- 3*d/2.
3*d*(d + 1)*(5*d - 1)/2
Determine i, given that 4*i**2 - 36*i + 72 = 0.
3, 6
Determine g, given that -g**5 + 63*g**4 - 958*g**3 - 1152*g**2 + 2048*g = 0.
-2, 0, 1, 32
Factor -5*r**3 + 210*r**2 + 455*r - 660.
-5*(r - 44)*(r - 1)*(r + 3)
Let -5*p**5 - 95*p**4 + 125*p**3 + 515*p**2 + 300*p = 0. Calculate p.
-20, -1, 0, 3
Factor q**3/2 + 16*q**2/5 + 37*q/10 + 1.
(q + 1)*(q + 5)*(5*q + 2)/10
What is m in -2*m**2/7 - 586*m/7 + 84 = 0?
-294, 1
Factor -h**4 + 3404*h**3 - 4345206*h**2 + 2465180204*h - 524467088401.
-(h - 851)**4
Factor -r**3/6 - 19*r**2/3 - 67*r/2 - 48.
-(r + 3)**2*(r + 32)/6
Suppose 170*f**2 - 2044*f/3 + 16/3 = 0. Calculate f.
2/255, 4
Suppose 3*y**4 - 99*y**3 + 96*y**2 = 0. What is y?
0, 1, 32
Factor -y**3 + 49*y**2 - 95*y + 47.
-(y - 47)*(y - 1)**2
Determine w so that w**2/5 - 1833*w/5 = 0.
0, 1833
Factor -3*z**3 - 126*z**2 - 1440*z - 2400.
-3*(z + 2)*(z + 20)**2
Factor -d**2/2 + 74*d - 2738.
-(d - 74)**2/2
Determine s so that -s**4/2 - 4*s**3 - s**2 + 16*s - 21/2 = 0.
-7, -3, 1
Determine l so that -l**4/5 + 38*l**3/5 + 83*l**2/5 - 24*l = 0.
-3, 0, 1, 40
Factor -3*l**2 - 369*l + 1134.
-3*(l - 3)*(l + 126)
Suppose f**4 - 51*f**3 - 105*f**2 - 53*f = 0. Calculate f.
-1, 0, 53
Factor 35*l**4 - 60*l**3 + 15*l**2 + 10*l.
5*l*(l - 1)**2*(7*l + 2)
Factor i**2 - 351*i + 350.
(i - 350)*(i - 1)
Determine x so that 1250*x**4 - 11050*x**3/3 + 20708*x**2/9 + 392*x/3 + 16/9 = 0.
-2/75, 1, 2
Suppose 2*d**4 + 78*d**3 - 346*d**2 - 78*d + 344 = 0. What is d?
-43, -1, 1, 4
Find v, given that 2*v**3/3 - 41*v**2/3 + 220*v/3 - 100/3 = 0.
1/2, 10
Let -27*x**2/5 - 5*x + 2/5 = 0. Calculate x.
-1, 2/27
Find a, given that -95*a**5 - 2100*a**4 - 2025*a**3 + 3800*a**2 + 420*a = 0.
-21, -2, -2/19, 0, 1
Solve -3*z**3 + 3*z**2 + 123*z - 315 = 0.
-7, 3, 5
Factor -2*i**3 - 80*i**2 + 166*i - 84.
-2*(i - 1)**2*(i + 42)
Factor -2*o**2/17 - 2*o/17.
-2*o*(o + 1)/17
Let 3*g**4/7 - 81*g**3/7 + 93*g**2 - 189*g - 294 = 0. Calculate g.
-1, 7, 14
Factor m**3/6 + 1598*m**2/3 - 6395*m/6 + 533.
(m - 1)**2*(m + 3198)/6
Factor -21*a**2/8 - 51*a/2 + 15/2.
-3*(a + 10)*(7*a - 2)/8
Factor y**3/7 + 41*y**2 + 20448*y/7 - 20736/7.
(y - 1)*(y + 144)**2/7
Factor 8*h**5 + 18*h**4 + 4*h**3 - 16*h**2 - 12*h - 2.
2*(h - 1)*(h + 1)**3*(4*h + 1)
Solve -k**4 + 26*k**3 - 189*k**2 + 216*k + 432 = 0 for k.
-1, 3, 12
Solve 3*p**5 + 36*p**4 + 90*p**3 + 84*p**2 + 27*p = 0 for p.
-9, -1, 0
Factor -35*j**3/6 + 835*j**2/6 - 820*j - 120.
-5*(j - 12)**2*(7*j + 1)/6
Let 5*t**4 - 25*t**3 - 30*t**2 = 0. What is t?
-1, 0, 6
Let 5*s**2 + 435*s + 1660 = 0. What is s?
-83, -4
Factor -4*r**4 - 1204*r**3 + 4*r**2 + 1204*r.
-4*r*(r - 1)*(r + 1)*(r + 301)
Factor -3625*w**2 + 210*w + 40.
-5*(25*w + 2)*(29*w - 4)
Let 5*d**3/2 - 30*d**2 + 145*d/2 + 105 = 0. Calculate d.
