2.
(a - 11)**3*(a - 2)*(a - 1)
Let 5*n**2 + 1685*n + 1680 = 0. Calculate n.
-336, -1
Factor -g**3 + 338*g**2/3 + 460*g/3 - 152.
-(g - 114)*(g + 2)*(3*g - 2)/3
Determine m so that -2*m**2/11 - 668*m/11 + 2022/11 = 0.
-337, 3
Suppose f**2 + 1100*f + 302500 = 0. Calculate f.
-550
Factor 5*r**2 + 65*r + 60.
5*(r + 1)*(r + 12)
Factor -60*w**2/13 + 1078*w/13 + 36/13.
-2*(w - 18)*(30*w + 1)/13
Factor f**2/4 - 88*f + 7744.
(f - 176)**2/4
Factor -4*x**3/7 + 3880*x**2/7 - 940900*x/7.
-4*x*(x - 485)**2/7
What is k in 2*k**4/9 + 2*k**3/3 - 32*k**2/9 - 32*k/3 = 0?
-4, -3, 0, 4
Suppose 3*x**3/2 + 21*x**2 + 129*x/2 + 45 = 0. Calculate x.
-10, -3, -1
Factor -20*s**3 - 452*s**2 - 2056*s + 896.
-4*(s + 7)*(s + 16)*(5*s - 2)
Determine y, given that 6*y**4 + 116*y**3 + 546*y**2 + 676*y = 0.
-13, -13/3, -2, 0
Suppose 2*s**5/5 + 22*s**4/5 - 6*s**3 - 14*s**2 + 28*s/5 + 48/5 = 0. What is s?
-12, -1, 1, 2
Factor 2*i**3 + 60*i**2 + 214*i + 156.
2*(i + 1)*(i + 3)*(i + 26)
Solve 2*t**4/5 - 8*t**3/5 - 4*t**2/5 + 24*t/5 + 18/5 = 0 for t.
-1, 3
Suppose -2*m**4/11 - 6*m**3/11 + 20*m**2/11 = 0. What is m?
-5, 0, 2
Factor 3*p**2 + 159*p - 330.
3*(p - 2)*(p + 55)
Factor c**3/5 - 167*c**2/5 + 331*c/5 - 33.
(c - 165)*(c - 1)**2/5
Suppose -2*l**2 - 212*l - 5618 = 0. What is l?
-53
What is d in 8*d**4/5 - 2*d**3/5 - 24*d**2/5 - 2*d + 4/5 = 0?
-1, 1/4, 2
Factor -2*m**2/11 - 1724*m/11 - 371522/11.
-2*(m + 431)**2/11
What is b in 5*b**5/2 + 15*b**4/2 - 95*b**3 + 60*b**2 + 160*b = 0?
-8, -1, 0, 2, 4
Factor 2*v**4/9 - 44*v**3/9 + 40*v**2/3 - 116*v/9 + 38/9.
2*(v - 19)*(v - 1)**3/9
Factor r**2 - 115*r + 114.
(r - 114)*(r - 1)
Suppose -2*j**2/3 + 220*j/3 + 448/3 = 0. What is j?
-2, 112
Suppose 2*m**5/11 + 18*m**4/11 + 42*m**3/11 + 38*m**2/11 + 12*m/11 = 0. Calculate m.
-6, -1, 0
Factor -73*o**4/3 - 150*o**3 - 24*o**2.
-o**2*(o + 6)*(73*o + 12)/3
Suppose 3*d**5/7 + 24*d**4/7 + 30*d**3/7 - 12*d**2 - 33*d/7 + 60/7 = 0. Calculate d.
-5, -4, -1, 1
Let 3*c**4/8 - 27*c**2/4 + 12*c - 45/8 = 0. Calculate c.
-5, 1, 3
Factor m**2/4 + 1465*m/2 + 2146225/4.
(m + 1465)**2/4
Solve -c**3/3 - 200*c**2/3 - 8692*c/3 + 44944 = 0 for c.
-106, 12
What is f in -2*f**5/3 - 16*f**4/3 - 32*f**3/3 - 4*f**2/3 + 34*f/3 + 20/3 = 0?
-5, -2, -1, 1
Factor s**4 - 6*s**3 - 3*s**2 + 20*s - 12.
(s - 6)*(s - 1)**2*(s + 2)
Find y such that -y**4/2 - 6*y**3 + 13*y**2/2 = 0.
-13, 0, 1
Solve 5*b**5 + 60*b**4 + 280*b**3 + 640*b**2 + 720*b + 320 = 0.
-4, -2
Factor -2*p**2/7 + 36*p - 1134.
-2*(p - 63)**2/7
Solve -3*d**2 - 42*d - 135 = 0.
-9, -5
Factor -2*k**3/9 + 548*k**2/9 - 12328*k/3 - 8464.
-2*(k - 138)**2*(k + 2)/9
Factor -t**2/8 - 7*t/4 - 33/8.
-(t + 3)*(t + 11)/8
Factor -3*k**4/8 + 33*k**3/8 - 15*k**2 + 18*k.
-3*k*(k - 4)**2*(k - 3)/8
Factor -5*h**4 + 5*h**3 + 10*h**2.
