that n**2 - 9*n + 8 = 0.
1, 8
Factor -3*j**3/2 - 9*j**2/2 + 27*j/2 + 81/2.
-3*(j - 3)*(j + 3)**2/2
Let 2*n**2/13 + 886*n/13 = 0. Calculate n.
-443, 0
Factor -4*s**4/5 - 76*s**3/5 - 468*s**2/5 - 1188*s/5 - 216.
-4*(s + 3)**3*(s + 10)/5
Factor -o**4/4 - 11*o**3/2 - o**2/4 + 483*o + 1323.
-(o - 9)*(o + 3)*(o + 14)**2/4
Find u such that -3*u**3 - 93*u**2 - 258*u - 168 = 0.
-28, -2, -1
Determine m so that -m**2/11 - 1038*m/11 + 1039/11 = 0.
-1039, 1
Suppose -6*a**2/5 + 13478*a/5 + 8988/5 = 0. What is a?
-2/3, 2247
Factor -4*t**2/5 + 106*t/5.
-2*t*(2*t - 53)/5
Determine b, given that 2*b**2/3 - 34*b/3 = 0.
0, 17
Determine x, given that -5*x**5/2 - 17*x**4/2 + 9*x**3/2 + 61*x**2/2 + 26*x + 6 = 0.
-3, -1, -2/5, 2
Solve 3*l**4 + 123*l**3 + 1320*l**2 + 1200*l = 0.
-20, -1, 0
Factor -3*a**2/4 - 2685*a - 2403075.
-3*(a + 1790)**2/4
Suppose 240*l**2 + 245*l + 5 = 0. Calculate l.
-1, -1/48
Suppose 3*q**4 - 132*q**3 - 222*q**2 + 36828*q + 233523 = 0. Calculate q.
-9, 31
Let -3*b**3 + 576*b**2 + 2340*b + 2352 = 0. Calculate b.
-2, 196
Determine s so that 3*s**2 - 534*s + 23763 = 0.
89
Factor 2*v**2 + 24*v + 54.
2*(v + 3)*(v + 9)
Solve 18*y**5/5 - 30*y**4 + 156*y**3/5 + 108*y**2/5 - 174*y/5 + 42/5 = 0.
-1, 1/3, 1, 7
Factor -5*m**2 + 35*m + 150.
-5*(m - 10)*(m + 3)
Factor -t**3 - 7*t**2 - 14*t - 8.
-(t + 1)*(t + 2)*(t + 4)
Factor u**3/3 + 2*u**2/3 - 8*u/3.
u*(u - 2)*(u + 4)/3
What is l in -2*l**4/9 + 20*l**3/9 + 8*l**2/9 - 80*l/9 = 0?
-2, 0, 2, 10
Factor d**3/11 - 16*d**2/11 + 13*d/11 + 30/11.
(d - 15)*(d - 2)*(d + 1)/11
Factor -2*t**3 + 820*t**2 + 822*t.
-2*t*(t - 411)*(t + 1)
Factor w**4/2 - w**3/8 - w**2/2 + w/8.
w*(w - 1)*(w + 1)*(4*w - 1)/8
Factor -27*i**3 + 84*i**2 + 27*i - 84.
-3*(i - 1)*(i + 1)*(9*i - 28)
Factor 4*c**4 + 248*c**3 + 236*c**2 - 488*c.
4*c*(c - 1)*(c + 2)*(c + 61)
Factor n**2/6 - 11*n/6 - 121/3.
(n - 22)*(n + 11)/6
Determine j, given that -108*j**5 - 30*j**4 + 1238*j**3/3 - 316*j**2/3 - 920*j/3 + 400/3 = 0.
-2, -1, 1/2, 10/9
Factor -y**5 - 27*y**4 - 43*y**3 + 171*y**2 - 100*y.
-y*(y - 1)**2*(y + 4)*(y + 25)
Solve f**2/2 + 43*f/2 - 22 = 0 for f.
-44, 1
Determine c so that -c**4/4 + 5*c**3/2 + 49*c**2/4 - 53*c/2 - 78 = 0.
-4, -2, 3, 13
Factor 5*n**2 + 325*n + 320.
5*(n + 1)*(n + 64)
Find i, given that -4*i**3/3 + 24*i**2 - 128*i + 512/3 = 0.
2, 8
Factor -96*x**4/11 - 80*x**3/11 - 2*x**2 - 2*x/11.
-2*x*(3*x + 1)*(4*x + 1)**2/11
Determine h, given that 8*h**3 - 614*h**2 - 778*h - 156 = 0.
-1, -1/4, 78
Factor -3*t**4 + 48*t**3 - 189*t**2 + 276*t - 132.
-3*(t - 11)*(t - 2)**2*(t - 1)
Determine h so that -12*h**5 - 274*h**4 + 956*h**3 - 824*h**2 + 208*h = 0.
-26, 0, 1/2, 2/3, 2
Factor v**4 - 9*v**3 + 24*v**2 - 16*v.
v*(v - 4)**2*(v - 1)
Determine t, given that 4*t**3 - 52*t**2 + 144*t = 0.
