463)/2
Factor 7*c**3/3 + c**2 - 7*c/3 - 1.
(c - 1)*(c + 1)*(7*c + 3)/3
Solve -2*k**3 - 244*k**2 - 7442*k = 0.
-61, 0
Determine q so that q**3/6 + 7*q**2/2 + 15*q = 0.
-15, -6, 0
Determine p so that 3*p**5/4 - 45*p**4/2 + 597*p**3/4 - 801*p**2/2 + 471*p - 198 = 0.
1, 2, 3, 22
Find y, given that -3*y**2 + 48 = 0.
-4, 4
Find s such that 2*s**3 + 108*s**2 + 1944*s + 11664 = 0.
-18
Solve 3*j**4/2 - 83*j**3 + 2403*j**2/2 - 1458*j = 0.
0, 4/3, 27
Determine f, given that 995*f**2 + 1985*f - 10 = 0.
-2, 1/199
Let -3*y**5/7 + 15*y**4 - 654*y**3/7 + 66*y**2/7 + 2529*y/7 + 243 = 0. What is y?
-1, 3, 7, 27
Factor 2*m**3 + 46*m**2 + 86*m + 42.
2*(m + 1)**2*(m + 21)
Factor g**2/3 + 14*g/3 + 49/3.
(g + 7)**2/3
What is w in 2*w**4/13 + 266*w**3/13 + 8150*w**2/13 - 46506*w/13 + 38088/13 = 0?
-69, 1, 4
Let -10*i**3 + 1856*i**2 + 2614*i + 748 = 0. Calculate i.
-1, -2/5, 187
Suppose h**3/4 - 3*h**2/2 + 11*h/4 - 3/2 = 0. Calculate h.
1, 2, 3
Determine h so that -80*h**2 + 40*h - 5 = 0.
1/4
Factor -q**2 - 107*q + 108.
-(q - 1)*(q + 108)
Suppose -u**2/3 + 68*u/3 - 1156/3 = 0. What is u?
34
Determine r, given that -3*r**2 + 999*r + 1002 = 0.
-1, 334
Factor 2*h**2/3 + 88*h/3 - 30.
2*(h - 1)*(h + 45)/3
Suppose -30*a**2 + 175*a + 30 = 0. Calculate a.
-1/6, 6
Factor 4*s**2 + 9040*s + 5107600.
4*(s + 1130)**2
Factor 3*c**5 - 15*c**4 - 24*c**3 + 36*c**2.
3*c**2*(c - 6)*(c - 1)*(c + 2)
Factor 15*a**2 + 1160*a + 3345.
5*(a + 3)*(3*a + 223)
Factor 2*c**3/9 - 76*c**2/9 - 26*c/3.
2*c*(c - 39)*(c + 1)/9
Factor 2*z**2/9 + 76*z/9 + 434/9.
2*(z + 7)*(z + 31)/9
Factor m**4/7 + 9*m**3/7 + 30*m**2/7 + 44*m/7 + 24/7.
(m + 2)**3*(m + 3)/7
Factor b**2 + 3*b.
b*(b + 3)
Let 35*o**5 - 1215*o**4 + 14665*o**3 - 67705*o**2 + 72600*o + 26620 = 0. What is o?
-2/7, 2, 11
Determine n so that -43*n**5/5 + 131*n**4/5 - 92*n**3/5 + 4*n**2/5 = 0.
0, 2/43, 1, 2
Find y such that -4*y**2/9 - 208*y/9 + 48 = 0.
-54, 2
Let c**2/5 - 13*c/5 + 22/5 = 0. Calculate c.
2, 11
Find g such that -110*g**4/7 + 68*g**3/7 + 74*g**2 - 380*g/7 - 96/7 = 0.
-24/11, -1/5, 1, 2
Factor 3*r**3/5 - 3*r**2/5 - 12*r/5 + 12/5.
3*(r - 2)*(r - 1)*(r + 2)/5
Factor -24*u**2 + 244*u - 40.
-4*(u - 10)*(6*u - 1)
Factor o**4/5 + 59*o**3/5 + 1071*o**2/5 + 3969*o/5 - 37044/5.
(o - 4)*(o + 21)**3/5
Factor 567*r**3/5 + 10242*r**2/5 + 9536*r + 2560.
(7*r + 2)*(9*r + 80)**2/5
Factor -94*j**3 - 180*j**2 - 78*j + 8.
-2*(j + 1)**2*(47*j - 4)
Find q such that 85*q**5 + 690*q**4 + 1525*q**3 + 1020*q**2 + 100*q = 0.
-5, -2, -1, -2/17, 0
Suppose -2*j**4 + 158*j**3 - 4680*j**2 + 61600*j - 304000 = 0. What is j?
19, 20
Factor -n**3 + 332*n**2 + 1003*n + 670.
-(n - 335)*(n + 1)*(n + 2)
Factor k**5/2 + k**4 - k**2 - k/2.
k*(k - 1)*(k + 1)**3/2
Factor -i**3/7 - 6*i**2/7 + 64*i/7 - 96/7.
