- 51*a**3 + 171*a**2 - 201*a + 78 = 0.
1, 2, 13
Find s, given that 2*s**4/3 - 344*s**3/9 - 26*s**2 + 116*s/9 = 0.
-1, 0, 1/3, 58
Solve -15*g**3 + 177*g**2 + 231*g + 39 = 0.
-1, -1/5, 13
What is j in -4*j**5/5 + 44*j**4 + 736*j**3/5 - 464*j**2 = 0?
-5, 0, 2, 58
Factor -p**3 + 2730*p**2 - 1860492*p - 3731912.
-(p - 1366)**2*(p + 2)
Factor -2*r**3 - 8*r**2 + 6*r + 36.
-2*(r - 2)*(r + 3)**2
Let -72*l**5/5 + 24*l**4/5 + 38*l**3 + 20*l**2 = 0. What is l?
-5/6, 0, 2
Suppose 4*k**3 + 4*k**2 = 0. What is k?
-1, 0
Let 27*b**5/5 - 4419*b**4/5 + 15789*b**3/5 + 8223*b**2/5 - 10092*b/5 + 384 = 0. Calculate b.
-1, 1/3, 4, 160
Solve 2*t**4/9 + 44*t**3/9 + 74*t**2/9 - 40*t/3 = 0 for t.
-20, -3, 0, 1
Suppose 4*n**5 - 2832*n**4 + 5648*n**3 + 8*n**2 - 5652*n + 2824 = 0. What is n?
-1, 1, 706
Factor j**4/5 + 2*j**3/5 - 36*j**2 + 230*j - 425.
(j - 5)**3*(j + 17)/5
Factor -3*p**3 + 1911*p**2 - 1902*p - 3816.
-3*(p - 636)*(p - 2)*(p + 1)
Factor 2*i**3 + 12*i**2 + 16*i.
2*i*(i + 2)*(i + 4)
Find z, given that -3*z**3 + 237*z**2 + 9135*z + 73575 = 0.
-15, 109
Factor -4*z**3/3 - 176*z**2/3 - 112*z.
-4*z*(z + 2)*(z + 42)/3
Determine v so that 2*v**3/7 + 1180*v**2/7 + 178674*v/7 + 1354896/7 = 0.
-291, -8
Let 2*s**5/9 - 134*s**4/9 + 914*s**3/3 - 16066*s**2/9 + 13456*s/9 = 0. Calculate s.
0, 1, 8, 29
Let -35*q**5 + 45*q**4 + 130*q**3 - 180*q**2 + 40*q = 0. Calculate q.
-2, 0, 2/7, 1, 2
Suppose l**4/6 - 11*l**3/6 + 16*l**2/3 - 14*l/3 = 0. What is l?
0, 2, 7
Determine m, given that 5*m**3 - 445*m**2 + 1300*m - 860 = 0.
1, 2, 86
Factor 112*b**3 - 124*b**2 + 103*b/4 - 3/2.
(7*b - 6)*(8*b - 1)**2/4
Suppose 108*z**5 + 36*z**4 - 72*z**3 - 56*z**2 - 44*z/3 - 4/3 = 0. Calculate z.
-1/3, 1
Factor -3*t**3/7 - 30*t**2/7 + 69*t/7 - 36/7.
-3*(t - 1)**2*(t + 12)/7
Let 256*t**3/5 + 192*t**2 - 300*t + 100 = 0. What is t?
-5, 5/8
Factor r**4/3 - 2*r**3/3 - 4*r**2 + 8*r/3 + 32/3.
(r - 4)*(r - 2)*(r + 2)**2/3
Let -g**2/3 + 136*g - 405 = 0. Calculate g.
3, 405
Determine u so that 21*u**5 - 165*u**4/4 - 276*u**3 - 867*u**2/4 + 12*u + 15 = 0.
-2, -1, -2/7, 1/4, 5
Find l such that 2*l**4 - 1124*l**3 + 210936*l**2 - 13288220*l + 13078406 = 0.
1, 187
Solve -5*d**4 + 1080*d**3 - 87480*d**2 + 3149280*d - 42515280 = 0.
54
Factor a**5/4 + 45*a**4 - 91*a**3.
a**3*(a - 2)*(a + 182)/4
Let z**2/2 + 67*z/2 - 105 = 0. What is z?
-70, 3
Factor -p**4/7 + 16*p**3/7 - 78*p**2/7 + 16*p - 7.
-(p - 7)**2*(p - 1)**2/7
Let 2*h**5/9 - 50*h**4/9 - 1066*h**3/9 + 16562*h**2/9 + 246064*h/9 + 228488/9 = 0. What is h?
-13, -1, 26
Factor -2*v**5/3 + 124*v**4/3 - 2354*v**3/3 + 4464*v**2 - 7776*v.
-2*v*(v - 27)**2*(v - 4)**2/3
Suppose 10*l**5 - 524*l**4 + 5848*l**3 + 26864*l**2 + 19712*l - 12544 = 0. Calculate l.
-2, 2/5, 28
Let 14*i**2/5 + 136*i/5 - 8 = 0. Calculate i.