-1, 6, 7
Factor -z**2/2 - 89*z + 179/2.
-(z - 1)*(z + 179)/2
Factor -3*p**2 + 282*p - 552.
-3*(p - 92)*(p - 2)
Factor -2*y**3/3 - 52*y**2 + 158*y/3.
-2*y*(y - 1)*(y + 79)/3
Find g, given that -g**4/2 + 3*g**3 + 4*g**2 - 3*g - 7/2 = 0.
-1, 1, 7
Factor 3*b**3 + 30*b**2 + 87*b + 60.
3*(b + 1)*(b + 4)*(b + 5)
Solve -2*h**2/3 + 1268*h/3 - 200978/3 = 0.
317
Solve 3*s**2 - 105*s + 102 = 0.
1, 34
Factor 2*v**3 - 8*v**2 - 18*v + 72.
2*(v - 4)*(v - 3)*(v + 3)
Factor 2*v**3/11 + 8*v**2/11 - 2*v + 12/11.
2*(v - 1)**2*(v + 6)/11
Factor 4*x**3 + 86*x**2 - 142*x - 92.
2*(x - 2)*(x + 23)*(2*x + 1)
Determine w, given that 2*w**3/9 + 46*w**2/9 - 70*w/3 + 18 = 0.
-27, 1, 3
Suppose 3*q**5/2 - 20*q**4 + 49*q**3/2 - 6*q**2 = 0. What is q?
0, 1/3, 1, 12
What is z in 9*z**5/2 + 15*z**4/4 - 81*z**3/2 + 231*z**2/4 - 63*z/2 + 6 = 0?
-4, 1/2, 2/3, 1
Suppose 5*o**5 + o**4 - 5*o**3 - o**2 = 0. Calculate o.
-1, -1/5, 0, 1
Factor u**5 - u**4.
u**4*(u - 1)
Factor -27*o**5/2 - 243*o**4 - 1584*o**3 - 4352*o**2 - 4096*o.
-o*(o + 2)*(3*o + 16)**3/2
Solve -w**2/3 + 46*w - 1587 = 0.
69
What is p in 4*p**4 + 88*p**3 + 332*p**2 - 1672*p + 1248 = 0?
-13, -12, 1, 2
Let -3*f**3 - 54*f**2 + 189*f = 0. Calculate f.
-21, 0, 3
Factor -49*w**2 + 84*w - 36.
-(7*w - 6)**2
Factor 35*l**4 - 165*l**3 + 160*l**2 + 60*l.
5*l*(l - 3)*(l - 2)*(7*l + 2)
Let 5*b**4 + 55*b**3 - 65*b**2 - 55*b + 60 = 0. Calculate b.
-12, -1, 1
Factor -9*n**3 - 24*n**2.
-3*n**2*(3*n + 8)
Factor -2*a**5/9 - 240*a**4 - 103680*a**3 - 22394880*a**2 - 2418647040*a - 104485552128.
-2*(a + 216)**5/9
Factor -i**2/3 + 803*i/3 - 534.
-(i - 801)*(i - 2)/3
Suppose -5*y**4 + 115*y**3 - 750*y**2 + 1780*y - 1400 = 0. Calculate y.
2, 5, 14
Find o, given that 2*o**2/3 + 4840*o + 8784600 = 0.
-3630
Suppose -18*z**4 - 14*z**3 + 166*z**2 + 126*z - 36 = 0. Calculate z.
-3, -1, 2/9, 3
Factor 5*s**3 + 16*s**2 + 13*s + 2.
(s + 1)*(s + 2)*(5*s + 1)
Factor 2*z**2/5 - 33024*z/5 + 136323072/5.
2*(z - 8256)**2/5
Let 5*a**3 - 2070*a**2 - 4155*a - 2080 = 0. Calculate a.
-1, 416
Factor 4*x**5 - 36*x**4 - 108*x**3 + 1316*x**2 - 1176*x.
4*x*(x - 7)**2*(x - 1)*(x + 6)
Let f**4 + 48*f**3 + 575*f**2 - 48*f - 576 = 0. What is f?
-24, -1, 1
Factor -q**2/2 - 61*q/2 + 63.
-(q - 2)*(q + 63)/2
Factor -5*j**4 - 65*j**3 - 50*j**2 + 120*j.
-5*j*(j - 1)*(j + 2)*(j + 12)
Determine q so that -3*q**4/4 + 13*q**3 - 173*q**2/4 + 13*q = 0.
0, 1/3, 4, 13
Factor 2*s**2/9 - 68*s/9 + 128/9.
2*(s - 32)*(s - 2)/9
Find f such that 4*f**3 - 288*f**2 + 548*f + 840 = 0.
-1, 3, 70
Solve -2*z**2/5 - 86*z/5 = 0.
-43, 0
Factor -5*m**3 - 11*m**2 + 118*m + 24.
-(m - 4)*(m + 6)*(5*m + 1)
Determine v so that 6*v**4 - 958*v**3/3 - 796*v**2/3 + 2168*v/3 - 144 = 0.
-2, 2/9, 1, 54
Let d**2/4 - 24*d + 576 = 0. What is d?
