7, -2, 4
Determine q so that 2*q**4 + 28*q**3 - 30*q**2 = 0.
-15, 0, 1
Suppose -k**3/7 + 31*k**2/7 - 41*k + 119 = 0. What is k?
7, 17
Factor 49*r**4 - 322*r**3 - 171*r**2 + 172*r - 28.
(r - 7)*(r + 1)*(7*r - 2)**2
Determine s so that -s**5/3 - 5*s**4 - 22*s**3/3 + 18*s**2 + 23*s/3 - 13 = 0.
-13, -3, -1, 1
Factor 2*i**2/7 + 116*i/7.
2*i*(i + 58)/7
Factor 2*o**5/9 - 20*o**4/9 + 16*o**3/3 - 44*o**2/9 + 14*o/9.
2*o*(o - 7)*(o - 1)**3/9
Factor f**3 + 9*f**2 + 14*f.
f*(f + 2)*(f + 7)
Factor 5*h**4 - 25*h**3 + 30*h**2.
5*h**2*(h - 3)*(h - 2)
Determine m, given that -m**4 + 11*m**3 + 17*m**2 - 63*m + 36 = 0.
-3, 1, 12
Factor -4*l**3/3 - 140*l**2/3 + 152*l/3 + 96.
-4*(l - 2)*(l + 1)*(l + 36)/3
Determine n so that n**4/5 - 13*n**3/5 - 64*n**2/5 - 68*n/5 = 0.
-2, 0, 17
Find m such that 28*m**4 - 106*m**3 + 116*m**2 - 26*m - 12 = 0.
-3/14, 1, 2
Find i such that 2*i**3/7 - 12*i**2 + 34*i - 156/7 = 0.
1, 2, 39
Find u, given that 4*u**3 - 148*u**2 + 1440*u - 1296 = 0.
1, 18
Let i**3/7 - 139*i**2/7 - 123*i - 1305/7 = 0. Calculate i.
-3, 145
Suppose -d**3/9 + d**2 + 10*d/9 - 56/3 = 0. Calculate d.
-4, 6, 7
Factor -18*b**2 + 429*b + 72.
-3*(b - 24)*(6*b + 1)
Factor 3*d**3/2 + 261*d**2/2 + 5805*d/2 + 5547/2.
3*(d + 1)*(d + 43)**2/2
What is l in 2*l**2/11 - 378*l/11 - 380/11 = 0?
-1, 190
Find t, given that -4*t**4 - 688*t**3 + 1388*t**2 - 696*t = 0.
-174, 0, 1
Factor 4*a**4 - 6068*a**3 + 2298252*a**2 + 2304324*a.
4*a*(a - 759)**2*(a + 1)
Solve -2*f**4/7 + 12*f**3/7 - 2*f**2 - 12*f/7 + 16/7 = 0 for f.
-1, 1, 2, 4
Solve -72*f**5/5 - 24*f**4 - 26*f**3/5 + 4*f**2 - 2*f/5 = 0 for f.
-1, 0, 1/6
Factor -2*i**2/19 + 106*i/19 - 204/19.
-2*(i - 51)*(i - 2)/19
Suppose -22*k**3/13 + 212*k**2/13 - 358*k/13 + 168/13 = 0. Calculate k.
1, 84/11
Factor -11*a**2/7 - 39*a/7 - 18/7.
-(a + 3)*(11*a + 6)/7
Find w such that 26*w**5/11 - 1036*w**4/11 + 12112*w**3/11 - 3232*w**2 + 27936*w/11 + 5184/11 = 0.
-2/13, 2, 18
Determine p, given that 9*p**3/2 - 480*p**2 - 646*p - 216 = 0.
-2/3, 108
Suppose -4*c**3 + 136*c**2 - 1540*c + 5808 = 0. What is c?
11, 12
Factor 5*y**3 - 15*y**2 - 230*y + 240.
5*(y - 8)*(y - 1)*(y + 6)
Factor -t**5/3 + 4*t**4/3 - 16*t**2/3 + 16*t/3.
-t*(t - 2)**3*(t + 2)/3
Factor 5*v**3 + 305*v**2 - 320*v - 620.
5*(v - 2)*(v + 1)*(v + 62)
What is v in -3*v**5/8 + 105*v**4/4 - 1947*v**3/8 = 0?
0, 11, 59
Suppose t**4 - 19*t**3 - 21*t**2 + 19*t + 20 = 0. Calculate t.
-1, 1, 20
Solve j**4/5 + 6*j**3 + 149*j**2/5 + 24*j = 0.
-24, -5, -1, 0
Solve 2*f**4/9 + 6*f**3 - 356*f**2/3 - 1120*f/9 = 0.
-40, -1, 0, 14
Solve -22*i**2/3 - 136*i/9 - 8/9 = 0 for i.
-2, -2/33
Find n such that 80*n**4 + 760*n**3 + 2645*n**2 + 3990*n + 2205 = 0.
-3, -7/4
Solve -2*a**3 + 348*a**2/5 - 594*a - 608/5 = 0.
