 1)
Factor 7*c**5/12 - 3*c**4/4 + c**3/6.
c**3*(c - 1)*(7*c - 2)/12
Factor -2*h**4 + 66*h**3 + 2*h**2 - 66*h.
-2*h*(h - 33)*(h - 1)*(h + 1)
Factor -2*r**2/5 + 16*r + 1792/5.
-2*(r - 56)*(r + 16)/5
Solve 2*j**2 - 2*j - 60 = 0 for j.
-5, 6
Solve -5*d**4 - 70*d**3 - 345*d**2 - 700*d - 500 = 0 for d.
-5, -2
Let 218*q**3/15 + 424*q**2/15 + 194*q/15 - 4/5 = 0. Calculate q.
-1, 6/109
Solve 2*z**5 - 158*z**4/15 + 212*z**3/15 - 8*z**2/15 - 16*z/5 = 0 for z.
-2/5, 0, 2/3, 2, 3
Factor -p**3/2 + 7*p**2 - 25*p/2 + 6.
-(p - 12)*(p - 1)**2/2
Find g, given that -2*g**2/3 - 34*g + 560/3 = 0.
-56, 5
Determine q, given that 3*q**3/4 + 99*q**2/4 - 675*q/4 + 1053/4 = 0.
-39, 3
Factor -3*v**2/4 + 87*v/4 + 585/2.
-3*(v - 39)*(v + 10)/4
Find j, given that j**4/7 + 51*j**3/7 + 765*j**2/7 + 2921*j/7 + 3174/7 = 0.
-23, -3, -2
Solve -4*n**5 - 16*n**4 + 12*n**3 + 136*n**2 + 208*n + 96 = 0 for n.
-2, -1, 3
Let o**2/2 + 75*o - 152 = 0. What is o?
-152, 2
Factor 3*g**2/4 + 27*g/4 + 15.
3*(g + 4)*(g + 5)/4
Factor 5*a**3/4 - 550*a**2 + 4385*a/4 - 1095/2.
5*(a - 438)*(a - 1)**2/4
Solve -45*d**5 + 120*d**4 + 85*d**3 - 100*d**2 - 60*d = 0.
-2/3, 0, 1, 3
Solve 2*o**2/13 - 732*o/13 + 66978/13 = 0 for o.
183
Determine p so that -2*p**4 + 40*p**3 - 36*p**2 - 40*p + 38 = 0.
-1, 1, 19
What is v in v**3 - 3*v**2 - 46*v + 48 = 0?
-6, 1, 8
Factor l**2/3 + 4678*l/3 + 5470921/3.
(l + 2339)**2/3
Factor -3*a**3 + 18*a**2.
-3*a**2*(a - 6)
Factor -2*i**4/9 + 4*i**3/3 + 10*i**2/3 + 16*i/9.
-2*i*(i - 8)*(i + 1)**2/9
Factor -i**3/2 + 5*i**2/2 + i/2 - 5/2.
-(i - 5)*(i - 1)*(i + 1)/2
Let 4*s**5 + 16*s**4 + 4*s**3 - 40*s**2 - 16*s + 32 = 0. What is s?
-2, 1
Factor 4*t**2 + 172*t.
4*t*(t + 43)
Factor -2*x**3 + 16*x**2 - 34*x + 20.
-2*(x - 5)*(x - 2)*(x - 1)
Find h such that 2*h**4 - 20*h**3/3 - 40*h**2/3 + 80*h/3 + 64/3 = 0.
-2, -2/3, 2, 4
Factor y**5 + 2*y**4 - 68*y**3 - 424*y**2 - 896*y - 640.
(y - 10)*(y + 2)**2*(y + 4)**2
Find n such that -4*n**5/5 + 104*n**4/5 - 72*n**3 + 32*n**2 + 364*n/5 - 264/5 = 0.
-1, 1, 3, 22
Factor 3*l**2 + 534*l - 537.
