.
-7, -4, 0
Factor -4*f**3 - 2*f**2 + 4*f + 2.
-2*(f - 1)*(f + 1)*(2*f + 1)
Factor -s**5/5 + 196*s**4/5 - 9406*s**3/5 - 19404*s**2/5 - 9801*s/5.
-s*(s - 99)**2*(s + 1)**2/5
Determine o, given that -3*o**2/2 + 33*o - 363/2 = 0.
11
Factor 4*z**3/5 + 284*z**2/5 + 1036*z + 980.
4*(z + 1)*(z + 35)**2/5
Solve -33*v**3 - 996*v**2 - 7605*v - 1350 = 0.
-15, -2/11
Suppose -n**3/4 + 540*n**2 - 388800*n + 93312000 = 0. Calculate n.
720
Determine q so that 5*q**2 - 4320*q = 0.
0, 864
Factor -2*s**4 + 8*s**3 + 64*s**2.
-2*s**2*(s - 8)*(s + 4)
Find k such that -2*k**4/9 - 22*k**3/9 + 80*k**2/3 + 3968*k/9 + 13312/9 = 0.
-8, 13
Factor -2*d**3/9 - 1514*d**2/9 - 3010*d/3 - 1502.
-2*(d + 3)**2*(d + 751)/9
Find u, given that -2*u**2/3 - 68*u/3 - 22 = 0.
-33, -1
Factor 5*w**3 - 1425*w**2 - 1430*w.
5*w*(w - 286)*(w + 1)
Factor -5*o**3 - 840*o**2.
-5*o**2*(o + 168)
Let 2*u**3 + 6*u**2 - 2898*u - 45494 = 0. What is u?
-23, 43
Factor y**2/5 + 27*y/5 + 26/5.
(y + 1)*(y + 26)/5
Solve d**3/6 + d**2 - 7*d/6 = 0 for d.
-7, 0, 1
Suppose 4*f**2/3 + 31*f/3 - 43 = 0. Calculate f.
-43/4, 3
Factor c**4/7 + 20*c**3/7 + 96*c**2/7 + 176*c/7 + 16.
(c + 2)**3*(c + 14)/7
Determine s, given that -2*s**3 - 20*s**2 - 34*s - 16 = 0.
-8, -1
Let -3*c**3/7 - 12*c**2/7 - 15*c/7 - 6/7 = 0. Calculate c.
-2, -1
Suppose 2*n**2/11 + 24*n + 792 = 0. What is n?
-66
Let 231*f**2 - 249*f + 18 = 0. What is f?
6/77, 1
Solve -5*l**2 - 400*l - 8000 = 0 for l.
-40
Find c, given that 12*c**4 - 128*c**3 - 204*c**2 + 128*c + 192 = 0.
-4/3, -1, 1, 12
Let 3*w**4/2 - 3*w**3/2 - 15*w**2/2 - 9*w/2 = 0. Calculate w.
-1, 0, 3
Determine b so that -2523*b**3/4 + 4785*b**2/4 - 2769*b/4 + 507/4 = 0.
13/29, 1
Find c, given that c**4/5 - 18*c**3/5 + 61*c**2/5 + 36*c + 20 = 0.
-1, 10
Find p such that -p**2 - 19*p + 20 = 0.
-20, 1
Factor -j**2 + 137*j + 278.
-(j - 139)*(j + 2)
Factor 16*s**3 - 4*s**2 - 20*s.
4*s*(s + 1)*(4*s - 5)
Let -3*h**4 + 165*h**3 - 3312*h**2 + 28416*h - 86016 = 0. What is h?
7, 16
Let k**5/2 + 2*k**4/3 - 2*k**3/3 - k**2 + k/6 + 1/3 = 0. Calculate k.
-1, 2/3, 1
Factor 5*y**4/6 - 895*y**3/3 + 26400*y**2 + 54000*y.
5*y*(y - 180)**2*(y + 2)/6
Let -8*o**2 - 362*o - 90 = 0. Calculate o.
-45, -1/4
Let -3*g**5/4 + 7*g**4/2 - g**3 - 9*g**2/2 + 7*g/4 + 1 = 0. What is g?
-1, -1/3, 1, 4
Factor -4*p**2 - 2824*p - 498436.
-4*(p + 353)**2
Factor -298*j**2/3 + j/3.
-j*(298*j - 1)/3
Factor -5*f**5 + 20*f**4 - 30*f**3 + 20*f**2 - 5*f.
-5*f*(f - 1)**4
Let -8*f**4/9 + 34*f**3/9 - 10*f**2/3 - 32*f/9 + 40/9 = 0. Calculate f.
-1, 5/4, 2
Factor w**4 + 5*w**3 + 8*w**2 + 4*w.
w*(w + 1)*(w + 2)**2
Find n such that 4*n**2 + 68*n + 288 = 0.
-9, -8
Determine s, given that 3*s**2/7 - 27*s/7 - 30/7 = 0.
-1, 10
Factor -5*y**4 - 135*y**3 - 485*y**2 - 585*y - 230.
