.
-2/27, 1/4
Factor 299*b**3/2 + 1197*b**2 + 2400*b + 16.
(b + 4)**2*(299*b + 2)/2
Solve -3*a**5/4 + 36*a**4 - 1419*a**3/4 - 3669*a**2/2 - 2457*a - 1014 = 0.
-2, -1, 26
Suppose x**3/3 - 4*x/3 = 0. Calculate x.
-2, 0, 2
Let 3*h**2 + 6*h = 0. Calculate h.
-2, 0
Find c such that 3*c**4 + 36*c**3 + 105*c**2 - 36*c - 108 = 0.
-6, -1, 1
Factor -5*x**3 - 870*x**2 + 4455*x - 3580.
-5*(x - 4)*(x - 1)*(x + 179)
Let 2*o**3/7 - 27*o**2/7 + 37*o/7 - 12/7 = 0. What is o?
1/2, 1, 12
Determine d so that 18*d**3 - 1226*d**2 + 20944*d - 2312 = 0.
1/9, 34
Suppose 4*i**3 + 132*i**2 - 144*i - 272 = 0. What is i?
-34, -1, 2
What is w in -10*w**5/3 + 3326*w**4/3 + 3804*w**3 + 4072*w**2/3 - 13424*w/3 - 1792 = 0?
-2, -2/5, 1, 336
Find c such that 4*c**4 + 57*c**3 + 142*c**2 - 480*c - 128 = 0.
-8, -1/4, 2
Find f, given that f**4/4 + 9*f**3/4 + 13*f**2/2 + 6*f = 0.
-4, -3, -2, 0
Factor 3*y**3/5 + 27*y**2/5 - 6*y.
3*y*(y - 1)*(y + 10)/5
Factor -4*s**2 + 184*s + 3360.
-4*(s - 60)*(s + 14)
Factor q**5/2 - 3*q**4/2 - q**3 + 6*q**2 - 4*q.
q*(q - 2)**2*(q - 1)*(q + 2)/2
Factor -3*m**3 + 9*m**2 - 12.
-3*(m - 2)**2*(m + 1)
Find w, given that -4*w**3 + 12*w + 8 = 0.
-1, 2
Factor 309*p**2 - 315*p + 6.
3*(p - 1)*(103*p - 2)
Factor p**2/3 + 17*p/3 + 16/3.
(p + 1)*(p + 16)/3
Suppose i**2/7 - 268*i/7 + 17956/7 = 0. What is i?
134
Factor -2*u**2/11 + 10108*u/11 - 12771458/11.
-2*(u - 2527)**2/11
Factor 3*y**5/7 + 354*y**4/7 + 1044*y**3/7 + 1038*y**2/7 + 345*y/7.
3*y*(y + 1)**3*(y + 115)/7
Factor -3*j**3/4 - 261*j**2/4 - 6669*j/4 - 41067/4.
-3*(j + 9)*(j + 39)**2/4
Factor -34*j**2/5 - 96*j - 56/5.
-2*(j + 14)*(17*j + 2)/5
Factor 2*t**4 - 278*t**3 - 1770*t**2 + 4366*t - 2320.
2*(t - 145)*(t - 1)**2*(t + 8)
Factor 14*q**3 + 78*q**2 + 76*q - 48.
2*(q + 2)*(q + 4)*(7*q - 3)
Factor -3*x**3 - 696*x**2 - 40368*x.
-3*x*(x + 116)**2
Let 5*l**4/3 + 53*l**3/3 + 46*l**2 + 76*l/3 - 56/3 = 0. Calculate l.
-7, -2, 2/5
Let q**4/4 + 37*q**3 + 293*q**2/4 + 73*q/2 = 0. Calculate q.
-146, -1, 0
What is w in 2*w**2/7 + 2400*w/7 + 720000/7 = 0?
-600
Suppose -2*i**4/7 + 124*i**3/7 + 240*i**2 + 6976*i/7 + 9472/7 = 0. Calculate i.
-4, 74
Factor -5*y**3 - 385*y**2 - 7955*y - 20535.
-5*(y + 3)*(y + 37)**2
Factor 27*a**3 + 30*a**2 + a - 2.
(a + 1)*(3*a + 1)*(9*a - 2)
Determine w, given that -w**2/4 - 6*w + 25/4 = 0.
-25, 1
Factor 14*q**4 + 37*q**3 + 33*q**2 + 11*q + 1.
(q + 1)**2*(2*q + 1)*(7*q + 1)
Factor 4*i**3/3 - 104*i**2/3 - 16*i/3 + 416/3.
4*(i - 26)*(i - 2)*(i + 2)/3
Factor 7*k**4 - 76*k**3 + 294*k**2 - 468*k + 243.
(k - 3)**2*(k - 1)*(7*k - 27)
Factor o**4/2 - 52*o**3 + 394*o**2 - 968*o + 768.
(o - 96)*(o - 4)*(o - 2)**2/2
Suppose -2*u**2/17 + 18*u/17 + 16 = 0. What is u?
-8, 17
Factor b**2/5 + 46*b/5 - 40.
