. What is c?
-3, 74
Solve q**5 - 31*q**3 + 106*q**2 - 132*q + 56 = 0 for q.
-7, 1, 2
Determine n so that n**5/2 - 5*n**4 + 7*n**3/2 + 9*n**2 = 0.
-1, 0, 2, 9
Factor 2*b**4/7 + 16*b**3/7 - 58*b**2/7 - 360*b/7.
2*b*(b - 5)*(b + 4)*(b + 9)/7
Determine v, given that -5*v**2 - 3080*v + 3085 = 0.
-617, 1
Factor -l**2/2 + 19*l/3 - 55/6.
-(l - 11)*(3*l - 5)/6
Factor -4*q**3 - 13*q**2 - 5*q/2 + 3/2.
-(q + 3)*(2*q + 1)*(4*q - 1)/2
Find l such that l**2/10 + 17*l/5 - 7/2 = 0.
-35, 1
Solve g**5 + 49*g**4/3 + 14*g**3/3 - 32*g**2/3 = 0 for g.
-16, -1, 0, 2/3
Determine q so that -q