 Calculate n.
-4, 0, 1
Factor 3*d**3 + 123*d**2 + 348*d + 228.
3*(d + 1)*(d + 2)*(d + 38)
Determine s, given that -s**3/3 + 17*s**2/3 + 464*s/3 + 704 = 0.
-8, 33
Solve -2*r**2/3 - 4342*r/3 = 0 for r.
-2171, 0
Solve -3*p**4 + 15*p**3 + 141*p**2 - 315*p + 162 = 0.
-6, 1, 9
Suppose 4*l**5 + 8*l**4 - 44*l**3 - 48*l**2 = 0. What is l?
-4, -1, 0, 3
Factor 4*l**2 - 25648*l + 41113744.
4*(l - 3206)**2
Solve g**2 - 412*g + 42436 = 0.
206
Let -t**3/5 - 7*t**2/5 + 88*t - 540 = 0. What is t?
-27, 10
Find y such that 4*y**2 - 2432*y = 0.
0, 608
Factor -2*q**2 - 11724*q - 17181522.
-2*(q + 2931)**2
Find b such that -4*b**5/5 - 36*b**4/5 - 92*b**3/5 - 12*b**2/5 + 144*b/5 = 0.
-4, -3, 0, 1
Suppose -7*m**4/3 - 20*m**3/9 + m**2/9 = 0. What is m?
-1, 0, 1/21
Factor -2*x**2/11 - 6*x/11 + 8/11.
-2*(x - 1)*(x + 4)/11
Factor -2*w**3 + 228*w**2 - 6264*w + 50544.
-2*(w - 78)*(w - 18)**2
Let -2*f**5/7 + 4*f**4/7 - 4*f**2/7 + 2*f/7 = 0. Calculate f.
-1, 0, 1
Let -2*x**3/5 - 12*x**2/5 + 738*x/5 + 748/5 = 0. What is x?
-22, -1, 17
Let 64*a**4 - 928*a**3 + 2052*a**2 - 1620*a + 432 = 0. Calculate a.
3/4, 1, 12
Find o such that 5*o**3/4 + 75*o**2/2 + 1125*o/4 + 625 = 0.
-20, -5
Factor -3*c**2/4 + 9*c/2 + 81/4.
-3*(c - 9)*(c + 3)/4
Solve 5*z**5 + 20*z**4 + 15*z**3 - 20*z**2 - 20*z = 0 for z.
-2, -1, 0, 1
Solve -2*g**2/7 - 18*g + 680/7 = 0 for g.
-68, 5
Find k such that -k**2 + 51*k - 50 = 0.
1, 50
Factor 3*f**4/5 - 24*f**3/5 + 54*f**2/5 - 48*f/5 + 3.
3*(f - 5)*(f - 1)**3/5
Find h such that 190*h**2/3 - 1714*h/9 + 4/3 = 0.
2/285, 3
What is i in 27*i**3 + 3*i**2 - 20*i + 4 = 0?
-1, 2/9, 2/3
Find v such that -v**2 - 160*v - 471 = 0.
-157, -3
Solve 28*z**2 - 32*z = 0.
0, 8/7
Let 2*z**2 - 1084*z + 1082 = 0. What is z?
1, 541
Solve -t**2/7 - 10*t/7 - 16/7 = 0.
-8, -2
Factor -2*r**2 + 30*r + 252.
-2*(r - 21)*(r + 6)
Determine i so that i**2/3 + 698*i/3 + 121801/3 = 0.
-349
Suppose 5*k**5 - 35*k**4 + 85*k**3 - 85*k**2 + 30*k = 0. What is k?
0, 1, 2, 3
Factor -l**2 + 2436*l - 1483524.
-(l - 1218)**2
Solve -k**2 + 3840*k - 3686400 = 0 for k.
1920
Solve -124*q**5 - 8*q**4 + 372*q**3 - 224*q**2 - 16*q = 0.
-2, -2/31, 0, 1
Let -3*d**4 - 16*d**3/3 + 13*d**2/3 + 16*d/3 - 4/3 = 0. What is d?
-2, -1, 2/9, 1
Factor -2*f**2 + 58*f + 1092.
-2*(f - 42)*(f + 13)
Factor -9*g**2/5 + 21*g/5 + 18/5.
-3*(g - 3)*(3*g + 2)/5
Let -8*y**5 + 31*y**4 + 28*y**3 - 141*y**2 - 18*y = 0. What is y?
-2, -1/8, 0, 3
Factor -4*p**4/3 + 8*p**3/3.
-4*p**3*(p - 2)/3
Let k**2/6 + 397*k/6 - 199/3 = 0. Calculate k.
-398, 1
Factor -3*a**4 + 33*a**3 - 42*a**2 - 240*a.
-3*a*(a - 8)*(a - 5)*(a + 2)
Factor 3*y**2/5 + 87*y/5 + 234/5.
3*(y + 3)*(y + 26)/5
Factor 3*s**3 + 234*s**2 + 225*s - 462.
3*(s - 1)*(s + 2)*(s + 77)
Factor 3*k**5 + 83*k**4 + 692*k**3 + 960*k**2 - 6400*k + 2000.
