r -6*r**4/7 - 48*r**3/7 - 18*r**2 - 108*r/7.
-6*r*(r + 2)*(r + 3)**2/7
Factor x**4/4 - 6*x**3 + 22*x**2 + 168*x + 196.
(x - 14)**2*(x + 2)**2/4
Let -2*w**2/7 + 12*w - 160/7 = 0. Calculate w.
2, 40
Let w**5/2 - 2*w**4 - 5*w**3/2 = 0. Calculate w.
-1, 0, 5
Solve -660*n**5 - 20585*n**4 - 77125*n**3 - 67025*n**2 - 9015*n + 810 = 0 for n.
-27, -3, -1, -1/4, 2/33
Factor -n**2/4 + 233*n/4 - 58.
-(n - 232)*(n - 1)/4
Factor 2*t**3/15 + 156*t**2/5 + 12168*t/5 + 316368/5.
2*(t + 78)**3/15
Factor -2*z**2/3 + 2*z - 4/3.
-2*(z - 2)*(z - 1)/3
Factor r**4/9 - 17*r**3/9.
r**3*(r - 17)/9
Suppose 3*c**5/4 + 9*c**4/2 + 3*c**3 - 9*c**2/2 - 15*c/4 = 0. What is c?
-5, -1, 0, 1
Solve 2*r**2 + 66*r + 124 = 0.
-31, -2
Determine f, given that -2*f**5/11 - 12*f**4/11 - 14*f**3/11 + 12*f**2/11 + 16*f/11 = 0.
-4, -2, -1, 0, 1
Factor -f**2/9 + 2*f/3 + 40/9.
-(f - 10)*(f + 4)/9
Factor 5*c**4 - 70*c**3 - 360*c**2.
5*c**2*(c - 18)*(c + 4)
Factor -2*z**2/15 + 32*z/15 + 32/3.
-2*(z - 20)*(z + 4)/15
Determine v, given that v**3/5 - 26*v**2 - 811*v/5 - 136 = 0.
-5, -1, 136
Find n such that 3*n**2/5 + 20*n + 817/5 = 0.
-19, -43/3
Find t, given that 5*t**4 - 25*t**3 - 270*t**2 - 620*t - 440 = 0.
-2, 11
Find j such that -4*j**2/7 - 48*j/7 - 80/7 = 0.
-10, -2
Factor -5*t**2/2 + 115*t/2 + 195.
-5*(t - 26)*(t + 3)/2
Factor 3*t**2/8 + 36*t + 1365/8.
3*(t + 5)*(t + 91)/8
Determine k so that -k**5/3 - 53*k**4/3 - 1015*k**3/3 - 8111*k**2/3 - 19720*k/3 + 28900/3 = 0.
-17, -10, 1
Factor -5*z**5 - 1020*z**4 - 67200*z**3 - 1274000*z**2 + 10290000*z.
-5*z*(z - 6)*(z + 70)**3
Factor -3*v**4/8 + 21*v**3/8 - 45*v**2/8 + 27*v/8.
-3*v*(v - 3)**2*(v - 1)/8
Factor -5*w**3/6 - 1175*w**2/3 - 276125*w/6.
-5*w*(w + 235)**2/6
Factor -3*p**3/5 + 183*p**2/5 - 2697*p/5 - 2883/5.
-3*(p - 31)**2*(p + 1)/5
Find s such that -3*s**2/8 - 915*s/2 - 279075/2 = 0.
-610
Determine k, given that 12*k**4/13 + 58*k**3/13 + 100*k**2/13 + 74*k/13 + 20/13 = 0.
-2, -1, -5/6
Find t, given that -t**3 + t**2 + t - 1 = 0.
-1, 1
Factor 2*y**3/3 - 104*y**2/3 - 110*y/3 + 212/3.
2*(y - 53)*(y - 1)*(y + 2)/3
Factor 2*x**3/5 - 16522*x**2/5 + 6826064*x - 6822760.
2*(x - 4130)**2*(x - 1)/5
Solve -100*b**3 + 13020*b**2 - 2576*b - 3120 = 0.
-2/5, 3/5, 130
Factor 3*k**2/7 - 13026*k/7 + 14139723/7.
3*(k - 2171)**2/7
Factor 2*r**4/3 + 20*r**3/3 + 26*r**2/3 - 40*r + 24.
2*(r - 1)**2*(r + 6)**2/3
Suppose -9*n**4 - 24*n**3 + 1305*n**2 - 1692*n + 420 = 0. Calculate n.
-14, 1/3, 1, 10
Factor 3*m**3/5 + 498*m**2/5 - 411*m - 510.
3*(m - 5)*(m + 1)*(m + 170)/5
Determine g, given that 630*g**2 - 9454*g/5 + 12/5 = 0.
2/1575, 3
Solve -c**2/4 - 45*c/4 + 23/2 = 0.
-46, 1
Find f such that -2*f**3/5 + 208*f**2/5 - 6888*f/5 + 14112 = 0.
20, 42
Find l, given that 64*l**3 + 268*l**2 - 272*l - 60 = 0.
