 1)
Factor 21*f**4 + 36*f**3 - 159*f**2 + 126*f - 24.
3*(f - 1)**2*(f + 4)*(7*f - 2)
Determine w so that 3*w**2 - 66*w + 288 = 0.
6, 16
Let -2*s**5/11 + 64*s**3/11 + 60*s**2/11 - 62*s/11 - 60/11 = 0. What is s?
-5, -1, 1, 6
Factor -5*h**4 - 95*h**3 - 520*h**2 - 700*h.
-5*h*(h + 2)*(h + 7)*(h + 10)
Let r**5/4 + r**4/2 - r**3/2 - r**2 + r/4 + 1/2 = 0. Calculate r.
-2, -1, 1
Factor -27*z**3/2 + 4020*z**2 + 894*z.
-3*z*(z - 298)*(9*z + 2)/2
Factor -2*o**4 + 8*o**3 - 12*o**2 + 8*o - 2.
-2*(o - 1)**4
Determine h, given that -3*h**3 - 96*h**2 - 180*h = 0.
-30, -2, 0
What is q in -q**5/5 + 9*q**4/5 + 36*q**3/5 + 4*q**2/5 - 48*q/5 = 0?
-2, 0, 1, 12
Factor -m**4/3 - 5*m**3/3 + 13*m**2/3 - 7*m/3.
-m*(m - 1)**2*(m + 7)/3
Factor -3*t**2/7 + 132*t - 921/7.
-3*(t - 307)*(t - 1)/7
Let -6*f**5 - 374*f**4 - 23060*f**3/3 - 50316*f**2 + 36162*f - 6174 = 0. Calculate f.
-21, 1/3
Factor 4*v**3/9 - 560*v**2/9 - 188*v/3.
4*v*(v - 141)*(v + 1)/9
What is k in k**4 - 1273*k**3/2 - 3191*k**2/2 - 2555*k/2 - 639/2 = 0?
-1, -1/2, 639
Factor i**2/2 - 1095*i + 1199025/2.
(i - 1095)**2/2
Solve -2*i**5/21 - 18*i**4/7 - 34*i**3/3 - 410*i**2/21 - 104*i/7 - 88/21 = 0 for i.
-22, -2, -1
Solve -2*b**3 + 42*b**2 - 240*b + 200 = 0 for b.
1, 10
Suppose 4*w**5 - 4*w**4 - 20*w**3 + 20*w**2 + 16*w - 16 = 0. Calculate w.
-2, -1, 1, 2
Factor -2178*f**4 - 2508*f**3 - 458*f**2 + 152*f - 8.
-2*(3*f + 2)**2*(11*f - 1)**2
Determine z so that -53138*z**3/13 - 160718*z**2/13 - 3920*z/13 - 24/13 = 0.
-3, -2/163
Suppose -5*c**2 + 390*c - 7605 = 0. What is c?
39
Factor -3*s**2 + 198*s - 744.
-3*(s - 62)*(s - 4)
Let 4*y**2/3 + 576*y + 62208 = 0. What is y?
-216
Suppose 2*g**2 - 60*g + 112 = 0. What is g?
2, 28
Solve 1369*q**2 - 74*q + 1 = 0 for q.
1/37
Find p, given that 2*p**3 + 16*p**2 - 158*p + 140 = 0.
-14, 1, 5
Let 3*k**5/2 + 16*k**4 + 58*k**3 + 89*k**2 + 121*k/2 + 15 = 0. Calculate k.
-5, -3, -1, -2/3
Let z**4 - z**3/2 - 3*z**2 = 0. Calculate z.
-3/2, 0, 2
Suppose 2*j**4/9 + 40*j**3/9 + 34*j**2/3 = 0. What is j?
-17, -3, 0
Let 7*c**5 - 47*c**4/2 + 28*c**3 - 13*c**2 + c + 1/2 = 0. Calculate c.
-1/7, 1/2, 1
Let -m**4/5 - m**3 + 3*m**2/5 + 17*m/5 + 2 = 0. What is m?
-5, -1, 2
Factor -z**2 + 1424*z - 506944.
-(z - 712)**2
Determine w so that 4*w**2 - 48*w + 144 = 0.
6
Solve 1474*u**2/5 - 4*u/5 = 0 for u.
0, 2/737
Let -4*z**2 - 484*z + 984 = 0. Calculate z.
-123, 2
Factor 123*l**2/2 + 249*l/4 + 3/4.
3*(l + 1)*(82*l + 1)/4
Factor 722*z**4 + 18620*z**3 + 118074*z**2 - 25480*z + 1352.
2*(z + 13)**2*(19*z - 2)**2
Factor -2*u**3/3 + 38*u**2/3 - 100*u/3 + 64/3.
-2*(u - 16)*(u - 2)*(u - 1)/3
Factor -3*d**5/8 + 3*d**4/4 - 3*d**3/8.
-3*d**3*(d - 1)**2/8
Suppose -5*n**3 - 800*n**2 - 2365*n - 1570 = 0. Calculate n.
-157, -2, -1
Factor -2*x**4 - 4*x**3 + 22*x**2 + 24*x - 72.