-5*(y + 1)**2*(y + 2)*(y + 23)
Suppose 2*p**5/25 + 18*p**4/25 - 66*p**3/25 + 14*p**2/5 - 24*p/25 = 0. Calculate p.
-12, 0, 1
Factor -2*j**2 - 366*j + 740.
-2*(j - 2)*(j + 185)
Factor 3*d**2 - 93*d + 174.
3*(d - 29)*(d - 2)
Suppose 4*a**5 + 16*a**4 - 80*a**3 + 40*a**2 + 76*a - 56 = 0. What is a?
-7, -1, 1, 2
Let -4*v**2/3 - 176*v - 516 = 0. What is v?
-129, -3
Factor 2*y**4/11 - 140*y**3/11 + 274*y**2/11 - 136*y/11.
2*y*(y - 68)*(y - 1)**2/11
Let 3*f**5/4 + 231*f**4/2 + 17319*f**3/4 - 9009*f**2 + 4563*f = 0. What is f?
-78, 0, 1
Solve g**2 + 435*g - 1756 = 0 for g.
-439, 4
Factor -b**3/3 - 137*b**2/3 - 4015*b/3 + 15987.
-(b - 9)*(b + 73)**2/3
Let 4*c**3 + 8*c**2 - 96*c = 0. Calculate c.
-6, 0, 4
Determine x so that x**4 - 15*x**3 + 38*x**2 - 24*x = 0.
0, 1, 2, 12
Factor m**3/2 + 3*m**2/2 - 2.
(m - 1)*(m + 2)**2/2
Factor n**4/5 - 2*n**3 - 23*n**2/5 - 12*n/5.
n*(n - 12)*(n + 1)**2/5
Solve -28*w**2/11 + 62*w/11 - 12/11 = 0.
3/14, 2
Suppose 20*t**3 - 195*t**2 + 130*t + 45 = 0. What is t?
-1/4, 1, 9
Let 12*q**5 + 100*q**4 + 84*q**3 - 644*q**2 - 240*q + 400 = 0. What is q?
-5, -1, 2/3, 2
Factor -x**3 + 373*x**2 + x - 373.
-(x - 373)*(x - 1)*(x + 1)
Find m such that 242*m**4 - 1672*m**3/3 + 3548*m**2/9 - 760*m/9 + 50/9 = 0.
5/33, 1
Factor 4*j**5 - 36*j**4 + 120*j**3 - 176*j**2 + 96*j.
4*j*(j - 3)*(j - 2)**3
Factor m**5/11 + 4*m**4 - 192*m**3/11 + 16*m**2/11 + 752*m/11 - 768/11.
(m - 2)**3*(m + 2)*(m + 48)/11
Factor 3*r**3/4 + 72*r**2 + 267*r - 828.
3*(r - 2)*(r + 6)*(r + 92)/4
Determine g, given that 2*g**3/5 + 122*g**2/5 + 406*g + 5046/5 = 0.
-29, -3
Solve -2*n**2/9 - 4*n/3 - 10/9 = 0 for n.
-5, -1
Solve -46*a**3/9 - 892*a**2/3 - 4350*a - 6728/9 = 0.
-29, -4/23
Solve 5*n**5/4 + n**4 - 3*n**3 - 5*n**2/2 + 7*n/4 + 3/2 = 0.
-1, 1, 6/5
Factor 5*o**2 + 185*o - 190.
5*(o - 1)*(o + 38)
Suppose -25*p**5/3 - 152*p**4/3 + 413*p**3/3 + 184*p**2/3 - 388*p/3 - 32/3 = 0. What is p?
-8, -1, -2/25, 1, 2
Let r**2 + 39*r - 40 = 0. What is r?
-40, 1
Factor 2*c**4 + 10*c**3 - 2*c**2 - 10*c.
2*c*(c - 1)*(c + 1)*(c + 5)
What is b in 5*b**2 - 108*b - 44 = 0?
-2/5, 22
Factor 22*p**2/13 + 68*p/13 + 6/13.
2*(p + 3)*(11*p + 1)/13
Let 16*d**5 + 20*d**4 - 24*d**3 - 32*d**2 + 8*d + 12 = 0. Calculate d.
-1, 3/4, 1
Factor -g**5 + 2*g**4 + 5*g**3 - 6*g**2.
-g**2*(g - 3)*(g - 1)*(g + 2)
Let 3*q**5/2 - 23*q**4/2 + 29*q**3 - 25*q**2 + 3*q/2 + 9/2 = 0. Calculate q.
-1/3, 1, 3
Factor 15*w**4 + 5*w**3.
5*w**3*(3*w + 1)
Factor -5*k**2 + 60*k - 180.
-5*(k - 6)**2
Factor -12*l**3 + 44*l**2 + 76*l + 20.
-4*(l - 5)*(l + 1)*(3*l + 1)
Factor v**2/6 - 656*v/3 + 215168/3.
(v - 656)**2/6
Determine y so that y**2 - 98*y - 624 = 0.
-6, 104
Determine k so that 2*k**3 - 26*k**2 = 0.
0, 13
Let -a**2 + 25*a = 0. What is a?
