termine y, given that -3*y**4 - 27*y**3 - 6*y**2 + 252*y - 216 = 0.
-6, 1, 2
Solve -5*r**3 + 1105*r**2 - 61600*r + 60500 = 0 for r.
1, 110
Factor -2*h**5/17 + 4*h**4/17 - 4*h**2/17 + 2*h/17.
-2*h*(h - 1)**3*(h + 1)/17
Let -2*o**5/3 + 4*o**4 - 8*o**3 + 16*o**2/3 = 0. Calculate o.
0, 2
Determine u so that 2*u**4/19 - 4*u**3/19 - 24*u**2/19 + 80*u/19 - 64/19 = 0.
-4, 2
Factor -x**3/2 + 5*x**2 + 53*x/2 + 21.
-(x - 14)*(x + 1)*(x + 3)/2
Factor 3*y**3 + 54*y**2 - 873*y - 924.
3*(y - 11)*(y + 1)*(y + 28)
Find v such that 22*v**5 - 26*v**4 - 14*v**3 + 18*v**2 = 0.
-9/11, 0, 1
Solve -2*b**2 + 206*b + 208 = 0 for b.
-1, 104
Find a such that -2*a**4/9 - 328*a**3/9 + 1004*a**2/9 + 328*a/9 - 334/3 = 0.
-167, -1, 1, 3
Determine w so that 3*w**2/2 - 1800*w + 540000 = 0.
600
Factor -3*a**5 - 129*a**4 - 912*a**3 - 2616*a**2 - 3408*a - 1680.
-3*(a + 2)**4*(a + 35)
Factor -f**2 - 115*f - 550.
-(f + 5)*(f + 110)
Suppose 3*t**5/2 + 24*t**4 + 153*t**3/2 + 54*t**2 = 0. Calculate t.
-12, -3, -1, 0
Factor 4*f**2 + 84*f - 288.
4*(f - 3)*(f + 24)
Find t such that -t**4/2 + 215*t**3 - 43573*t**2/2 - 285090*t - 879138 = 0.
-6, 221
Suppose h**2/4 - 271*h/4 + 267 = 0. Calculate h.
4, 267
Solve 12*a**4 + 86*a**3 + 84*a**2 - 2*a - 12 = 0.
-6, -1, -1/2, 1/3
Let -2*k**4/3 - 8*k**3/3 + 26*k**2/3 + 8*k/3 - 8 = 0. Calculate k.
-6, -1, 1, 2
Factor -3*j**2/7 - 7848*j/7 - 5132592/7.
-3*(j + 1308)**2/7
Solve r**5/3 - 30*r**4 + 835*r**3 - 22060*r**2/3 + 26000*r - 32448 = 0.
4, 39
Determine u, given that -u**2/2 + 354*u + 709/2 = 0.
-1, 709
What is s in 3*s**2 + 282*s + 279 = 0?
-93, -1
Determine s so that 3*s**4/2 - 3*s**3 - 219*s**2/2 - 105*s = 0.
-7, -1, 0, 10
Solve -2*o**2/11 - 34*o/11 + 120/11 = 0 for o.
-20, 3
Factor -5*y**5 + 90*y**3 - 405*y.
-5*y*(y - 3)**2*(y + 3)**2
Suppose -3*l**4 - 27*l**3 - 66*l**2 + 96 = 0. What is l?
-4, -2, 1
Find x, given that -21*x**4 + 300*x**3 - 357*x**2 + 78*x = 0.
0, 2/7, 1, 13
Factor -3*b**2 - 372*b + 375.
-3*(b - 1)*(b + 125)
Find t, given that -t**2 + 173*t = 0.
0, 173
Solve -4*t**2 - 464*t = 0.
-116, 0
Solve -p**5/4 - 11*p**4/2 - 121*p**3/4 = 0.
-11, 0
Factor 4*z**5/3 + 500*z**4/3 + 488*z**3.
4*z**3*(z + 3)*(z + 122)/3
Determine f, given that -f**2/10 + 21*f/2 - 558/5 = 0.
12, 93
Find s, given that -15*s**5 + 33*s**4/7 + 30*s**3/7 = 0.
-2/5, 0, 5/7
Determine p, given that 2*p**2 + 464*p + 462 = 0.
-231, -1
Factor 2*k**2/3 + 14*k - 92/3.
2*(k - 2)*(k + 23)/3
Factor 3*r**4/2 + 189*r**3/2 - 294*r**2 + 198*r.
3*r*(r - 2)*(r - 1)*(r + 66)/2
Factor 3*r**2/7 - 12*r - 1140/7.
3*(r - 38)*(r + 10)/7
Factor 4*v**5 - 28*v**3 + 24*v**2.
4*v**2*(v - 2)*(v - 1)*(v + 3)
Solve -a**5 - 287*a**4 - 26458*a**3 - 683694*a**2 + 8967915*a - 24257475 = 0 for a.
-99, 5
Suppose -3*l**2 - 45*l + 2442 = 0. What is l?
-37, 22
What is i in i**4/4 + 3*i**3 + 45*i**2/4 + 29*i/2 + 6 = 0?