(k - 2)*(k + 10)**3*(3*k - 1)
Find a such that -5*a**5/4 + 25*a**4/4 + 35*a**3/4 - 205*a**2/4 + 75*a/2 = 0.
-3, 0, 1, 2, 5
Find h such that h**4/6 + 4*h**3/3 + h**2 - 20*h/3 + 25/6 = 0.
-5, 1
Factor 5*u**5 - 60*u**4 + 180*u**3.
5*u**3*(u - 6)**2
Factor i**4/3 - 28*i**3/3 + 155*i**2/3 - 152*i/3 - 112.
(i - 21)*(i - 4)**2*(i + 1)/3
Determine c so that -3*c**2/5 + 177*c/5 - 2442/5 = 0.
22, 37
Suppose -15*b**3 + 185*b**2 - 705*b + 855 = 0. Calculate b.
3, 19/3
What is l in 2*l**2/7 - 6612*l/7 + 5464818/7 = 0?
1653
Let 2*h**2/17 + 4396*h/17 + 2415602/17 = 0. What is h?
-1099
Factor 2*r**3/9 - 26*r/9 + 8/3.
2*(r - 3)*(r - 1)*(r + 4)/9
Suppose 200*j**2/9 - 40*j/9 + 2/9 = 0. What is j?
1/10
Solve r**2/2 + 3*r/2 + 1 = 0.
-2, -1
Factor 5*p**2 + 108*p.
p*(5*p + 108)
Solve -5*t**2 - 15*t + 440 = 0 for t.
-11, 8
Factor 7*b**4/2 - 391*b**3 + 10864*b**2 + 3136*b.
b*(b - 56)**2*(7*b + 2)/2
Determine u, given that 3*u**4 - 36*u**3 + 102*u**2 + 36*u - 105 = 0.
-1, 1, 5, 7
Factor 3*r**2 - 96*r.
3*r*(r - 32)
Factor 4*b**4 - 4*b**3 - 24*b**2 + 16*b + 32.
4*(b - 2)**2*(b + 1)*(b + 2)
Let 4*n**2 - 488*n + 4068 = 0. What is n?
9, 113
Factor -14*u**2/17 - 298*u/17 - 84/17.
-2*(u + 21)*(7*u + 2)/17
What is r in -3*r**2/5 + 3*r - 18/5 = 0?
2, 3
Suppose p**4 - 1297*p**3 + 419903*p**2 + 421201*p = 0. What is p?
-1, 0, 649
Factor -4*p**4 + 20*p**3 + 4*p**2 - 20*p.
-4*p*(p - 5)*(p - 1)*(p + 1)
Factor k**2/3 + 39*k + 114.
(k + 3)*(k + 114)/3
Find w such that w**3 + 721*w**2 + 130320*w + 129600 = 0.
-360, -1
Let i**4 + 3*i**3 + 2*i**2 = 0. Calculate i.
-2, -1, 0
Solve 12*r**5 + 9*r**4 - 15*r**3 - 9*r**2 + 3*r = 0.
-1, 0, 1/4, 1
Factor 2*t**4 + 376*t**3 + 16500*t**2 - 110968*t + 94090.
2*(t - 5)*(t - 1)*(t + 97)**2
Solve -2*u**4/5 + 132*u**3/5 - 2306*u**2/5 + 4224*u/5 - 2048/5 = 0.
1, 32
Determine h, given that -h**2/4 + 461*h/2 - 212521/4 = 0.
461
Factor i**2/3 - 167*i/3 - 56.
(i - 168)*(i + 1)/3
Factor -z**2/3 - 2*z/3 + 1.
-(z - 1)*(z + 3)/3
Let -5*u**3 + 5*u**2 + 5*u - 5 = 0. Calculate u.
-1, 1
Factor 98*h**5 - 5348*h**4 + 98288*h**3 - 626400*h**2 + 334368*h - 46656.
2*(h - 18)**3*(7*h - 2)**2
Factor -45*p**3 - 3540*p**2 + 4780*p - 1600.
-5*(p + 80)*(3*p - 2)**2
Factor 200*d**5 - 840*d**4 + 162*d**3 - 8*d**2.
2*d**2*(d - 4)*(10*d - 1)**2
What is l in -2*l**2/23 - 10*l/23 - 12/23 = 0?
-3, -2
Factor 3*y**5/4 + 15*y**4/2 + 51*y**3/4 + 6*y**2.
3*y**2*(y + 1)**2*(y + 8)/4
Let -3*v**3/2 - 213*v**2/2 + 108*v = 0. What is v?
-72, 0, 1
Suppose -q**3/4 + 165*q**2/4 - 7623*q/4 + 65219/4 = 0. What is q?
11, 77
Let -4*v**2 + 26648*v - 44382244 = 0. What is v?
3331
Let 2*g**2/13 - 168*g/13 - 1472/13 = 0. Calculate g.
-8, 92
Find i such that -5*i**3 - 245*i**2 - 3120*i - 2880 = 0.
-24, -1
Factor -o**4 + 13*o**3 - 62*o**2 + 128*o - 96.
