-1
Factor -2*c**2/11 - 162*c/11 + 164/11.
-2*(c - 1)*(c + 82)/11
Factor -4*l**2 - 2652*l + 2656.
-4*(l - 1)*(l + 664)
Find m such that 4*m**4 - 1038*m**3 + 1550*m**2 - 516*m = 0.
0, 1/2, 1, 258
Factor 4*x**3 + 44*x**2 - 224*x + 240.
4*(x - 2)**2*(x + 15)
Factor -2*s**3 + 38*s**2 + 232*s + 192.
-2*(s - 24)*(s + 1)*(s + 4)
Let -2*i**4/7 + 38*i**3/7 - 232*i**2/7 + 64*i = 0. What is i?
0, 4, 7, 8
Find u such that -2*u**5/3 + 22*u**4/3 - 16*u**3 = 0.
0, 3, 8
Determine d so that 2*d**3/9 + 8*d**2/3 + 40*d/9 = 0.
-10, -2, 0
Determine p, given that p**2/4 + 733*p/2 + 537289/4 = 0.
-733
Factor -w**4 + 94*w**3 - 2893*w**2 + 32148*w - 116964.
-(w - 38)**2*(w - 9)**2
Factor c**2/5 + 2067*c/5 - 2068/5.
(c - 1)*(c + 2068)/5
Factor -203404644*x**2 + 114096*x - 16.
-4*(7131*x - 2)**2
Let j**2/4 - 77*j/4 + 19 = 0. What is j?
1, 76
Factor 2754*m**2/7 - 3*m/7.
3*m*(918*m - 1)/7
Let t**2/9 + 47*t/3 = 0. Calculate t.
-141, 0
Determine g so that 2*g**2 - 42*g - 144 = 0.
-3, 24
What is r in -20*r**5/9 - 124*r**4/9 - 88*r**3/3 - 208*r**2/9 - 32*r/9 = 0?
-2, -1/5, 0
Find a, given that 2*a**2/13 + 76*a/13 + 672/13 = 0.
-24, -14
Factor -12*a**2 - 51*a + 360.
-3*(a + 8)*(4*a - 15)
Find s, given that 2*s**4 + 16*s**3 + 4*s**2 - 160*s - 150 = 0.
-5, -1, 3
Find a, given that -3*a**5/7 + 9*a**4 - 42*a**3 - 426*a**2/7 + 297*a/7 + 363/7 = 0.
-1, 1, 11
Solve -h**2 + 13*h - 12 = 0.
1, 12
Determine i so that -5*i**4 - 540*i**3 + 1095*i**2 - 550*i = 0.
-110, 0, 1
Factor 1805*z**3 - 3800*z**2 + 385*z - 10.
5*(z - 2)*(19*z - 1)**2
Factor c**5/9 - 5*c**4/9 - 2*c**3/3 + 32*c**2/9 + 32*c/9.
c*(c - 4)**2*(c + 1)*(c + 2)/9
Suppose d**2 - 45*d + 396 = 0. What is d?
12, 33
Let 2*l**5/3 - 20*l**4/3 + 6*l**3 = 0. What is l?
0, 1, 9
Solve d**3 + 8*d**2/3 - 5*d + 4/3 = 0.
-4, 1/3, 1
Suppose 5*x**2 - 1885*x + 1880 = 0. Calculate x.
1, 376
Solve -22*p**3 + 356*p**2 + 1190*p - 228 = 0.
-3, 2/11, 19
Factor -j**3/4 - 17*j**2/4.
-j**2*(j + 17)/4
Suppose -4*r**4/3 - 40*r**3/3 - 28*r**2 + 160*r/3 + 400/3 = 0. Calculate r.
-5, -2, 2
Factor 8*x**2/3 + 232*x + 5046.
2*(2*x + 87)**2/3
Factor -3*o**3 - 9525*o**2 - 7555704*o + 7565232.
-3*(o - 1)*(o + 1588)**2
Suppose 5*g**3 + 55*g**2 - 230*g - 280 = 0. What is g?
-14, -1, 4
Factor 2*q**4 + 26*q**3 - 108*q**2 - 720*q.
2*q*(q - 6)*(q + 4)*(q + 15)
Factor y**3/2 + 33*y**2 + 989*y/2 + 462.
(y + 1)*(y + 21)*(y + 44)/2
Let 5*p**2 + 1430*p = 0. What is p?
-286, 0
Determine s, given that 2*s**2/9 - 28*s - 2720/9 = 0.
-10, 136
Factor c**2/7 + 6456*c/7 + 10419984/7.
(c + 3228)**2/7
Factor 2*a**3/3 - 82*a**2/3 - 28*a.
2*a*(a - 42)*(a + 1)/3
Factor -192*d**4/7 - 3216*d**3/7 - 2340*d**2/7 - 579*d/7 - 48/7.
-3*(d + 16)*(4*d + 1)**3/7
Let -h**3/2 + 216*h**2 + 433*h/2 = 0. Calculate h.
-1, 0, 433
Determine y, given that -2*y**2 + 12*y + 14 = 0.