(b - 4)*(b + 50)/5
Factor -g**3/6 - 29*g**2/2 - 361*g/3 - 260.
-(g + 4)*(g + 5)*(g + 78)/6
Determine p so that -4*p**4/5 - 832*p**3/5 - 2472*p**2/5 - 2464*p/5 - 164 = 0.
-205, -1
What is b in -b**3/4 + 7*b/4 + 3/2 = 0?
-2, -1, 3
Find o, given that 6*o**2/7 - 90*o/7 + 324/7 = 0.
6, 9
Let -4*n**4/3 - 112*n**3/3 - 848*n**2/3 + 640*n/3 + 6400 = 0. What is n?
-12, -10, 4
Determine l, given that -2*l**5/3 - 2*l**4/3 + 2*l**3/3 + 2*l**2/3 = 0.
-1, 0, 1
Solve 4*n**2 - 376*n + 1780 = 0 for n.
5, 89
Solve -2*m**3/9 + 16*m**2/9 - 8*m/9 - 32/3 = 0 for m.
-2, 4, 6
Factor -c**4 + 41*c**3 - 427*c**2 + 1323*c.
-c*(c - 27)*(c - 7)**2
Suppose 3*d**2 - 36*d - 39 = 0. What is d?
-1, 13
Factor -5*y**2 + 195*y - 370.
-5*(y - 37)*(y - 2)
Factor 3*o**3 + 5*o**2 + 2*o.
o*(o + 1)*(3*o + 2)
Suppose -4*s**5 + 128*s**4 + 136*s**3 - 128*s**2 - 132*s = 0. Calculate s.
-1, 0, 1, 33
Solve 2*u**3/9 - 130*u**2/3 + 8450*u/3 - 549250/9 = 0.
65
Let -11*p**5 - 28*p**4 - 23*p**3 - 6*p**2 = 0. What is p?
-1, -6/11, 0
Factor -g**4/4 + 19*g**3/2 + 88*g**2 + 184*g.
-g*(g - 46)*(g + 4)**2/4
Factor -x**4 + 112*x**3 - 3022*x**2 - 6384*x - 3249.
-(x - 57)**2*(x + 1)**2
Solve o**4/2 + 15*o**3/2 - 35*o**2/2 - 15*o/2 + 17 = 0 for o.
-17, -1, 1, 2
Factor -2*r**4 - 40*r**3 + 150*r**2 + 4500*r.
-2*r*(r - 10)*(r + 15)**2
Suppose -2*i**4/11 + 2*i**3 + 4*i**2/11 - 312*i/11 - 432/11 = 0. What is i?
-2, 6, 9
Factor -2*z**2/5 + 64*z - 2142/5.
-2*(z - 153)*(z - 7)/5
Suppose -4*m**4 - 220*m**3 - 3124*m**2 - 2484*m + 5832 = 0. Calculate m.
-27, -2, 1
Determine t, given that -2*t**2/7 - 134*t/7 - 732/7 = 0.
-61, -6
Factor -3*x**5 + 945*x**4 - 75825*x**3 + 221835*x**2 - 219960*x + 73008.
-3*(x - 156)**2*(x - 1)**3
Determine k so that 3*k**4/2 + 57*k**3/8 + 9*k**2/8 - 51*k/4 + 3 = 0.
-4, -2, 1/4, 1
Find w, given that -w**2/2 - w + 3/2 = 0.
-3, 1
Factor 15*h**2 - 410*h - 280.
5*(h - 28)*(3*h + 2)
Suppose 4*r**4 - 96*r**3 + 252*r**2 + 16*r - 336 = 0. What is r?
-1, 2, 21
Suppose -2*r**5/23 + 8*r**3/23 - 4*r**2/23 - 6*r/23 + 4/23 = 0. What is r?
-2, -1, 1
Let -u**2/5 - 18*u/5 + 8 = 0. What is u?
-20, 2
Factor -5*z**3 - 105*z**2 - 540*z.
-5*z*(z + 9)*(z + 12)
Suppose 36*r**3 + 226*r**2 + 56*r - 24 = 0. Calculate r.
-6, -1/2, 2/9
Let 5*y**3 + 1025*y**2 = 0. Calculate y.
-205, 0
Suppose 4*b**4 + 221*b**3 + 687*b**2 + 574*b + 104 = 0. Calculate b.
-52, -2, -1, -1/4
Factor -4*h**2 + 856*h - 1696.
-4*(h - 212)*(h - 2)
Factor -a**3/2 - 4*a**2 - 8*a.
-a*(a + 4)**2/2
Find z, given that -z**2/3 + 338*z/3 - 28561/3 = 0.
169
Let 6*z**3/5 + 9*z**2/5 - 3*z - 18/5 = 0. What is z?
-2, -1, 3/2
Solve -5*p**5 - 1070*p**4 + 1075*p**3 = 0 for p.
-215, 0, 1
Determine s so that -3*s**2/8 + 27*s/8 + 15/4 = 0.
-1, 10
Factor -c**3 - 18*c**2 + 39*c - 20.
-(c - 1)**2*(c + 20)
What is v in 2*v**5 + 16*v**4 + 26*v**3 - 60*v**2 - 144*v = 0?
