 = 0.
-3, -2/7, 0, 1, 25
Find o such that 9*o**4/2 - 3*o**3/2 - 48*o**2 - 66*o - 24 = 0.
-2, -1, -2/3, 4
Factor 18*v**4/13 - 96*v**3/13 + 8*v**2 - 32*v/13.
2*v*(v - 4)*(3*v - 2)**2/13
Find r, given that -r**5/12 + r**4/2 - 11*r**3/12 + r**2/6 + r - 2/3 = 0.
-1, 1, 2
Suppose -16*r**3 - 60*r**2 - 68*r - 24 = 0. Calculate r.
-2, -1, -3/4
Factor 2*a**3 + 137*a**2/2 - 53*a - 35/2.
(a - 1)*(a + 35)*(4*a + 1)/2
Let 2*b**3/5 - 6*b**2/5 + 6*b/5 - 2/5 = 0. What is b?
1
Factor -j**4/2 - 5*j**3/2 + 47*j**2 + 208*j - 576.
-(j - 9)*(j - 2)*(j + 8)**2/2
Determine k, given that 2*k**4/17 - 62*k**3/17 + 30*k**2 - 1450*k/17 + 1000/17 = 0.
1, 5, 20
Find j such that 5*j**4 - 210*j**3 + 3245*j**2 - 21840*j + 54080 = 0.
8, 13
Factor 5*l**3 - 640*l**2 + 1265*l - 630.
5*(l - 126)*(l - 1)**2
Suppose y**2/3 - 11*y/3 + 10/3 = 0. Calculate y.
1, 10
Factor -4*r**2 - 104*r.
-4*r*(r + 26)
Factor -12*i**2 + 81*i - 135.
-3*(i - 3)*(4*i - 15)
Solve -2*x**4/5 + 10*x**3 - 366*x**2/5 + 110*x + 968/5 = 0 for x.
-1, 4, 11
Factor 4*p**4/3 + 85*p**3/3 + 101*p**2/3 + 20*p/3.
p*(p + 1)*(p + 20)*(4*p + 1)/3
Let 8*w**2 - 910*w - 2802 = 0. Calculate w.
-3, 467/4
Factor -4*f**3 + 68*f**2 - 236*f - 308.
-4*(f - 11)*(f - 7)*(f + 1)
Factor 9*x**4 - 6*x**3 - 27*x**2 + 36*x - 12.
3*(x - 1)**2*(x + 2)*(3*x - 2)
Determine q, given that -2*q**4 + 2100*q**3 = 0.
0, 1050
Find g such that -2*g**3/11 - 74*g**2/11 = 0.
-37, 0
Factor 2*a**4/3 + 17*a**3/3 + 32*a**2/3 + 4*a.
a*(a + 2)*(a + 6)*(2*a + 1)/3
Factor -r**5 + 9*r**4 - 27*r**3 + 23*r**2 + 24*r - 36.
-(r - 3)**2*(r - 2)**2*(r + 1)
What is h in 4*h**3 - 190*h**2/7 + 262*h/7 - 60/7 = 0?
2/7, 3/2, 5
Determine u so that 35*u**2 - 1915*u - 550 = 0.
-2/7, 55
Let -4*q**2 + 24*q + 28 = 0. What is q?
-1, 7
What is x in -3*x**2 + x = 0?
0, 1/3
Determine s, given that 243*s**4 - 594*s**3 - 501*s**2 + 300*s - 36 = 0.
-1, 2/9, 3
Suppose 2*l**5/5 - 4*l**4/5 - 22*l**3/5 + 8*l**2/5 + 56*l/5 + 32/5 = 0. Calculate l.
-2, -1, 2, 4
Factor 2*v**2/9 + 2396*v/9 + 717602/9.
2*(v + 599)**2/9
Find o such that 8*o**2/15 + 5558*o/15 - 278/3 = 0.
-695, 1/4
Solve x**2/5 + 89*x/5 = 0.
-89, 0
Factor 2*h**2/7 + 6*h + 40/7.
2*(h + 1)*(h + 20)/7
Determine k, given that k**5/9 + 2*k**4 - 62*k**3/9 + 8*k**2/3 + 61*k/9 - 14/3 = 0.
-21, -1, 1, 2
Factor 3*n**3/4 - 7*n**2/4 - 11*n/2 + 2.
(n - 4)*(n + 2)*(3*n - 1)/4
Factor 5*c**4 + 600*c**3 + 17995*c**2 - 600*c - 18000.
5*(c - 1)*(c + 1)*(c + 60)**2
Find q, given that -3*q**2 - 237*q - 4410 = 0.
-49, -30
Factor -n**2 + 1039*n - 3108.
-(n - 1036)*(n - 3)
Factor m**3 - 51*m**2 - 2601*m + 132651.
(m - 51)**2*(m + 51)
Solve -8*q**3 + 20*q**2 + 72*q - 180 = 0 for q.
-3, 5/2, 3
Let -4*f**2 + 22160*f - 30691600 = 0. Calculate f.
2770
Factor 3*t**3 - 84*t**2 + 81*t.