-1/5, 16, 19
Determine u, given that -u**3/4 + 421*u**2/2 - 44099*u - 89042 = 0.
-2, 422
Solve 2*r**2 - 44*r + 242 = 0 for r.
11
Factor k**5 - 5*k**4 - 7*k**3 + 5*k**2 + 6*k.
k*(k - 6)*(k - 1)*(k + 1)**2
Suppose -3*f**4 + 2184*f**3 - 2181*f**2 = 0. What is f?
0, 1, 727
Suppose -2*k**3/3 - 4*k**2/3 + 10*k = 0. Calculate k.
-5, 0, 3
Factor -p**2/4 + 47*p/4 + 49/2.
-(p - 49)*(p + 2)/4
Determine a, given that 2*a**5/11 - 2*a**4/11 - 34*a**3/11 - 38*a**2/11 + 32*a/11 + 40/11 = 0.
-2, -1, 1, 5
Factor c**4 - 40*c**3 - c**2 + 40*c.
c*(c - 40)*(c - 1)*(c + 1)
Factor g**3 - 3*g**2 - 196*g - 192.
(g - 16)*(g + 1)*(g + 12)
Find a, given that -5*a**3 - 40*a**2 + 45*a = 0.
-9, 0, 1
Factor -w**3/5 + 11*w**2/5 - 3*w - 27/5.
-(w - 9)*(w - 3)*(w + 1)/5
Find k such that 5*k**3 + 58*k**2/3 + 52*k/3 - 8/3 = 0.
-2, 2/15
Determine t so that 5*t**2 - 55*t + 140 = 0.
4, 7
Factor -j**2/4 - 19*j/2 - 361/4.
-(j + 19)**2/4
Solve 2*i**5 + 2*i**4 - 2*i**3 - 2*i**2 = 0.
-1, 0, 1
Factor -4*q**3 - 60*q**2 - 192*q + 256.
-4*(q - 1)*(q + 8)**2
Let 3*s**3/5 - 27*s**2/5 + 24*s/5 + 36 = 0. Calculate s.
-2, 5, 6
Factor -3*v**3 + 6*v**2 + 3*v - 6.
-3*(v - 2)*(v - 1)*(v + 1)
Find c such that -49*c**2 + 70*c - 25 = 0.
5/7
Factor -3*f**2/2 - 417*f/2 + 210.
-3*(f - 1)*(f + 140)/2
Factor o**4/4 - 3*o**3/2 - 15*o**2/4 - 2*o.
o*(o - 8)*(o + 1)**2/4
Factor -r**3 - 15*r**2 - 39*r + 55.
-(r - 1)*(r + 5)*(r + 11)
Suppose -3*a**5 + 213*a**4 - 4239*a**3 + 15147*a**2 + 19602*a = 0. What is a?
-1, 0, 6, 33
Let -34*p**4/5 + 582*p**3/5 - 408*p**2/5 - 3224*p/5 + 384/5 = 0. Calculate p.
-2, 2/17, 3, 16
Factor o**2 + 79*o + 504.
(o + 7)*(o + 72)
Factor -2*v**4 - 36*v**3 - 216*v**2 - 476*v - 294.
-2*(v + 1)*(v + 3)*(v + 7)**2
Solve 20*r**3 + 146*r**2/7 + 6*r/7 = 0 for r.
-1, -3/70, 0
Solve 3*b**5 + 24*b**4 + 66*b**3 + 72*b**2 + 27*b = 0 for b.
-3, -1, 0
Find h, given that -2*h**5/21 - 8*h**4/21 + 10*h**3/21 + 24*h**2/7 + 24*h/7 = 0.
-3, -2, 0, 3
Let -2*d**2 - 286*d - 1904 = 0. What is d?
-136, -7
Factor -4*q**4 - 24*q**3 - 44*q**2 - 24*q.
-4*q*(q + 1)*(q + 2)*(q + 3)
Factor -u**4/5 - 37*u**3/5 - 47*u**2 + 2037*u/5 - 1764/5.
-(u - 4)*(u - 1)*(u + 21)**2/5
Factor -2*p**2/3 - 2*p/3.
-2*p*(p + 1)/3
Factor 3*q**2/4 + 141*q/4 + 135/2.
3*(q + 2)*(q + 45)/4
Determine m, given that m**2/6 - 302*m/3 + 45602/3 = 0.
302
Let b**2/3 + 34*b + 867 = 0. Calculate b.
-51
Let -x**5/2 + 7*x**4/2 - 15*x**3/2 + 13*x**2/2 - 2*x = 0. What is x?
0, 1, 4
Find d, given that 2*d**4/19 + 44*d**3/19 + 120*d**2/19 + 116*d/19 + 2 = 0.
-19, -1
Find s such that -11*s**3 - 41*s**2 + 12*s = 0.
-4, 0, 3/11
Suppose 4*o**5 + 48*o**4 + 176*o**3 + 168*o**2 - 180*o - 216 = 0. Calculate o.
-6, -3, -1, 1
Factor 3*x**4 + 21*x**3 + 15*x**2 - 21*x - 18.