-5*h**2*(h - 2)*(h + 1)
Suppose 3*w**2 + 330*w - 672 = 0. What is w?
-112, 2
Suppose l**4/6 + 361*l**3/6 + 14637*l**2/2 + 1855091*l/6 + 3370318/3 = 0. What is l?
-119, -4
Solve -2*g**4/9 - 58*g**3/3 - 1444*g**2/3 - 23360*g/9 - 6400/3 = 0 for g.
-40, -6, -1
What is d in 3*d**5 - 3*d**4 - 30*d**3 + 30*d**2 + 27*d - 27 = 0?
-3, -1, 1, 3
Suppose 2*d**3/3 + 8*d**2/3 + 10*d/3 + 4/3 = 0. What is d?
-2, -1
Solve 7*d**3 - 11*d**2 + 4*d = 0 for d.
0, 4/7, 1
Factor -164*t**2 - 40*t.
-4*t*(41*t + 10)
Let 3*r**4 + 6*r**3 - 3*r**2 - 6*r = 0. What is r?
-2, -1, 0, 1
What is t in -t**4/2 - 5*t**3/2 + 13*t**2/2 - 7*t/2 = 0?
-7, 0, 1
Solve -3*u**5 - 12*u**4 + 60*u**3 - 30*u**2 - 57*u + 42 = 0 for u.
-7, -1, 1, 2
What is t in -4*t**2 + 45488*t - 129322384 = 0?
5686
Factor -5*p**4 + 2670*p**3 - 13245*p**2 + 10580*p.
-5*p*(p - 529)*(p - 4)*(p - 1)
Factor 3*z**2 - 36*z + 96.
3*(z - 8)*(z - 4)
Find l such that 33*l**4/7 - 3261*l**3/7 + 107217*l**2/7 - 166617*l - 215622/7 = 0.
-2/11, 33
Determine q, given that -q**3 - 5*q**2 - 6*q = 0.
-3, -2, 0
Factor 5*m**3/3 - 118*m**2 - 267*m - 146/3.
(m - 73)*(m + 2)*(5*m + 1)/3
Factor -5*u**3 + 15*u - 10.
-5*(u - 1)**2*(u + 2)
Determine j, given that -74*j**2/11 - 226*j/11 - 12/11 = 0.
-3, -2/37
Let 4*j**4/5 - 56*j**3/5 + 48*j**2/5 + 56*j/5 - 52/5 = 0. What is j?
-1, 1, 13
Determine t so that -3*t**3 - 111*t**2 - 312*t - 204 = 0.
-34, -2, -1
Suppose 2*p**2/9 - 764*p/9 + 72962/9 = 0. Calculate p.
191
Let 33*m**3/4 - 51*m**2/2 + 75*m/4 - 3/2 = 0. What is m?
1/11, 1, 2
Find o, given that 2*o**3/5 + 106*o**2/5 - 8*o/5 - 424/5 = 0.
-53, -2, 2
Factor 2*r**3/5 - 18*r**2/5 + 22*r/5 + 42/5.
2*(r - 7)*(r - 3)*(r + 1)/5
Factor -5*z**3 + 570*z**2 - 1120*z.
-5*z*(z - 112)*(z - 2)
Factor 2*j**4/9 + 2*j**3/9 - 38*j**2/3 - 226*j/9 - 112/9.
2*(j - 8)*(j + 1)**2*(j + 7)/9
Factor -n**4/4 + 5*n**3/4 - 3*n**2/2 - n + 2.
-(n - 2)**3*(n + 1)/4
Factor -5*w**2 - 40*w + 100.
-5*(w - 2)*(w + 10)
Determine v, given that 4*v**3 - 28*v - 24 = 0.
-2, -1, 3
Let 2*j**2/5 + 4*j/5 = 0. What is j?
-2, 0
Factor -u**2 - 61*u.
-u*(u + 61)
Factor 2*f**5 - 8*f**4 + 8*f**3.
2*f**3*(f - 2)**2
Factor -20*c**3 + 720*c**2 - 2025*c + 1485.
-5*(c - 33)*(2*c - 3)**2
Factor -3*z**3/5 + 399*z**2/5 - 2613*z - 13467/5.
-3*(z - 67)**2*(z + 1)/5
Factor -4*c**4 + 372*c**3 - 368*c**2.
-4*c**2*(c - 92)*(c - 1)
Let -80*n**5 - 360*n**4 - 165*n**3 - 20*n**2 = 0. Calculate n.
-4, -1/4, 0
Solve -7*j**3/6 - 3*j**2 + 19*j/2 - 16/3 = 0.
-32/7, 1
Let -4*a**5/7 + 204*a**4/7 - 1628*a**3/7 + 5028*a**2/7 - 6624*a/7 + 432 = 0. Calculate a.
1, 2, 3, 42
Solve -2*p**5/13 - 34*p**4/13 - 188*p**3/13 - 336*p**2/13 = 0.
-7, -6, -4, 0
Find o, given that 6*o**2/7 + 444*o/7 - 1872/7 = 0.
