 given that 68*t**2/7 - 66*t/7 - 2/7 = 0.
-1/34, 1
Find b such that -b**4/2 + b**3/2 + 59*b**2/2 - 249*b/2 + 135 = 0.
-9, 2, 3, 5
Let 5*x**5 - 445*x**4 - 465*x**3 + 1345*x**2 + 460*x - 900 = 0. What is x?
-2, -1, 1, 90
Let -r**5 - 14*r**4 + 31*r**3 - 16*r**2 = 0. What is r?
-16, 0, 1
Solve 4*x**4 - 124*x**3 + 312*x**2 + 704*x - 896 = 0 for x.
-2, 1, 4, 28
Factor -5*l**3 + 70*l**2 - 300*l + 360.
-5*(l - 6)**2*(l - 2)
Solve -9*x**4 - 30*x**3 - 21*x**2 + 12*x + 12 = 0 for x.
-2, -1, 2/3
Factor 3*p**2 + 72*p - 75.
3*(p - 1)*(p + 25)
Suppose 8*x**2/3 - 2*x/3 = 0. Calculate x.
0, 1/4
Factor -4*f**4 + 132*f**3 + 296*f**2 - 528*f - 1120.
-4*(f - 35)*(f - 2)*(f + 2)**2
Factor 3*h**4/7 + 48*h**3/7 + 240*h**2/7 + 384*h/7.
3*h*(h + 4)**2*(h + 8)/7
Factor q**3/2 + 19*q**2/2 - 410*q + 400.
(q - 20)*(q - 1)*(q + 40)/2
Suppose -3*k**5/7 + 327*k**4/7 + 666*k**3/7 + 6*k**2/7 - 663*k/7 - 333/7 = 0. Calculate k.
-1, 1, 111
Factor 2*s**2/17 - 852*s/17 + 90738/17.
2*(s - 213)**2/17
Suppose -2*i**4/19 + 1600*i**3/19 - 326318*i**2/19 + 2520144*i/19 - 2195424/19 = 0. What is i?
1, 7, 396
Factor -2*s**3/3 - 68*s**2 - 2312*s - 78608/3.
-2*(s + 34)**3/3
Factor 35*m**2 + 115*m + 30.
5*(m + 3)*(7*m + 2)
Suppose 3*c**4/5 + 3*c**3 + 3*c**2/5 - 63*c/5 - 54/5 = 0. What is c?
-3, -1, 2
Factor 2*r**2/5 + 320*r + 6368/5.
2*(r + 4)*(r + 796)/5
Solve 4*v**5/7 - 20*v**4 + 1420*v**3/7 - 3460*v**2/7 + 3200*v/7 - 1024/7 = 0.
1, 16
Factor -r**4 + 1202*r**3 + 2412*r**2 - 4808*r - 9632.
-(r - 1204)*(r - 2)*(r + 2)**2
Solve 5*z**5/2 - 10*z**4 - 30*z**3 - 5*z**2 + 55*z/2 + 15 = 0 for z.
-1, 1, 6
Find h such that h**3/10 + 3*h**2/10 - h/10 - 3/10 = 0.
-3, -1, 1
Determine u so that -5*u**2 - 225*u - 430 = 0.
-43, -2
Let -o**2/3 - 38*o/3 - 361/3 = 0. What is o?
-19
Solve -u**2/3 + 323*u = 0 for u.
0, 969
Let -2*y**3/9 + 34*y**2/9 = 0. Calculate y.
0, 17
Factor w**3/8 - 3*w**2/8 - 5*w/4 + 3.
(w - 4)*(w - 2)*(w + 3)/8
Determine n, given that n**3/3 + 9*n**2 + 17*n + 25/3 = 0.
-25, -1
Find d such that 22*d**2/7 - 64*d/7 - 6/7 = 0.
-1/11, 3
Find b such that -2*b**2/7 + 20*b/7 - 18/7 = 0.
1, 9
Factor 46*a**3/3 + 224*a**2/9 + 34*a/9 - 52/9.
2*(a + 1)**2*(69*a - 26)/9
Factor 4*i**2 + 64*i + 112.
4*(i + 2)*(i + 14)
Let 2*j**4 + 242*j**3/3 - 416*j**2/3 + 56*j = 0. Calculate j.
-42, 0, 2/3, 1
Factor 3*a**4 + 27*a**3 - 9*a**2 - 75*a + 54.
3*(a - 1)**2*(a + 2)*(a + 9)
Factor 3*x**3 + 12*x**2 + 12*x.
3*x*(x + 2)**2
Solve 3*w**3/5 - 9*w**2/5 - 3*w/5 + 9/5 = 0 for w.
-1, 1, 3
Factor -2*n**3/3 + 10*n**2 + 64*n + 160/3.
-2*(n - 20)*(n + 1)*(n + 4)/3
Factor a**3/3 + 11*a**2/3 - 25*a/3 + 13/3.
(a - 1)**2*(a + 13)/3
Determine v so that 153027*v**4 - 87738*v**3 + 12660*v**2 - 24*v = 0.
0, 2/1041, 2/7
Factor 3*y**3 - 54*y**2 - 183*y - 126.