3*(l - 1)*(l + 179)
Factor -3*b**4/4 + 15*b**3 - 75*b**2.
-3*b**2*(b - 10)**2/4
Factor -37*v**3/7 + 367*v**2/7 - 895*v/7 - 75/7.
-(v - 5)**2*(37*v + 3)/7
Suppose -2*f**5/17 + 2*f**4/17 + 10*f**3/17 + 6*f**2/17 = 0. What is f?
-1, 0, 3
Factor -4*f**2 - 11480*f - 8236900.
-4*(f + 1435)**2
Factor q**5 - 74*q**4 + 1573*q**3 - 7548*q**2 + 10404*q.
q*(q - 34)**2*(q - 3)**2
Find y, given that -4*y**3/3 + 128*y**2/3 - 1024*y/3 = 0.
0, 16
Factor h**2/5 - 42*h/5 + 392/5.
(h - 28)*(h - 14)/5
Let -3*v**3/2 + 3423*v**2/2 - 974697*v/2 - 978123/2 = 0. Calculate v.
-1, 571
Factor -l**3/5 - 82*l**2/5 - 833*l/5 + 38416/5.
-(l - 16)*(l + 49)**2/5
Factor -5*w**5 - 65*w**4 - 245*w**3 - 395*w**2 - 290*w - 80.
-5*(w + 1)**3*(w + 2)*(w + 8)
Factor -2*j**3 + 110*j**2/3 - 12*j.
-2*j*(j - 18)*(3*j - 1)/3
Let t**2/3 + 55*t/3 + 68 = 0. Calculate t.
-51, -4
Suppose -9*u**4/7 - 3*u**3/7 + 96*u**2/7 - 132*u/7 + 48/7 = 0. What is u?
-4, 2/3, 1, 2
Factor -2*d**2/7 + 46*d/7 - 12.
-2*(d - 21)*(d - 2)/7
Factor z**4 + 10*z**3 + 24*z**2 + 22*z + 7.
(z + 1)**3*(z + 7)
Factor -o**5/8 - 17*o**4/2 + 231*o**3/2 - 360*o**2.
-o**2*(o - 6)**2*(o + 80)/8
Factor -2*s**5 - 2*s**4 + 6*s**3 + 10*s**2 + 4*s.
-2*s*(s - 2)*(s + 1)**3
Suppose -4*c**4 - 528*c**3 - 16888*c**2 + 35376*c - 17956 = 0. Calculate c.
-67, 1
Find i such that -4780*i**5/7 - 12458*i**4/7 - 8682*i**3/7 + 902*i**2/7 + 274*i + 12/7 = 0.
-1, -3/478, 2/5
What is q in -32*q**4/13 + 9840*q**3/13 - 753986*q**2/13 - 378840*q/13 - 47432/13 = 0?
-1/4, 154
Find i such that -5*i**5 - 40*i**4 + 1780*i**3 + 5530*i**2 + 5585*i + 1870 = 0.
-22, -1, 17
Factor -b**4/4 - 11*b**3/2 - 33*b**2 - 85*b/2 + 325/4.
-(b - 1)*(b + 5)**2*(b + 13)/4
Solve 3*a**4/7 - 2844*a**3/7 + 1011042*a**2/7 - 159744636*a/7 + 9464869683/7 = 0 for a.
237
Determine t so that t**2/6 - 40*t/3 + 79/6 = 0.
1, 79
Factor -867*y**3/5 - 9282*y**2/5 - 2592*y + 69984/5.
-3*(y - 2)*(17*y + 108)**2/5
Factor -g**4/3 - 4*g**3 - 43*g**2/3 - 8*g + 80/3.
-(g - 1)*(g + 4)**2*(g + 5)/3
Factor 3*w**5 - 24*w**4 - 18*w**3 + 168*w**2 - 201*w + 72.
