 2
Factor 2*f**4/23 + 4*f**3/23 - 2*f**2 - 48*f/23 + 288/23.
2*(f - 3)**2*(f + 4)**2/23
Factor -3*z**3 - 30*z**2 - 9*z + 162.
-3*(z - 2)*(z + 3)*(z + 9)
Factor -5*r**2 - 3830*r - 733445.
-5*(r + 383)**2
Determine m, given that 2*m**2/9 - 418*m/9 = 0.
0, 209
Factor -v**2 - 5*v - 4.
-(v + 1)*(v + 4)
Factor -2*w**3/3 + 138*w**2 - 1330*w + 9850/3.
-2*(w - 197)*(w - 5)**2/3
Determine m, given that m**4/3 - 14*m**3/3 - 55*m**2/3 + 68*m/3 = 0.
-4, 0, 1, 17
Factor y**5/7 + 16*y**4/7 + 16*y**3/7 - 640*y**2/7 - 1024*y/7 + 8192/7.
(y - 4)**2*(y + 8)**3/7
Factor -3*x**2 - 36*x + 399.
-3*(x - 7)*(x + 19)
Factor -3*r**3 - 23*r**2 - 28*r + 12.
-(r + 2)*(r + 6)*(3*r - 1)
Suppose -4*g**2/5 - 264*g/5 + 268/5 = 0. Calculate g.
-67, 1
Determine w, given that 5*w**2 + 50*w - 375 = 0.
-15, 5
Factor -5*f**3 + 25*f**2 - 10*f - 40.
-5*(f - 4)*(f - 2)*(f + 1)
Solve -g**4/2 - 629*g**3/6 + 845*g**2/6 + 209*g/6 - 211/3 = 0 for g.
-211, -2/3, 1
Factor -3*c**3 - 87*c**2 + 12*c + 348.
-3*(c - 2)*(c + 2)*(c + 29)
Suppose 8*s**3/7 + 60*s**2/7 + 108*s/7 + 40/7 = 0. What is s?
-5, -2, -1/2
Suppose -4*u**2/3 + 3256*u/3 - 662596/3 = 0. What is u?
407
Let 7*r**4/2 + 5*r**3 = 0. Calculate r.
-10/7, 0
Factor 4*g**2 + 1224*g + 93636.
4*(g + 153)**2
Factor -3*u**2/4 + 69*u/4 + 75/2.
-3*(u - 25)*(u + 2)/4
Factor 3*t**5 + 141*t**4 + 534*t**3 + 786*t**2 + 519*t + 129.
3*(t + 1)**4*(t + 43)
Factor r**2/5 + 167*r/5.
r*(r + 167)/5
Factor -r**4 + 2*r**2 - 1.
-(r - 1)**2*(r + 1)**2
Factor -v**2 + 24*v - 23.
-(v - 23)*(v - 1)
Determine j, given that -2*j**3/11 + 204*j**2/11 - 5400*j/11 + 10000/11 = 0.
2, 50
Factor 3*l**5 + 12*l**4 - 45*l**3 - 54*l**2.
3*l**2*(l - 3)*(l + 1)*(l + 6)
Find w such that 8*w**4/3 + 50*w**3/3 - 452*w**2 - 1554*w - 360 = 0.
-15, -3, -1/4, 12
Let 65*h**4 - 250*h**3 + 220*h**2 + 40*h = 0. Calculate h.
-2/13, 0, 2
Factor -r**3/5 + 3*r**2/5.
-r**2*(r - 3)/5
Factor -33*o**4 + 312*o**3 - 645*o**2 - 450*o.
-3*o*(o - 5)**2*(11*o + 6)
Factor -2*s**2/5 - 14*s/5 - 24/5.
-2*(s + 3)*(s + 4)/5
Factor j**4 - 8*j**3 + 7*j**2.
j**2*(j - 7)*(j - 1)
Let -2*q**3 + 16*q**2 - 24*q = 0. Calculate q.
