60.
-5*(k + 1)*(k + 2)**2*(k + 13)
Let -45*w**3 + 4355*w**2 - 3350*w - 960 = 0. What is w?
-2/9, 1, 96
Determine g so that -18*g**4 - 1428*g**3 + 2416*g**2 - 1132*g + 162 = 0.
-81, 1/3, 1
Find u such that -4*u**2/9 + 296*u/3 - 576 = 0.
6, 216
Factor 2*w**2/3 + 164*w/3 + 54.
2*(w + 1)*(w + 81)/3
Factor s**5 - 32*s**4 - 67*s**3 - 34*s**2.
s**2*(s - 34)*(s + 1)**2
Determine h, given that -4*h**4 - 72*h**3 + 484*h**2 + 552*h = 0.
-23, -1, 0, 6
Solve -3*v**4 + 69*v**3 - 354*v**2 - 576*v + 864 = 0 for v.
-2, 1, 12
Factor 5*f**4 + 8440*f**3 + 4746090*f**2 + 887513200*f - 892267735.
5*(f - 1)*(f + 563)**3
Suppose -2*q**2/11 - 18*q - 388/11 = 0. Calculate q.
-97, -2
Solve 3*t**2/5 + 123*t + 612/5 = 0.
-204, -1
Factor 4*g**3 + 8*g**2.
4*g**2*(g + 2)
Factor -w**2/2 - 95*w/2 + 147.
-(w - 3)*(w + 98)/2
Let 2*q**3 + 34*q**2 + 62*q + 30 = 0. What is q?
-15, -1
Solve -2*w**3/11 + 170*w**2/11 - 1532*w/11 + 2400/11 = 0.
2, 8, 75
Let -250*b**3 + 166050*b**2 - 36763470*b + 2713144086 = 0. What is b?
1107/5
Determine r so that -r**4 - 12*r**3 - 50*r**2 - 84*r - 45 = 0.
-5, -3, -1
Factor 3*w**3 + 69*w**2 + 381*w + 315.
3*(w + 1)*(w + 7)*(w + 15)
Find z such that 4*z**4 - 1048*z**3 - 3168*z**2 - 3176*z - 1060 = 0.
-1, 265
Solve 5*d**2 - 50*d - 55 = 0.
-1, 11
Factor 2*w**3/9 - 22*w**2/9 - 50*w/9 - 26/9.
2*(w - 13)*(w + 1)**2/9
Let -3*o**3 - 753*o**2 + 1518*o = 0. Calculate o.
-253, 0, 2
Factor 2*m**3 + 122*m**2 + 352*m + 232.
2*(m + 1)*(m + 2)*(m + 58)
Factor -5*w**4 - 25*w**3 + 30*w**2.
-5*w**2*(w - 1)*(w + 6)
Determine c, given that -3*c**2 + 24*c = 0.
0, 8
Suppose j**4/10 - 3*j**3/5 - 8*j**2/5 = 0. What is j?
-2, 0, 8
Factor 125*f**3 - 470*f**2 + 380*f + 120.
5*(f - 2)**2*(25*f + 6)
Suppose 8*m**4/11 + 42*m**3/11 + 6*m**2 + 38*m/11 + 6/11 = 0. What is m?
-3, -1, -1/4
Suppose -34347*r**4 - 206724*r**3 - 312978*r**2 - 5796*r - 27 = 0. What is r?
-3, -1/107
Let 2*l**3/5 + 906*l**2/5 + 136806*l/5 + 6885902/5 = 0. What is l?
-151
Factor -2*y**2/7 - 18*y/7 - 36/7.
-2*(y + 3)*(y + 6)/7
Find a such that -6*a**5 + 142*a**4 - 1154*a**3 + 3786*a**2 - 4968*a + 1944 = 0.
2/3, 2, 3, 9
Determine t, given that -2*t**2 + 2*t + 40 = 0.
-4, 5
Determine v, given that 4*v**3 + 1204*v**2 + 83616*v - 1070784 = 0.
-156, 11
Determine r, given that -2*r**2/13 - 304*r/13 = 0.