-4, -3, 0, 2
What is c in -2*c**5/13 - 12*c**4/13 + 4*c**3/13 + 24*c**2/13 - 2*c/13 - 12/13 = 0?
-6, -1, 1
Determine s, given that 4*s**2/5 + 76*s/5 - 16 = 0.
-20, 1
Find u, given that -50*u**5/11 - 760*u**4/11 - 3858*u**3/11 - 6532*u**2/11 + 1792*u/11 + 9408/11 = 0.
-28/5, -3, -2, 1
Factor -10*c**2/3 - 3455*c/3 + 1730/3.
-5*(c + 346)*(2*c - 1)/3
Factor 2*n**4 - 2*n**3 - 26*n**2 + 50*n - 24.
2*(n - 3)*(n - 1)**2*(n + 4)
Suppose 5*i**3 - 90*i**2 + 85*i = 0. What is i?
0, 1, 17
Factor r**3/6 + 35*r**2 + 3675*r/2.
r*(r + 105)**2/6
Find t, given that 2*t**2 - 4456*t + 8904 = 0.
2, 2226
Factor -i**2/6 - i + 20/3.
-(i - 4)*(i + 10)/6
Solve u**4 - 4*u**3 - 6*u**2 + 4*u + 5 = 0 for u.
-1, 1, 5
Solve -5*w**5/4 - 10*w**4 + 155*w**3/4 - 55*w**2/2 = 0 for w.
-11, 0, 1, 2
Determine x so that 45*x**5 + 42*x**4 - 279*x**3 + 12*x**2 + 36*x = 0.
-3, -1/3, 0, 2/5, 2
Factor 9*p**4/5 - 479*p**3/5 + 574*p**2/5 - 104*p/5.
p*(p - 52)*(p - 1)*(9*p - 2)/5
Find c, given that c**5/8 - 9*c**4/8 + 21*c**3/8 - 19*c**2/8 + 3*c/4 = 0.
0, 1, 6
Factor -2*p**5 + 30*p**4 - 52*p**3 - 4*p**2 + 54*p - 26.
-2*(p - 13)*(p - 1)**3*(p + 1)
Factor 5000*o**5 + 33500*o**4 + 86150*o**3 + 106245*o**2 + 63180*o + 14580.
5*(o + 2)**2*(10*o + 9)**3
Factor 4*r**3 + 72*r**2 + 240*r + 224.
4*(r + 2)**2*(r + 14)
Factor 2*o**2/5 + 56*o/5 - 58/5.
2*(o - 1)*(o + 29)/5
Factor -4*v**3/7 - 36*v**2 - 960*v/7 - 944/7.
-4*(v + 2)**2*(v + 59)/7
Factor -17*c**3 - 7*c**2 + 17*c + 7.
-(c - 1)*(c + 1)*(17*c + 7)
Factor 3*u**2 - 9*u - 264.
3*(u - 11)*(u + 8)
Find q, given that -9*q**4/2 - 195*q**3/2 - 1023*q**2/2 + 363*q/2 = 0.
-11, 0, 1/3
Factor 5*k**2 - 450*k + 10125.
5*(k - 45)**2
Solve 3*a**4/4 - 3*a**3/2 - 36*a**2 - 189*a/2 - 243/4 = 0.
-3, -1, 9
Let 2*y**4 + 136*y**3 + 3468*y**2 + 39304*y + 167042 = 0. What is y?
-17
Solve 3*f**5 - 2*f**4/3 - 9*f**3 + 8*f**2 - 4*f/3 = 0 for f.
-2, 0, 2/9, 1
Find g, given that 24*g**5/5 - 26*g**4 + 146*g**3/15 + 22*g**2/15 - 2*g/3 = 0.
-1/4, 0, 1/3, 5
Solve -4*f**3 + 244*f**2 + 516*f - 756 = 0 for f.
-3, 1, 63
Factor -h**4/2 - 179*h**3 - 32749*h**2/2 - 63366*h - 62658.
-(h + 2)**2*(h + 177)**2/2
Factor -882*c**2 - 10752*c - 32768.
-2*(21*c + 128)**2
What is o in o**3/4 + 65*o**2/4 - 133*o/4 + 67/4 = 0?
-67, 1
Factor -8*q**3/5 - 21*q**2/5 - 13*q/5.
-q*(q + 1)*(8*q + 13)/5
Factor -2*w**3 - 30*w**2 + 74*w + 102.
-2*(w - 3)*(w + 1)*(w + 17)
Suppose l**3/7 - 9*l**2/7 + 27*l/7 - 27/7 = 0. Calculate l.
3
Find m such that -3*m**5 - 36*m**4 + 573*m**3 - 1854*m**2 + 1320*m = 0.
-22, 0, 1, 4, 5
What is y in -y**4/4 + y**3/4 + y**2/4 - y/4 = 0?
-1, 0, 1
Solve -2*u**2 + 2348*u - 689138 = 0 for u.
587
Find n such that 4*n**2/9 + 20*n + 224 = 0.
-24, -21
Factor 3*f**5 + 255*f**4 + 5790*f**3 + 15870*f**2 