-(i - 4)*(i - 2)*(i + 12)/7
Factor 6*a**2 + 315*a - 159.
3*(a + 53)*(2*a - 1)
Let 3*g**2 - 3171*g - 3174 = 0. Calculate g.
-1, 1058
Factor b**3/9 + 9743*b**2/9 + 7908880*b/3 - 2637376.
(b - 1)*(b + 4872)**2/9
Find x, given that 4*x**4 - 16*x**3 - 20*x**2 = 0.
-1, 0, 5
Solve -2*i**4 + 10*i**3 + 6*i**2 - 34*i + 20 = 0.
-2, 1, 5
Suppose 5*g**5 - 20*g**4 + 10*g**3 + 20*g**2 - 15*g = 0. What is g?
-1, 0, 1, 3
Factor -2*g**2/3 + 140*g/3 - 750.
-2*(g - 45)*(g - 25)/3
What is c in 5*c**4 + 1045*c**3 - 1055*c**2 - 1045*c + 1050 = 0?
-210, -1, 1
Factor 16*g**4 - 189592*g**3 + 561595201*g**2 + 280833150*g + 35105625.
(g - 5925)**2*(4*g + 1)**2
Let 2*u**3/9 - 10*u**2/3 + 124*u/9 - 32/3 = 0. Calculate u.
1, 6, 8
Factor -4*c**3/9 + 4*c**2/9.
-4*c**2*(c - 1)/9
Let 4*l**3 + 572*l**2 + 568*l = 0. Calculate l.
-142, -1, 0
Factor -36*g**3 + 748*g**2 + 1824*g + 368.
-4*(g - 23)*(g + 2)*(9*g + 2)
Factor y**3 - 44*y**2 + 43*y.
y*(y - 43)*(y - 1)
Factor 5*h**5 + 170*h**4 + 325*h**3 + 160*h**2.
5*h**2*(h + 1)**2*(h + 32)
Factor 3*v**2/4 + 309*v/2 - 621/4.
3*(v - 1)*(v + 207)/4
Suppose b**3 + 137*b**2 + 4623*b - 4761 = 0. Calculate b.
-69, 1
Factor -4*a**2 + 2304*a - 6876.
-4*(a - 573)*(a - 3)
What is t in t**5/12 - t**4/4 + t**2/3 = 0?
-1, 0, 2
Find t such that 3*t**4 - 18*t**3 - 153*t**2 + 348*t - 180 = 0.
-6, 1, 10
Factor 4*f**2/7 - 40*f/7 + 64/7.
4*(f - 8)*(f - 2)/7
Factor -5*a**3 - 7372*a**2 + 4427*a + 2950.
-(a - 1)*(a + 1475)*(5*a + 2)
Solve -3*q**5 - 96*q**4 + 243*q**3 + 1356*q**2 + 1020*q = 0.
-34, -2, -1, 0, 5
Factor -4*i**2 - 288*i + 6916.
-4*(i - 19)*(i + 91)
Determine p so that -p**2 + 27*p - 176 = 0.
11, 16
Factor -2*u**3/19 - 656*u**2/19 - 54442*u/19 - 106276/19.
-2*(u + 2)*(u + 163)**2/19
Determine y so that -y**5 + 67*y**4 - 1331*y**3 + 6965*y**2 - 10200*y + 4500 = 0.
1, 5, 30
What is q in q**5/5 + 19*q**4/5 + 14*q**3 - 4*q**2 - 296*q/5 - 224/5 = 0?
-14, -4, -2, -1, 2
Solve -c**5 + 254*c**4/7 - 3124*c**3/7 + 14984*c**2/7 - 3712*c + 896 = 0 for c.
2/7, 4, 14
Factor x**2/6 + 862*x/3 + 371522/3.
(x + 862)**2/6
Find t such that -5*t**3 - 140*t**2 + 340*t + 1200 = 0.
-30, -2, 4
Factor -2*h**2 + 34652*h - 150095138.
-2*(h - 8663)**2
Factor 3*h**2 + 48*h + 192.
3*(h + 8)**2
Find j, given that -j**2 + 1784*j - 1783 = 0.
1, 1783
Factor -n**2/3 - 7*n/3 + 6.
-(n - 2)*(n + 9)/3
Factor -2*h**2/5 + 112*h/5 + 882/5.
-2*(h - 63)*(h + 7)/5
Factor -q**4 - q**3 + 36*q**2 + 124*q + 112.
-(q - 7)*(q + 2)**2*(q + 4)
Let 12*l**5/5 - 536*l**4/5 - 192*l**3/5 + 536*l**2/5 + 36*l = 0. Calculate l.
-1, -1/3, 0, 1, 45
Suppose 6*g**5/7 + 120*g**4/7 + 90*g**3 + 1140*g**2/7 + 624*g/7 = 0. Calculate g.
-13, -4, -2, -1, 0
Factor -2*c**3/23 + 234*c**2/23 + 236*c/23.
-2*c*(c - 118)*(c + 1)/23
Let 5*b**3 + 675*b**2 + 1330*b = 0. What is b?