3*(w - 8)*(w - 1)**3*(w + 3)
Find k such that -k**5/4 - 3*k**4/4 - k**3/4 + 3*k**2/4 + k/2 = 0.
-2, -1, 0, 1
Suppose -6*s**5 + 10*s**4 + 10*s**3 - 10*s**2 - 4*s = 0. Calculate s.
-1, -1/3, 0, 1, 2
Factor -1083*f**4 - 4446*f**3 - 4791*f**2 - 468*f - 12.
-3*(f + 2)**2*(19*f + 1)**2
Let -4*h**4 + 68*h**3 + 276*h**2 - 740*h + 400 = 0. What is h?
-5, 1, 20
Factor 29*v**3/4 - 25*v**2/2 - 4*v.
v*(v - 2)*(29*v + 8)/4
Factor 5*k**5 - 85*k**3 - 180*k**2 - 100*k.
5*k*(k - 5)*(k + 1)*(k + 2)**2
Solve -t**5/3 + 17*t**4/3 - 104*t**3/3 + 280*t**2/3 - 112*t + 48 = 0 for t.
1, 2, 6
Let -3*g**3/4 + 181*g**2/2 + 123*g/4 - 121/2 = 0. Calculate g.
-1, 2/3, 121
Determine v, given that -3*v**2 + 642*v + 6720 = 0.
-10, 224
Let -s**3 + 31*s**2 + 213*s + 333 = 0. What is s?
-3, 37
Find f, given that 3*f**2 - 474*f - 3984 = 0.
-8, 166
Factor 2*u**3 + 4950*u**2 + 9894*u + 4946.
2*(u + 1)**2*(u + 2473)
Let -4*s**5 + 108*s**4 - 1080*s**3 + 4968*s**2 - 10692*s + 8748 = 0. Calculate s.
3, 9
Suppose -2*z**4/7 + 4*z**3/7 + 234*z**2/7 + 180*z/7 - 1296/7 = 0. What is z?
-9, -3, 2, 12
Factor -3*h**2 + 14*h + 5.
-(h - 5)*(3*h + 1)
Factor -4*d**2/3 + 64*d - 188/3.
-4*(d - 47)*(d - 1)/3
Let 2*o**3 + 404*o**2 + 802*o + 400 = 0. What is o?
-200, -1
Determine p, given that -2*p**2 + 10*p = 0.
0, 5
Factor 9*i**2 + 195*i - 66.
3*(i + 22)*(3*i - 1)
Factor -a**3 - 126*a**2 - 249*a - 124.
-(a + 1)**2*(a + 124)
Find y, given that -y**3 + 63*y**2 - 123*y + 61 = 0.
1, 61
Solve -2*z**2/5 + 62*z/5 = 0 for z.
0, 31
Suppose 15*s**4 + 25*s**3 - 5*s**2 - 25*s - 10 = 0. Calculate s.
-1, -2/3, 1
Let 4*h**5 - 24*h**4 + 56*h**3 - 64*h**2 + 36*h - 8 = 0. Calculate h.
1, 2
Find h, given that -15*h**2/7 - 687*h/7 + 138/7 = 0.
-46, 1/5
Factor 2*z**3/5 - 32*z/5.
2*z*(z - 4)*(z + 4)/5
Suppose -4*c**2/3 + 68*c/3 - 64/3 = 0. What is c?
1, 16
Find m such that 16*m**4 - 228*m**3 + 212*m**2 = 0.
0, 1, 53/4
Factor -3*m**2/5 - 15*m - 138/5.
-3*(m + 2)*(m + 23)/5
Factor 5*n**2/4 - 61*n/4 + 3.
(n - 12)*(5*n - 1)/4
Factor -2*u**3/5 - 28*u**2/5 + 154*u/5 + 36.
-2*(u - 5)*(u + 1)*(u + 18)/5
Suppose 2*q**3/5 + 4*q**2/5 - 2*q/5 - 4/5 = 0. What is q?