-10, 2/7
Factor -2*n**4/5 - 1568*n**3/5 - 307328*n**2/5.
-2*n**2*(n + 392)**2/5
Factor 3*n**3 + 720*n**2 + 43911*n + 84966.
3*(n + 2)*(n + 119)**2
What is c in -3*c**3 - 21*c**2 + 51*c - 27 = 0?
-9, 1
Factor s**4 + 38*s**3 + 101*s**2 - 140*s.
s*(s - 1)*(s + 4)*(s + 35)
Suppose -2*p**4/13 - 2504*p**3/13 - 1175628*p**2/13 - 245314376*p/13 - 19195849922/13 = 0. Calculate p.
-313
Let 5*y**2 + 295*y - 300 = 0. Calculate y.
-60, 1
Let -4*a**3 - 72*a**2 - 348*a - 280 = 0. What is a?
-10, -7, -1
Find a such that 3*a**2 + 105*a + 102 = 0.
-34, -1
Determine r, given that -4*r**3 - 8*r**2 + 52*r - 40 = 0.
-5, 1, 2
Find a, given that -4*a**2/3 + 2876*a/3 + 5768/3 = 0.
-2, 721
Factor 3*f**4/7 - 9*f**3/7 - 30*f**2/7.
3*f**2*(f - 5)*(f + 2)/7
Suppose -4*z**3 - 32*z**2 - 68*z - 40 = 0. Calculate z.
-5, -2, -1
Factor -2*o**3/11 - 140*o**2/11 - 1138*o/11 - 2440/11.
-2*(o + 4)*(o + 5)*(o + 61)/11
Factor 8*u**3/3 + 230*u**2 - 524*u/3 - 58.
2*(u - 1)*(u + 87)*(4*u + 1)/3
Let 4*g**5 - 76*g**4 + 344*g**3 - 416*g**2 = 0. Calculate g.
0, 2, 4, 13
Find t such that -8*t**2 + 69*t/4 - 5/2 = 0.
5/32, 2
Determine q, given that 5*q**3/3 - 400*q**2/3 + 355*q + 2310 = 0.
-3, 6, 77
Suppose i**3/5 + 153*i**2/5 + 30*i - 304/5 = 0. What is i?
-152, -2, 1
Let -9*q**5/8 + 21*q**4/8 - 3*q**3/8 - 21*q**2/8 + 3*q/2 = 0. What is q?
-1, 0, 1, 4/3
Solve -5*f**4 - 35*f**3 + 150*f**2 = 0.
-10, 0, 3
Factor 5*v**2 - 110*v - 240.
5*(v - 24)*(v + 2)
Factor k**3/5 + 11*k**2/5 - 14*k/5 - 24/5.
(k - 2)*(k + 1)*(k + 12)/5
Factor k**2/11 + 32*k/11 - 3.
(k - 1)*(k + 33)/11
Determine h so that -h**3 + 153*h**2 + 309*h + 155 = 0.
-1, 155
Let -j**4/5 + 12*j**3/5 + 146*j**2/5 - 1092*j/5 - 8281/5 = 0. Calculate j.
-7, 13
Factor -3*u**2 - 3834*u - 1224963.
-3*(u + 639)**2
Suppose 6*j**2/7 - 192*j/7 + 186/7 = 0. Calculate j.
1, 31
Factor -l**4/6 + 5*l**3/3 - 11*l**2/2 + 20*l/3 - 8/3.
-(l - 4)**2*(l - 1)**2/6
Find q such that 4*q**3 - 56*q**2 + 172*q - 120 = 0.
1, 3, 10
Factor r**5 + 27*r**4 + 50*r**3.
r**3*(r + 2)*(r + 25)
Solve 5*s**5 + 5*s**4 - 105*s**3 - 5*s**2 + 100*s = 0 for s.
-5, -1, 0, 1, 4
Factor 33*d**2/2 + 60*d + 63/2.
3*(d + 3)*(11*d + 7)/2
Find w such that 235*w**2 + 1395*w - 90 = 0.
-6, 3/47
Factor 3*w**5 - 108*w**4 + 96*w**3 + 330*w**2 - 531*w + 210.
3*(w - 35)*(w - 1)**3*(w + 2)
Determine o so that 2*o**4 + 12*o**3 - 62*o**2 - 72*o = 0.
-9, -1, 0, 4
Find p, given that -7*p**4/5 - 68*p**3/5 - 204*p**2/5 - 32*p + 64/5 = 0.
-4, -2, 2/7
Factor 5*r**5 + 20*r**4 - 15*r**3 - 70*r**2 - 40*r.
5*r*(r - 2)*(r + 1)**2*(r + 4)
Factor -5*h**2/2 + 1170*h - 136890.
-5*(h - 234)**2/2
Suppose -m**3/10 - 187*m**2/10 - 1767*m/2 - 8649/10 = 0. What is m?
-93, -1
Find t such that -21*t**3/4 + 193*t**2/2 + 525*t/4 + 59/2 = 0.
-1, -2/7, 59/3
Factor 3*c**2 - 3240*c + 874800.