-6, -4, -1
Determine n so that n**3/5 + 84*n**2 + 11760*n + 548800 = 0.
-140
What is z in -12*z**3 - 9*z**2 + 27*z - 6 = 0?
-2, 1/4, 1
What is m in -5*m**5 - 5*m**4 + 50*m**3 - 40*m**2 = 0?
-4, 0, 1, 2
Factor -18*g**3 + 68*g**2 + 16*g.
-2*g*(g - 4)*(9*g + 2)
Find u such that -4*u**2/5 + 24*u/5 + 44 = 0.
-5, 11
Factor 3*f**4 + 186*f**3 + 1611*f**2 + 2676*f + 1248.
3*(f + 1)**2*(f + 8)*(f + 52)
Factor -3*r**4/5 + 192*r**3/5 - 3258*r**2/5 + 5952*r/5 - 2883/5.
-3*(r - 31)**2*(r - 1)**2/5
Factor 9*w**5/5 - 12*w**4/5 + 3*w**3/5.
3*w**3*(w - 1)*(3*w - 1)/5
Factor -2*p**4 + 8*p**3 - 10*p**2 + 4*p.
-2*p*(p - 2)*(p - 1)**2
Factor -h**3/3 - 10*h**2/9 - h/3.
-h*(h + 3)*(3*h + 1)/9
Find j, given that 4*j**4 + 640*j**3 + 24288*j**2 - 104960*j + 107584 = 0.
-82, 2
Factor -3*f**3 + 60*f**2 + 81*f - 378.
-3*(f - 21)*(f - 2)*(f + 3)
Determine t, given that 2*t**5 + 24*t**4 + 84*t**3 + 40*t**2 - 150*t = 0.
-5, -3, 0, 1
Factor 4*n**3 + 100*n**2 + 492*n + 684.
4*(n + 3)**2*(n + 19)
Let 3*h**4/2 - 57*h**3/4 - 42*h**2 - 141*h/4 - 9 = 0. Calculate h.
-1, -1/2, 12
Factor 2*m**4/5 - 22*m**3/5 - 8*m**2/5 + 88*m/5.
2*m*(m - 11)*(m - 2)*(m + 2)/5
Determine l so that 2*l**5 - 96*l**4 + 186*l**3 - 92*l**2 = 0.
0, 1, 46
Suppose -k**2 - 2*k + 35 = 0. What is k?
-7, 5
Factor -2*s**3 + 27*s**2 + 47*s - 30.
-(s - 15)*(s + 2)*(2*s - 1)
Let q**3/8 - q**2/2 + 5*q/8 - 1/4 = 0. What is q?
1, 2
Suppose -2*f**2 + 3772*f - 1778498 = 0. Calculate f.
943
Suppose 33*v**3/7 - 15*v**2/7 - 18*v/7 = 0. What is v?
-6/11, 0, 1
Factor -5*n**2/2 + 85*n/2 - 105.
-5*(n - 14)*(n - 3)/2
Factor -2*o**2/7 - 48*o/7 - 216/7.
-2*(o + 6)*(o + 18)/7
Factor 2*g**2 + 5068*g + 3210578.
2*(g + 1267)**2
Factor 65*s**3 - 848*s**2 + 37*s + 26.
(s - 13)*(5*s - 1)*(13*s + 2)
Determine b so that b**3 + 10*b**2 + 28*b + 24 = 0.
-6, -2
Factor -2*v**3/11 - 122*v**2/11 - 1920*v/11 - 1800/11.
-2*(v + 1)*(v + 30)**2/11
Let -b**4/3 + 2*b**3 - 8*b**2/3 = 0. Calculate b.
0, 2, 4
Factor t**2/3 + 20*t/3 + 100/3.
(t + 10)**2/3
Factor -5*x**3 - 135*x**2 + 5*x + 135.
-5*(x - 1)*(x + 1)*(x + 27)
Suppose f**2/3 - 37*f/3 - 38/3 = 0. Calculate f.
-1, 38
Find s, given that s**4/9 - 163*s**3/9 - 55*s**2/3 + 163*s/9 + 164/9 = 0.
-1, 1, 164
Factor 2*j**2 - 42*j + 180.
2*(j - 15)*(j - 6)
Factor 3*m**3/2 - 63*m**2 + 1251*m/2 + 690.
3*(m - 23)*(m - 20)*(m + 1)/2
Factor -y**5/3 - 63*y**4 + 190*y**3/3.
-y**3*(y - 1)*(y + 190)/3
Suppose -2*t**3/9 - 550*t**2/3 + 1102*t/3 - 1654/9 = 0. Calculate t.
-827, 1
Let -3*s**4 - 252*s**3 - 738*s**2 - 732*s - 243 = 0. What is s?
-81, -1
Suppose b**5/2 + 134*b**4 + 399*b**3 + 398*b**2 + 265*b/2 = 0. Calculate b.
-265, -1, 0
Suppose -44*z**5 + 226*z**4/3 - 338*z**3/9 + 58*z**2/9 - 2*z/9 = 0. What is z?