-5, -3/16, 1
Factor 3*b**5/7 - 57*b**4/7.
3*b**4*(b - 19)/7
Factor 27*j**3 + 48*j**2 - 93*j + 18.
3*(j - 1)*(j + 3)*(9*j - 2)
Factor q**3/5 - 9*q**2/5 - 16*q/5 + 144/5.
(q - 9)*(q - 4)*(q + 4)/5
Suppose 20*p**4 + 40*p**3 - 15*p**2 - 45*p = 0. Calculate p.
-3/2, 0, 1
Factor -5*h**5 + 5*h**3.
-5*h**3*(h - 1)*(h + 1)
What is a in -2*a**4 - 52*a**3 - 280*a**2 + 784*a = 0?
-14, 0, 2
What is v in -4*v**2 - 40*v + 156 = 0?
-13, 3
Determine k so that -2*k**4/3 + 2*k**3 + 64*k**2/3 + 40*k + 64/3 = 0.
-2, -1, 8
Let -4*s**2 + 1752*s + 3520 = 0. What is s?
-2, 440
Factor -19*w**3/2 - w**2 + 19*w/2 + 1.
-(w - 1)*(w + 1)*(19*w + 2)/2
Suppose -r**4/7 + 15*r**3/7 - 13*r**2/7 - 15*r/7 + 2 = 0. What is r?
-1, 1, 14
Factor 3*b**3 - 39*b**2 + 105*b + 147.
3*(b - 7)**2*(b + 1)
Let 5*j**4 + 15*j**3 - 60*j**2 - 100*j + 240 = 0. What is j?
-4, -3, 2
Factor 2*x**2 + 1890*x - 1892.
2*(x - 1)*(x + 946)
Solve x**2 - x - 6 = 0.
-2, 3
Factor -6*h**2 - 447*h - 222.
-3*(h + 74)*(2*h + 1)
Suppose p**3 - 43*p**2 - p + 43 = 0. Calculate p.
-1, 1, 43
Factor -n**5 + 5*n**4 - 7*n**3 + 3*n**2.
-n**2*(n - 3)*(n - 1)**2
Let -104*j**5/7 + 96*j**4/7 + 86*j**3/7 - 46*j**2/7 - 30*j/7 - 2/7 = 0. What is j?
-1/2, -1/13, 1
Factor o**2/5 - 148*o/5 + 5476/5.
(o - 74)**2/5
Factor 2*l**2/7 + 6036*l/7 + 4554162/7.
2*(l + 1509)**2/7
Solve -2*s**2/5 - 2*s - 12/5 = 0.
-3, -2
Factor 4*j**3/5 - 5*j**2 + 3*j/5 + 18/5.
(j - 6)*(j - 1)*(4*j + 3)/5
Factor 7*w**2/6 + 163*w/2 + 69.
(w + 69)*(7*w + 6)/6
Suppose -w**4/11 + 15*w**3/11 + 18*w**2/11 - 32*w/11 = 0. What is w?
-2, 0, 1, 16
Factor 11*a**2 - 40*a.
a*(11*a - 40)
Factor a**2/5 - 39*a/5.
a*(a - 39)/5
Factor -u**3/4 - 105*u**2/2 + 427*u/4 + 159.
-(u - 3)*(u + 1)*(u + 212)/4
Factor 10*j**3 + 5*j**2 - 10*j - 5.
5*(j - 1)*(j + 1)*(2*j + 1)
Factor -45*g**3 - 6425*g**2 + 7910*g - 1440.
-5*(g - 1)*(g + 144)*(9*g - 2)
Let -3*s**2/7 - 543*s/7 - 540/7 = 0. Calculate s.
-180, -1
Let -5*m**5/3 - 40*m**4/3 + 95*m**3 - 500*m**2/3 + 260*m/3 = 0. What is m?
-13, 0, 1, 2
Factor -3*s**4 - 54*s**3 - 264*s**2 + 1536.
-3*(s - 2)*(s + 4)*(s + 8)**2
Let 1500*l**5 - 2553*l**4 + 624*l**3 + 411*l**2 + 18*l = 0. What is l?
-1/4, -6/125, 0, 1
Let -15*y**2/2 + 36*y + 15/2 = 0. What is y?
-1/5, 5
Solve -5*q**3 + 4210*q**2 - 8405*q + 4200 = 0 for q.
1, 840
What is u in 3*u**2 + 1119*u + 1116 = 0?
-372, -1
Find c such that -31*c**2/2 - 1583*c/2 - 51 = 0.
-51, -2/31
Solve -x**4/2 + 11*x**3/2 - 33*x**2/2 + 37*x/2 - 7 = 0 for x.
1, 2, 7
Factor -3*i**2 - 138*i + 2088.
-3*(i - 12)*(i + 58)
Factor 2*a**2/9 - 8*a/3 + 8.
2*(a - 6)**2/9
Suppose 2*p**2/3 - 140*p/3 + 1298/3 = 0. Calculate p.
11, 59
Find s such that 2*s**5/3 + 88*s**4/3 + 208*s**3 + 1792*s**2/3 + 2336*s/3 + 384 = 0.