-1, 7
Factor -2*g**3 + 138*g**2 - 1230*g - 43706.
-2*(g - 41)**2*(g + 13)
Factor -3*r**3 - 327*r**2 - 645*r - 321.
-3*(r + 1)**2*(r + 107)
Factor 5*l**4 - 145*l**3 + 140*l**2.
5*l**2*(l - 28)*(l - 1)
Suppose n**3/4 - 5*n**2 - 1843*n/4 - 10469/2 = 0. Calculate n.
-19, 58
Factor r**4/2 + 300*r**3 + 597*r**2/2 - 599*r.
r*(r - 1)*(r + 2)*(r + 599)/2
Suppose 3*l**4 + 2268*l**3 + 2262*l**2 - 2268*l - 2265 = 0. Calculate l.
-755, -1, 1
Factor -2*n**3/3 + 34*n**2 - 416*n + 4480/3.
-2*(n - 35)*(n - 8)**2/3
Factor -3*p**4 - 15*p**3 + 36*p**2 + 132*p - 240.
-3*(p - 2)**2*(p + 4)*(p + 5)
Solve -j**3/2 + 999*j**2/2 - 124500*j - 125000 = 0 for j.
-1, 500
Let -u**4/2 - 175*u**3/8 + 427*u**2/2 - 52*u = 0. What is u?
-52, 0, 1/4, 8
Determine z, given that -28*z**4 + 5524*z**3 + 15168*z**2 + 6416*z - 3200 = 0.
-2, -1, 2/7, 200
Find n such that 3*n**4/5 - 12*n**3/5 + 3*n**2 - 6*n/5 = 0.
0, 1, 2
Let -s**2/4 + 123*s/2 + 247/4 = 0. What is s?
-1, 247
Factor -4*i**4 + 4*i**2.
-4*i**2*(i - 1)*(i + 1)
Factor -4*j**4/7 + 1052*j**3/7.
-4*j**3*(j - 263)/7
Factor -9*z**4 + 52*z**3 + 147*z**2 + 102*z + 16.
-(z - 8)*(z + 1)**2*(9*z + 2)
Factor 2*i**2 - 212*i + 5618.
2*(i - 53)**2
Factor 2*q**2 + 62*q - 132.
2*(q - 2)*(q + 33)
Factor 3*z**4 + 1230*z**3 - 3717*z**2 + 12*z + 4956.
3*(z - 2)**2*(z + 1)*(z + 413)
Determine w so that -8*w**2/7 + 26*w/7 + 24/7 = 0.
-3/4, 4
Solve -c**2 + 84*c - 1764 = 0 for c.
42
Suppose -2*y**4/15 - 4*y**3/5 - 2*y**2/15 + 16*y/5 - 32/15 = 0. Calculate y.
-4, 1
Factor i**2/6 - 14*i/3.
i*(i - 28)/6
Factor -2*i**3/5 + 6*i/5 - 4/5.
-2*(i - 1)**2*(i + 2)/5
Let -2*b**2 - 58*b - 56 = 0. What is b?
-28, -1
Factor -b**2 + 1059*b - 1058.
-(b - 1058)*(b - 1)
Let 100*f**5 + 260*f**4 - 1016*f**3 + 872*f**2 - 236*f + 20 = 0. Calculate f.
-5, 1/5, 1
Suppose 20*s**4 + 45*s**3 - 150*s**2 - 40*s = 0. Calculate s.
-4, -1/4, 0, 2
Factor v**3 + 80*v**2 + 148*v - 624.
(v - 2)*(v + 4)*(v + 78)
Factor -2*v**3/3 - 14*v**2/3 + 56*v/3 - 40/3.
-2*(v - 2)*(v - 1)*(v + 10)/3
Factor -2*s**2/11 - 642*s/11 - 2536/11.
-2*(s + 4)*(s + 317)/11
Factor 5*c**3 + 20*c**2 + 20*c.
5*c*(c + 2)**2
Factor x**5 + 2*x**4 - 6*x**3 - 20*x**2 - 19*x - 6.
(x - 3)*(x + 1)**3*(x + 2)
Factor 2*w**4/7 - 3380*w**3/7 + 1441506*w**2/7 - 11370320*w/7 + 22632992/7.
2*(w - 841)**2*(w - 4)**2/7
Factor -4*b**3 + 389*b**2 + 295*b - 98.
-(b - 98)*(b + 1)*(4*b - 1)
Suppose 3*i**4/5 + 114*i**3/5 - 72*i**2 + 366*i/5 - 123/5 = 0. What is i?
-41, 1
Suppose 2*q**4 + 2*q**3 - 86*q**2 - 170*q - 84 = 0. What is q?
-6, -1, 7
Factor -5*o**2 + 7820*o - 7815.
-5*(o - 1563)*(o - 1)
What is c in 4*c**3 + 764*c**2 - 8004*c + 7236 = 0?
-201, 1, 9
Suppose 11*u**3 - 827*u**2 - 3326*u + 632 = 0. Calculate u.
-4, 2/11, 79
Solve -10*a**5/3 + 19*a**4/3 + 79*a**3/3 - 169*a**2/3 + 33*a - 6 = 0 for a.
