at -2*g**2 + 44*g - 242 = 0.
11
Factor -6*j**3/7 + 6*j**2/7 + 30*j/7 + 18/7.
-6*(j - 3)*(j + 1)**2/7
Solve v**2/3 - 283*v/3 + 2200/3 = 0.
8, 275
Let s**5/8 + s**4 + 23*s**3/8 + 7*s**2/2 + 3*s/2 = 0. Calculate s.
-3, -2, -1, 0
Factor -k**3 - 7*k**2/6 - k/6.
-k*(k + 1)*(6*k + 1)/6
Factor 2*u**3/11 - 6*u**2 - 140*u/11.
2*u*(u - 35)*(u + 2)/11
Factor -12*s**3 - 20*s**2 + 128*s + 240.
-4*(s + 2)*(s + 3)*(3*s - 10)
Factor 5*w**5/6 - 10*w**4/3 + 35*w**2/3 - 85*w/6 + 5.
5*(w - 3)*(w - 1)**3*(w + 2)/6
What is k in 3*k**2 + 330*k - 6477 = 0?
-127, 17
Suppose -s**3 - 4*s**2 = 0. Calculate s.
-4, 0
Solve -2*z**4/5 - 68*z**3/5 + 6*z**2/5 + 40*z - 136/5 = 0.
-34, -2, 1
Factor -k**3/9 + 50*k**2/9 - 97*k/9 + 16/3.
-(k - 48)*(k - 1)**2/9
Determine p, given that -3*p**3 - 45*p**2 + 3*p + 45 = 0.
-15, -1, 1
Factor -2*g**2/17 - 8*g/17 - 6/17.
-2*(g + 1)*(g + 3)/17
Find j such that -8*j**4/3 - 1000*j**3/3 - 3646*j**2 - 10192*j/3 - 2486/3 = 0.
-113, -11, -1/2
Let -596*v**5 - 604*v**4 - 8*v**3 = 0. Calculate v.
-1, -2/149, 0
Factor n**3/3 - 70*n**2/3 + 384*n + 864.
(n - 36)**2*(n + 2)/3
Determine c so that 3*c**2/5 - 642*c + 171735 = 0.
535
Solve -2*t**5/7 + 8*t**4/7 - 4*t**2 + 34*t/7 - 12/7 = 0.
-2, 1, 3
Let -2*k**5/3 - 10*k**4/3 - 4*k**3 + 4*k**2/3 + 14*k/3 + 2 = 0. Calculate k.
-3, -1, 1
Find z such that 3*z**4/7 - 27*z**3/7 - 99*z**2/7 - 15*z - 36/7 = 0.
-1, 12
Factor 4*g**4 - 8*g**3.
4*g**3*(g - 2)
Determine w, given that -3*w**5/4 - 27*w**4/2 - 117*w**3/2 + 42*w**2 + 837*w/4 + 243/2 = 0.
-9, -1, 2
Determine a so that a**2/8 + 225*a/2 + 50625/2 = 0.
-450
Suppose -l**4/3 + 16*l**3/3 - 13*l**2/3 - 10*l = 0. Calculate l.
-1, 0, 2, 15
Factor 3*c**3 + 195*c**2.
3*c**2*(c + 65)
Find i, given that -2*i**2/7 + 290*i/7 - 276 = 0.
7, 138
Factor -a**3 - 61*a**2 - 231*a - 171.
-(a + 1)*(a + 3)*(a + 57)
Factor -75*r**2/2 - 147*r/2 + 3.
-3*(r + 2)*(25*r - 1)/2
Let 5*t**5 - 125*t**4 + 115*t**3 + 125*t**2 - 120*t = 0. Calculate t.
-1, 0, 1, 24
Solve -245*j**4 + 2100*j**3 - 1140*j**2 + 160*j = 0 for j.
0, 2/7, 8
Factor i**3 - 4*i**2 - 31*i + 70.
(i - 7)*(i - 2)*(i + 5)
Factor -x**3 + 30*x**2 + 31*x.
-x*(x - 31)*(x + 1)
Factor -q**4/2 + 3*q**3 + 12*q**2 - 32*q.
-q*(q - 8)*(q - 2)*(q + 4)/2
Find b such that b**2/3 + 1888*b + 2673408 = 0.
-2832
Find s such that -3*s**4/8 + 24*s**3 + 3*s**2/8 - 24*s = 0.
-1, 0, 1, 64
Let -32*z**4/3 + 26*z**3/3 + 9*z**2 - 26*z/3 + 5/3 = 0. Calculate z.
-1, 5/16, 1/2, 1
Factor 2*k**4 - 340*k**3 + 17706*k**2 - 276760*k + 1325192.
2*(k - 74)**2*(k - 11)**2
Solve -2*x**5/9 - 2*x**4/9 + 4*x**3/9 + 4*x**2/9 - 2*x/9 - 2/9 = 0.
-1, 1
Find j, given that 10*j**5/9 - 293*j**4/9 + 209*j**3/3 - 18*j**2 = 0.
0, 3/10, 2, 27
Let k**5/4 + k**4/4 - 11*k**3/4 - 29*k**2/4 - 13*k/2 - 2 = 0. What is k?