3*(x - 1)*(x + 1)**2*(x + 6)
Find w, given that -w**5/2 - 907*w**4 - 411323*w**3 + 2722*w**2 + 2471575*w/2 + 822649 = 0.
-907, -1, 2
Solve t**3/2 + 735*t**2/2 + 135423*t/2 + 134689/2 = 0 for t.
-367, -1
Solve -3*r**2 + 546*r - 1080 = 0.
2, 180
Let -3*z**2/4 + 1107*z/2 = 0. What is z?
0, 738
Factor 4*t**4/3 - 440*t**3/3 + 16900*t**2/3 - 88000*t + 480000.
4*(t - 40)**2*(t - 15)**2/3
Factor -x**4/6 - 5*x**3/6 + 7*x**2/2 + 85*x/6 - 50/3.
-(x - 4)*(x - 1)*(x + 5)**2/6
Determine o, given that -o**2 - 11*o = 0.
-11, 0
Factor -m**2/4 + 43*m/2 + 44.
-(m - 88)*(m + 2)/4
Let 2*m**4/21 + 1016*m**3/21 - 2038*m**2/21 + 340*m/7 = 0. Calculate m.
-510, 0, 1
Determine v, given that -2*v**3 + 2930*v**2/3 - 11696*v/9 + 3896/9 = 0.
2/3, 487
Solve -80*j**5 - 908*j**4 - 2264*j**3 + 1776*j**2 - 288*j = 0.
-6, 0, 1/4, 2/5
Determine o, given that o**5/8 + 113*o**4/8 + 406*o**3 + 392*o**2 = 0.
-56, -1, 0
Factor -z**2 - 61*z - 118.
-(z + 2)*(z + 59)
Factor -r**5/2 - 3*r**4 - r**3 + 18*r**2 + 27*r/2 - 27.
-(r - 2)*(r - 1)*(r + 3)**3/2
Factor -216*u**3 - 1170*u**2 - 3675*u/8 - 375/8.
-3*(u + 5)*(24*u + 5)**2/8
Suppose -10*r**5/7 + 12*r**4 - 22*r**3/7 - 12*r**2 + 32*r/7 = 0. What is r?
-1, 0, 2/5, 1, 8
Factor -507*x**3 + 351*x**2 + 144*x + 12.
-3*(x - 1)*(13*x + 2)**2
Factor -2*v**3/9 + 24*v - 96.
-2*(v - 6)**2*(v + 12)/9
Solve -5*h**3 - 170*h**2 - 1725*h - 4500 = 0 for h.
-15, -4
What is x in -5*x**2 + 2290*x - 262205 = 0?
229
Determine x, given that 30*x**5 + 147*x**4 + 225*x**3 + 96*x**2 - 12*x = 0.
-2, -1, 0, 1/10
Suppose 19321*j**3/5 - 278*j**2/5 + j/5 = 0. Calculate j.
0, 1/139
Determine y, given that 2*y**5/5 + 22*y**4/5 - 34*y**3/5 - 126*y**2/5 - 72*y/5 = 0.
-12, -1, 0, 3
Factor 44*q**2 + 1338*q + 540.
2*(q + 30)*(22*q + 9)
Find q, given that 930*q**2/11 + 48*q/11 = 0.
-8/155, 0
Suppose -k**2 - 458*k - 52441 = 0. What is k?
-229
Factor -a**2/4 - 317*a/4 - 315/2.
-(a + 2)*(a + 315)/4
Let 3*d**2 + 456*d + 17328 = 0. Calculate d.
-76
Factor -4*o**2/9 - 68*o.
-4*o*(o + 153)/9
Factor x**2/2 - 2.
(x - 2)*(x + 2)/2
Factor -2*q**3/13 - 24*q**2/13 + 242*q/13 - 456/13.
-2*(q - 4)*(q - 3)*(q + 19)/13
Let 457773282*l**4 + 29773872*l**3 + 726192*l**2 + 7872*l + 32 = 0. What is l?
-2/123
Factor z**3/6 - 211*z**2/6 - 425*z/6 - 71/2.
(z - 213)*(z + 1)**2/6
Factor 35*c**3 - 885*c**2 + 4240*c - 1140.
5*(c - 19)*(c - 6)*(7*c - 2)
Determine x so that 2*x**3 - 1728*x**2 = 0.
0, 864
Suppose -y**3/3 - 518*y**2/3 + 2084*y/3 - 696 = 0. What is y?
-522, 2
Factor w**3/7 + 9*w**2/7 - w/7 - 9/7.
(w - 1)*(w + 1)*(w + 9)/7
Let x**2 + 1710*x = 0. Calculate x.
-1710, 0
Determine n so that -10*n**5/13 - 184*n**4/13 - 842*n**3/13 - 308*n**2/13 = 0.
-11, -7, -2/5, 0
Factor 2*t**5 + 34*t**4 - 114*t**3 + 118*t**2 - 40*t.
2*t*(t - 1)**3*(t + 20)
Solve -4*o**2 + 128*o + 132 = 0.
-1, 33
Solve t**2 + 192*t + 752 