-36, -2
Factor -2*l**3 + 22*l**2 - 70*l + 50.
-2*(l - 5)**2*(l - 1)
Factor 5*z**2/3 - 13310*z + 26573415.
5*(z - 3993)**2/3
Determine g so that -3*g**2 - 2032*g - 677 = 0.
-677, -1/3
Let -5*v**2 + 5090*v - 1295405 = 0. What is v?
509
Solve -4*z**2 + 740*z = 0 for z.
0, 185
Determine j so that 10*j**5/13 + 168*j**4 + 121842*j**3/13 + 283828*j**2/13 + 210816*j/13 + 46656/13 = 0.
-108, -1, -2/5
Find j such that 2*j**2/3 - 74*j/3 + 208 = 0.
13, 24
Factor 5*x**3 - 170*x**2 - 3055*x.
5*x*(x - 47)*(x + 13)
Suppose -3*b**2 - 12*b + 63 = 0. Calculate b.
-7, 3
Find g, given that 5*g**2 + 75*g - 80 = 0.
-16, 1
Let j**2/11 + 43*j/11 + 120/11 = 0. What is j?
-40, -3
What is i in -i**5/6 - 11*i**4/12 - i**3/3 + 53*i**2/12 + 4*i - 3 = 0?
-3, -2, 1/2, 2
Factor 2*z**2 + 28340*z + 100394450.
2*(z + 7085)**2
Solve -3*j**5 + 70*j**4 - 446*j**3 + 372*j**2 + 649*j - 242 = 0 for j.
-1, 1/3, 2, 11
Factor -2*f**3 - 16*f**2 - 38*f - 24.
-2*(f + 1)*(f + 3)*(f + 4)
Factor -2*m**2/7 + 16*m/7 - 32/7.
-2*(m - 4)**2/7
Find l such that -3*l**2 + 36*l - 105 = 0.
5, 7
Factor -2*c**5/11 - 20*c**4/11 - 72*c**3/11 - 108*c**2/11 - 54*c/11.
-2*c*(c + 1)*(c + 3)**3/11
Determine r, given that 5*r**4 - 880*r**3 + 36875*r**2 + 166500*r - 202500 = 0.
-5, 1, 90
Let -11*l**2 + 39*l + 20 = 0. What is l?
-5/11, 4
Factor 2*l**4/5 - 26*l**3/5 + 58*l**2/5 + 266*l/5 - 588/5.
2*(l - 7)**2*(l - 2)*(l + 3)/5
Factor -2*b**4/5 + 16*b**3.
-2*b**3*(b - 40)/5
Solve -v**3 - 36*v**2 + v + 36 = 0 for v.
-36, -1, 1
Solve o**4/2 - 1371*o**3/4 + 234611*o**2/4 + 118335*o/4 - 117649/4 = 0 for o.
-1, 1/2, 343
Let -150*j**2 - 148*j + 2 = 0. Calculate j.
-1, 1/75
Factor -15*j**3 + 6*j**2.
-3*j**2*(5*j - 2)
Factor -3*v**4 + 32394*v**3 - 116607600*v**2 + 139967967606*v - 139851392397.
-3*(v - 3599)**3*(v - 1)
Determine m, given that -6*m**2 + 280*m - 184 = 0.
2/3, 46
Factor g**3/2 - 19*g**2/2 - 97*g/2 + 115/2.
(g - 23)*(g - 1)*(g + 5)/2
Factor m**4 + 125*m**3 - 4*m**2 - 500*m.
m*(m - 2)*(m + 2)*(m + 125)
Factor 2*o**2/3 - 112*o + 4704.
2*(o - 84)**2/3
Find k such that 7*k**3/3 - 18526*k**2 + 36770140*k + 31521800/3 = 0.
-2/7, 3970
Factor 4*f**3 + 372*f**2 - 1152*f.
4*f*(f - 3)*(f + 96)
Factor 4*a**4 - 804*a**3 + 53868*a**2 - 1203052*a.
4*a*(a - 67)**3
Find m, given that -3*m**2/8 + 9*m/4 + 6 = 0.
-2, 8
Let 4*a**3 - 160*a**2 - 336*a = 0. What is a?
-2, 0, 42
Let -2*g**2 - 13*g - 11 = 0. What is g?
-11/2, -1
Let u**2/2 + 527*u = 0. What is u?
-1054, 0
Factor 7*l**4/3 - 6276*l**3 + 4219265*l**2 + 3618050*l/3.
l*(l - 1345)**2*(7*l + 2)/3
Determine h so that -9*h**5/2 + 489*h**4/2 - 5691*h**3/2 - 25677*h**2/2 - 14790*h - 5046 = 0.
-2, -1, -2/3, 29
Factor 3*z**2 + 27*z + 24.
3*(z + 1)*(z + 8)
Find d, given that 4*d**5 - 16*d**4 - 16*d**3 + 136*d**2 - 180*d + 72 = 0.
-3, 1, 2, 3
Factor -432*a**3 + 1368*a**2 - 219