-152, 0
Solve d**4/4 + 7*d**3/4 - 17*d**2/2 - 10*d = 0 for d.
-10, -1, 0, 4
Determine g so that g**4/4 + g**3/2 - 19*g**2/4 + 7*g - 3 = 0.
-6, 1, 2
Solve -5*q**2/4 + 1065*q/4 - 265 = 0.
1, 212
Let 5*t**4 - 20*t**3 - 330*t**2 - 580*t - 275 = 0. What is t?
-5, -1, 11
Determine i, given that 242*i**2 - 10032*i + 103968 = 0.
228/11
Let 3*n**3/4 - 3*n**2 - 3*n/4 + 3 = 0. Calculate n.
-1, 1, 4
Factor -3*d**3 - 21*d**2 - 18*d.
-3*d*(d + 1)*(d + 6)
Suppose -3*j**2 + 54*j + 120 = 0. Calculate j.
-2, 20
What is a in 2*a**4/5 - 394*a**3/5 + 234*a**2 - 1166*a/5 + 388/5 = 0?
1, 194
Factor 3*r**2/5 - 1869*r/5 - 1872/5.
3*(r - 624)*(r + 1)/5
Find p such that -7*p**3/3 + 58*p**2/3 + 719*p/3 - 70 = 0.
-7, 2/7, 15
Factor 2*n**3/15 + 2*n**2/3 - 16*n/15 - 8/5.
2*(n - 2)*(n + 1)*(n + 6)/15
Factor w**5 + 8*w**4 + 12*w**3 - 2*w**2 - 13*w - 6.
(w - 1)*(w + 1)**3*(w + 6)
Suppose 58*k**4 + 1570*k**3 + 14202*k**2 + 43254*k + 2916 = 0. What is k?
-9, -2/29
Determine r so that r**5/5 + 11*r**4 - r**3/5 - 11*r**2 = 0.
-55, -1, 0, 1
Factor -x**3 - 7*x**2 + 714*x + 720.
-(x - 24)*(x + 1)*(x + 30)
Let 4*b**2/5 + 8*b/5 - 96/5 = 0. Calculate b.
-6, 4
Factor 5*r**5 - 40*r**4 + 120*r**3 - 160*r**2 + 80*r.
5*r*(r - 2)**4
Factor y**2 - 50*y + 49.
(y - 49)*(y - 1)
Suppose -2*x**2 - 82*x + 84 = 0. Calculate x.
-42, 1
Suppose 2*t**2/11 + 50*t/11 - 108/11 = 0. What is t?
-27, 2
Solve -2*z**3 - 2058*z**2 - 12294*z - 18414 = 0 for z.
-1023, -3
Factor 2*h**4 - 32*h**3 - 300*h**2 - 496*h - 230.
2*(h - 23)*(h + 1)**2*(h + 5)
Find y such that -5*y**2 + 4200*y - 4195 = 0.
1, 839
Let 1106*p**4/17 + 818*p**3/17 - 296*p**2/17 - 8*p/17 = 0. Calculate p.
-1, -2/79, 0, 2/7
Factor w**4/6 + 53*w**3/6 + 76*w**2/3 + 50*w/3.
w*(w + 1)*(w + 2)*(w + 50)/6
Factor -o**2/2 + 27*o/2.
-o*(o - 27)/2
Solve -2*t**5/7 - 22*t**4/7 + 2*t**3/7 + 22*t**2/7 = 0.
-11, -1, 0, 1
Factor 44*u**3/7 + 696*u**2/7 + 384*u - 512/7.
4*(u + 8)**2*(11*u - 2)/7
Factor 10*i**4 + 71*i**3 + 67*i**2 + 6*i.
i*(i + 1)*(i + 6)*(10*i + 1)
Find y, given that 2*y**5/13 - 274*y**4/13 + 9520*y**3/13 - 9248*y**2/13 = 0.
0, 1, 68
What is o in o**2/5 + 26*o - 131/5 = 0?
-131, 1
Factor -m**3 - 82*m**2 + 167*m - 84.
-(m - 1)**2*(m + 84)
Find s such that -5*s**3 - 10*s**2 + 155*s - 140 = 0.