-2, -1, 4
Factor -2*z**2/5 - 3124*z/5 - 1219922/5.
-2*(z + 781)**2/5
Factor -4*l**2 - 132*l - 864.
-4*(l + 9)*(l + 24)
Factor -h**3/2 + 36*h**2 + 475*h/2 - 273.
-(h - 78)*(h - 1)*(h + 7)/2
Factor -9*b**2 - 24*b.
-3*b*(3*b + 8)
Factor 4*v**4 - 76*v**3 - 80*v**2.
4*v**2*(v - 20)*(v + 1)
Factor k**3 + 7*k**2 + 7*k - 15.
(k - 1)*(k + 3)*(k + 5)
Suppose 5*u**2 - 1890*u + 178605 = 0. Calculate u.
189
Factor -10*v**3 - 525*v**2 - 4035*v + 2150.
-5*(v + 10)*(v + 43)*(2*v - 1)
Find y, given that y**4/6 + 5*y**3/6 + y**2/2 - 5*y/6 - 2/3 = 0.
-4, -1, 1
Let -3*q**3/7 - 5913*q**2/7 - 3884841*q/7 - 850780179/7 = 0. Calculate q.
-657
Factor -2*c**2 - 230*c + 232.
-2*(c - 1)*(c + 116)
Factor p**4/5 - 8*p**3/5 + 17*p**2/5 - 2*p.
p*(p - 5)*(p - 2)*(p - 1)/5
Factor -3*b**3 - 117*b**2 - 1242*b - 2040.
-3*(b + 2)*(b + 17)*(b + 20)
Factor 2*m**3 - 8*m**2/5 - 18*m + 72/5.
2*(m - 3)*(m + 3)*(5*m - 4)/5
Factor 4*a**3 - 52*a**2 + 176*a - 128.
4*(a - 8)*(a - 4)*(a - 1)
Factor 5*n**2/2 + 73*n/2 - 15.
(n + 15)*(5*n - 2)/2
Factor -56*a**2/3 - 130*a/3 + 62.
-2*(a - 1)*(28*a + 93)/3
Factor b**4/5 + 23*b**3/5 - 104*b**2/5 + 108*b/5.
b*(b - 2)**2*(b + 27)/5
Factor 5*g**2/6 + 10525*g/3 + 22155125/6.
5*(g + 2105)**2/6
Factor 3*y**4 - 21*y**3 - 201*y**2 + 1785*y - 2646.
3*(y - 7)**2*(y - 2)*(y + 9)
Factor -3*u**2 - 4329*u.
-3*u*(u + 1443)
Find l such that -3*l**4/4 + 159*l**3/4 - 153*l**2/4 - 159*l/4 + 39 = 0.
-1, 1, 52
Let -9*s**2/5 - 74*s/5 - 16/5 = 0. Calculate s.
-8, -2/9
Solve -3*h**4/2 - 339*h**3 + 2070*h**2 - 4164*h + 2784 = 0 for h.
-232, 2
Suppose 2*l**2 + 12*l = 0. What is l?
-6, 0
Factor 3*p**4 - 21*p**2 - 18*p.
3*p*(p - 3)*(p + 1)*(p + 2)
Factor 5*j**3 + 1015*j**2 - 2045*j + 1025.
5*(j - 1)**2*(j + 205)
Suppose w**2 - 6300*w + 9922500 = 0. What is w?
3150
Factor a**2 + 8*a - 20.
(a - 2)*(a + 10)
Let 2*h**2 - 14*h = 0. Calculate h.
0, 7
Let -2*i**2/9 - 40*i + 728/9 = 0. Calculate i.
-182, 2
Let b**3/2 + 5052*b**2 + 17015136*b + 19102326016 = 0. Calculate b.
-3368
Determine m, given that -5*m**4 - 195*m**3 - 540*m**2 + 20*m + 720 = 0.
-36, -2, 1
Determine i so that -14*i**3/11 + 144*i**2/11 - 24*i + 64/11 = 0.
2/7, 2, 8
Factor 2*o**4 + 1210*o**3 + 182402*o**2 - 186042*o - 367236.
2*(o - 2)*(o + 1)*(o + 303)**2
Determine b so that b**3/5 + 4*b**2/5 - b/5 - 4/5 = 0.
-4, -1, 1
Suppose -380*u**2/3 + 32*u - 4/3 = 0. What is u?
1/19, 1/5
Factor -2*u**3/7 + 76*u**2/7 + 74*u + 440/7.
-2*(u - 44)*(u + 1)*(u + 5)/7
Determine d so that -d**5/4 + 5*d**4/2 + 23*d**3/4 + 3*d**2 = 0.
-1, 0, 12
Find n such that -3*n**5 + 6*n**4 + 3*n**3 - 6*n**2 = 0.
-1, 0, 1, 2
Find u such that -5*u**2 - 280*u = 0.
-56, 0
Factor n**2/2 + 69*n + 4761/2.
(n + 69)**2/2
Factor -i**5/6 + 7*i**4/6 - 5*i**3/2 + 3*i**2/2.