0, 2, 6
Factor i**3 - 309*i**2.
i**2*(i - 309)
Let 4*i**3/3 - 8540*i**2 + 18232900*i - 38927241500/3 = 0. Calculate i.
2135
Factor -3*s**5/2 - 2361*s**4/2 - 465705*s**3/2 - 463347*s**2/2.
-3*s**2*(s + 1)*(s + 393)**2/2
Find u such that 5*u**4 + 945*u**3 - 950*u**2 = 0.
-190, 0, 1
Factor 5*c**4/6 + 20*c**3/3 + 115*c**2/6 + 70*c/3 + 10.
5*(c + 1)*(c + 2)**2*(c + 3)/6
Factor -3*y**3 + 21*y - 18.
-3*(y - 2)*(y - 1)*(y + 3)
Factor 36*m**2 - 68*m + 32.
4*(m - 1)*(9*m - 8)
Suppose 2*v**4/5 + 2*v**3/5 - 14*v**2/5 - 26*v/5 - 12/5 = 0. What is v?
-2, -1, 3
Determine q so that 81*q**5 + 756*q**4 + 2241*q**3 + 1842*q**2 - 1012*q - 968 = 0.
-11/3, -2, -2/3, 2/3
Let -245*r**5 - 5740*r**4 - 25325*r**3 + 98710*r**2 - 49660*r + 6760 = 0. What is r?
-13, 2/7, 2
Factor 4*v**2 + 528*v + 17424.
4*(v + 66)**2
Let 4*u**4/3 - 19*u**3/3 + 11*u**2/3 + 4*u/3 = 0. What is u?
-1/4, 0, 1, 4
Factor -q**2/7 + 180*q/7 - 179/7.
-(q - 179)*(q - 1)/7
Factor -t**2/3 - 26*t/3 - 25/3.
-(t + 1)*(t + 25)/3
Factor -512*w**2/3 + 2557*w/3 + 5.
-(w - 5)*(512*w + 3)/3
Factor 21*j**4/4 - 15*j**3/4 - 3*j**2/2.
3*j**2*(j - 1)*(7*j + 2)/4
Solve -5*u**3 - 45*u**2 + 405*u - 675 = 0 for u.
-15, 3
Determine w so that -2*w**2/5 + 6*w/5 + 8/5 = 0.
-1, 4
Let 10*u**4/7 - 2494*u**3/7 - 1504*u**2/7 + 1000*u/7 = 0. Calculate u.
-1, 0, 2/5, 250
Factor -3*x**3/8 - 141*x**2/8.
-3*x**2*(x + 47)/8
Factor -u**2/4 + 805*u/2 - 648025/4.
-(u - 805)**2/4
Determine y so that -2*y**3/7 - 4*y**2/7 + 22*y/7 + 24/7 = 0.
-4, -1, 3
Let u**4 - 14*u**3 + 33*u**2 + 4*u - 44 = 0. Calculate u.
-1, 2, 11
Factor 2*q**2 - 426*q + 1260.
2*(q - 210)*(q - 3)
Solve 2*j**3/13 + 110*j**2/13 + 950*j/13 + 2250/13 = 0.
-45, -5
Find v, given that -25*v**3 + 1790*v**2 - 31680*v - 12960 = 0.
-2/5, 36
Factor 5*o**2 - 670*o + 22445.
5*(o - 67)**2
Suppose -t**4/6 + 7*t**2/6 + t = 0. Calculate t.
-2, -1, 0, 3
Solve -3*o**2/5 - 381*o/5 - 378/5 = 0 for o.
-126, -1
Solve -4*n**3 + 2112*n**2 + 2116*n = 0 for n.
-1, 0, 529
Suppose -294*s**5 + 1904*s**4 - 2378*s**3 + 1072*s**2 - 160*s = 0. What is s?