3*(c - 540)**2
Find b such that 4*b**5 + 316*b**4 + 2296*b**3 + 1672*b**2 - 2300*b - 1988 = 0.
-71, -7, -1, 1
Find n, given that -25*n**5 - 140*n**4 + 75*n**3 + 90*n**2 = 0.
-6, -3/5, 0, 1
Factor 2*o**3/11 + 26*o**2/11 - 146*o/11 - 170/11.
2*(o - 5)*(o + 1)*(o + 17)/11
Factor -9*m**4 + m**3 + 27*m**2 + 15*m - 2.
-(m - 2)*(m + 1)**2*(9*m - 1)
Suppose -j**2/6 - 4*j/3 + 51/2 = 0. What is j?
-17, 9
Find p, given that -2*p**3/7 - 284*p**2/7 - 2658*p/7 - 2376/7 = 0.
-132, -9, -1
Let -y**4 - 60*y**3 - 771*y**2 + 3904*y - 3072 = 0. What is y?
-32, 1, 3
Solve -c**3 + 42*c**2 + 241*c - 282 = 0.
-6, 1, 47
Factor r**3/3 - 2*r**2 - 5*r - 8/3.
(r - 8)*(r + 1)**2/3
Solve 2*j**4 - 6*j**3 + 6*j**2 - 2*j = 0.
0, 1
Suppose 2*h**5/5 - 21*h**4/5 + 58*h**3/5 - 68*h**2/5 + 36*h/5 - 7/5 = 0. Calculate h.
1/2, 1, 7
Factor f**2/3 - 161*f/3 - 54.
(f - 162)*(f + 1)/3
Let 25*w**4/9 - 20*w**3/9 - 13*w**2 + 68*w/9 + 44/9 = 0. Calculate w.
-2, -2/5, 1, 11/5
Suppose 21*g**5/5 - 104*g**4/5 + 161*g**3/5 - 66*g**2/5 - 4*g + 8/5 = 0. What is g?
-1/3, 2/7, 1, 2
Find s such that 5*s**2 + 3655*s - 3660 = 0.
-732, 1
Factor -3*z**3 + 42*z**2 + 63*z - 270.
-3*(z - 15)*(z - 2)*(z + 3)
Let 2*j**3 + 8*j**2 - 56*j + 64 = 0. What is j?
-8, 2
Factor v**3/4 + 67*v**2/4 + 247*v/4 - 315/4.
(v - 1)*(v + 5)*(v + 63)/4
Find u such that -9*u**3 + 2706*u**2 - 1801*u + 300 = 0.
1/3, 300
Factor 5*h**4 - 20*h**3 - 10*h**2 + 60*h + 45.
5*(h - 3)**2*(h + 1)**2
Solve 5*g**5 - 205*g**4 + 2535*g**3 - 8595*g**2 + 3240*g + 14580 = 0 for g.
-1, 3, 18
Solve s**3/5 - 8*s**2/5 - 4*s = 0 for s.
-2, 0, 10
Let 2*r**2 - 80*r + 800 = 0. What is r?
20
Suppose 2*h**3/9 + 4*h**2/3 - 98*h/9 + 44/3 = 0. What is h?
-11, 2, 3
Solve 2*t**5/13 + 68*t**4/13 - 74*t**3/13 - 140*t**2/13 = 0 for t.
-35, -1, 0, 2
Determine b so that -b**5/8 + b**4/2 + 17*b**3/8 - 4*b**2 - 31*b/2 - 10 = 0.
-2, -1, 4, 5
Solve -2*q**5/7 - 130*q**4/7 - 36*q**3 + 4*q**2/7 + 254*q/7 + 18 = 0 for q.
-63, -1, 1
Suppose f**4/6 - f**2/6 = 0. Calculate f.
-1, 0, 1
Solve -8*p**4/9 - 482*p**3/9 - 64*p**2 + 830*p/9 + 236/9 = 0.
-59, -2, -1/4, 1
Find w such that 55*w**4 - 155*w**3 - 30*w**2 + 220*w + 40 = 0.
-1, -2/11, 2
Let -3*n**5/7 - 12*n**4/7 + 27*n**3/7 + 48*n**2/7 - 60*n/7 = 0. What is n?
-5, -2, 0, 1, 2
Let d**3/3 + 2*d**2/3 - 7*d/3 + 4/3 = 0. Calculate d.
-4, 1
Find q, given that 4*q**5 + 68*q**4 - 96*q**3 - 432*q**2 = 0.
-18, -2, 0, 3
Suppose -15*v**4 + 140*v**3 - 270*v**2 + 180*v - 35 = 0. What is v?
1/3, 1, 7
Factor 2*z**3/3 + 26*z**2/3 + 14*z/3 - 110.
2*(z - 3)*(z + 5)*(z + 11)/3
Find q, given that q**5 + 20*q**4 + 108*q**3 + 144*q**2 = 0.
-12, -6, -2, 0
Factor 3*x**3/4 + 273*x**2/4 - 1719*x/4 + 2619/4.
3*(x - 3)**2*(x + 97)/4
Factor 3*o**4/2 - 39*o**3/2.
3*o**3*(o - 