-2, -1, 1
Factor -5*o**2/3 + 20*o + 75.
-5*(o - 15)*(o + 3)/3
Let 4*d**3 - 56*d**2 + 140*d + 200 = 0. What is d?
-1, 5, 10
Find f, given that -4*f**5/7 - 8*f**4/7 + 4*f**3 + 32*f**2/7 - 48*f/7 = 0.
-3, -2, 0, 1, 2
Solve -v**4/7 + 114*v**3/7 = 0.
0, 114
Factor -k**2/4 + 39*k/2 - 1521/4.
-(k - 39)**2/4
Factor -s**3 - s**2.
-s**2*(s + 1)
Determine z so that 147*z**5 - 3297*z**4 + 9693*z**3 - 2019*z**2 - 3840*z - 684 = 0.
-2/7, 1, 3, 19
Solve 4*w**2 + 1220*w + 2424 = 0.
-303, -2
Suppose -f**2/3 - 88*f/3 + 89/3 = 0. Calculate f.
-89, 1
Factor 3*m**4/4 - 6933*m**3 + 48066489*m**2/2 - 37027218693*m + 85569902399523/4.
3*(m - 2311)**4/4
Factor 4*m**5 + 8*m**4 + 4*m**3.
4*m**3*(m + 1)**2
Factor -2*f**2 - 1180*f - 174050.
-2*(f + 295)**2
Factor 4*b**4 - 132*b**3 - 1404*b**2 - 4428*b - 4536.
4*(b - 42)*(b + 3)**3
Factor -2*v**4/5 - 2232*v**3/5 - 620492*v**2/5 + 1247688*v/5 - 624962/5.
-2*(v - 1)**2*(v + 559)**2/5
Factor -2*n**4 - 2*n**3 + 34*n**2 - 30*n.
-2*n*(n - 3)*(n - 1)*(n + 5)
Solve -2*p**4/5 - 42*p**3/5 - 228*p**2/5 + 8*p + 240 = 0.
-10, -3, 2
Factor -4*s**4/5 - 64*s**3/5 - 208*s**2/5 - 192*s/5.
-4*s*(s + 2)**2*(s + 12)/5
Solve -2*i**5/9 - 4*i**4/9 + 2*i**3/9 + 4*i**2/9 = 0 for i.
-2, -1, 0, 1
Solve -5*g**4/2 + 175*g**3 - 6785*g**2/2 + 11550*g - 10890 = 0 for g.
2, 33
Factor w**2/2 + 27*w/2.
w*(w + 27)/2
Find s such that 5*s**4 - 160*s**3 + 1440*s**2 - 5120*s + 6400 = 0.
4, 20
Let 8*m**5/7 - 110*m**4/7 - 1200*m**3/7 - 560*m**2 - 5440*m/7 - 2784/7 = 0. Calculate m.
-2, 87/4
What is p in -32*p**4/11 + 7696*p**3/11 + 75854*p**2/11 + 36482*p/11 + 4500/11 = 0?
-9, -1/4, 250
Factor -6*j**2 - 1022*j + 1720.
-2*(j + 172)*(3*j - 5)
Solve -2*t**3/11 - 4*t**2/11 + 8*t/11 + 16/11 = 0 for t.
-2, 2
What is r in 15*r**3/4 - 103*r**2/4 - 67*r/2 - 4 = 0?
-1, -2/15, 8
Suppose y**5 - 7*y**3 - 2*y**2 + 12*y + 8 = 0. What is y?
-2, -1, 2
Factor 3*a**3/5 - 54*a**2 + 1620*a - 16200.
3*(a - 30)**3/5
Suppose 4*w**2/13 + 3202*w/13 - 1602/13 = 0. Calculate w.
-801, 1/2
Let -p**2/5 + 809*p/5 = 0. Calculate p.
0, 809
Solve -3*