-2*(x - 2)**2*(x + 3)**2
Factor -2*b**2 - 2456*b - 753992.
-2*(b + 614)**2
Let 2*k**2/5 + 92*k/5 + 1058/5 = 0. What is k?
-23
Factor -3*p**3/2 - 261*p**2/2 + 1014*p + 2538.
-3*(p - 9)*(p + 2)*(p + 94)/2
Factor 3*h**2 + 15*h - 42.
3*(h - 2)*(h + 7)
Suppose a**5/10 - 9*a**4/10 + a**3 + 3*a**2 - 11*a/10 - 21/10 = 0. Calculate a.
-1, 1, 3, 7
Factor -b**3 + 2943*b**2 - 2887083*b + 944076141.
-(b - 981)**3
What is l in -5*l**2 + 210*l + 3575 = 0?
-13, 55
Factor y**2/4 + 83*y/4 - 21.
(y - 1)*(y + 84)/4
Find p such that 4*p**5 + 40*p**4 + 104*p**3 + 32*p**2 - 108*p - 72 = 0.
-6, -3, -1, 1
Let 7*o**5/3 + 466*o**4 - 1814*o**3/3 - 332*o**2 + 1807*o/3 - 134 = 0. What is o?
-201, -1, 2/7, 1
Suppose -5*k**4 - 1250*k**3 - 6165*k**2 - 9820*k - 4900 = 0. Calculate k.
-245, -2, -1
Factor u**3 + 55*u**2 + 667*u - 2523.
(u - 3)*(u + 29)**2
Factor -2*d**4/7 + 10*d**3/7 + 48*d**2/7.
-2*d**2*(d - 8)*(d + 3)/7
Factor 145*h**3 + 20890*h**2 + 753120*h + 51840.
5*(h + 72)**2*(29*h + 2)
Factor 4*g**2 + 844*g - 848.
4*(g - 1)*(g + 212)
Find t such that -2*t**2 - 36*t = 0.
-18, 0
Factor -n**2/2 - 501*n/2 + 1010.
-(n - 4)*(n + 505)/2
Find y, given that -2*y**2 + 86*y - 84 = 0.
1, 42
What is q in -3*q**2/4 + 21*q/2 - 18 = 0?
2, 12
Find u such that -u**3 - 265*u**2 + 1073*u - 807 = 0.
-269, 1, 3
Factor 2*w**3/19 - 2*w**2/19 - 12*w/19.
2*w*(w - 3)*(w + 2)/19
Find o, given that 3*o**2 + 165*o - 342 = 0.
-57, 2
Suppose c**4/3 - 4*c**3/3 + c**2/3 + 2*c = 0. What is c?
-1, 0, 2, 3
Find w, given that -2*w**4/7 - 2*w**3 - 2*w**2 + 30*w/7 = 0.
-5, -3, 0, 1
Let -3*g**2 + 21*g = 0. Calculate g.
0, 7
Factor -5*f**2 - 365*f - 360.
-5*(f + 1)*(f + 72)
Factor -o**3/4 + o**2/2.
-o**2*(o - 2)/4
Solve 3*n**4/5 - 12*n**3 + 396*n**2/5 - 192*n + 768/5 = 0 for n.
2, 8
Determine m, given that -5*m**3 + 80*m = 0.
-4, 0, 4
Suppose 2*z**3 + 15*z**2/2 - 51*z/2 - 65 = 0. What is z?
-5, -2, 13/4
Factor 3*d**4/4 - 51*d**3/4 + 57*d**2 - 45*d.
3*d*(d - 10)*(d - 6)*(d - 1)/4
Suppose 4*q**2/7 + 276*q/7 - 40 = 0. Calculate q.
-70, 1
Factor -4*w**2 - 1360*w.
-4*w*(w + 340)
Factor -15*t**3 - 305*t**2 + 215*t + 105.
-5*(t - 1)*(t + 21)*(3*t + 1)
Solve 4*d**4 - 32*d**3 + 20*d**2 + 152*d + 96 = 0.
-1, 4, 6
Suppose -5*m**5 + 5*m**4 + 275*m**3 + 715*m**2 + 450*m = 0. What is m?
-5, -2, -1, 0, 9
Let -3*m**5/2 + 33*m**4/2 - 63*m**3 + 96*m**2 - 48*m = 0. What is m?
0, 1, 2, 4
Factor -2*s**2/11 - 628*s/11 - 49298/11.
-2*(s + 157)**2/11
Factor 3*o**2/7 - 7590*o/7.
3*o*(o - 2530)/7
Factor 3*k**3/4 - 75*k**2/2 + 504*k - 864.
3*(k - 24)**2*(k - 2)/4
Determine i, given that -i**4/2 + 21*i**3 - 157*i**2/2 + 96*i - 38 = 0.
1, 2, 38
Factor 5*m**3 + 2575*m**2 + 332815*m + 330245.
5*(m + 1)*(m + 257)**2
Factor 4*m**2 - 408*m - 1260.
4*(m - 105)*(m + 3)
Let -28*p**4 + 444*p**3 + 64*p**2 = 0. What is p?
