*3 - 919*c**2 + 614*c.
-c*(c + 307)*(3*c - 2)
Factor -2*t**2 + 176*t.
-2*t*(t - 88)
Find i, given that -2*i**4 + 60*i**3 - 312*i**2 + 592*i - 384 = 0.
2, 24
Factor -4*a**3 - 28*a**2 + 196*a + 220.
-4*(a - 5)*(a + 1)*(a + 11)
Factor m**2/3 + 118*m/3 - 80.
(m - 2)*(m + 120)/3
Determine s so that -2*s**5 + 82*s**4 - 1092*s**3 + 4312*s**2 + 5488*s = 0.
-1, 0, 14
Factor -3*v**4/7 + 150*v**3/7 - 2559*v**2/7 + 17100*v/7 - 38988/7.
-3*(v - 19)**2*(v - 6)**2/7
Find r such that 4*r**4 - 552*r**3 + 1092*r**2 - 544*r = 0.
0, 1, 136
Factor -3*u**2 + 9*u + 30.
-3*(u - 5)*(u + 2)
Factor 3*w**4 - 1668*w**3 + 235152*w**2 - 914112*w.
3*w*(w - 276)**2*(w - 4)
Factor g**3/2 + 35*g**2/2 - 637*g/2 + 2401/2.
(g - 7)**2*(g + 49)/2
Factor -2*g**3 + 88*g**2 + 90*g.
-2*g*(g - 45)*(g + 1)
Factor -10*x**3/7 + 25226*x**2/7 - 15916342*x/7 + 9540726/7.
-2*(x - 1261)**2*(5*x - 3)/7
Suppose -4*j**4 + 128*j**3 + 1380*j**2 - 50128*j - 51376 = 0. What is j?
-19, -1, 26
Factor 2*s**5 - 6*s**4 - 106*s**3 + 222*s**2 - 112*s.
2*s*(s - 8)*(s - 1)**2*(s + 7)
Determine n, given that -2*n**3/9 - 68*n**2/3 - 640*n - 3072 = 0.
-48, -6
Factor -v**4/6 + 91*v**3/6 - 89*v**2/6 - 91*v/6 + 15.
-(v - 90)*(v - 1)**2*(v + 1)/6
Find k such that -15*k**5 + 365*k**4 - 105*k**3 - 365*k**2 + 120*k = 0.
-1, 0, 1/3, 1, 24
Let 4*c**3 - 1844*c**2 + 5496*c = 0. What is c?
0, 3, 458
Let h**3/2 - 6*h**2 - 277*h/2 - 132 = 0. What is h?
-11, -1, 24
Factor 3*n**2 - 108*n - 228.
3*(n - 38)*(n + 2)
Factor -c**4/2 + 23*c**3/2 - 35*c**2/2 - 143*c/2 - 42.
-(c - 21)*(c - 4)*(c + 1)**2/2
Suppose 2*b**3/9 - 32*b**2/9 + 142*b/9 - 112/9 = 0. What is b?
1, 7, 8
Solve -56*y**5/5 - 82*y**4/5 + 98*y**3/5 + 64*y**2/5 - 24*y/5 = 0 for y.
-2, -3/4, 0, 2/7, 1
Factor -d**3/3 - 5*d**2/3 + 22*d/3 + 56/3.
-(d - 4)*(d + 2)*(d + 7)/3
Factor -150*v**5/11 + 162*v**4/11 - 12*v**3/11.
-6*v**3*(v - 1)*(25*v - 2)/11
Factor -3*o**4 - 2*o**3 + 7*o**2 - 2*o.
-o*(o - 1)*(o + 2)*(3*o - 1)
Factor 4*h**3/7 + 1216*h**2/7 + 1212*h/7.
4*h*(h + 1)*(h + 303)/7
Factor 2*o**3 - 10*o**2 + 6*o + 18.
2*(o - 3)**2*(o + 1)
Find b such that b**3/2 + 735*b**2/2 + 180075*b/2 + 14706125/2 = 0.
-245
Factor -g**5/2 - 4*g**4 + 6*g**3 + 11*g**2 - 43*g/2 + 9.
-(g - 1)**3*(g + 2)*(g + 9)/2
Factor -5*s**2 + 75*s - 70.
-5*(s - 14)*(s - 1)
Factor 4*d**3 - 11400*d**2 + 22788*d - 11392.
4*(d - 2848)*(d - 1)**2
Solve -k**4/9 + 8*k**3/9 + 34*k**2/9 - 8*k/9 - 11/3 = 0 for k.
-3, -1, 1, 11
Factor -6*s**3 - 1312*s**2 - 72158*s - 47524.
-2*(s + 109)**2*(3*s + 2)
What is k in 2*k**2/3 + 418*k/3 - 2140/3 = 0?
-214, 5
Factor t**4/3 + 17*t**3/3 + 21*t**2 - 27*t.
t*(t - 1)*(t + 9)**2/3
Factor 2*u**3/3 + 46*u**2 + 90*u + 134/3.
2*(u + 1)**2*(u + 67)/3
Let 2*b**4/13 + 16*b**3/13 - 158*b**2/13 + 140*b/13 = 0. What is b?