-133, -2, 0
Suppose 20*d**3/9 - 28*d**2/9 - 32*d/9 + 16/9 = 0. What is d?
-1, 2/5, 2
Factor -5*h**4 + 25*h**3 - 5*h**2 - 105*h + 90.
-5*(h - 3)**2*(h - 1)*(h + 2)
Factor 2*i**2/5 + 212*i/5 + 42.
2*(i + 1)*(i + 105)/5
Factor 2*z**5/3 - 10*z**4/3 + 20*z**3/3 - 20*z**2/3 + 10*z/3 - 2/3.
2*(z - 1)**5/3
Factor 4*d**2 + 168*d + 1764.
4*(d + 21)**2
Factor 3*a**2/5 + 312*a/5 + 309/5.
3*(a + 1)*(a + 103)/5
Find n such that n**2 + 224*n + 444 = 0.
-222, -2
Determine v, given that -v**4 - 37*v**3 - 35*v**2 + 37*v + 36 = 0.
-36, -1, 1
Let 4*y**2 + 952*y - 2892 = 0. What is y?
-241, 3
Factor -2*h**2/5 - 26*h/5 - 72/5.
-2*(h + 4)*(h + 9)/5
Factor 2*k**5/9 - 32*k**4/9 + 128*k**3/9.
2*k**3*(k - 8)**2/9
What is o in o**5/8 + o**4/8 - 3*o**3/4 - 7*o**2/4 - 11*o/8 - 3/8 = 0?
-1, 3
Factor x**5/4 + 15*x**4/2 + 63*x**3 + 98*x**2.
x**2*(x + 2)*(x + 14)**2/4
Factor 2*h**3/3 - 18*h**2 + 48*h.
2*h*(h - 24)*(h - 3)/3
Factor -4*q**3 + 464*q**2 - 460*q.
-4*q*(q - 115)*(q - 1)
Solve 2*u**2 - 4572*u + 2612898 = 0.
1143
Factor -b**3/3 - 6*b**2 - 27*b.
-b*(b + 9)**2/3
Factor -243*o**2/7 - 4752*o/7 - 23232/7.
-3*(9*o + 88)**2/7
What is v in 2*v**2/7 + 52*v/7 - 54/7 = 0?
-27, 1
Let -27*m**4 + 2787*m**3 - 618*m**2 = 0. What is m?
0, 2/9, 103
Factor 2*l**3 + l**2 - 13*l + 6.
(l - 2)*(l + 3)*(2*l - 1)
Factor -d**2/2 + 173*d/2 + 264.
-(d - 176)*(d + 3)/2
Factor -q**4/4 - q**3/4 + 5*q**2/4 - 3*q/4.
-q*(q - 1)**2*(q + 3)/4
Find y such that -5*y**2 + 33230*y - 55211645 = 0.
3323
Factor -4*z**3 + 104*z**2 - 364*z + 264.
-4*(z - 22)*(z - 3)*(z - 1)
Factor 2*a**4 + 188*a**3 + 5098*a**2 + 31648*a + 44376.
2*(a + 2)*(a + 6)*(a + 43)**2
Solve -5*n**3 + 80*n**2 + 525*n = 0 for n.
-5, 0, 21
Suppose 5*k**4 + 695*k**3 + 665*k**2 - 3435*k + 2070 = 0. What is k?
-138, -3, 1
Factor 3*d**5/5 - 234*d**4/5 + 4563*d**3/5 - 26364*d**2/5.
3*d**2*(d - 52)*(d - 13)**2/5
Let 2*h**4 - 30*h**2 - 20*h + 48 = 0. What is h?
-3, -2, 1, 4
Factor -2*f**2/5 - 74*f/5 - 28.
-2*(f + 2)*(f + 35)/5
Let 4*d**2 + 1400*d + 122500 = 0. Calculate d.
-175
Find f, given that 3*f**5 + 27*f**4 - 54*f**3 - 582*f**2 + 819*f + 1323 = 0.
-7, -1, 3
Find v such that v**4/2 - 11*v**3 - 24*v**2 = 0.
-2, 0, 24
Determine f so that -f**3/4 + 51*f**2/4 + 225*f/4 - 275/4 = 0.
-5, 1, 55
Factor -a**5/3 + 5*a**4 - 16*a**3 - 64*a**2/3.
-a**2*(a - 8)**2*(a + 1)/3
Find s, given that 3*s**3 - 54*s**2 + 135*s = 0.
0, 3, 15
Solve -3*a**5 + 1314*a**4 - 139887*a**3 - 875136*a**2 - 1325340*a - 591408 = 0 for a.
-4, -1, 222
Let 4*x**4 + 48*x**3 - 36*x**2 - 432*x = 0. What is x?
-12, -3, 0, 3
Determine c, given that 25*c**3 + 105*c**2 - 96*c + 20 = 0.
-5, 2/5
Factor 5*c**3 + 65*c**2 + 220*c + 160.
5*(c + 1)*(c + 4)*(c + 8)
Solve 3*i**5 + 522*i**4 - 6*i**3 - 1044*i**2 + 3*i + 522 = 0.
-174, -