3*t*(t - 27)*(t - 1)
Factor -2*t**2 - 4894*t - 9780.
-2*(t + 2)*(t + 2445)
Factor -3*y**4/5 + 25413*y**3/5 - 71749368*y**2/5 + 67492221888*y/5 + 67563996672/5.
-3*(y - 2824)**3*(y + 1)/5
Solve 3*f**3/7 + 123*f**2/7 - 267*f/7 - 387/7 = 0 for f.
-43, -1, 3
Factor 2*z**2/9 + 532*z/9.
2*z*(z + 266)/9
Find d such that d**4 + 3*d**3 - 13*d**2 - 15*d = 0.
-5, -1, 0, 3
Factor -2*n**4/7 + 20*n**3/7 - 50*n**2/7.
-2*n**2*(n - 5)**2/7
Factor -2*p**2/7 - 22*p/7 - 48/7.
-2*(p + 3)*(p + 8)/7
Factor -3*c**2 + 186*c - 696.
-3*(c - 58)*(c - 4)
Let -o**3/6 - 5*o**2/6 + 2*o/3 + 10/3 = 0. What is o?
-5, -2, 2
Factor 4*k**3 + 3044*k**2 + 15144*k + 18144.
4*(k + 2)*(k + 3)*(k + 756)
Factor -l**3/6 + 196*l**2 - 1173*l/2.
-l*(l - 1173)*(l - 3)/6
Find v such that 2*v**2/7 - 456*v/7 - 920/7 = 0.
-2, 230
Solve y**5/4 - 3*y**4 + 27*y**3/2 - 27*y**2 + 81*y/4 = 0 for y.
0, 3
Factor -21*u**3 - 573*u**2 - 2094*u - 552.
-3*(u + 4)*(u + 23)*(7*u + 2)
Let 2*x**5/5 + 2*x**4/5 - 22*x**3/5 + 14*x**2/5 + 4*x - 16/5 = 0. What is x?
-4, -1, 1, 2
Find j such that -2*j**3/3 + 16*j**2/3 + 518*j/3 + 2156/3 = 0.
-7, 22
What is o in -4*o**4/5 + 146*o**3/5 - 298*o**2 + 2686*o/5 + 1734/5 = 0?
-1/2, 3, 17
Factor c**2/10 - 5*c/2 + 42/5.
(c - 21)*(c - 4)/10
Suppose j**3/3 + 5*j**2/3 + 4*j/3 = 0. Calculate j.
-4, -1, 0
Factor -2*j**4 + 38*j**3 + 240*j**2.
-2*j**2*(j - 24)*(j + 5)
Suppose 4*i**2 - 24*i + 20 = 0. What is i?
1, 5
Factor -4*b**3 + 216*b**2 - 596*b - 816.
-4*(b - 51)*(b - 4)*(b + 1)
Factor -16*d**4 + 156*d**3 - 104*d**2 - 36*d.
-4*d*(d - 9)*(d - 1)*(4*d + 1)
Factor -f**4/2 + 19*f**3/2 + 696*f**2.
-f**2*(f - 48)*(f + 29)/2
Factor -5*a**2 - 350*a - 6125.
-5*(a + 35)**2
Factor y**5/3 - 7*y**4/3 - 8*y**3/3 + 128*y**2/3 - 128*y/3 - 256/3.
(y - 4)**3*(y + 1)*(y + 4)/3
Find t, given that -4*t**2/3 + 184*t/3 + 188/3 = 0.
-1, 47
Determine i, given that -25*i**3 + 335*i**2 - 130*i = 0.
0, 2/5, 13
Suppose 2*w**3/5 - 2*w**2 - 26*w/5 - 14/5 = 0. Calculate w.
-1, 7
What is r in 3*r**5 - 160*r**4 - 634*r**3 + 388*r**2 + 631*r - 228 = 0?
-4, -1, 1/3, 1, 57
Factor 658*b**2/9 + 146*b - 4/9.
2*(b + 2)*(329*b - 1)/9
Suppose 2*j**3 - 18*j**2 + 28*j = 0. What is j?
0, 2, 7
Factor -8*w**2/19 + 2690*w/19 + 2022/19.
-2*(w - 337)*(4*w + 3)/19
Factor 2*a**5 + 22*a**4 + 36*a**3 - 4*a**2 - 38*a - 18.
2*(a - 1)*(a + 1)**3*(a + 9)
Factor 3*o**4 - 3*o**3 - 6*o**2.
3*o**2*(o - 2)*(o + 1)
Factor 2*a**5 + 12*a**4 + 16*a**3 - 12*a**2 - 18*a.
2*a*(a - 1)*(a + 1)*(a + 3)**2
Factor -2*u**4 - 4932*u**3 - 14784*u**2 - 14780*u - 4926.
-2*(u + 1)**3*(u + 2463)
Let b**4/3 + 97*b**3/3 + 711*b**2 + 5913*b + 17010 = 0. Calculate b.
-70, -9
Find t, given that -3*t**3/7 - 6*t**2/7 = 0.
-2, 0
What is l in 2*l**4 - 40*l**3 - 288*l**2 - 608*l - 416 = 0?
