 + 13)
Factor -2*m**4 + 20*m**3 - 58*m**2 + 16*m + 96.
-2*(m - 4)**2*(m - 3)*(m + 1)
Solve 3*r**4 - 30*r**3 - 9*r**2 + 420*r + 588 = 0 for r.
-2, 7
Factor 1643524*x**3/3 - 1664036*x**2/3 + 20576*x/3 - 64/3.
4*(x - 1)*(641*x - 4)**2/3
Solve 5*z**3 - 155*z**2 + 795*z - 1125 = 0 for z.
3, 25
Determine r so that 4*r**4/9 - 80*r**3/9 - 4*r**2/9 + 80*r/9 = 0.
-1, 0, 1, 20
Let 25*x**3 + 815*x**2 + 4670*x - 2000 = 0. Calculate x.
-25, -8, 2/5
Factor -h**2/3 + 31*h + 96.
-(h - 96)*(h + 3)/3
Solve -2*v**5/5 - 54*v**4/5 - 316*v**3/5 + 428*v**2/5 + 318*v/5 - 374/5 = 0 for v.
-17, -11, -1, 1
Factor -8*p**2/5 + 372*p - 928/5.
-4*(p - 232)*(2*p - 1)/5
Suppose 44*t**3 + 140*t**2 - 672*t + 432 = 0. What is t?
-6, 9/11, 2
Determine c so that c**5/3 - 3*c**4 - 61*c**3/3 + 259*c**2 - 480*c - 756 = 0.
-9, -1, 6, 7
Factor -21*k**4 - 18*k**3 + 180*k**2 - 222*k + 81.
-3*(k - 1)**3*(7*k + 27)
Factor 7*o**2/5 - 2*o/5 - 9/5.
(o + 1)*(7*o - 9)/5
Factor 3*j**3 - 4536*j**2 + 2286144*j - 384072192.
3*(j - 504)**3
Suppose 30*g**2 - 515*g + 85 = 0. Calculate g.
1/6, 17
Find h such that -10*h**5 + 716*h**4 - 2496*h**3 + 3292*h**2 - 1910*h + 408 = 0.
3/5, 1, 68
Suppose w**2/2 + 21*w/2 - 296 = 0. What is w?
-37, 16
Let -4*l**2 + 36*l - 72 = 0. Calculate l.
3, 6
Determine p so that p**3/2 + 7*p**2 + 13*p/2 = 0.
-13, -1, 0
Let -j**4/4 + 5*j**3/4 + 2*j**2 - 3*j = 0. Calculate j.
-2, 0, 1, 6
Factor -2*a**2 + 36*a + 80.
-2*(a - 20)*(a + 2)
Factor 3*s**4 - 27*s**3 - 36*s**2 + 60*s.
3*s*(s - 10)*(s - 1)*(s + 2)
Let -4*s**2 - 4156*s - 4152 = 0. What is s?
-1038, -1
Let 3*f**2 - 4542*f + 4539 = 0. What is f?
1, 1513
Factor 2*h**4/5 - 6*h**3/5 - 84*h**2/5 - 40*h - 144/5.
2*(h - 9)*(h + 2)**3/5
Factor 2*k**2/5 - 122*k/5.
2*k*(k - 61)/5
Factor 9*l**3/5 + 156*l**2/5 - 468*l/5 + 48.
3*(l - 2)*(l + 20)*(3*l - 2)/5
What is y in -4*y**3 + 1988*y**2 - 248000*y + 246016 = 0?
1, 248
Factor -3*r**3/8 - 111*r**2/8 - 969*r/8 + 1083/8.
-3*(r - 1)*(r + 19)**2/8
Let s**4/4 - s**3/2 = 0. Calculate s.
0, 2
Factor d**2 - 94*d - 192.
(d - 96)*(d + 2)
Factor -p**2/5 + 28*p/5 - 147/5.
-(p - 21)*(p - 7)/5
Solve 2*v**4/7 + 22*v**3/7 - 12*v**2 + 8*v/7 + 16 = 0.
-14, -1, 2
Find w such that -4*w**2 + 11592*w - 8398404 = 0.
1449
Factor -3*u**2 - 57*u - 54.
-3*(u + 1)*(u + 18)
Let 2*v**5/9 - 94*v**4/9 + 614*v**3/9 + 1238*v**2 + 4368*v + 4704 = 0. Calculate v.
-3, 28
Factor -5*w**5 - 50*w**4 - 20*w**3 + 410*w**2 - 535*w + 200.
-5*(w - 1)**3*(w + 5)*(w + 8)
Determine r, given that -224*r**4/5 + 288*r**3/5 + 62*r**2/5 - 162*r/5 + 36/5 = 0.
-3/4, 2/7, 3/4, 1
Suppose -11*p**3/4 - 5*p**2/2 + 23*p/4 - 1/2 = 0. Calculate p.
-2, 1/11, 1
Factor 36*g**5 - 96*g**4 + 52*g**3 - 8*g**2.
4*g**2*(g - 2)*(3*g - 1)**2
Factor s**3/2 - 2*s.
s*(s - 2)*(s + 2)/2
Find i, given that -4*i**5/11 + 34*i**4/11 - 62*i**3/11 + 8*i**2/11 + 24*i/11 = 0.
