 1)/2
Factor 2*f**4/5 - 8*f**3/5 + 6*f**2/5 + 8*f/5 - 8/5.
2*(f - 2)**2*(f - 1)*(f + 1)/5
Factor o**3/8 + 351*o**2/8 + 30975*o/8 + 30625/8.
(o + 1)*(o + 175)**2/8
Factor -c**2 + 226*c - 12769.
-(c - 113)**2
Factor 3*g**2 - 264*g + 5508.
3*(g - 54)*(g - 34)
Factor -4*a**3 - 50*a**2/3 + 136*a/3 + 8.
-2*(a - 2)*(a + 6)*(6*a + 1)/3
Find o, given that o**2 - 51*o + 230 = 0.
5, 46
Suppose 3*l**2 + 702*l + 41067 = 0. Calculate l.
-117
Factor k**4/2 + 20*k**3 + 303*k**2/2 - 1078*k - 1210.
(k - 5)*(k + 1)*(k + 22)**2/2
Suppose -5*o**2/3 + 765*o - 4570/3 = 0. Calculate o.
2, 457
Find i, given that i**3/2 - 21*i**2 + 221*i/2 - 90 = 0.
1, 5, 36
Solve 4*g**4/3 - 32*g**3/3 - 40*g**2/3 + 32*g/3 + 12 = 0 for g.
-1, 1, 9
What is o in o**4 - o**3 - 9*o**2 - 11*o - 4 = 0?
-1, 4
Solve -6*b**4/11 + 28*b**3/11 + 208*b**2/11 + 228*b/11 + 54/11 = 0 for b.
-3, -1, -1/3, 9
Suppose -2*o**4/3 + 10*o**3/3 + 20*o**2/3 - 40*o/3 - 16 = 0. What is o?
-2, -1, 2, 6
Solve 4*q**3 - 2012*q**2 - 4036*q - 2020 = 0 for q.
-1, 505
Determine o so that 12*o**3/7 + 6351*o**2/7 + 7923*o/7 + 1584/7 = 0.
-528, -1, -1/4
Solve -4*t**2/5 - 618*t/5 - 244 = 0 for t.
-305/2, -2
Factor -3*u**3/2 + 381*u**2 - 49875*u/2 + 93750.
-3*(u - 125)**2*(u - 4)/2
Factor -15*a**4 - 80*a**3 - 115*a**2 - 30*a.
-5*a*(a + 2)*(a + 3)*(3*a + 1)
Factor 4*b**2 + 640*b - 644.
4*(b - 1)*(b + 161)
Factor -i**5 + 100*i**4 - 3696*i**3 + 59584*i**2 - 351232*i.
-i*(i - 28)**3*(i - 16)
Suppose 3*w**2/4 + 165*w/4 + 159/2 = 0. What is w?
-53, -2
Factor -2*u**2 + 72*u.
-2*u*(u - 36)
Find h, given that 14*h**5 - 132*h**4 + 330*h**3/7 + 424*h**2/7 + 72*h/7 = 0.
-2/7, 0, 1, 9
Find b, given that 6*b**5 - 105*b**4 + 312*b**3 + 1263*b**2 + 1140*b + 300 = 0.
-1, -1/2, 10
Factor 4*m**3 + 132*m**2 - 136*m.
4*m*(m - 1)*(m + 34)
Let i**4/9 - 2*i**3 - 20*i**2/9 + 2*i + 19/9 = 0. What is i?
-1, 1, 19
Factor -20*n**3 - 155*n**2 + 40*n.
-5*n*(n + 8)*(4*n - 1)
Factor -2*c**2/11 + 226*c/11 - 4140/11.
-2*(c - 90)*(c - 23)/11
Factor 2*w**4/3 - 16*w**3 + 66*w**2 - 152*w/3.
2*w*(w - 19)*(w - 4)*(w - 1)/3
Find r, given that 5*r**5/2 + 27*r**4/2 - 115*r**3/2 - 75*r**2/2 + 55*r + 24 = 0.
-8, -1, -2/5, 1, 3
Solve 3*f**5/2 + 12*f**4 + 33*f**3 + 36*f**2 + 27*f/2 = 0 for f.
-3, -1, 0
Let -2*a**3/9 - 74*a**2/9 + 76*a/9 = 0. Calculate a.
-38, 0, 1
Factor 25*r**3 + 720*r**2 + 3645*r + 5130.
5*(r + 3)**2*(5*r + 114)
What is s in -s**3 - 1221*s**2 - 496947*s - 67419143 = 0?
-407
What is o in 2*o**3/3 - 134*o**2/3 - 274*o/3 - 46 = 0?
-1, 69
Factor 2*r**3/3 + 2*r**2 - 44*r/3 - 16.
2*(r - 4)*(r + 1)*(r + 6)/3
Solve -c**5 - 13*c**4 - 15*c**3 + 73*c**2 - 44*c = 0.
-11, -4, 0, 1
Suppose -4*a**5 - 32*a**4 + 348*a**3 + 1208*a**2 + 832*a = 0. What is a?
