525*b**2/4 - 58529*b/4 + 34347/2.
(b - 107)**2*(b - 3)*(b - 2)/4
Factor 3*f**3/7 - 2883*f**2/7 + 2880*f/7.
3*f*(f - 960)*(f - 1)/7
Suppose -4*i**5 - 116*i**4 - 412*i**3 - 284*i**2 + 416*i + 400 = 0. Calculate i.
-25, -2, -1, 1
Factor 3*x**3 + 111*x**2 + 480*x.
3*x*(x + 5)*(x + 32)
Find u such that -u**2 - 1750*u - 1749 = 0.
-1749, -1
Solve 2*y**5 - 36*y**4 + 110*y**3 + 420*y**2 - 112*y - 384 = 0 for y.
-2, -1, 1, 8, 12
Factor 2*k**4 + 56*k**3 + 170*k**2 - 3468*k.
2*k*(k - 6)*(k + 17)**2
What is l in 5*l**4 - 560*l**3 + 13305*l**2 + 28310*l + 14440 = 0?
-1, 38, 76
Factor 3*r**4/4 - 45*r**3/4 + 21*r**2/2.
3*r**2*(r - 14)*(r - 1)/4
Let -y**4 - 11*y**3 - 42*y**2 - 68*y - 40 = 0. Calculate y.
-5, -2
Solve -2*r**2/5 - 36*r - 720 = 0.
-60, -30
Solve 2*m**4/7 - 664*m**3/7 + 1322*m**2/7 - 660*m/7 = 0 for m.
0, 1, 330
Factor -m**3/3 - 3*m**2 + 25*m/3 + 11.
-(m - 3)*(m + 1)*(m + 11)/3
Determine q, given that 18*q**3/7 + 5718*q**2/7 - 7648*q/7 + 2552/7 = 0.
-319, 2/3
Factor -4*n**3/3 - 23*n**2/6 - 13*n/6 + 1/3.
-(n + 1)*(n + 2)*(8*n - 1)/6
Factor 21*w**3/5 + 699*w**2/5 - 1272*w/5 - 84.
3*(w - 2)*(w + 35)*(7*w + 2)/5
Let 4*q**3 + 20*q**2 - 3000*q = 0. Calculate q.
-30, 0, 25
Factor -108*c**3 + 532*c**2 + 2632*c + 192.
-4*(c - 8)*(c + 3)*(27*c + 2)
What is t in t**4/4 + 12*t**3 - 49*t**2/4 = 0?
-49, 0, 1
Factor -2*k**4/5 + 6*k**3/5 + 98*k**2/5 + 18*k.
-2*k*(k - 9)*(k + 1)*(k + 5)/5
Find i such that 56*i**3/3 - 450*i**2 + 142*i/3 + 16 = 0.
-1/7, 1/4, 24
Solve 48*c**4 - 218*c**3 + 362*c**2 - 262*c + 70 = 0.
7/8, 1, 5/3
Find q, given that -4*q**5/5 - 21*q**4/5 + 47*q**3/5 - 3*q**2 - 7*q/5 = 0.
-7, -1/4, 0, 1
Let -16*t**5/3 - 104*t**4/3 - 209*t**3/3 - 58*t**2/3 + 75*t + 54 = 0. Calculate t.
-9/4, -2, -1, 1
Suppose -3*y**5 + 27*y**4 - 69*y**3 + 21*y**2 + 72*y - 48 = 0. Calculate y.
-1, 1, 4
Factor -2*g**4 - 8*g**3 - 4*g**2 + 8*g + 6.
-2*(g - 1)*(g + 1)**2*(g + 3)
Determine r, given that 2*r**4/9 + 58*r**3/9 + 208*r**2/3 + 2944*r/9 + 5120/9 = 0.
-8, -5
Factor 3*w**3 + 54*w**2 + 45*w - 102.
3*(w - 1)*(w + 2)*(w + 17)
Determine a, given that a**4/2 + 203*a**3/2 - 309*a**2 = 0.
-206, 0, 3
Suppose -v**3 + v**2 + 182*v = 0. Calculate v.
-13, 0, 14
Factor -2*b**2/17 - 76*b/17 - 74/17.
-2*(b + 1)*(b + 37)/17
Solve s**2/3 - 8522*s/3 + 18156121/3 = 0.
4261
Solve 3*b**2 + 144*b = 0.
-48, 0
What is a in 2*a**5/3 - 7*a**4/3 - a**3 + 25*a**2/3 - 23*a/3 + 2 = 0?
-2, 1/2, 1, 3
Suppose 4*i**2 + 3996*i - 8008 = 0. What is i?
-1001, 2
Find g such that 5*g**4 - 25*g**2 + 20 = 0.
-2, -1, 1, 2
Determine i so that 2*i**4/5 + 94*i**3/15 + 178*i**2/15 - 382*i/15 + 104/15 = 0.
-13, -4, 1/3, 1
Factor 2*k**4/3 - 232*k**3 - 2848*k**2 - 34432*k/3 - 15360.
2*(k - 360)*(k + 4)**3/3
Find k, given that 3*k**2/5 + 36*k/5 + 12 = 0.