-i**2*(i - 3)**2*(i - 1)/6
Factor 2*w**3/11 - 18*w**2/11 - 32*w/11 + 120/11.
2*(w - 10)*(w - 2)*(w + 3)/11
Solve -4*m**5 + 28*m**4 + 772*m**3 + 2708*m**2 - 768*m - 2736 = 0 for m.
-6, -1, 1, 19
Determine c, given that 24*c**2/7 - 597*c/7 - 702/7 = 0.
-9/8, 26
Factor -r**4 + 26*r**3 + 27*r**2.
-r**2*(r - 27)*(r + 1)
Solve 3*i**3/7 - 735*i**2 = 0 for i.
0, 1715
Factor 4*s**4 + 388*s**3 + 3276*s**2 + 9612*s + 9504.
4*(s + 3)**3*(s + 88)
Find c, given that -3*c**3 + 57*c**2 = 0.
0, 19
What is x in -x**4/3 + 14*x**3/3 - 44*x**2/3 - 110*x/3 + 175 = 0?
-3, 5, 7
Factor -3*d**4 + 147*d**3 + 3*d**2 - 147*d.
-3*d*(d - 49)*(d - 1)*(d + 1)
Find r, given that 3*r**3/5 - 186*r**2/5 + 363*r/5 - 36 = 0.
1, 60
Suppose -y**5/3 + 5*y**4/3 + 4*y**3/3 - 20*y**2/3 = 0. Calculate y.
-2, 0, 2, 5
Let 3*x**2 - 42*x + 39 = 0. What is x?
1, 13
Suppose 243*f**3/5 + 97*f**2 + 241*f/5 - 1/5 = 0. What is f?
-1, 1/243
Determine v so that -4*v**4 + 32*v**3 - 64*v**2 = 0.
0, 4
Suppose -f**2/2 - 2527*f - 6385729/2 = 0. Calculate f.
-2527
Factor -3*m**2 + 69*m.
-3*m*(m - 23)
Determine x so that -10*x**2 - 15*x + 135 = 0.
-9/2, 3
Let 98*d**2/19 - 3360*d/19 + 28800/19 = 0. What is d?
120/7
Factor -2*v**4/7 + 2*v**2/7.
-2*v**2*(v - 1)*(v + 1)/7
Factor 2*y**3/5 - 4*y**2/5 - 2*y/5 + 4/5.
2*(y - 2)*(y - 1)*(y + 1)/5
Suppose i**5/5 + 8*i**4/5 - 2*i**3/5 - 16*i**2/5 + i/5 + 8/5 = 0. Calculate i.
-8, -1, 1
Factor -f**5 + 8*f**4 + 19*f**3 + 10*f**2.
-f**2*(f - 10)*(f + 1)**2
Suppose i**2 - 24*i - 25 = 0. Calculate i.
-1, 25
Determine f, given that 3*f**4 + 600*f**3 + 1779*f**2 + 1182*f = 0.
-197, -2, -1, 0
Find u such that 2*u**3 - 6*u**2 - 12*u + 16 = 0.
-2, 1, 4
Factor -2*g**4/5 - 262*g**3/5.
-2*g**3*(g + 131)/5
Suppose -84*u**5 - 200*u**4 + 148*u**3 - 24*u**2 = 0. Calculate u.
-3, 0, 2/7, 1/3
What is n in n**4/3 + 5*n**3 + 43*n**2/3 - 5*n - 44/3 = 0?
-11, -4, -1, 1
Factor 4*c**3 - 108*c**2 + 204*c - 100.
4*(c - 25)*(c - 1)**2
Factor g**4/3 - 8*g**3/3 - 10*g**2/3 + 8*g/3 + 3.
(g - 9)*(g - 1)*(g + 1)**2/3
Factor 2*m**2/5 + 16*m/5 + 6.
2*(m + 3)*(m + 5)/5
Find v, given that -v**4/4 - 3*v**3 - 13*v**2 - 24*v - 16 = 0.
-4, -2
Factor -3*p**3/4 - 10701*p**2/4.
-3*p**2*(p + 3567)/4
Suppose 64*n**5 + 752*n**4 - 228*n**3 - 443*n**2 - 133*n - 12 = 0. Calculate n.
-12, -1/4, 1
Factor x**4/2 + 2*x**3 - 8*x**2 - 32*x.
x*(x - 4)*(x + 4)**2/2
Factor -2*c**3/15 + 104*c**2/15 + 118*c/15 - 212/5.
-2*(c - 53)*(c - 2)*(c + 3)/15
Determine z, given that -2*z**3/9 + 438*z**2 - 648130*z/3 + 1940450/9 = 0.
1, 985
Determine k so that 4*k**2 + 4*k - 8 = 0.
-2, 1
Factor 2*j**2/3 - 8*j.
2*j*(j - 12)/3
Let -4*q**3 + 384*q**2 - 12288*q + 131072 = 0. Calculate q.
32
Find j such that 2*j**3/3 - 136*j**2/3 + 2266*j/3 - 11132/3 = 0.
11, 46
Determine r, given that 2*r**2/7 + 2*r = 0.
-7, 0
Facto