-14, 0, 1, 5
Let -2*n**4/3 - 106*n**3/3 - 104*n**2/3 = 0. What is n?
-52, -1, 0
Factor -3*i**3 + 6*i**2 + 9*i.
-3*i*(i - 3)*(i + 1)
Let m**4 + 6*m**3 + 13*m**2 + 12*m + 4 = 0. What is m?
-2, -1
Suppose -3*n**5/2 - 21*n**4/2 + 222*n**3 + 1590*n**2 - 1800*n = 0. Calculate n.
-10, 0, 1, 12
Let -2*t**2 - 2984*t - 1113032 = 0. What is t?
-746
Factor -h**3/5 - 72*h**2/5 - 1053*h/5 + 9126/5.
-(h - 6)*(h + 39)**2/5
Suppose 2*p**2/9 - 88*p/3 + 968 = 0. What is p?
66
Solve 405*w**2 - 1440*w + 1280 = 0 for w.
16/9
Suppose -4*c**4/9 + 52*c**3/9 - 56*c**2/3 + 32*c/9 + 256/9 = 0. Calculate c.
-1, 2, 4, 8
Factor -5*w**3 - 615*w**2.
-5*w**2*(w + 123)
Factor -5*k**3 - 120*k**2 - 225*k - 110.
-5*(k + 1)**2*(k + 22)
What is g in -g**3 + 121*g**2 - 2059*g - 105861 = 0?
-21, 71
Find b, given that -4*b**3 - 224*b**2 - 4116*b - 24696 = 0.
-21, -14
Determine q, given that 45*q**3/4 - 195*q**2/2 - 145*q - 50 = 0.
-2/3, 10
Factor -2*r**2/5 - 54*r/5 + 936/5.
-2*(r - 12)*(r + 39)/5
Factor 2*v**4/3 + 4*v**3/3 - 2*v**2.
2*v**2*(v - 1)*(v + 3)/3
Factor -25*p**4 + 90*p**3 - 56*p**2 - 90*p + 81.
-(p - 1)*(p + 1)*(5*p - 9)**2
Let -p**2/3 + p - 2/3 = 0. Calculate p.
1, 2
Factor -33*l**3 + 6*l**2/7.
-3*l**2*(77*l - 2)/7
What is t in -363*t**4/4 - 1683*t**3/4 - 201*t**2 + 117*t - 12 = 0?
-4, -1, 2/11
Let 8*h**4 - 41*h**3 - 43*h**2 + 6*h = 0. Calculate h.
-1, 0, 1/8, 6
Factor 2*g**5/9 + 20*g**4/9 + 20*g**3/3 + 80*g**2/9 + 50*g/9 + 4/3.
2*(g + 1)**4*(g + 6)/9
Solve -q**2 + 484*q - 58564 = 0.
242
Factor 4*d**3 - 588*d**2 - 592*d.
4*d*(d - 148)*(d + 1)
Factor -3*r**2/5 - 201*r/5 + 204/5.
-3*(r - 1)*(r + 68)/5
Solve -125*i**4 - 740*i**3 + 560*i**2 + 2960*i - 240 = 0.
-6, -2, 2/25, 2
Factor -a**4 + 8*a**3 + 17*a**2 - 204*a + 180.
-(a - 6)**2*(a - 1)*(a + 5)
Determine x so that 10*x**5 - 15*x**4 - 60*x**3 + 35*x**2 + 30*x = 0.
-2, -1/2, 0, 1, 3
Factor -3*f**3/4 + 24219*f**2/4 - 65173329*f/4 + 58460476113/4.
-3*(f - 2691)**3/4
Let -1500*r**5 + 1300*r**4 + 2885*r**3 + 1050*r**2 - 20*r - 40 = 0. What is r?
-1/2, -2/5, 1/6, 2
Suppose -3*s**3 - 50*s**2 - 31*s + 16 = 0. Calculate s.
-16, -1, 1/3
Let p**2/6 + 3*p/2 - 6 = 0. What is p?
-12, 3
Find s such that -2*s**3/9 - 734*s**2/3 - 244*s + 4400/9 = 0.
-1100, -2, 1
Factor 2*s**4/7 - 4262*s**3/7 + 3028860*s**2/7 - 718846600*s/7 + 715822000/7.
2*(s - 710)**3*(s - 1)/7
Factor -d**3 - 23*d**2.
-d**2*(d + 23)
What is m in 2*m**3/5 - 4*m**2/5 - 66*m/5 + 36 = 0?
-6, 3, 5
Factor -2*f**4/11 - 12*f**3/11 + 30*f**2/11 - 16*f/11.
-2*f*(f - 1)**2*(f + 8)/11
Factor -2*p**2/11 + 2*p + 84/11.
-2*(p - 14)*(p + 3)/11
Suppose -2*x**5 - 12*x**4 + 14*x**3 + 96*x**2 + 72*x = 0. Calculate x.
-6, -2, -1, 0, 3
Let 6*z**5/7 + 78*z**4/7 - 516*z**3/7 + 432*z**2/7 = 0. Calculate z.