0, 1/3, 4/7, 5
Factor -2*s**3/3 + 34*s**2/3 - 80*s/3 - 200.
-2*(s - 10)**2*(s + 3)/3
Factor -14*j**3/9 + 110*j**2/9 - 152*j/9 - 8/3.
-2*(j - 6)*(j - 2)*(7*j + 1)/9
Determine s so that 3*s**5/5 + 21*s**4/5 + 6*s**3/5 - 84*s**2/5 - 72*s/5 = 0.
-6, -2, -1, 0, 2
Determine q, given that -q**4/4 + 9*q**3/2 - 27*q**2 + 119*q/2 - 147/4 = 0.
1, 3, 7
Let -3*j**3/2 - 351*j**2/2 + 3*j/2 + 351/2 = 0. What is j?
-117, -1, 1
Solve 5*l**5/4 - 5*l**4 - 25*l**3/4 + 25*l**2 + 5*l - 20 = 0 for l.
-2, -1, 1, 2, 4
Factor -3*c**2 + 3.
-3*(c - 1)*(c + 1)
What is g in 9*g**5 + 303*g**4 + 1713*g**3 - 16011*g**2 - 14934*g + 43320 = 0?
-19, -2, 4/3, 5
Determine h, given that -4*h**2 + 176*h - 492 = 0.
3, 41
Solve 2*g**5 - 130*g**4 - 266*g**3 - 134*g**2 = 0.
-1, 0, 67
Determine z so that -3*z**4/5 + 3*z**3/5 + 3*z**2/5 - 3*z/5 = 0.
-1, 0, 1
Factor 2*t**3/17 - 118*t**2/17 + 528*t/17 + 648/17.
2*(t - 54)*(t - 6)*(t + 1)/17
What is m in -2*m**3 + 46*m**2/5 + 4*m = 0?
-2/5, 0, 5
Factor -2*i**2/13 - 36*i/13 - 10.
-2*(i + 5)*(i + 13)/13
Suppose q**5 - 502*q**4 - 3035*q**3 - 6592*q**2 - 6092*q - 2032 = 0. What is q?
-2, -1, 508
What is w in -14*w**3/5 - 6*w**2/5 + 14*w/5 + 6/5 = 0?
-1, -3/7, 1
Factor -z**4 + 8*z**3 - 17*z**2 + 10*z.
-z*(z - 5)*(z - 2)*(z - 1)
Solve -2*i**2 + 184*i = 0.
0, 92
Factor -b**3 + 2*b**2 + 8*b.
-b*(b - 4)*(b + 2)
Suppose 3*o**3/2 - 39*o**2/2 - 231*o/2 + 3267/2 = 0. Calculate o.
-9, 11
Solve 3*k**5 + 87*k**4 + 957*k**3 + 4977*k**2 + 12312*k + 11664 = 0.
-9, -4, -3
What is p in -p**3/9 - 4*p**2 - 215*p/9 + 28 = 0?
-28, -9, 1
Factor -2*s**5 + 38*s**4 - 70*s**3 + 34*s**2.
-2*s**2*(s - 17)*(s - 1)**2
Factor 5*y**2 - 45.
5*(y - 3)*(y + 3)
Suppose 2*g**4/5 - 14*g**3/5 - 8*g**2/5 + 56*g/5 = 0. What is g?
-2, 0, 2, 7
What is y in -5*y**4/4 - 7*y**3/2 - 3*y**2 - y/2 + 1/4 = 0?
-1, 1/5
Solve -d**3/4 - 15*d**2/4 + 37*d/4 + 51/4 = 0 for d.
-17, -1, 3
Factor -3*v**5/8 - 3*v**4/4 + 9*v**3/8.
-3*v**3*(v - 1)*(v + 3)/8
Find d such that 348*d**2 - 712*d + 32 = 0.
4/87, 2
Let -2*r**5/7 + 18*r**4/7 - 2*r**3 - 18*r**2/7 + 16*r/7 = 0. What is r?