-13, -2, -1, 0, 8
Factor -4*a**2/7 + 41784*a/7 - 109118916/7.
-4*(a - 5223)**2/7
Determine k, given that 16*k**5/5 + 984*k**4/5 + 1165*k**3 + 5702*k**2/5 - 801*k + 110 = 0.
-55, -5, -2, 1/4
Factor 2*w**2/11 - 66*w.
2*w*(w - 363)/11
Find f, given that 2*f**2/7 + 72*f = 0.
-252, 0
Solve 8*c**5/3 + 110*c**4/3 - 277*c**3/3 + 176*c**2/3 - c/3 - 16/3 = 0 for c.
-16, -1/4, 1/2, 1
Factor -2*q**2/7 - 384*q/7 - 382/7.
-2*(q + 1)*(q + 191)/7
Factor t**4/10 + 2*t**3/5 - 2*t**2/5 - 8*t/5.
t*(t - 2)*(t + 2)*(t + 4)/10
Let 3*l**3/2 + 36*l**2 + 69*l/2 = 0. Calculate l.
-23, -1, 0
Factor 2*p**4/3 - 110*p**3 - 332*p**2/3.
2*p**2*(p - 166)*(p + 1)/3
Solve 2*a**4/7 - 24*a**3/7 + 86*a**2/7 - 48*a/7 - 160/7 = 0 for a.
-1, 4, 5
Determine q, given that -20*q**5 - 68*q**4 - 64*q**3 - 16*q**2 = 0.
-2, -1, -2/5, 0
Factor b**4 + 9*b**3 + 30*b**2 + 44*b + 24.
(b + 2)**3*(b + 3)
Determine z so that -z**2/2 + 39*z/2 - 37 = 0.
2, 37
What is r in -r**2 - 9018*r + 9019 = 0?
-9019, 1
What is k in -4*k**5 + 740*k**4 - 28252*k**3 - 549796*k**2 - 2480800*k - 1960000 = 0?
-7, -1, 100
Factor u**3/4 + 365*u**2/4 - 551*u/2 + 184.
(u - 2)*(u - 1)*(u + 368)/4
Determine l, given that 3*l**2 + 378*l + 11907 = 0.
-63
Solve -2*x**2/17 - 70*x/17 = 0.
-35, 0
Suppose -4*g**2 + 692*g + 1400 = 0. Calculate g.
-2, 175
Factor -m**3 - 1244*m**2/5 - 991*m/5 + 248/5.
-(m + 1)*(m + 248)*(5*m - 1)/5
Factor -2*d**3/23 - 182*d**2/23 - 3920*d/23.
-2*d*(d + 35)*(d + 56)/23
Factor -3*u**4 - 90*u**3 - 879*u**2 - 2952*u - 2160.
-3*(u + 1)*(u + 5)*(u + 12)**2
Let -2*f**2/5 - 74*f/5 = 0. Calculate f.
-37, 0
Suppose -2*p**4 + 1776*p**3 - 591408*p**2 + 87528384*p - 4857825312 = 0. What is p?
222
Factor -4*n**4 + 96*n**3 - 576*n**2 + 1024*n.
-4*n*(n - 16)*(n - 4)**2
Let -3*i**2 - 93*i + 198 = 0. What is i?
-33, 2
Let 5*l**2/3 + 375*l = 0. Calculate l.
-225, 0
Factor -2*q**2/11 + 13824*q/11 - 23887872/11.
-2*(q - 3456)**2/11
Find c such that c**5/2 - 33*c**4 + 607*c**3 - 2078*c**2 + 4929*c/2 - 961 = 0.
1, 2, 31
Factor -s**2/4 + 33*s/2 + 34.
-(s - 68)*(s + 2)/4
What is h in -3*h**2/2 + 15*h - 24 = 0?
2, 8
Solve 2*k**4/11 - 248*k**3/11 + 7688*k**2/11 = 0 for k.
0, 62
Factor -4*i**3 - 56*i**2 + 16*i + 224.
-4*(i - 2)*(i + 2)*(i + 14)
Factor -h**4/4 - 7*h**3/2 - 45*h**2/4 - 13*h - 5.
-(h + 1)**2*(h + 2)*(h + 10)/4
Find n, given that -2*n**4/5 - 154*n**3/5 - 1956*n**2/5 + 40832*n/5 - 7744 = 0.
-44, 1, 10
Let -x**2 + 205*x + 206 = 0. What is x?
-1, 206
Solve -2*h**3 - 22*h**2 - 38*h - 18 = 0.
-9, -1
Find z such that -z**3/2 + 70*z**2 - 4757*z/2 - 5041 = 0.
-2, 71
Factor 2*m**2/3 + 8*m/9 + 2/9.
2*(m + 1)*(3*m + 1)/9
Factor -2*a**2 + 266*a - 780.
-2*(a - 130)*(a - 3)
Find n such that n**2 - 420*n + 44100 = 0.
210
Factor -f**2/4 + 165*f/4.
-f*(f - 165)/4
Factor -z**4/9 + 49*z**3/9 - 47*z**2/9 - 49*z/9 + 16/3.