-1/2, 0, 1, 2, 6
Factor 2*h**2/3 + 28*h.
2*h*(h + 42)/3
Let -52*k**2/19 - 4314*k/19 + 166/19 = 0. What is k?
-83, 1/26
Suppose 3*j**5/8 - 3*j**3/2 = 0. What is j?
-2, 0, 2
Suppose 4*q**2 - 92*q - 432 = 0. Calculate q.
-4, 27
Factor 3*m**2/5 - 6*m + 15.
3*(m - 5)**2/5
Solve -2*f**3/5 + 2*f**2 + 4*f/5 - 48/5 = 0 for f.
-2, 3, 4
Find r, given that 44*r**5 - 96*r**4 - 116*r**3 + 200*r**2 + 144*r - 32 = 0.
-1, 2/11, 2
Find o, given that -o**2/3 - 19*o + 60 = 0.
-60, 3
Factor -12*y**2/11 + 74*y + 136/11.
-2*(y - 68)*(6*y + 1)/11
Factor 2*t**4/5 - 1884*t**3/5 + 117936*t**2 - 12145140*t - 37507050.
2*(t - 315)**3*(t + 3)/5
Find k such that -k**3/4 - 17*k**2 + 755*k/4 - 975/2 = 0.
-78, 5
Factor -4*m**4 + 756*m**3 - 46020*m**2 + 794300*m + 6591000.
-4*(m - 65)**3*(m + 6)
Factor j**2/8 + 247*j/4 + 61009/8.
(j + 247)**2/8
Factor 2*q**2/5 - 132*q/5 - 134/5.
2*(q - 67)*(q + 1)/5
Determine d, given that 3*d**5 + d**4 - 11*d**3 - 9*d**2 + 4*d + 4 = 0.
-1, 2/3, 2
Factor 2*q**2/3 + 4*q + 16/3.
2*(q + 2)*(q + 4)/3
Factor -12*j**2 - 1527*j - 381.
-3*(j + 127)*(4*j + 1)
Factor -2*k**4 - 33*k**3 - 126*k**2 + 64*k + 672.
-(k - 2)*(k + 4)**2*(2*k + 21)
Find u such that -u**2/4 - 17*u/2 + 111/4 = 0.
-37, 3
Solve -2*r**3/9 - 416*r**2/9 - 7070*r/3 + 4900 = 0.
-105, 2
Factor d**5/4 + d**4/4 - d**3/2 - d**2/2 + d/4 + 1/4.
(d - 1)**2*(d + 1)**3/4
Find n such that n**2 - 10*n + 9 = 0.
1, 9
Suppose 100*c**4 - 860*c**3 - 2556*c**2 - 916*c - 88 = 0. Calculate c.
-2, -1/5, 11
Solve -122*c**2/19 + 118*c/19 + 4/19 = 0.
-2/61, 1
Find q such that 38*q**3/3 + 24*q**2 + 10*q - 4/3 = 0.
-1, 2/19
Suppose 2*d**2/7 - 26932*d/7 + 90666578/7 = 0. Calculate d.
6733
Solve 3*l**3 - 129*l**2 - 867*l - 735 = 0 for l.
-5, -1, 49
Suppose 5*w**4 - 7700*w**3 + 2979860*w**2 - 11827200*w + 11796480 = 0. Calculate w.
2, 768
Let -w**2/2 + 8*w - 14 = 0. What is w?
2, 14
Let 3*n**2/2 + 4359*n/8 + 1089/8 = 0. What is n?
-363, -1/4
Solve -20*u**5 - 68*u**4 - 12*u**3 + 36*u**2 = 0.
-3, -1, 0, 3/5
Factor -2*s**2 - 8*s + 792.
-2*(s - 18)*(s + 22)
Factor 2*r**5/7 - 2*r**4/7 - 12*r**3/7 - 4*r**2/7 + 10*r/7 + 6/7.
2*(r - 3)*(r - 1)*(r + 1)**3/7
Solve -14*h**3/11 - 94*h**2 + 3382*h/11 - 42 = 0.
-77, 1/7, 3
Factor -t**4/3 + 11*t**3/3 + t**2 - 35*t/3 + 22/3.
-(t - 11)*(t - 1)**2*(t + 2)/3
Solve 2*p**5/3 + 8*p**4 + 64*p**3/3 - 140*p**2/3 - 150*p + 500/3 = 0.
-5, 1, 2
Factor 2*j**4 - 2*j**3 - 6*j**2 + 10*j - 4.
2*(j - 1)**3*(j + 2)
Suppose 4*q**4/7 - 1644*q**3/7 - 236*q**2 + 1644*q/7 + 1648/7 = 0. Calculate q.
-1, 1, 412
Factor 2*h**3/3 - 4864*h**2 + 11829248*h - 28768731136/3.
2*(h - 2432)**3/3
Factor 4*f**5/3 - 4*f**4/3 - 12*f**3 - 44*f**2/3 - 16*f/3.