-10, -2
Let 3*r**4 - 48*r**3 - 51*r**2 = 0. Calculate r.
-1, 0, 17
Solve 4*u**2/3 + 52*u = 0 for u.
-39, 0
Factor -z**2/2 + 21*z/2 + 36.
-(z - 24)*(z + 3)/2
Solve -10*v**2/11 + 2*v/11 + 8/11 = 0.
-4/5, 1
Find t such that 4*t**2 + 68024*t + 289204036 = 0.
-8503
Determine v so that -3*v**3/7 - 39*v**2/7 + 45*v - 513/7 = 0.
-19, 3
Solve -2*i**4/3 - 10*i**3 + 2*i**2 + 86*i/3 - 20 = 0 for i.
-15, -2, 1
Factor -3*j**3 + 30*j**2 - 33*j - 210.
-3*(j - 7)*(j - 5)*(j + 2)
Suppose 3*s**3 - 42*s**2 + 123*s + 168 = 0. What is s?
-1, 7, 8
What is h in -h**2 + 30*h - 125 = 0?
5, 25
Factor u**2/7 + 68*u/7 + 1156/7.
(u + 34)**2/7
Let a**3 - 158*a**2 + 157*a = 0. What is a?
0, 1, 157
Factor 4*d**3 + 36*d**2 + 104*d + 96.
4*(d + 2)*(d + 3)*(d + 4)
Factor 551*o**3/4 - 1101*o**2/2 + 549*o + 2.
(o - 2)**2*(551*o + 2)/4
Suppose -2*k**3/5 + 4*k**2 + 46*k/5 + 24/5 = 0. What is k?
-1, 12
Suppose 28*u**5 + 456*u**4 + 2592*u**3 + 6080*u**2 + 5568*u + 1152 = 0. What is u?
-6, -2, -2/7
Find n, given that -7*n**5/2 - 69*n**4/2 - 23*n**3 + 228*n**2 - 32*n = 0.
-8, -4, 0, 1/7, 2
Factor -n**2/2 - 101*n - 10201/2.
-(n + 101)**2/2
Find p, given that 405*p**5 + 1195*p**4 + 750*p**3 - 40*p**2 = 0.
-2, -1, 0, 4/81
Factor 3*c**4 + 38*c**3 + 84*c**2 + 40*c.
c*(c + 2)*(c + 10)*(3*c + 2)
Find v such that 2*v**4/3 + 28*v**3/3 + 128*v**2/3 + 76*v + 42 = 0.
-7, -3, -1
Determine o so that -11*o**5 + 46*o**4 - 19*o**3 - 64*o**2 + 12*o = 0.
-1, 0, 2/11, 2, 3
Factor -72*f**2 + 196*f + 60.
-4*(f - 3)*(18*f + 5)
What is u in -3*u**5/4 - 39*u**4/4 + 213*u**3/4 + 99*u**2/4 - 459*u/2 = 0?
-17, -2, 0, 3
What is s in 2*s**3/3 + 10*s**2/3 - 24*s = 0?
-9, 0, 4
What is g in 2*g**3/5 - 512*g**2/5 + 33274*g/5 - 64516/5 = 0?
2, 127
Suppose -14*s**4/11 + 1278*s**3/11 + 4914*s**2/11 + 2482*s/11 - 1140/11 = 0. What is s?
-3, -1, 2/7, 95
What is n in 3*n**3/4 - 21*n**2 + 75*n - 72 = 0?
2, 24
Determine y so that -2*y**5/5 - 14*y**4/5 - 6*y**3 - 2*y**2 + 32*y/5 + 24/5 = 0.
-3, -2, -1, 1
Determine y, given that -35*y**3 + 920*y**2 - 6175*y + 1690 = 0.
2/7, 13
Factor -5*n**2/4 - 5*n/2 + 10.
-5*(n - 2)*(n + 4)/4
Factor -2*l**4/5 - 3614*l**3/5 - 326886*l**2 - 1630818*l/5.
-2*l*(l + 1)*(l + 903)**2/5
Determine s so that -s**4/5 - 11*s**3/5 + 12*s**2/5 + 256*s/5 - 256/5 = 0.
-8, 1, 4
Factor -4*v**4 + 16*v**3 - 20*v**2 + 8*v.
-4*v*(v - 2)*(v - 1)**2
Let -f**2/2 + 16*f - 78 = 0. Calculate f.
6, 26
Let 3*j**3 - 6*j**2 + 3*j = 0. Calculate j.
0, 1
Factor 5*m**2/3 - 515*m/3 + 170.
5*(m - 102)*(m - 1)/3
Solve -10*c**4/3 + 134*c**3/3 - 272*c**2/3 + 88*c/3 = 0 for c.
0, 2/5, 2, 11
Factor -3*t**2/4 - 3*t/4 + 3/2.
-3*(t - 1)*(t + 2)/4
Factor -261*b**2 - 525*b - 6.
-3*(b + 2)*(87*b + 1)
Factor -2*m**3/9 + 478*m**2/9 - 476*m/9.