0, 4, 9
Solve 2*h**3 + 10*h**2 - 8*h - 40 = 0 for h.
-5, -2, 2
Factor u**2 - 96*u.
u*(u - 96)
Suppose -12*o**4 + 399*o**3 - 855*o**2 + 561*o - 93 = 0. Calculate o.
1/4, 1, 31
Suppose -2*q**3/7 - 128*q**2/7 + 262*q/7 - 132/7 = 0. What is q?
-66, 1
Factor 5*r**3 - 225*r**2 + 435*r - 215.
5*(r - 43)*(r - 1)**2
Find w, given that -15*w**3 + 273*w**2 - 546*w + 288 = 0.
1, 6/5, 16
Determine a, given that 3*a**3/5 + 81*a**2/5 - 96*a = 0.
-32, 0, 5
Determine j, given that j**2 - 90*j + 2025 = 0.
45
Factor -4*p**3/9 + 28*p**2 - 1280*p/3 - 4096/9.
-4*(p - 32)**2*(p + 1)/9
Suppose -3*a**2 - 57*a + 126 = 0. What is a?
-21, 2
Factor -3*d**5 + 3*d**4 + 3*d**3 - 3*d**2.
-3*d**2*(d - 1)**2*(d + 1)
Solve -2*s**2/13 + 1708*s/13 + 3424/13 = 0 for s.
-2, 856
Let -p**2/4 - 2765*p/2 - 7645225/4 = 0. What is p?
-2765
Let 5*k**3 - 95*k**2 - 440*k - 460 = 0. What is k?
-2, 23
Suppose -2*f**2/7 - 484*f/7 - 29282/7 = 0. Calculate f.
-121
Factor -9*t**2/7 + 2*t.
-t*(9*t - 14)/7
Factor 2*j**2/9 - 128*j/9 + 14.
2*(j - 63)*(j - 1)/9
Solve 3*n**3/4 - 42*n**2 + 528*n - 1920 = 0 for n.
8, 40
Factor 16*d**3/15 + 82*d**2/15 - 8*d/15 - 6.
2*(d - 1)*(d + 5)*(8*d + 9)/15
Factor -10*f**3 - 186*f**2 + 276*f - 80.
-2*(f - 1)*(f + 20)*(5*f - 2)
Find n such that n**5/9 + 11*n**4/9 - 3*n**3 - 203*n**2/9 - 286*n/9 - 40/3 = 0.
-12, -2, -1, 5
Let 3*h**3 - 168*h**2 = 0. What is h?
0, 56
Factor 5*k**3 - 60*k**2 + 240*k - 320.
5*(k - 4)**3
Solve -s**3/4 - 6165*s**2/4 - 9498723*s/4 + 9504889/4 = 0.
-3083, 1
Factor -5*s**3 - 30770*s**2 - 47339645*s.
-5*s*(s + 3077)**2
Factor c**4/8 + 23*c**3/2 + 2205*c**2/8 + 2025*c/4.
c*(c + 2)*(c + 45)**2/8
Factor 4*c**2 + 64*c - 420.
4*(c - 5)*(c + 21)
Let -25*c**4 + 365*c**3 - 1025*c**2 - 2045*c - 630 = 0. What is c?
-1, -2/5, 7, 9
Factor -s**2/2 + 47*s/2.
-s*(s - 47)/2
Suppose 5*u**4 + 5*u**3 - 65*u**2 - 5*u + 60 = 0. Calculate u.
-4, -1, 1, 3
Let -4*g**4/7 - 4*g**3 + 40*g**2/7 + 64*g/7 = 0. Calculate g.
-8, -1, 0, 2
Determine u, given that 18*u**3 + 573*u**2 + 4512*u - 768 = 0.
-16, 1/6
Factor -5*y**2 + 10*y + 2415.
-5*(y - 23)*(y + 21)
Solve -3*a**5 + 18*a**4 + 36*a**3 - 318*a**2 + 207*a + 540 = 0 for a.
-4, -1, 3, 5
Determine w so that 4*w**5/5 - 24*w**4/5 - 36*w**3/5 + 56*w**2/5 = 0.
-2, 0, 1, 7
Factor c**5 - 21*c**4 + 75*c**3 + 217*c**2 + 120*c.
c*(c - 15)*(c - 8)*(c + 1)**2
Factor 4*n**2/7 + 138*n/7 + 198/7.
2*(n + 33)*(2*n + 3)/7
Factor 25*n**2 - 9505*n - 7620.
5*(n - 381)*(5*n + 4)
Find b such that -4*b**3 - 188*b**2 - 2012*b + 2204 = 0.
-29, -19, 1
Let -5*f**5/6 + 20*f**4/3 + 110*f**3/3 + 40*f**2 = 0. What is f?
-2, 0, 12
Find l, given that -16*l**4 - 56*l**3 + 132*l**2 + 198*l - 324 = 0.
-9/2, -2, 3/2
What is k in 30*k**4 + 117*k**3 + 138*k**2 + 45*k - 6 = 0?