-78, 4
Determine n, given that -2*n**3 - 4788*n**2 + 9582*n - 4792 = 0.
-2396, 1
Find v such that -5*v**3 - 145*v**2 + 480*v = 0.
-32, 0, 3
Determine u, given that 4*u**5/11 - 34*u**4/11 + 96*u**3/11 - 104*u**2/11 + 32*u/11 = 0.
0, 1/2, 2, 4
Suppose 5*t**5 - 90*t**4 + 80*t**3 + 90*t**2 - 85*t = 0. What is t?
-1, 0, 1, 17
Factor -4*c**3 + 20*c**2 - 16*c.
-4*c*(c - 4)*(c - 1)
Factor 44*z**3 - 256*z**2 + 348*z + 72.
4*(z - 3)**2*(11*z + 2)
Suppose -y**5/2 - 15*y**4 + 52*y**3 + 81*y**2 - 103*y/2 - 66 = 0. Calculate y.
-33, -1, 1, 4
Factor x**2/3 + 17*x/9 + 8/3.
(x + 3)*(3*x + 8)/9
Determine p so that 5*p**3/4 - 40*p**2 + 285*p/4 + 225/2 = 0.
-1, 3, 30
What is s in -s**2/6 - 61*s/6 - 10 = 0?
-60, -1
Factor d**2/3 + 40*d/3 + 77.
(d + 7)*(d + 33)/3
Let -u**3 - 320*u**2 - 25600*u = 0. Calculate u.
-160, 0
Let 2*g**5/5 + 24*g**4/5 - 84*g**3/5 + 88*g**2/5 - 6*g = 0. What is g?
-15, 0, 1
Let a**2/3 - 125*a/3 = 0. Calculate a.
0, 125
Find q, given that 4*q**3/3 + 7*q**2/3 - 2*q/3 = 0.
-2, 0, 1/4
What is h in -3*h**2/5 - 84*h/5 + 87/5 = 0?
-29, 1
Solve -2*m**5/5 + 26*m**4/5 + 8*m**3 - 32*m**2 - 128*m/5 + 224/5 = 0.
-2, 1, 2, 14
Factor 2*q**4/3 + 16*q**3/3 + 12*q**2 - 18.
2*(q - 1)*(q + 3)**3/3
Let -p**4 - 3*p**3 + 4*p = 0. What is p?
-2, 0, 1
Find r such that 2*r**2/17 - 308*r + 201586 = 0.
1309
Find s, given that 2*s**3/15 - 52*s**2/3 - 176*s/5 = 0.
-2, 0, 132
Factor -3*j**3 + 1524*j**2 - 195063*j + 384054.
-3*(j - 253)**2*(j - 2)
Find o such that 2*o**3/3 + 38*o**2 = 0.
-57, 0
Factor -h**4/2 - 3*h**3 - 11*h**2/2 - 3*h.
-h*(h + 1)*(h + 2)*(h + 3)/2
Let -p**3 + 29*p**2 - 28*p = 0. Calculate p.
0, 1, 28
Solve -24*i**5 + 308*i**4 - 456*i**3 - 340*i**2 + 336*i + 176 = 0.
-2/3, -1/2, 1, 2, 11
What is d in -2*d**3/9 - 4*d**2/3 - 2*d - 8/9 = 0?
-4, -1
Find a, given that -4*a**5 - 2*a**4 + 22*a**3 - 22*a**2 + 6*a = 0.
-3, 0, 1/2, 1
Suppose -4*j**3 + 84*j - 80 = 0. What is j?
-5, 1, 4
Find i, given that -4*i**4 + 308*i**3 - 4256*i**2 + 10672*i - 6720 = 0.
1, 2, 14, 60
Suppose -3*r**2 + 3282*r - 897627 = 0. What is r?
547
Determine z, given that 3*z**4 - 39*z**3 + 165*z**2 - 225*z = 0.
0, 3, 5
Factor -2*a**5/17 - 26*a**4/17 + 28*a**3/17.
-2*a**3*(a - 1)*(a + 14)/17
Solve 3*m**4 - 15*m**3 - 378*m**2 - 324*m + 4536 = 0.
-6, 3, 14
Solve -4*p**2 - 72*p = 0 for p.
-18, 0
What is d in 5*d**3 - 6755*d**2 + 2278120*d + 2284880 = 0?
-1, 676
Factor -w**3 - w**2.
-w**2*(w + 1)
What is g in 3*g**3/5 + 36*g**2/5 + 63*g/5 + 6 = 0?
-10, -1
Suppose 2*i**5/7 - 30*i**4/7 + 30*i**3/7 + 310*i**2/7 - 312*i/7 = 0. What is i?
-3, 0, 1, 4, 13
Factor -5*n**4 - 1485*n**3 - 147015*n**2 - 4851495*n.
-5*n*(n + 99)**3
Suppose g**5/3 + 19*g**4/3 + 115*g**3/3 + 241*g**2/3 + 208*g/3 + 64/3 = 0. What is g?
-8, -1
Suppose z**3 - 54*z**2 + 297*z - 432 = 0. Calculate z.
3, 48
Solve 4*d**5 + 40*d*