48
Factor -25*p**4 + 35*p**3 - 10*p**2.
-5*p**2*(p - 1)*(5*p - 2)
Suppose -o**2/2 - 13*o/2 + 150 = 0. What is o?
-25, 12
Factor 4*g**5 - 12*g**4 + 12*g**3 - 4*g**2.
4*g**2*(g - 1)**3
Find f such that -4*f**5/5 - 22*f**4/5 - 18*f**3/5 + 76*f**2/5 + 136*f/5 + 48/5 = 0.
-3, -2, -1/2, 2
Determine s so that -2*s**3/5 - 16*s**2/5 - 24*s/5 = 0.
-6, -2, 0
Find a, given that 2*a**5/7 - 114*a**4 + 2382*a**3/7 - 2378*a**2/7 + 792*a/7 = 0.
0, 1, 396
Suppose 15*t**2 + 21*t/2 - 9/2 = 0. Calculate t.
-1, 3/10
Determine x so that -4*x**5/5 - 28*x**4/5 - 76*x**3/5 - 20*x**2 - 64*x/5 - 16/5 = 0.
-2, -1
What is i in -2*i**3 - 40*i**2 - 38*i = 0?
-19, -1, 0
Determine a so that 3*a**5 + 9*a**4 - 126*a**3 - 570*a**2 - 261*a + 945 = 0.
-5, -3, 1, 7
Factor 3*w**3 + 39*w**2 - 42*w.
3*w*(w - 1)*(w + 14)
Suppose 3*a**5/4 - 15*a**4/4 + 9*a**3/2 + 3*a**2 - 6*a = 0. What is a?
-1, 0, 2
Factor s**5/6 + 9*s**4/2 + 97*s**3/3 + 188*s**2/3 - 112*s - 1088/3.
(s - 2)*(s + 4)**3*(s + 17)/6
Let -2*m**2/7 + 54*m/7 + 180/7 = 0. Calculate m.
-3, 30
Find h such that 2*h**2/7 + 248*h/7 + 7688/7 = 0.
-62
Factor 2*a**2/3 - 146*a + 436/3.
2*(a - 218)*(a - 1)/3
Find m such that 3*m**2 - 83*m + 130 = 0.
5/3, 26
Factor -2*b**3/3 - 236*b**2/3 - 7192*b/3 - 13456/3.
-2*(b + 2)*(b + 58)**2/3
Factor y**3 - 3*y**2 + 3*y - 1.
(y - 1)**3
Suppose -2*a**4/17 - 48*a**3/17 - 126*a**2/17 = 0. Calculate a.
-21, -3, 0
Suppose -p**2/6 - 2*p/3 + 5/6 = 0. What is p?
-5, 1
Solve 5*n**3 - 210*n**2 + 2805*n - 11560 = 0 for n.
8, 17
Factor k**3/2 - 5*k**2/2 - 56*k + 352.
(k - 8)**2*(k + 11)/2
Factor 4*z**3 - 24*z**2 + 12*z + 40.
4*(z - 5)*(z - 2)*(z + 1)
Determine g, given that 20*g**4 + 328*g**3 + 1088*g**2 + 384*g = 0.
-12, -4, -2/5, 0
Let 5*o**3 + 145*o**2 + 140*o = 0. What is o?
-28, -1, 0
Factor 3*s**5/5 - 2784*s**4/5 + 859323*s**3/5 - 17529198*s**2 - 35576220*s - 17874600.
3*(s - 310)**3*(s + 1)**2/5
What is d in -d**4/3 - 5*d**3/3 + 2*d**2/3 + 8*d = 0?
-4, -3, 0, 2
Factor 20*x**4 + 15*x**3 - 165*x**2 - 200*x + 60.
5*(x - 3)*(x + 2)**2*(4*x - 1)
Factor -2*d**3/7 - 220*d**2/7 - 646*d/7 - 428/7.
-2*(d + 1)*(d + 2)*(d + 107)/7
Suppose 2*x**5/23 + 8*x**4/23 - 4*x**3/23 - 24*x**2/23 + 18*x/23 = 0. What is x?
-3, 0, 1
Determine q, given that 5*q**4 - 60*q**3 + 185*q**2 - 210*q + 80 = 0.
1, 2, 8
Let 5*p**5 + 250*p**4 + 950*p**3 + 1400*p**2 + 925*p + 230 = 0. Calculate p.
-46, -1
Let 5*y**2 - 5*y - 100 = 0. What is y?
-4, 5
Let -20*n**3 + 3765*n**2 - 940*n = 0. What is n?
0, 1/4, 188
Let y**3 + 2*y**2 = 0. What is y?
-2, 0
Factor y**3/5 - 11*y**2/5 + 36*y/5 - 36/5.
(y - 6)*(y - 3)*(y - 2)/5
Factor -i**2/12 + 139*i/12 - 230.
-(i - 115)*(i - 24)/12
Determine c, given that -5*c**3 - 595*c**2 - 16560*c - 134460 = 0.
-83, -18
Factor 4*h**2/5 + 22696*h/5 + 3