-18, 0, 1, 4
Let 3*c**3/4 + 117*c**2/4 + 621*c/4 + 891/4 = 0. Calculate c.
-33, -3
Find f, given that -5*f**5 - 55*f**4 - 95*f**3 + 215*f**2 + 100*f - 160 = 0.
-8, -4, -1, 1
Factor 180*i**2 + 956*i/5 + 56/5.
4*(i + 1)*(225*i + 14)/5
Factor 4*o**5 - 60*o**4 + 104*o**3 + 8*o**2 - 108*o + 52.
4*(o - 13)*(o - 1)**3*(o + 1)
Determine p so that -9*p**3/5 + 292*p**2/5 - 557*p/5 + 274/5 = 0.
1, 274/9
Factor -x**5 + 22*x**4 - 169*x**3 + 532*x**2 - 640*x + 256.
-(x - 8)**2*(x - 4)*(x - 1)**2
Find f, given that -2*f**3/9 - 238*f**2/9 + 1048*f/3 = 0.
-131, 0, 12
Factor p**4 - 5*p**3.
p**3*(p - 5)
Find j such that -102*j**2 - 2349*j - 69 = 0.
-23, -1/34
Find f, given that f**5/6 - 15*f**4/2 + 43*f**3/2 - 127*f**2/6 + 7*f = 0.
0, 1, 42
Determine j so that -j**3 - 2*j**2 + 4*j + 8 = 0.
-2, 2
Factor 2*u**2 + 7200*u.
2*u*(u + 3600)
Suppose 4*m**5/5 + 16*m**4/5 - 72*m**3/5 + 16*m**2 - 28*m/5 = 0. Calculate m.
-7, 0, 1
Factor -4*q**3 - 68*q**2 - 320*q - 256.
-4*(q + 1)*(q + 8)**2
Factor -5*d**3/6 - 137*d**2/6 + 43*d/3 + 28/3.
-(d - 1)*(d + 28)*(5*d + 2)/6
Factor -2*v**2/5 + 204*v/5 - 5202/5.
-2*(v - 51)**2/5
Solve 6*r**3/5 + 17178*r**2/5 + 2457312*r - 12303744/5 = 0 for r.
-1432, 1
Suppose -2*i**5/3 + 164*i**4/3 - 3674*i**3/3 + 4264*i**2 - 4056*i = 0. Calculate i.
0, 2, 39
Factor 4*r**2 - 12*r - 432.
4*(r - 12)*(r + 9)
Factor -2*x**2/3 - 620*x/3 - 48050/3.
-2*(x + 155)**2/3
Determine r so that r**2/3 - 20*r/3 - 224/3 = 0.
-8, 28
Determine l, given that 45*l**3 - 235*l**2 + 230*l - 40 = 0.
2/9, 1, 4
Factor -2*f**3/7 + 6812*f**2/7 - 13618*f/7 + 6808/7.
-2*(f - 3404)*(f - 1)**2/7
Suppose 3*n**2 + 1365*n - 1368 = 0. What is n?
-456, 1
What is u in -2*u**5 + 30*u**4 + 82*u**3 - 198*u**2 - 656*u - 408 = 0?
-2, -1, 3, 17
Find z such that 2*z**2/19 + 4*z = 0.
-38, 0
Find m, given that -3*m**5/8 + 33*m**3/4 + 9*m**2/2 - 351*m/8 - 81/2 = 0.
-3, -1, 3, 4
Let -3*k**4 + 12*k**3 + 9*k**2 - 30*k - 24 = 0. What is k?
-1, 2, 4
Factor 12*w**3 + 40*w**2 - 828*w - 280.
4*(w - 7)*(w + 10)*(3*w + 1)
Solve 3*v**3/2 - 339*v**2/2 + 9405*v/2 + 9747/2 = 0 for v.
-1, 57
Determine b, given that -b**3 - 77*b**2 + 157*b - 79 = 0.
-79, 1
Solve -4*q**2/5 - 1632*q/5 - 166464/5 = 0 for q.
-204
Factor 2*b**3/9 + 88*b**2/3 - 1646*b/9 + 460/3.
2*(b - 5)*(b - 1)*(b + 138)/9
Factor -5*n**2/3 + 365*n/3 - 670.
-5*(n - 67)*(n - 6)/3
Factor -12769*c**2/8 + 113*c/4 - 1/8.
-(113*c - 1)**2/8
Suppose 5*z**2/4 + 205*z/4 + 50 = 0. What is z?
-40, -1
Factor -3*q**4 - 111*q**3 - 306*q**2 + 12*q + 408.
-3*(q - 1)*(q + 2)**2*(q + 34)
Let 5*y**5/2 + 459*y**4/4 + 1997*y**3/4 - 529*y**2/4 - 1527*y/4 - 205/2 = 0. Calculate y.
-41, -5, -1/2, -2/5, 1
Solve c**5/4 - c**4/2 + c**3/4 = 0 for c.
0, 1
Factor 6*f**2/13 + 10*f - 44/13.
2*(f + 22)*(3*f - 1)/13
Let -4*c**5 + 200*c**4 - 3460*c**3 + 22720*c*