-2*m*(m - 238)*(m - 1)/9
What is i in -i**3 - 8*i**2 + i + 8 = 0?
-8, -1, 1
Factor 3*u**3/5 + 177*u**2/5 + 2484*u/5.
3*u*(u + 23)*(u + 36)/5
Determine v, given that 3*v**4 - 3*v**3 = 0.
0, 1
Factor n**4 - 5*n**3 + 6*n**2 + 4*n - 8.
(n - 2)**3*(n + 1)
Determine b so that 2*b**4/5 + 2*b**3 - 26*b**2/5 + 14*b/5 = 0.
-7, 0, 1
Suppose 4*d**2/3 + 2304*d + 995328 = 0. What is d?
-864
Find y, given that 2*y**5/9 + 2*y**4/9 - 4*y**3/9 - 4*y**2/9 + 2*y/9 + 2/9 = 0.
-1, 1
Suppose k**4/3 - k**3 - k**2 + 11*k/3 - 2 = 0. What is k?
-2, 1, 3
Factor -5*v**3/3 - 246*v**2 + 296*v/3.
-v*(v + 148)*(5*v - 2)/3
Find u such that u**2 + 332*u - 2720 = 0.
-340, 8
Determine k, given that k**3 + 11*k**2 - k - 11 = 0.
-11, -1, 1
Suppose k**2 + 15*k - 2296 = 0. What is k?
-56, 41
Solve -3375*w**4/2 + 65475*w**3/2 - 12915*w**2 + 1714*w - 76 = 0.
2/15, 19
Factor 2*x**3 - 50*x**2 + 48*x.
2*x*(x - 24)*(x - 1)
Factor -405*n**3 - 9360*n**2 + 8560*n - 1920.
-5*(n + 24)*(9*n - 4)**2
Solve -2*j**2 + 2*j + 40 = 0 for j.
-4, 5
Factor -3*z**3/2 - 9*z**2/2 + 6*z.
-3*z*(z - 1)*(z + 4)/2
Factor 3*h**5 - 669*h**4 + 55062*h**3 - 1929906*h**2 + 20556423*h + 158340015.
3*(h - 57)**4*(h + 5)
Factor 6*n**2 - 183*n/5 + 252/5.
3*(n - 4)*(10*n - 21)/5
Factor -5*x**5 + 385*x**4 - 755*x**3 + 375*x**2.
-5*x**2*(x - 75)*(x - 1)**2
Solve 5*x**4 - 1020*x**3 + 78030*x**2 - 2653020*x + 33826005 = 0.
51
Suppose z**3/5 - 45*z**2 + 888*z/5 - 884/5 = 0. What is z?
2, 221
Factor f**4/2 - 19*f**3 + 18*f**2 + 19*f - 37/2.
(f - 37)*(f - 1)**2*(f + 1)/2
Factor 48*f**2 + 20*f + 2.
2*(4*f + 1)*(6*f + 1)
Factor -5*n**2 - 12540*n - 7862580.
-5*(n + 1254)**2
Solve -3*g**5 - 27*g**4 + 210*g**3 + 1962*g**2 + 4401*g + 2673 = 0 for g.
-11, -3, -1, 9
Factor -4*m**3 - 60*m**2 - 188*m - 132.
-4*(m + 1)*(m + 3)*(m + 11)
Factor -3*t**5/2 + 3*t**3/2.
-3*t**3*(t - 1)*(t + 1)/2
Factor -a**4/5 + 14*a**3/5 - 33*a**2/5 - 112*a/5 - 64/5.
-(a - 8)**2*(a + 1)**2/5
Determine r so that 4*r**4 - 84*r**3 - 600*r**2 - 1264*r - 864 = 0.
-2, 27
Factor m**4 + 33*m**3 + 206*m**2 - 240*m.
m*(m - 1)*(m + 10)*(m + 24)
Factor 2*x**2 + 572*x + 40898.
2*(x + 143)**2
Factor 2*k**2 - 1330*k + 1328.
2*(k - 664)*(k - 1)
Find l, given that 3*l**2/2 - 39*l/2 - 2775 = 0.
-37, 50
Factor -3*v**3 - 21*v**2 + 120*v - 132.
-3*(v - 2)**2*(v + 11)
Solve -25*b**5/3 - 5*b**4 + 34*b**3/3 + 14*b**2/3 - 3*b + 1/3 = 0 for b.
-1, 1/5, 1
Determine m, given that -8*m**3 - 2*m**2 + m = 0.
-1/2, 0, 1/4
Factor 3*w**3/2 + 21*w**2/2 + 21*w/2 - 45/2.
3*(w - 1)*(w + 3)*(w + 5)/2
Let -2*s**3/3 + 446*s**2/3 + 452*s/3 - 896/3 = 0. Calculate s.
-2, 1, 224
Determine k so that 21*k**3 + 72*k**2 + 69*k + 18 = 0.
-2, -1, -3/7
Determine m so that -m**4 + 7*m**3 + 753*m**2 + 1481*m + 736 = 0.
-23, -1, 32
Find x, given that -56*x**4 - 142*x**3 - 120*x**2 - 38*x - 4 = 0.
-1