6
Factor -3*a**3/2 + 9*a**2/2 + 195*a - 396.
-3*(a - 12)*(a - 2)*(a + 11)/2
Factor -3*r**3 + 111*r**2 + 1335*r + 3525.
-3*(r - 47)*(r + 5)**2
Determine n so that -n**4/3 + 116*n**3/3 + 118*n**2/3 - 116*n/3 - 39 = 0.
-1, 1, 117
Find q, given that -9*q**4/4 - 69*q**3/4 - 139*q**2/4 + 21*q/4 + 49 = 0.
-4, -7/3, 1
Let -4*f**2 - 176*f - 336 = 0. Calculate f.
-42, -2
Suppose 3*y**5 + 50*y**4 + 311*y**3 + 920*y**2 + 1308*y + 720 = 0. What is y?
-20/3, -3, -2
Determine j so that -405*j**3 - 2418*j**2 - 3573*j + 108 = 0.
-3, 4/135
Factor -3*j**2 - 33*j + 78.
-3*(j - 2)*(j + 13)
Factor 5*q**3/4 - 10*q**2 + 65*q/4 - 15/2.
5*(q - 6)*(q - 1)**2/4
Solve 20*z**5 - 68*z**4 + 12*z**3 + 116*z**2 - 32*z - 48 = 0.
-1, -3/5, 1, 2
Suppose -2*y**3/9 - 26*y**2 - 1474*y/3 - 22990/9 = 0. What is y?
-95, -11
Factor 2*f**5/3 + 2*f**4/3 - 4*f**3/3 - 4*f**2/3 + 2*f/3 + 2/3.
2*(f - 1)**2*(f + 1)**3/3
Find o such that -6750*o**4/17 + 32400*o**3/17 - 23040*o**2/17 + 5888*o/17 - 512/17 = 0.
4/15, 4
Suppose 2*o**4/5 + 1036*o**3 + 15528*o**2/5 + 15524*o/5 + 5174/5 = 0. What is o?
-2587, -1
Let -i**2/4 - 461*i/2 - 212521/4 = 0. What is i?
-461
Factor -2*u**2 - 70*u + 72.
-2*(u - 1)*(u + 36)
Factor 2*s**2 + 44*s + 42.
2*(s + 1)*(s + 21)
Factor 5*l**2 - 225*l + 2530.
5*(l - 23)*(l - 22)
Find d, given that -2*d**4/7 + 17*d**3/7 - 50*d**2/7 + 57*d/7 - 18/7 = 0.
1/2, 2, 3
Suppose 5*w**3 - 235*w**2 + 2140*w + 2380 = 0. Calculate w.
-1, 14, 34
Factor 2*n**4 - 192*n**3 + 4394*n**2 + 11172*n - 38416.
2*(n - 49)**2*(n - 2)*(n + 4)
Factor -2*s**3/5 - 84*s**2 - 810*s - 2000.
-2*(s + 5)**2*(s + 200)/5
Suppose 7*w**2/2 + 1235*w - 353/2 = 0. What is w?
-353, 1/7
What is u in -3*u**5 + 30*u**4 - 84*u**3 + 30*u**2 + 87*u - 60 = 0?
-1, 1, 4, 5
Find c such that 5*c**3 - 75*c**2 + 190*c - 120 = 0.
1, 2, 12
Determine g so that 2*g**5/7 - 20*g**4/7 - 2*g**3 + 344*g**2/7 + 264*g/7 - 576/7 = 0.
-3, -2, 1, 6, 8
Solve -6*f**4/7 - 66*f**3/7 - 60*f**2/7 = 0.
-10, -1, 0
Solve -4*a**3/3 - 928*a**2/3 - 8980*a/3 - 7400 = 0.
-222, -5
Solve -j**4/2 - 118*j**3 - 117*j**2 + 118*j + 235/2 = 0 for j.
-235, -1, 1
Find w, given that -4*w**2 - 1160*w = 0.
-290, 0
Factor -4*w**3/3 + 1720*w**2/3 - 3424*w/3.
-4*w*(w - 428)*(w - 2)/3
Let -4*z**5/5 + 352*z**4/5 - 3216*z**3/5 + 7576*z**2/5 - 6892*z/5 + 2184/5 = 0. What is z?
1, 7, 78
Solve 3*x**2/5 + 99*x/5 + 186/5 = 0 for x.
-31, -2
Factor y**2/6 + 11*y/6 - 21.
(y - 7)*(y + 18)/6
Find d, given that -2*d**5 + 102*d**4 + 1148*d**3 + 4284*d**2 + 6534*d + 3294 = 0.
-3, -1, 61
Factor 5*b**2/4 - 3*b/2.
b*(5*b - 6)/4
Solve -8*t**3 + 10*t**2 + 44*t + 26 = 0.
-1, 13/4
Factor 4*u**5 - 96*u**4 + 468*u**3 - 648*u**2.
4*u**2*(u - 18)*(u - 3)**2
Factor -2*m**4/17 - 32*m**3/17 - 160*m**2/17 - 256*m/17.
-2*m*(m + 4)**2*(m + 8)/17
Let -3*m**2/8 + 5847*m/4 - 11395803/8 = 0. Calculate m.