-3, 2/5, 1/2, 1, 3
Find j, given that 4*j**5/7 + 110*j**4/7 - 62*j**3/7 - 166*j**2/7 + 58*j/7 + 8 = 0.
-28, -1, -1/2, 1
Factor 20*f**3 + 772*f**2 + 4904*f + 5952.
4*(f + 6)*(f + 31)*(5*f + 8)
Let 45*a**5/4 + 65*a**4 - 735*a**3 + 1240*a**2 - 240*a = 0. Calculate a.
-12, 0, 2/9, 2, 4
Factor 2*p**3 + 30*p**2 + 28*p.
2*p*(p + 1)*(p + 14)
Factor 2*p**4 - 20*p**3 + 54*p**2 - 36*p.
2*p*(p - 6)*(p - 3)*(p - 1)
Find a, given that -108*a**5/7 - 15003*a**4/7 + 6720*a**3 - 34920*a**2/7 + 1728*a/7 + 3408/7 = 0.
-142, -1/4, 2/3, 2
Factor 3*j**2 - 96*j - 1107.
3*(j - 41)*(j + 9)
Factor 5*d**3 - 10*d**2 - 20*d + 40.
5*(d - 2)**2*(d + 2)
What is j in 4*j**2 - 56*j + 52 = 0?
1, 13
Let -x**5 + 3*x**4 - 3*x**3 + x**2 = 0. Calculate x.
0, 1
Find x such that -2*x**2/5 - x - 2/5 = 0.
-2, -1/2
Suppose -a**3/2 + 3*a**2 - 4*a = 0. Calculate a.
0, 2, 4
Find z, given that 3*z**2/4 - 105*z/4 = 0.
0, 35
What is y in -2*y**2/5 - 1266*y/5 - 1264/5 = 0?
-632, -1
Factor 98*u**3/15 - 112*u**2/3 - 166*u/15 - 4/5.
2*(u - 6)*(7*u + 1)**2/15
Factor r**2 + 170*r - 171.
(r - 1)*(r + 171)
Determine s, given that s**4/2 - 9*s**3/2 + 10*s**2 = 0.
0, 4, 5
Determine z so that 4*z**4 - 4*z**3 - 4*z**2 + 4*z = 0.
-1, 0, 1
Factor 39*k**2/2 - k/5.
k*(195*k - 2)/10
Factor -6*y**3 - 8*y**2 + 50*y + 84.
-2*(y - 3)*(y + 2)*(3*y + 7)
Let -2*s**5/5 + 22*s**4/5 - 86*s**3/5 + 138*s**2/5 - 72*s/5 = 0. Calculate s.
0, 1, 3, 4
Factor -2*i**4/9 + 110*i**3/9 - 106*i**2/3 + 314*i/9 - 104/9.
-2*(i - 52)*(i - 1)**3/9
Factor 1369*q**4 - 2442*q**3 + 793*q**2 + 264*q + 16.
(q - 1)**2*(37*q + 4)**2
Factor 3*j**4 + 321*j**3 - 2370*j**2 + 2784*j + 5472.
3*(j - 4)**2*(j + 1)*(j + 114)
Factor 25*k**5 + 10*k**4 - 99*k**3 - 40*k**2 - 4*k.
k*(k - 2)*(k + 2)*(5*k + 1)**2
Determine d, given that d**2 + 53*d - 54 = 0.
-54, 1
Factor -2*o**3/9 + 140*o**2/9 + 592*o/9.
-2*o*(o - 74)*(o + 4)/9
Factor -5*t**4 - 510*t**3 - 1500*t**2 - 1490*t - 495.
-5*(t + 1)**3*(t + 99)
Solve -a**4 + 20*a**3 - 128*a**2 + 256*a = 0 for a.
0, 4, 8
Factor -2*o**4 - 50*o**3 - 374*o**2 - 726*o.
-2*o*(o + 3)*(o + 11)**2
Determine s so that -10*s**5/9 - 38*s**4/3 - 194*s**3/9 + 70*s**2/3 + 12*s = 0.
-9, -3, -2/5, 0, 1
What is m in 14*m**4 - 68*m**3/3 - 184*m**2/3 + 208*m/3 + 64 = 0?
-12/7, -2/3, 2
Find x, given that -x**3/8 - 19*x**2/2 - 489*x/8 - 207/4 = 0.
-69, -6, -1
Factor 3*g**5/5 - 207*g**4/5 + 3672*g**3/5 - 3468*g**2/5.
3*g**2*(g - 34)**2*(g - 1)/5
Factor -25*d**3/3 + 125140*d**2/3 - 156575165*d/3 - 62650090/3.
-5*(d - 2503)**2*(5*d + 2)/3
Find l such that -2*l**5 - 88*l**4/5 - 252*l**3/5 - 256*l**2/5 - 58*l/5 + 24/5 = 0.
-4, -3, -1, 1/5
Factor g**3/4 + 3*g**2/4 - 9*g/2.
g*(g - 3)*(g + 6)/4
Factor -2*r**2/7 - 1181*r/7 + 591