0, 1/22, 1/3, 1
Factor s**4/7 - 32*s**3/7 - 47*s**2 + 360*s/7.
s*(s - 40)*(s - 1)*(s + 9)/7
Factor 2*d**5/7 - 94*d**4/7 + 270*d**3/7 - 38*d**2 + 88*d/7.
2*d*(d - 44)*(d - 1)**3/7
Factor -j**2/5 + 76*j/5 - 15.
-(j - 75)*(j - 1)/5
Solve 2*w**4/9 + 4*w**3/3 + 2*w**2/9 - 16*w/3 + 32/9 = 0 for w.
-4, 1
What is m in m**2/7 + 498*m/7 + 71 = 0?
-497, -1
Let m**2/2 - 21*m + 76 = 0. What is m?
4, 38
Solve -3*v**3/5 + 74*v**2/5 - 96*v + 288/5 = 0 for v.
2/3, 12
Solve b**5/6 - 2*b**4/3 - 11*b**3/6 - b**2 = 0 for b.
-1, 0, 6
Factor -4*w**4/7 - 20*w**3/7 - 4*w**2 - 12*w/7.
-4*w*(w + 1)**2*(w + 3)/7
Factor 4*l**5 + 16*l**4 + 8*l**3 - 16*l**2 - 12*l.
4*l*(l - 1)*(l + 1)**2*(l + 3)
Factor -5*c**3 + 435*c**2 - 400*c - 2580.
-5*(c - 86)*(c - 3)*(c + 2)
Factor 3*p**5 + 21*p**4 - 54*p**3 + 6*p**2 + 51*p - 27.
3*(p - 1)**3*(p + 1)*(p + 9)
Suppose f**3/3 + 3*f**2 + 9*f + 9 = 0. Calculate f.
-3
Find n, given that 2*n**3/3 + 28*n**2 + 234*n + 620/3 = 0.
-31, -10, -1
Find m, given that -m**4/3 + 2*m**3/9 + 4*m**2/9 - 2*m/9 - 1/9 = 0.
-1, -1/3, 1
Let -4*t**5 - 86*t**4 - 198*t**3 - 154*t**2 - 38*t = 0. What is t?
-19, -1, -1/2, 0
Factor 5*j**2 - 10090*j.
5*j*(j - 2018)
Factor 7*p**3 - 30*p**2 + 8*p.
p*(p - 4)*(7*p - 2)
Find k such that k**4/7 + 145*k**3/7 + 5469*k**2/7 + 2201*k + 10082/7 = 0.
-71, -2, -1
Solve 5*w**5/3 + 5*w**4/3 - 20*w**3 - 140*w**2/3 - 80*w/3 = 0.
-2, -1, 0, 4
Factor -14*b**4 - 66*b**3 - 64*b**2 + 24*b.
-2*b*(b + 2)*(b + 3)*(7*b - 2)
Let n**4/2 - n**3/2 - 27*n**2/2 - 27*n/2 + 27 = 0. What is n?
-3, 1, 6
Factor -3*f**3 - 72*f**2 - 576*f - 1536.
-3*(f + 8)**3
Factor -t**4 - 11*t**3.
-t**3*(t + 11)
Determine t, given that 3*t**3/2 - 597*t**2/2 + 36465*t/2 - 628575/2 = 0.
29, 85
Solve -4*r**4 - 124*r**3 - 1432*r**2 - 7296*r - 13824 = 0.
-9, -8, -6
Factor 21*k**3/2 + 1032*k**2 + 294*k.
3*k*(k + 98)*(7*k + 2)/2
Find f such that -35*f**3 + 1481*f**2 - 456*f - 252 = 0.
-2/7, 3/5, 42
Factor -2*c**2 - 2540*c + 2542.
-2*(c - 1)*(c + 1271)
Solve -2*k**5/3 + 66*k**4 - 2178*k**3 + 23958*k**2 = 0.
0, 33
Determine a, given that -5*a**5 + 80*a**4 - 290*a**3 + 140*a**2 + 295*a - 220 = 0.
-1, 1, 4, 11
Factor -18*v**3 + 38*v**2 - 4*v.
-2*v*(v - 2)*(9*v - 1)
Find b, given that b**3/8 + 27*b**2/2 - 565*b/8 = 0.
-113, 0, 5
Determine u, given that 6*u**5/5 - 15*u**4 - 561*u**3/5 + 1761*u**2/5 - 417*u/5 - 714/5 = 0.
-7, -1/2, 1, 2, 17
What is i in -2*i**3 - 36*i**2 - 34*i = 0?
-17, -1, 0
Factor 4*a**2 + 80*a - 624.
4*(a - 6)*(a + 26)
Find a such that -45*a**5 - 12*a**4 + 187*a**3 + 50*a**2 - 28*a - 8 = 0.
-2, -1/3, 2/5, 2
Factor -2*i**2 + 7124*i - 6343922.
-2*(i - 1781)**2
Determine n so that -4*n**2 - 3176*n - 630436 = 0.
-397
Factor -9*o**2 - 2364*o - 1572.
-3*(o + 262)*(3*o + 2)
Factor -