1949
Solve 3*g**4/4 - 57*g**3/4 + 189*g**2/2 - 243*g + 162 = 0.
1, 6
Find r such that -2*r**5/5 + 32*r**4/5 - 86*r**3/5 - 24*r**2 = 0.
-1, 0, 5, 12
Suppose -n**3 - 244*n**2/3 + 55*n + 82/3 = 0. Calculate n.
-82, -1/3, 1
Find a such that -2*a**2 - 304*a = 0.
-152, 0
Let 2*v**4/9 + 22*v**3/9 + 10*v**2/3 - 6*v = 0. Calculate v.
-9, -3, 0, 1
Find q such that 4*q**4 - 88*q**3 - 3568*q**2 - 25256*q - 21780 = 0.
-11, -1, 45
Factor -r**3/2 + 31*r**2/2 + 16*r.
-r*(r - 32)*(r + 1)/2
Find p such that 2*p**5/19 - 128*p**4/19 + 714*p**3/19 - 1036*p**2/19 - 488*p/19 + 1392/19 = 0.
-1, 2, 3, 58
Factor i**5/4 + 5*i**4/4 + 3*i**3/4 - 5*i**2/4 - i.
i*(i - 1)*(i + 1)**2*(i + 4)/4
Find i such that -5*i**4 - 35*i**3 - 90*i**2 - 100*i - 40 = 0.
-2, -1
Factor 4*y**4 - 8*y**3 - 16*y**2 + 8*y + 12.
4*(y - 3)*(y - 1)*(y + 1)**2
Factor 6*m**4 - 63*m**3 + 213*m**2 - 261*m + 105.
3*(m - 5)*(m - 1)**2*(2*m - 7)
What is v in 28*v**2 - 32*v - 60 = 0?
-1, 15/7
Factor -5*f**2 - 23740*f - 28179380.
-5*(f + 2374)**2
Let -j**3/4 - 23*j**2/4 - 171*j/4 - 405/4 = 0. What is j?
-9, -5
Factor -3*i**2 + 20040*i - 33466800.
-3*(i - 3340)**2
Factor 192*n**4 - 720*n**3/7 + 108*n**2/7 - 3*n/7.
3*n*(4*n - 1)**2*(28*n - 1)/7
Factor -4*w**3/7 - 26*w**2/7 - 40*w/7 - 18/7.
-2*(w + 1)**2*(2*w + 9)/7
Solve -3*x**3/8 - 9*x**2/4 + 3*x/8 + 45/4 = 0 for x.
-5, -3, 2
Find j such that -8*j**5/5 + 316*j**4/5 - 3032*j**3/5 - 1916*j**2/5 + 608*j + 320 = 0.
-1, -1/2, 1, 20
Factor 2*x**2/7 - 1208*x/7.
2*x*(x - 604)/7
What is v in 2*v**5/7 + 44*v**4/21 + 116*v**3/21 + 136*v**2/21 + 10*v/3 + 4/7 = 0?
-3, -2, -1, -1/3
Factor m**2 + 7*m - 44.
(m - 4)*(m + 11)
What is q in 3*q**5 - 18*q**4 + 6*q**3 + 48*q**2 - 9*q - 30 = 0?
-1, 1, 2, 5
Factor -5*g**3 + 19480*g**2 - 18973520*g.
-5*g*(g - 1948)**2
Determine x, given that 12*x**4 + 7*x**3 - 11*x**2 - 7*x - 1 = 0.
-1, -1/3, -1/4, 1
Factor -2*k**2 + 224*k - 6272.
-2*(k - 56)**2
Let t**3/10 - 126*t**2/5 - 254*t/5 = 0. What is t?
-2, 0, 254
Let -4*x**5 + 4*x**4 + 40*x**3 + 32*x**2 = 0. Calculate x.
-2, -1, 0, 4
Let 5*r**2 + 85*r - 190 = 0. Calculate r.
-19, 2
Factor -4*r**3 - 36*r**2 + 196*r - 156.
-4*(r - 3)*(r - 1)*(r + 13)
Factor 2*f**3/9 - 230*f**2/9 - 52*f.
2*f*(f - 117)*(f + 2)/9
What is w in 21*w**2/5 - 27*w/5 + 6/5 = 0?
2/7, 1
Solve s**4/2 + 5*s**3/4 - 31*s**2/2 - 56*s - 24 = 0 for s.
-4, -1/2, 6
Solve -3*l**3 + 234*l**2 - 4788*l + 8664 = 0 for l.
2, 38
Factor 3*s**3/5 + 198*s**2/5 - 621*s/5.
3*s*(s - 3)*(s + 69)/5
Let o**3/4 + 9*o**2/4 - 27 = 0. What is o?
-6, 3
Find s, given that -2*s**3/5 + 22*s**2/5 + 144*s/5 - 72 = 0.
-6, 2, 15
Let -5*a**3 + 1255*a**2 - 3720*a = 0. Calculate a.
0, 3, 248
Let -2*g**3/17 + 530*g**2/17 + 1066*g/17 + 534/17 = 0. Calculate g.