3*(y - 21)*(y + 1)*(y + 2)
Suppose -f**3/3 + f**2/3 + 2*f/3 = 0. Calculate f.
-1, 0, 2
Factor 4*i**5 + 12*i**4 + 4*i**3 - 12*i**2 - 8*i.
4*i*(i - 1)*(i + 1)**2*(i + 2)
Factor -2*t**3/5 - 14*t**2 - 614*t/5 - 546/5.
-2*(t + 1)*(t + 13)*(t + 21)/5
Determine k so that 5*k**2 - 750*k - 2295 = 0.
-3, 153
Suppose -4*x**4/5 - 12*x**3 + 132*x**2/5 - 68*x/5 = 0. What is x?
-17, 0, 1
Factor -4*d**3 - 208*d**2 + 2444*d - 2232.
-4*(d - 9)*(d - 1)*(d + 62)
Solve 6*d**4 + 286*d**3 + 462*d**2 + 90*d - 92 = 0 for d.
-46, -1, 1/3
Determine d so that -2*d**3 + 46*d**2 + 1528*d + 2856 = 0.
-17, -2, 42
Factor -v**4 + 11*v**3 - 33*v**2 + 5*v + 50.
-(v - 5)**2*(v - 2)*(v + 1)
Factor y**3/6 - 5*y**2/6 - 13*y/6 - 7/6.
(y - 7)*(y + 1)**2/6
Suppose 2*n**3/5 - 4*n**2 - 14*n/5 + 392/5 = 0. Calculate n.
-4, 7
Factor 243*m**3 - 1404*m**2 + 1920*m - 768.
3*(m - 4)*(9*m - 8)**2
Factor 3*n**4 + 36*n**3 - 42*n**2 - 36*n + 39.
3*(n - 1)**2*(n + 1)*(n + 13)
Factor -5*y**3 + 70*y**2 + 885*y - 3150.
-5*(y - 21)*(y - 3)*(y + 10)
Factor -4*a**5/3 + 168*a**4 - 5612*a**3 + 59536*a**2/3.
-4*a**2*(a - 61)**2*(a - 4)/3
Factor 2*t**4/7 + 16*t**3/7 - 384*t**2/7 + 256*t - 2560/7.
2*(t - 4)**3*(t + 20)/7
Factor -b**4/2 + b**3/2 + 3*b**2/2 - b/2 - 1.
-(b - 2)*(b - 1)*(b + 1)**2/2
Factor 108*x**3/5 - 504*x**2/5 - 177*x/5 - 3.
3*(x - 5)*(6*x + 1)**2/5
Factor 46*r**2/7 + 338*r/7 + 292/7.
2*(r + 1)*(23*r + 146)/7
Factor 4*q**4 + 296*q**3 + 2868*q**2 - 6640*q + 3472.
4*(q - 1)**2*(q + 14)*(q + 62)
What is f in -2*f**4/11 - 4*f**3/11 + 158*f**2/11 - 104*f/11 - 840/11 = 0?
-10, -2, 3, 7
Suppose -2*g**2 - 2*g + 24 = 0. What is g?
-4, 3
Find y, given that -y**3/4 - 21*y**2/4 - 95*y/4 - 75/4 = 0.
-15, -5, -1
Factor -5*q**3/3 + 20*q**2/3 + 35*q.
-5*q*(q - 7)*(q + 3)/3
Find p such that 2*p**3/5 - 166*p**2/5 = 0.
0, 83
Factor -2*m**5/11 - 4*m**4 - 194*m**3/11 + 48*m**2 - 288*m/11.
-2*m*(m - 1)**2*(m + 12)**2/11
Factor j**3/5 - 357*j**2/5 + 31683*j/5 + 32041/5.
(j - 179)**2*(j + 1)/5
Solve -3*t**2 - 12894*t - 13854603 = 0 for t.
-2149
Factor o**5/8 - 3*o**4 + 209*o**3/8 - 369*o**2/4 + 135*o/2 + 189.
(o - 7)*(o - 6)**3*(o + 1)/8
Factor 5*n**2 - 335*n + 330.
5*(n - 66)*(n - 1)
Factor -7*t**2 + 213*t - 90.
-(t - 30)*(7*t - 3)
Factor 5*f**3 + 195*f**2 + 1495*f + 1305.
5*(f + 1)*(f + 9)*(f + 29)
What is l in l**2/3 - 400*l + 120000 = 0?
600
Factor 52*x**2 + 26892*x + 4136.
4*(x + 517)*(13*x + 2)
Factor 5*j**5 - 2990*j**4 + 455885*j**3 - 2655120*j**2 + 3942720*j.
5*j*(j - 296)**2*(j - 3)**2
Find j such that 4*j**5 - 24*j**4 + 44*j**3 - 24*j**2 = 0.
0, 1, 2, 3
Factor 2*j**3/19 + 1768*j**2/19 + 5290*j/19 + 3524/19.
2*(j + 1)*(j + 2)*(j + 881)/19
Factor -12*l**2 - 2876*l - 1912.
-4*(l + 239)*(3*l + 2)
What is r in 2*r**3/5 - 108*r**2/5 = 0?