-1, 0, 1, 8
Factor -g**2/2 + 200*g - 20000.
-(g - 200)**2/2
Solve 14*c**4/5 + 456*c**3/5 - 342*c**2 + 648*c/5 = 0 for c.
-36, 0, 3/7, 3
Factor -5*i**4 - 230*i**3 + 2080*i**2 - 4320*i.
-5*i*(i - 4)**2*(i + 54)
Factor 2*f**2/9 - 52*f/9 + 46/3.
2*(f - 23)*(f - 3)/9
Determine k, given that -2*k**4 - 122*k**3 + 378*k**2 - 382*k + 128 = 0.
-64, 1
Let s**4/6 - s**3/3 = 0. Calculate s.
0, 2
Solve -5*z**3 - 215*z**2 + 925*z - 705 = 0 for z.
-47, 1, 3
Factor -n**4/3 - 13*n**3/3 - 11*n**2/3 + 13*n/3 + 4.
-(n - 1)*(n + 1)**2*(n + 12)/3
Solve 3*d**4 + 54*d**3 - 345*d**2 - 6300*d + 13500 = 0 for d.
-15, 2, 10
Factor -d**5/4 + 12*d**4 + 99*d**3/4 + 25*d**2/2.
-d**2*(d - 50)*(d + 1)**2/4
Solve u**4/2 + 35*u**3/2 - 417*u**2/2 - 935*u/2 - 242 = 0 for u.
-44, -1, 11
Solve -1342*z**3 - 2688*z**2 - 1350*z - 4 = 0.
-1, -2/671
Let -4*n**3/7 - 22*n**2/7 - 26*n/7 - 8/7 = 0. Calculate n.
-4, -1, -1/2
Find p, given that 4*p**2 - 96*p + 476 = 0.
7, 17
Solve 2*q**5/15 + 16*q**4/15 - 4*q**3/15 - 32*q**2/15 + 2*q/15 + 16/15 = 0 for q.
-8, -1, 1
Solve -4*c**2/3 - 92*c/3 = 0.
-23, 0
Solve 3*c**3/5 - 972*c**2/5 + 104976*c/5 - 3779136/5 = 0.
108
Factor -2*j**5/5 - 2*j**4/5 + 4*j**3/5 + 4*j**2/5 - 2*j/5 - 2/5.
-2*(j - 1)**2*(j + 1)**3/5
Factor -r**5/4 - 3*r**4/4 + 7*r**3/4 + 7*r**2/4 - 9*r/2 + 2.
-(r - 1)**3*(r + 2)*(r + 4)/4
Find d, given that 2*d**5 + 14*d**4 + 22*d**3 - 14*d**2 - 24*d = 0.
-4, -3, -1, 0, 1
Factor 3*x**3/7 - 171*x**2 + 22743*x - 1008273.
3*(x - 133)**3/7
Solve -5*r**5 + 90*r**4 - 440*r**3 + 630*r**2 - 275*r = 0.
0, 1, 5, 11
Determine p so that p**4/5 - 2*p**3 + p**2/5 + 24*p = 0.
-3, 0, 5, 8
Factor -27*j**3 + 7308*j**2 + 9780*j + 3264.
-3*(j - 272)*(3*j + 2)**2
Let i**4/5 - 9*i**3/5 + 3*i**2 - 7*i/5 = 0. What is i?
0, 1, 7
Suppose 3*l**3 - 3*l**2 - 12*l + 12 = 0. Calculate l.
-2, 1, 2
Factor -9*p**3/2 + 15225*p**2/2 - 3218184*p - 1073574.
-3*(p - 846)**2*(3*p + 1)/2
Let p**5/12 - 43*p**4/4 - 137*p**3/12 + 303*p**2/4 + 34*p/3 - 65 = 0. What is p?
-3, -1, 1, 2, 130
Determine y so that 3*y**5 + 132*y**4 + 1449*