-1, 267
Solve -845*d**5/12 + 247*d**4/12 + 34*d**3/3 + d**2 = 0 for d.
-2/13, 0, 3/5
Factor 2*r**3/7 + 10*r**2 + 112*r + 392.
2*(r + 7)*(r + 14)**2/7
Factor 5*p**3 - 30*p**2 + 45*p.
5*p*(p - 3)**2
Factor 24*u**2 + 167*u - 7.
(u + 7)*(24*u - 1)
Factor -3*l**3/4 + 249*l**2/4 - 489*l/4 + 243/4.
-3*(l - 81)*(l - 1)**2/4
Factor a**2/6 - a/6 - 10/3.
(a - 5)*(a + 4)/6
Determine b so that 2*b**2/7 + 1634*b/7 + 1632/7 = 0.
-816, -1
Factor -p**3/4 + 9*p**2/4 - 9*p/2.
-p*(p - 6)*(p - 3)/4
Factor -2*j**2/19 + 34*j/19 + 36/19.
-2*(j - 18)*(j + 1)/19
Find m such that -2*m**3/3 + 7*m**2/3 - 7*m/3 + 2/3 = 0.
1/2, 1, 2
Solve -4*h**3/3 - 16*h**2 - 164*h/3 - 56 = 0 for h.
-7, -3, -2
Factor 4*a**3 + 60*a**2 + 108*a - 972.
4*(a - 3)*(a + 9)**2
Suppose 2*v**3/9 + 4*v**2 + 118*v/9 + 28/3 = 0. Calculate v.
-14, -3, -1
Suppose 2*s**5/5 - 4*s**4/5 - 6*s**3/5 + 16*s**2/5 - 8*s/5 = 0. What is s?
-2, 0, 1, 2
What is q in -560*q**3 - 5596*q**2 - 13960*q + 100 = 0?
-5, 1/140
Factor 4*a**4 - 4976*a**3 + 2321304*a**2 - 481283696*a + 37419807364.
4*(a - 311)**4
Find s such that -12*s**5/5 + 27*s**4/5 + 42*s**3/5 - 36*s**2/5 - 6*s + 9/5 = 0.
-1, 1/4, 1, 3
Factor 4*u**5 + 30*u**4 + 48*u**3 - 32*u**2.
2*u**2*(u + 4)**2*(2*u - 1)
Find t such that 1682*t**2/9 - 116*t/3 + 2 = 0.
3/29
Solve 2*f**3/5 + 28*f**2/5 + 88*f/5 + 16 = 0 for f.
-10, -2
Factor 2*s**3/9 + 2*s**2/3 + 2*s/3 + 2/9.
2*(s + 1)**3/9
Factor 28*o**2 + 236*o + 208.
4*(o + 1)*(7*o + 52)
What is b in -75*b**5 - 306*b**4 - 174*b**3 + 288*b**2 + 249*b + 18 = 0?
-3, -1, -2/25, 1
Solve 4*u**5 - 102*u**4 - 404*u**3 - 72*u**2 + 400*u + 174 = 0.
-3, -1, -1/2, 1, 29
Suppose -o**4/2 - o**3/2 + 79*o**2/2 + 289*o/2 + 105 = 0. What is o?
-7, -3, -1, 10
Factor -3*m**4 + 6*m**3 + 12*m**2 - 6*m - 9.
-3*(m - 3)*(m - 1)*(m + 1)**2
Solve 2*i**2 + 2*i - 12 = 0 for i.
-3, 2
Let -10*g**4/3 - 38*g**3/21 - 4*g**2/21 = 0. What is g?
-2/5, -1/7, 0
Factor 3*b**2 - 465*b + 6300.
3*(b - 140)*(b - 15)
Find f, given that f**5/10 - 9*f**4/10 - 23*f**3/10 + 21*f**2/2 + 119*f/5 + 12 = 0.
-3, -1, 4, 10
Let -o**5 + 3*o**4 - 2*o**3 = 0. What is o?
0, 1, 2
Suppose 4*v**4 - 148*v**3 + 284*v**2 - 140*v = 0. What is v?
0, 1, 35
Factor -6750*z**4 + 237600*z**3 - 47340*z**2 + 3152*z - 70.
-2*(z - 35)*(15*z - 1)**3
Factor 3*l**3 - 378*l**2 - 381*l.
3*l*(l - 127)*(l + 1)
Determine v so that 9*v**5 + 51*v**4 + 57*v**3 - 63*v**2 - 54*v = 0.
-3, -2/3, 0, 1
Factor 3*r**3/7 - 3*r**2 + 45*r/7 - 27/7.
3*(r - 3)**2*(r - 1)/7
Find b, given that -2*b**5/15 - 2*b**4/15 + 2*b**3/3 + 2*b**2/15 - 16*b/15 + 8/15 = 0.
-2, 1
Factor 3*r**3/7 - 18*r**2 - 264*r - 5184/7.
3*(r - 54)*(r + 4)*(r + 8)/7
Determine i so that -15*i**3 + 651*i**2 + 1092*i - 540 = 0.
-2, 2/5, 45
Find n, given that -2*n**4 - 10*n**3 - 