-2, -1, 1/10
Factor 4*i**3/7 - 24*i**2/7 + 20*i/7 + 48/7.
4*(i - 4)*(i - 3)*(i + 1)/7
Find h such that 4*h**5/3 - 20*h**4 + 64*h**3 + 256*h**2/3 = 0.
-1, 0, 8
Factor -2*j**5/11 + 56*j**4/11 - 204*j**3/11 + 296*j**2/11 - 194*j/11 + 48/11.
-2*(j - 24)*(j - 1)**4/11
Factor 23*l**3/6 + 31*l**2/2 - 37*l/2 - 5/6.
(l - 1)*(l + 5)*(23*l + 1)/6
Factor -2*k**2/17 + 6*k - 1288/17.
-2*(k - 28)*(k - 23)/17
Solve 20*s**2 - 1795*s - 450 = 0.
-1/4, 90
Suppose -3*g**4/8 - 3*g**3/2 + 63*g**2/8 - 3*g/2 - 21/2 = 0. Calculate g.
-7, -1, 2
Factor 2*d**4 - 18*d**3 + 16*d**2.
2*d**2*(d - 8)*(d - 1)
Factor -2*t**2/11 + 24*t - 792.
-2*(t - 66)**2/11
Determine q so that 7*q**2 + 79*q + 72 = 0.
-72/7, -1
Factor -2*r**4/3 + 2*r**3 + 18*r**2 - 90*r + 108.
-2*(r - 3)**3*(r + 6)/3
Factor -c**2/7 + 3*c/7 + 10.
-(c - 10)*(c + 7)/7
Let 2*s**4/11 + 14*s**3 + 148*s**2/11 - 304*s/11 = 0. Calculate s.
-76, -2, 0, 1
Factor -2*l**4/13 - 64*l**3/13 - 570*l**2/13 - 900*l/13.
-2*l*(l + 2)*(l + 15)**2/13
Factor j**2 + 3142*j + 2468041.
(j + 1571)**2
Solve -j**5/11 + 10*j**4/11 - 25*j**3/11 - 20*j**2/11 + 80*j/11 + 64/11 = 0.
-1, 4
Determine t, given that -2*t**3 - 204*t**2 - 4992*t + 10816 = 0.
-52, 2
Factor 4*c**4 + 4*c**3 - 36*c**2 - 36*c.
4*c*(c - 3)*(c + 1)*(c + 3)
Factor -3*y**3 + 1275*y**2 - 136104*y + 134832.
-3*(y - 212)**2*(y - 1)
Determine l so that 1444*l**2/7 - 456*l/7 + 36/7 = 0.
3/19
Find q such that -q**3/9 - 2*q**2/9 + q/9 + 2/9 = 0.
-2, -1, 1
Solve a**4/6 + 7*a**3 + 98*a**2 + 1372*a/3 = 0.
-14, 0
Solve 3*b**4/7 - 108*b**2/7 - 96*b/7 + 576/7 = 0 for b.
-4, 2, 6
Find f, given that -f**2/3 + 104*f - 8112 = 0.
156
Suppose -80*p**4 + 316*p**3 - 304*p**2 - 16*p = 0. Calculate p.
-1/20, 0, 2
Find g such that 5*g**3 + 43*g**2/3 - 22*g + 8/3 = 0.
-4, 2/15, 1
Factor 60*p**3 + 639*p**2 + 396*p + 60.
3*(p + 10)*(4*p + 1)*(5*p + 2)
Suppose p**2/6 + 65*p/6 = 0. Calculate p.
-65, 0
Factor -l**3 + 8*l**2 + l - 8.
-(l - 8)*(l - 1)*(l + 1)
Suppose -4*x**2/3 - 5056*x/3 - 1597696/3 = 0. Calculate x.
-632
Solve 40*r**4 + 2276*r**3 + 4224*r**2 + 2428*r + 440 = 0 for r.
-55, -1, -1/2, -2/5
Factor r**2 - 652*r - 653.
(r - 653)*(r + 1)
Suppose -50*x**3/13 + 10630*x**2/13 + 4258*x/13 + 426/13 = 0. What is x?
-1/5, 213
Solve -4*n**4 - 12*n**3 = 0.
-3, 0
Factor l**4 - 210*l**3 + 12397*l**2 - 144060*l + 470596.
(l - 98)**2*(l - 7)**2
Factor -4*q**2 - 2896*q - 524176.
-4*(q + 362)**2
Determine m, given that -m**5/2 + 12*m**4 - 67*m**3 + 44*m**2 + 135*m/2 - 56 = 0.
-1, 1, 7, 16
Factor -4*j**4 + 720*j**3 - 48600*j**2 + 1458000*j - 16402500.
-4*(j - 45)**4
Factor -w**4/9 + 5*w**3/3 + 38*w**2/3 + 244*w/9 + 56/3.
-(w - 21)*(w + 2)**3/9
Let -4*w**2 + 20*w = 0. What is w?
0, 5
Factor 2*p**5/13 + 8*p**4/13 - 46*p**3/13 - 76*p**2/13 + 440*p/13 - 400/13.
2*(p - 2)**3*(p +