-1/7, 0, 16
Factor 4*n**2/9 - 14008*n/3 + 12264004.
4*(n - 5253)**2/9
Factor 16*y**3 - 68*y**2 - 100*y + 200.
4*(y - 5)*(y + 2)*(4*y - 5)
What is h in 2*h**5/5 - 16*h**4/5 + 2*h**3 + 20*h**2 = 0?
-2, 0, 5
Factor 5*i**2 - 820*i.
5*i*(i - 164)
Factor 2*a**3 - 328*a**2/3 + 648*a - 384.
2*(a - 48)*(a - 6)*(3*a - 2)/3
Factor 3*l**3 - 33*l**2 + 69*l + 105.
3*(l - 7)*(l - 5)*(l + 1)
Let 310*a**2 + 988*a/7 + 48/7 = 0. Calculate a.
-2/5, -12/217
Find s such that -5*s**5/2 + 5*s**4/2 + 5*s**3 = 0.
-1, 0, 2
Factor -2*k**3/3 + 220*k**2/3 - 5824*k/3 - 12544/3.
-2*(k - 56)**2*(k + 2)/3
Factor 6*v**3/5 + 54*v**2/5 - 126*v/5 + 66/5.
6*(v - 1)**2*(v + 11)/5
Solve 2*o**2 - 48*o + 288 = 0.
12
Solve 2*h**5 - 2*h**4 - 12*h**3 + 8*h**2 + 16*h = 0 for h.
-2, -1, 0, 2
Factor 5*z**3 - 465*z**2 + 14415*z - 148955.
5*(z - 31)**3
Determine c so that 4*c**2 + 1388*c - 2792 = 0.
-349, 2
Find j, given that -j**4 - 16*j**3 - 42*j**2 - 40*j - 13 = 0.
-13, -1
Let -3*s**5 + 27*s**4 + 156*s**3 + 48*s**2 - 576*s - 624 = 0. What is s?
-2, 2, 13
Factor 5*x**5 - 15*x**4 - 265*x**3 + 1275*x**2 - 1000*x.
5*x*(x - 5)**2*(x - 1)*(x + 8)
Factor 2*j**4/7 - 22*j**3 + 152*j**2/7.
2*j**2*(j - 76)*(j - 1)/7
Solve 14*u**5 + 4*u**4/3 - 98*u**3 + 224*u**2/3 + 8*u = 0 for u.
-3, -2/21, 0, 1, 2
Suppose -h**2/2 + 77*h - 5929/2 = 0. What is h?
77
Find w such that 60*w**4 - 28045*w**3 + 11645*w**2 + 14005*w + 2335 = 0.
-1/3, -1/4, 1, 467
Factor -2*h**2/15 - 14*h/15 - 4/5.
-2*(h + 1)*(h + 6)/15
Solve 6*f**3 - 40*f**2 + 72*f - 32 = 0 for f.
2/3, 2, 4
Let 2*u**5 - 76*u**4 + 610*u**3 + 2800*u**2 - 12000*u = 0. Calculate u.
-5, 0, 3, 20
What is a in 2*a**3/7 - 18*a**2/7 + 54*a/7 - 54/7 = 0?
3
Determine k so that 5*k**2 - 215*k/2 - 910 = 0.
-13/2, 28
Solve -3*b**5 - 81*b**4 - 411*b**3 + 1845*b**2 - 1350*b = 0 for b.
-15, 0, 1, 2
Determine k, given that 2*k**2/21 - 4*k/3 - 10/7 = 0.
-1, 15
Factor -3*m**5 + 9*m**4 - 6*m**3.
-3*m**3*(m - 2)*(m - 1)
Factor 3*u**4/4 + 23*u**3/4 + 19*u**2/2 - 8*u - 8.
(u - 1)*(u + 4)**2*(3*u + 2)/4
Factor -3*b**5 - 9*b**4 + 30*b**3 - 6*b**2 - 27*b + 15.
-3*(b - 1)**3*(b + 1)*(b + 5)
Let y**3/2 + 11*y**2/2 + 31*y/2 + 21/2 = 0. Calculate y.
-7, -3, -1
Determine u, given that -3*u**5 + 24*u**4 + 93*u**3 + 66*u**2 = 0.
-2, -1, 0, 11
Factor 25*g**4 + 40*g**3 + 5*g**2 - 10*g.
5*g*(g + 1)**2*(5*g - 2)
Determine w so that -44*w**2/3 + 13120*w/3 - 2384/3 = 0.
2/11, 298
Suppose -2*s**5/3 + 22*s**4/3 - 52*s**3/3 + 32*s**2/3 = 0. What is s?
0, 1, 2, 8
Suppose 2*h**3/3 - 112*h**2/9 + 88*h/3 - 128/9 = 0. What is h?
2/3, 2, 16
Let -19*k**4 - 339*k**3/2 + 825*k**2/2 - 481*k/2 + 33/2 = 0. Calculate k.
-11, 3/38, 1
Suppose -m**3 - 9*m**2 + 52*m = 0. What is m?
-13, 0, 4
Factor -