-(z - 48)*(z - 1)**2*(z + 1)/9
Factor a**4/4 - 178*a**3 + 31684*a**2.
a**2*(a - 356)**2/4
Determine x so that -x**5/3 - x**4 - x**3 - x**2/3 = 0.
-1, 0
Factor 3*n**4 - 3*n**2.
3*n**2*(n - 1)*(n + 1)
Factor 2*s**3/13 + 48*s**2/13 + 90*s/13 + 44/13.
2*(s + 1)**2*(s + 22)/13
Determine o so that -27*o**2/2 - 51*o + 12 = 0.
-4, 2/9
Determine f, given that 2*f**5/15 + 42*f**4/5 + 82*f**3/5 + 122*f**2/15 = 0.
-61, -1, 0
Factor y**4/5 - 70*y**3 + 6125*y**2.
y**2*(y - 175)**2/5
Factor 3*a**3 - 294*a**2 + 7488*a - 13824.
3*(a - 48)**2*(a - 2)
Find i such that -2*i**2/17 - 858*i/17 = 0.
-429, 0
Suppose 198*q**3/5 - 5772*q**2/5 + 858*q/5 + 348/5 = 0. Calculate q.
-2/11, 1/3, 29
Find n such that 22*n**4/7 - 114*n**3/7 + 108*n**2/7 - 16*n/7 = 0.
0, 2/11, 1, 4
Suppose -5*l**2 - 1220*l + 1225 = 0. What is l?
-245, 1
Factor 3*w**4/5 + 13*w**3/5 - 92*w**2/5 - 32*w/5.
w*(w - 4)*(w + 8)*(3*w + 1)/5
Factor 4*l**3 - 5376*l**2 + 1806336*l.
4*l*(l - 672)**2
Suppose -2*y**4/5 - 194*y**3/5 - 6256*y**2/5 - 67048*y/5 = 0. What is y?
-34, -29, 0
Factor 5*m**3/2 - 520*m**2 - 2095*m/2 - 525.
5*(m - 210)*(m + 1)**2/2
Determine d, given that 4*d**2/7 - 172*d/7 = 0.
0, 43
What is m in -2*m**4/15 + 116*m**3/15 - 416*m**2/3 + 2300*m/3 - 1250 = 0?
3, 5, 25
Suppose 5*g**4/3 + 20*g**3/3 - 5*g**2/3 - 80*g/3 - 20 = 0. What is g?
-3, -2, -1, 2
Factor -u**3/2 - 117*u**2/2 - 3363*u/2 + 3481/2.
-(u - 1)*(u + 59)**2/2
Solve -2*c**3/7 + 422*c**2/7 - 22048*c/7 - 22472/7 = 0.
-1, 106
Factor -r**4 - 88*r**3 - 2610*r**2 - 26912*r - 24389.
-(r + 1)*(r + 29)**3
Solve -2*x**2 + 17456*x - 38088992 = 0.
4364
Suppose -8*u**5 + 4*u**4 + 8*u**3 - 4*u**2 = 0. What is u?
-1, 0, 1/2, 1
Suppose -r**4 - 31*r**3 - 158*r**2 + 256*r + 384 = 0. What is r?
-24, -8, -1, 2
Factor -g**3 + 21*g**2 - 147*g + 343.
-(g - 7)**3
Let -12*k**3 - 140*k**2 - 448*k - 240 = 0. What is k?
-6, -5, -2/3
Factor 3*n**3/2 - 1458*n**2 + 2913*n/2.
3*n*(n - 971)*(n - 1)/2
Find p, given that p**5/9 - 66*p**4 - 1793*p**3/9 + 394*p**2/3 + 7156*p/9 + 1592/3 = 0.
-2, -1, 2, 597
Factor -6*v**3/7 - 24*v**2/7 - 24*v/7.
-6*v*(v + 2)**2/7
Factor -2*j**2 + 104*j + 106.
-2*(j - 53)*(j + 1)
Find g such that 7*g**3/4 - g**2 - 17*g/4 - 3/2 = 0.
-1, -3/7, 2
Let -6*w**5/7 - 18*w**4/7 + 96*w**3/7 + 312*w**2/7 - 384/7 = 0. Calculate w.
-4, -2, 1, 4
Find c, given that c**2/3 - 202*c/3 + 264 = 0.
4, 198
Suppose v**5/3 - 5*v**4/3 + 5*v**3/3 + 5*v**2/3 - 2*v = 0. Calculate v.
-1, 0, 1, 2, 3
Suppose -15*n**5 - 39*n**4 + 87*n**3 + 363*n**2 + 360*n + 108 = 0. What is n?
-2, -1, -3/5, 3
Let 2*s**5/5 + 3*s**4/5 - 8*s**3/5 + 3*s**2/5 = 0. Calculate s.
-3, 0, 1/2, 1
Let 11*r**3/3 - 14*r**2/3 + r = 0. What is r?
0, 3/11, 1
Factor 4*z**5 + 96*z**4 + 664*z**3 + 1056*z**2 + 484*z.
4*z*(z + 1)**2*(z + 11)**2
Factor 