-(o - 4)**2*(o - 3)*(o - 2)
Factor v**5/9 + 13*v**4/9 + 23*v**3/9 + 11*v**2/9.
v**2*(v + 1)**2*(v + 11)/9
Let -7*y**5/4 - 4*y**4 + 41*y**3 + 12*y**2 = 0. Calculate y.
-6, -2/7, 0, 4
Factor 4*t**3 + 244*t**2 + 3600*t.
4*t*(t + 25)*(t + 36)
Determine u so that -18*u**5/7 - 48*u**4/7 + 244*u**3/7 + 824*u**2/7 + 66*u + 72/7 = 0.
-3, -1/3, 4
Let -5*a**3 + 220*a**2 - 425*a + 210 = 0. Calculate a.
1, 42
Find q such that -20000*q**2 - 1200*q - 18 = 0.
-3/100
Factor 5*i**4 - 15*i**3 - 45*i**2 + 115*i - 60.
5*(i - 4)*(i - 1)**2*(i + 3)
Let 2*t**2 - 192*t = 0. What is t?
0, 96
Find k, given that 2*k**3/17 + 38*k**2/17 + 200*k/17 + 264/17 = 0.
-11, -6, -2
Solve -a**5/3 - 5*a**4/3 - a**3 + 5*a**2/3 + 4*a/3 = 0.
-4, -1, 0, 1
Find z such that z**3 + 161*z**2 + 318*z = 0.
-159, -2, 0
Factor -64296980*b**3 - 35860*b**2 - 5*b.
-5*b*(3586*b + 1)**2
Factor k**4 - 10*k**3 + 9*k**2.
k**2*(k - 9)*(k - 1)
Find b such that 24*b**3/5 + 14*b**2/5 - 388*b/15 + 32/15 = 0.
-8/3, 1/12, 2
Factor -n**4/4 - 6*n**3 - 75*n**2/2 - 50*n + 375/4.
-(n - 1)*(n + 5)**2*(n + 15)/4
Factor -3*a**4 - 18*a**3 + 96*a.
-3*a*(a - 2)*(a + 4)**2
Factor 2*t**2 + 4352*t + 2367488.
2*(t + 1088)**2
Determine s so that 6*s**4 + 40*s**3 + 72*s**2 + 32*s = 0.
-4, -2, -2/3, 0
Factor 4*r**3 + 32*r**2 + 44*r - 80.
4*(r - 1)*(r + 4)*(r + 5)
Solve -10*x**2 - 8714*x - 3484 = 0.
-871, -2/5
Find j such that 2*j**2/3 + 152*j/3 + 2888/3 = 0.
-38
Factor 5*s**3 - 70*s**2.
5*s**2*(s - 14)
Factor -2*u**5/7 - 22*u**4/7 - 2*u**3 + 42*u**2.
-2*u**2*(u - 3)*(u + 7)**2/7
Solve -2*d**2 + 372*d = 0.
0, 186
Factor 2*w**3/11 - 194*w**2/11 + 3006*w/11 - 12798/11.
2*(w - 79)*(w - 9)**2/11
Determine f so that 10*f**5 + 15*f**4 - 5*f**3 - 15*f**2 - 5*f = 0.
-1, -1/2, 0, 1
Solve -2*w**2/11 - 332*w/11 + 672/11 = 0 for w.
-168, 2
Let g**3/3 - 23*g**2/3 - g/3 + 23/3 = 0. Calculate g.
-1, 1, 23
Solve 3*r**3 - 30*r**2 + 69*r - 42 = 0 for r.
1, 2, 7
Factor 4*w**3 - 16*w**2.
4*w**2*(w - 4)
Factor -2*a**3/5 - 12*a**2/5 + 6*a + 40.
-2*(a - 4)*(a + 5)**2/5
Factor -4*t**2/3 - 32*t/3 - 16.
-4*(t + 2)*(t + 6)/3
Determine x, given that 5*x**3 - 100*x**2 - 220*x = 0.
-2, 0, 22
Suppose -f**5/3 - 7*f**4/3 + 127*f**3/3 + 55*f**2/3 - 266*f - 240 = 0. What is f?
-15, -2, -1, 3, 8
Let -552*q**5 + 4425*q**4/2 - 3330*q**3 + 2235*q**2 - 570*q + 9/2 = 0. Calculate q.
3/368, 1
Suppose -4*b**5/9 + 10*b**4/3 + 2*b**3 - 16*b**2/9 = 0. What is b?
-1, 0, 1/2, 8
What is c in 3*c**2/8 + 15*c/8 + 3/2 = 0?
-4, -1
Find b, given that 387*b**3 + 402*b**2 + 15*b = 0.
-1, -5/129, 0
Solve f**2 - 7*f + 12 = 0 for f.
3, 4
Solve 6*q**5 - 152*q**4 + 838*q**3 - 812*q**2 - 312*q + 432 = 0 for q.
-2/3, 1, 6, 18
Factor k**4/4 - 283*k**3/2 + 423*k**2 - 845*k/2 + 563/4.
(k - 563)*(k - 1)**3/4
Fac