0, 54
Factor -m**5 - 25*m**4 - 235*m**3 - 1015*m**2 - 1960*m - 1372.
-(m + 2)**2*(m + 7)**3
Find b such that -2*b**4/7 - 2*b**3 - 2*b**2 + 30*b/7 = 0.
-5, -3, 0, 1
What is y in -5*y**4 + 10*y**3 + 1195*y**2 - 1200*y = 0?
-15, 0, 1, 16
Factor 3*h**4/4 - 41*h**3/4 + 25*h**2/4 + 13*h/4.
h*(h - 13)*(h - 1)*(3*h + 1)/4
Solve -3*t**3/5 + 27*t**2/5 - 6*t/5 - 144/5 = 0 for t.
-2, 3, 8
Determine b so that -5*b**3 - 40*b**2 + 20*b + 160 = 0.
-8, -2, 2
Determine l, given that -5*l**5 - 1210*l**4 - 71940*l**3 + 158600*l**2 + 595360*l = 0.
-122, -2, 0, 4
Factor -2*y**2 - 676*y.
-2*y*(y + 338)
Factor -2*x**2/5 - 7548*x/5 - 7121538/5.
-2*(x + 1887)**2/5
Factor -270*t**3 - 785*t**2 - 465*t + 50.
-5*(t + 1)*(t + 2)*(54*t - 5)
Find h, given that 2*h**4/5 - 2*h**3/5 - 14*h**2/5 + 2*h/5 + 12/5 = 0.
-2, -1, 1, 3
Factor -2*p**3 + 266*p**2 - 526*p + 262.
-2*(p - 131)*(p - 1)**2
Determine h, given that -2*h**5/11 + 8*h**4/11 + 42*h**3/11 = 0.
-3, 0, 7
Find j, given that j**4/6 - j**3 - 117*j**2/2 + 180*j + 5400 = 0.
-12, 15
Determine m, given that 5*m**5 + 10*m**4 - 10*m**2 - 5*m = 0.
-1, 0, 1
Let -6*t**3/11 + 8*t**2/11 + 10*t/11 - 4/11 = 0. Calculate t.
-1, 1/3, 2
Determine w so that -9*w**5/5 + 33*w**4/5 - 24*w**3/5 - 12*w**2/5 = 0.
-1/3, 0, 2
Determine b, given that 4*b**3 - 2*b**2 - 46*b - 40 = 0.
-5/2, -1, 4
Determine x so that -3*x**2 + 1107*x + 1110 = 0.
-1, 370
Determine l so that 21*l**5 + 174*l**4 + 426*l**3 + 108*l**2 - 567*l - 162 = 0.
-3, -2/7, 1
Factor -a**3/7 - 25*a**2/7 - 43*a/7 + 69/7.
-(a - 1)*(a + 3)*(a + 23)/7
Let r**3/4 + 13*r**2/4 + 8*r + 5 = 0. Calculate r.
-10, -2, -1
Determine k, given that 5*k**2 - 40*k + 60 = 0.
2, 6
Suppose -2*u**3 + 8*u**2 + 330*u = 0. Calculate u.
-11, 0, 15
Factor 5*z**3 + 260*z**2 + 3145*z - 3410.
5*(z - 1)*(z + 22)*(z + 31)
Factor b**5/4 - 21*b**4/4 + 39*b**3/4 - 19*b**2/4.
b**2*(b - 19)*(b - 1)**2/4
Let -2*i**4/3 - 53*i**3/6 - 71*i**2/2 - 137*i/3 - 28/3 = 0. What is i?
-7, -4, -2, -1/4
Suppose 5*o**4 - 85*o**3 + 275*o**2 - 195*o = 0. Calculate o.
0, 1, 3, 13
Factor -64*y**3 - 372*y**2 + 72*y.
-4*y*(y + 6)*(16*y - 3)
Let -b**5/2 - 3*b**4/2 - b**3/2 + 3*b**2/2 + b = 0. What is b?
-2, -1, 0, 1
Find q, given that 2*q**2 - 18*q - 20 = 0.
-1, 10
Factor -z**3 + 14*z**2 - 25*z + 12.
-(z - 12)*(z - 1)**2
Determine w, given that -5*w**3/2 - 30*w**2 - 175*w/2 = 0.
-7, -5, 0
Solve 14*l**2/3 + 100*l/3 + 14/3 = 0 for l.
-7, -1/7
Suppose 56*s**3 - 40*s**2 + 50*s/7 = 0. What is s?
0, 5/14
Find j, given that -21*j**3 + 57*j**2 - 24*j - 12 = 0.
-2/7, 1, 2
Let -4*a**2/3 + 40*a/3 + 3500/3 = 0. Calculate a.
-25, 35
Factor -2*j**2/11 - 1010*j/11 - 2012/11.
-2*(j + 2)*(j + 503)/11
Suppose -u**4/10 - 6*u**3/5 - 8*u**2/5 + 24*u/5 + 8 = 0. Calculate u.
-10, -2, 2
Let 12*x**3 + 225*x**2 - 849*x + 198 = 0. Calcu