-2, 26
Factor -2*q**3 + 26*q**2 - 102*q + 126.
-2*(q - 7)*(q - 3)**2
Let 2*d**5 - 20*d**4 - 612*d**3 + 8096*d**2 + 4114*d - 239580 = 0. What is d?
-18, -5, 11
Factor 4*g**2 - 47*g - 12.
(g - 12)*(4*g + 1)
Solve -2*y**3/5 - 1678*y**2/5 + 2*y/5 + 1678/5 = 0.
-839, -1, 1
Determine s so that -s**2/2 - 2020*s - 2040200 = 0.
-2020
Find g such that 50*g**4 - 138*g**2 - 112*g - 24 = 0.
-1, -3/5, -2/5, 2
Factor -2*d**2/7 - 18*d/7 + 20/7.
-2*(d - 1)*(d + 10)/7
Find r, given that 5*r**2 - 720*r + 25920 = 0.
72
Determine r so that -r**4 + 3*r**3 - 3*r**2 + r = 0.
0, 1
Suppose 20*t**5/7 + 24*t**4 + 452*t**3/7 + 384*t**2/7 - 16*t - 192/7 = 0. Calculate t.
-4, -2, -1, 3/5
Let 27*y**2 - 105*y - 150 = 0. What is y?
-10/9, 5
Suppose -2*g**3/3 + 16*g**2/3 + 62*g/3 + 44/3 = 0. What is g?
-2, -1, 11
Solve 2*u**2 - 466*u - 1416 = 0.
-3, 236
Factor 2*r**5/9 - 16*r**4/9 + 4*r**3 - 32*r**2/9 + 10*r/9.
2*r*(r - 5)*(r - 1)**3/9
Solve -3*p**2/5 - 3*p + 18/5 = 0.
-6, 1
Factor 3*z**4 - 75*z**3 - 159*z**2 - 81*z.
3*z*(z - 27)*(z + 1)**2
Factor 3*t**4 + 39*t**3 - 1161*t**2 + 6405*t - 8526.
3*(t - 7)**2*(t - 2)*(t + 29)
Factor -2*i**3 - 38*i**2 - 70*i - 34.
-2*(i + 1)**2*(i + 17)
Suppose -5*u**4 + 50*u**3 + 65*u**2 - 110*u = 0. What is u?
-2, 0, 1, 11
Let 4*f**3/7 - 788*f**2/7 + 37600*f/7 + 120000/7 = 0. Calculate f.
-3, 100
Find d, given that -2*d**5 + 1352*d**4 + 8158*d**3 + 17708*d**2 + 16360*d + 5456 = 0.
-2, -1, 682
Solve j**4/5 - 66*j**3/5 + 129*j**2/5 - 64*j/5 = 0 for j.
0, 1, 64
Determine h, given that 20*h**3 + 88*h**2 + 32*h = 0.
-4, -2/5, 0
Factor 3*h**2/4 + 11982*h + 47856108.
3*(h + 7988)**2/4
Factor 3*x**4 + 906*x**3 + 67491*x**2 - 137712*x + 69312.
3*(x - 1)**2*(x + 152)**2
Factor -4*o**3/5 + 564*o**2/5 - 2208*o/5 + 2192/5.
-4*(o - 137)*(o - 2)**2/5
Solve 2*o**2 + 968*o + 1928 = 0 for o.
-482, -2
Suppose 8*r**5/11 - 50*r**4/11 + 52*r**3/11 + 86*r**2/11 - 24*r/11 = 0. What is r?
-1, 0, 1/4, 3, 4
Let i**5/6 + 5*i**4/6 + i**3/3 - 10*i**2/3 - 4*i = 0. What is i?
-3, -2, 0, 2
Factor b**4 + 90*b**3 + 2024*b**2 - 90*b - 2025.
(b - 1)*(b + 1)*(b + 45)**2
Let c**4/6 - 31*c**3/6 - 71*c**2/2 - 329*c/6 - 74/3 = 0. Calculate c.
-4, -1, 37
Let -16*a**2 + 116*a - 120 = 0. Calculate a.
5/4, 6
Factor t**2/3 - 53*t/3 - 56.
(t - 56)*(t + 3)/3
Determine c, given that 71*c**2/4 + 145*c/4 + 3/2 = 0.
-2, -3/71
Factor -p**2 - 17*p + 578.
-(p - 17)*(p + 34)
Factor -j**3/6 + 125*j**2/6 - 1856*j/3 - 2048.
-(j - 64)**2*(j + 3)/6
Factor -3*i**3 + 177*i**2 - 2325*i - 8649.
-3*(i - 31)**2*(i + 3)
Factor -4*k**3 + 256*k**2 - 3604*k - 3864.
-4*(k - 42)*(k - 23)*(k + 1)
Factor -6*u**3/5 + 33*u**2 - 1092*u/5 - 588/5.
-3*(u - 14)**2*(2*u + 1)/5
Let -3*j**2/7 - 33*j - 228/7 = 0. What is j?
-76, -1
Find i, given that 14*i**5/19 + 92*i**4/19 + 84*i**3/19 - 8*i**2 - 98*i/19 + 60/