0, 25
Let -r**2 + 941*r + 1886 = 0. Calculate r.
-2, 943
Suppose 20*x**4 + 105*x**3 - 415*x**2 + 210*x + 80 = 0. Calculate x.
-8, -1/4, 1, 2
Find h such that -4*h**3 - 936*h**2 - 3696*h - 3680 = 0.
-230, -2
Factor g**4/4 - 23*g**3/4 - 105*g**2.
g**2*(g - 35)*(g + 12)/4
Factor 5*b**3/3 + 95*b**2/3 + 575*b/3 + 375.
5*(b + 5)**2*(b + 9)/3
Find w, given that 2*w**2/3 + 2540*w + 2419350 = 0.
-1905
Factor 3*n**5/5 - 3*n**4/5 - 3*n**3 + 3*n**2/5 + 24*n/5 + 12/5.
3*(n - 2)**2*(n + 1)**3/5
Factor 5*k**5 - 35*k**4 + 30*k**3 + 140*k**2 - 200*k.
5*k*(k - 5)*(k - 2)**2*(k + 2)
Factor -b**4 - 10*b**3 - 12*b**2 + 40*b + 64.
-(b - 2)*(b + 2)**2*(b + 8)
Suppose 2*l**3/3 + 10*l**2 + 32*l - 128/3 = 0. What is l?
-8, 1
What is h in h**2/4 - 47*h/2 + 2209/4 = 0?
47
Solve -2*c**2/5 + 2312*c/5 - 668168/5 = 0.
578
Let -4*t**2 - 36*t - 56 = 0. What is t?
-7, -2
Determine z, given that -3*z**4 + 42*z**3 - 99*z**2 - 336*z - 192 = 0.
-1, 8
What is k in -2*k**3/21 - 664*k**2/7 = 0?
-996, 0
Determine v, given that -4*v**2 + 13636*v/3 - 4544/3 = 0.
1/3, 1136
Factor -s**4 + 191*s**3 - 9762*s**2 + 61088*s - 84640.
-(s - 92)**2*(s - 5)*(s - 2)
Factor -2*f**2/3 - 286*f/3 - 2660/3.
-2*(f + 10)*(f + 133)/3
Let -5*p**4 + 115*p**3 - 380*p**2 = 0. Calculate p.
0, 4, 19
Solve j**5 + 12*j**4 + 56*j**3 + 126*j**2 + 135*j + 54 = 0.
-3, -2, -1
Find a such that -4*a**5 - 1268*a**4 + 2548*a**3 - 1276*a**2 = 0.
-319, 0, 1
Let -65610*m**2 + 648*m - 8/5 = 0. What is m?
2/405
Suppose 2*g**2/3 - 274*g/3 + 180 = 0. What is g?
2, 135
Factor 3*f**2/5 - 1422*f + 842535.
3*(f - 1185)**2/5
Factor 28*h**4/5 + 22*h**3 + 104*h**2/5 - 8*h/5.
2*h*(h + 2)**2*(14*h - 1)/5
Let -3*k**2 - 528*k - 23232 = 0. Calculate k.
-88
Factor -4*c**4 - 36*c**3 + 4*c**2 + 564*c + 1008.
-4*(c - 4)*(c + 3)**2*(c + 7)
Factor -2*y**4/25 - 558*y**3/25.
-2*y**3*(y + 279)/25
Factor -2*h**5/9 + 344*h**4/9 - 14792*h**3/9.
-2*h**3*(h - 86)**2/9
Find a such that 2*a**2 + 34*a + 60 = 0.
-15, -2
Find g such that g**5/2 - 7*g**4/2 - 51*g**3 - 127*g**2 - 235*g/2 - 75/2 = 0.
-5, -1, 15
Suppose -4*h**3/3 + 52*h**2 + 224*h + 688/3 = 0. What is h?
-2, 43
Factor 4*i**5 + 40*i**4 + 16*i**3 - 544*i**2 - 1408*i - 1024.
4*(i - 4)*(i + 2)**3*(i + 8)
Factor a**3 - 2*a**2 - 168*a.
a*(a - 14)*(a + 12)
Factor -6*x**3/7 - 40*x**2/7 + 2*x.
-2*x*(x + 7)*(3*x - 1)/7
Factor 192*z**3 - 10512*z**2 + 191844*z - 1167051.
3*(4*z - 73)**3
Determine y, given that -y**3/4 - 3687*y**2/2 = 0.
-7374, 0
Determine i so that 2*i**3 - 36*i**2 - 134*i + 168 = 0.
-4, 1, 21
Solve 2*m**3/3 - 82*m**2/9 + 212*m/9 + 80/9 = 0 for m.
-1/3, 4, 10
What is x in -2*x**3 + 12*x**2 - 10*x = 0?
0, 1, 5
Determine x so that -44*x**3 + 84*x**2 - 36*x - 4 = 0.
-1/11, 1
Suppose -p**3/4 - 19*p**2/4 - 19*p + 24 = 0. What is p?
-12, -8, 1
Factor 15*d**3/2 + 6*d**2 