4*f*(f - 4)*(f + 1)**3/3
Suppose b**3/3 - 7*b**2/3 - 10*b/3 + 16/3 = 0. Calculate b.
-2, 1, 8
Determine r so that r**2/12 - 155*r/12 - 13 = 0.
-1, 156
Factor -r**4/7 - 579*r**3/7 - 2304*r**2/7 - 2300*r/7.
-r*(r + 2)**2*(r + 575)/7
Factor 5*x**3 - 20*x**2 - 55*x - 30.
5*(x - 6)*(x + 1)**2
Determine x so that -2*x**3/7 + 578*x**2/7 - 1150*x/7 + 82 = 0.
1, 287
Find s such that -15*s**4/4 + 33*s**3/2 - 9*s**2/4 - 33*s/2 + 6 = 0.
-1, 2/5, 1, 4
Factor -2*q**2/7 + 1216*q/7 - 184832/7.
-2*(q - 304)**2/7
What is b in 5*b**4 - 5*b**3 - 15*b**2 + 5*b + 10 = 0?
-1, 1, 2
What is u in 5*u**3 + 90*u**2 + 165*u + 80 = 0?
-16, -1
Solve -k**2/2 - 2096*k - 2196608 = 0.
-2096
Factor -2*t**3/5 + 26*t**2/5 - 24*t/5.
-2*t*(t - 12)*(t - 1)/5
Find n, given that 3*n**5/4 + 7*n**4/4 - n**3/4 - 7*n**2/4 - n/2 = 0.
-2, -1, -1/3, 0, 1
Factor -4*o**2/3 + 1240*o/3 - 96100/3.
-4*(o - 155)**2/3
Solve 5*m**3/6 + 25*m**2/3 - 560*m/3 - 400 = 0.
-20, -2, 12
Determine w, given that -10*w**4 - 36*w**3 - 24*w**2 + 16*w = 0.
-2, 0, 2/5
Solve 5*l**4 + 165*l**3 + 1275*l**2 - 1445*l = 0 for l.
-17, 0, 1
Find u, given that -2*u**5 + 6*u**3 - 4*u**2 = 0.
-2, 0, 1
What is j in 3*j**4 + 108*j**3 + 831*j**2 - 3078*j - 8664 = 0?
-19, -2, 4
Suppose -2*s**4/7 + 22*s**3/7 + 4*s**2 - 48*s/7 = 0. What is s?
-2, 0, 1, 12
Factor h**2 + 24*h + 135.
(h + 9)*(h + 15)
Suppose 9*u**4/4 - 57*u**3 + 249*u**2/2 - 87*u + 69/4 = 0. Calculate u.
1/3, 1, 23
Factor -m**5/6 - 157*m**4/2 - 9125*m**3 + 83543*m**2/3 - 56011*m/2 + 18723/2.
-(m - 1)**3*(m + 237)**2/6
Find s, given that -s**3/8 + 7*s**2/8 - 7*s/8 - 15/8 = 0.
-1, 3, 5
Factor -2*a**2/3 + 14*a - 76/3.
-2*(a - 19)*(a - 2)/3
Solve 5*p**3 - 170*p**2 + 325*p - 160 = 0.
1, 32
Let -2*n**5/3 + 62*n**3/3 - 28*n**2 - 48*n = 0. What is n?
-6, -1, 0, 3, 4
Factor -2*p**2/3 + 128*p/3 - 2048/3.
-2*(p - 32)**2/3
Factor -2*f**3 + 12*f**2 + 144*f.
-2*f*(f - 12)*(f + 6)
Suppose 3*c**4 - 89*c**3/5 - 488*c**2/5 - 404*c/5 + 192/5 = 0. Calculate c.
-2, 1/3, 48/5
Suppose -3*o**2 - 462*o + 3381 = 0. Calculate o.
-161, 7
Let 5*x**5 + 15*x**4 - 115*x**3 + 165*x**2 - 70*x = 0. Calculate x.
-7, 0, 1, 2
Suppose 2*y**2/3 - 172*y = 0. What is y?
0, 258
What is s in 5*s**5 - 60*s**3 - 80*s**2 = 0?
-2, 0, 4
Let -361*h**3/4 + 57*h**2/2 + 297*h - 242 = 0. Calculate h.
-2, 22/19
Factor 6*a**3 - 219*a**2/2 - 1023*a + 525/2.
3*(a - 25)*(a + 7)*(4*a - 1)/2
Suppose i**3 + 21*i**2 + 72*i - 432 = 0. Calculate i.
-12, 3
Find j such that 4*j**5 - 8*j**4 - 108*j**3 - 208*j**2 - 112*j = 0.
-2, -1, 0, 7
Determine c so that 315*c**4/4 - 2001*c**3/4 + 1155*c**2/2 - 231*c + 30 = 0.
2/7, 2/5, 2/3, 5
Solve -b**4/8 - b**3/2 + b**2/8 + b/2 = 0.
-4, -1, 0, 1
Let -3*t**2/2 - 63*t + 1860 = 0. Calculate t.
-62, 20
Suppose -3*y**2 + 117*y - 420 = 0. Calculate y.
4, 35
Factor -u**5 - 3*u**4 