-7, 1, 4
Suppose 14*p**5/5 - 128*p**4/5 + 312*p**3/5 - 308*p**2/5 + 122*p/5 - 12/5 = 0. Calculate p.
1/7, 1, 6
Factor -4*a**2/3 + 2448*a - 1123632.
-4*(a - 918)**2/3
Factor -4*v**2 - 124*v - 232.
-4*(v + 2)*(v + 29)
Factor 4*u**2/3 + 184*u/3 + 364.
4*(u + 7)*(u + 39)/3
Solve z**2 - 592*z + 87616 = 0 for z.
296
Solve -z**5 + 29*z**4 - 102*z**3 + 46*z**2 + 103*z - 75 = 0 for z.
-1, 1, 3, 25
Factor -2994003*a**4/2 - 2988009*a**3 - 2970039*a**2/2 + 5982*a - 6.
-3*(a + 1)**2*(999*a - 2)**2/2
Factor 2*d**4/3 + 4*d**3/3 - 14*d**2/3 - 40*d/3 - 8.
2*(d - 3)*(d + 1)*(d + 2)**2/3
Suppose n**3 + 21*n**2 + 20*n = 0. What is n?
-20, -1, 0
Find o, given that -5*o**2 + 15*o + 20 = 0.
-1, 4
Factor 4*h**3 + 4*h**2 - 16*h - 16.
4*(h - 2)*(h + 1)*(h + 2)
Find f, given that -2*f**2 + 124*f = 0.
0, 62
What is n in -n**5 + 112*n**4 + 818*n**3 + 1772*n**2 + 1543*n + 476 = 0?
-4, -1, 119
Find d such that 2*d**5/7 - 8*d**4/7 + 6*d**3/7 + 8*d**2/7 - 8*d/7 = 0.
-1, 0, 1, 2
Factor 5*z**2 + 170*z - 975.
5*(z - 5)*(z + 39)
Determine k, given that k**5 - 52*k**4/5 + 79*k**3/5 + 52*k**2/5 - 84*k/5 = 0.
-1, 0, 1, 2, 42/5
Suppose 9*o**2/8 + 195*o/8 + 63/4 = 0. What is o?
-21, -2/3
Solve 28*u**3 - 118*u**2 + 108*u - 18 = 0 for u.
3/14, 1, 3
Factor 2*c**4/3 - 128*c**3/3 - 2*c**2/3 + 128*c/3.
2*c*(c - 64)*(c - 1)*(c + 1)/3
Let 4*n**4/5 + 408*n**3/5 + 2688*n**2 + 25480*n - 102900 = 0. What is n?
-35, 3
Suppose -2*n**5 + 16*n**4 - 34*n**3 + 20*n**2 = 0. Calculate n.
0, 1, 2, 5
Factor 18*o**4 + 48*o**3 - 34*o**2 - 40*o + 24.
2*(o + 1)*(o + 3)*(3*o - 2)**2
Factor 3*i**3 + 369*i**2 + 5670*i.
3*i*(i + 18)*(i + 105)
Solve -2*i**3/7 - 36*i**2/7 - 192*i/7 - 320/7 = 0 for i.
-10, -4
What is x in 21*x**3/2 + 127*x**2/2 + 86*x - 30 = 0?
-10/3, -3, 2/7
Solve 5*a**5 + 10*a**4 - 25*a**3 - 50*a**2 + 20*a + 40 = 0.
-2, -1, 1, 2
Find b, given that b**2/3 + 173*b/3 + 114 = 0.
-171, -2
Factor 2*k**3/11 - 1810*k**2/11 + 1808*k/11.
2*k*(k - 904)*(k - 1)/11
Factor 2*i**3/3 + 116*i**2/3 + 1280*i/3 - 4096.
2*(i - 6)*(i + 32)**2/3
Solve -r**2 + 214*r/5 + 43/5 = 0.
-1/5, 43
Factor -q**3/3 + 68*q**2/3 + 71*q/3 - 46.
-(q - 69)*(q - 1)*(q + 2)/3
Let 2*b**2 + 348*b + 15138 = 0. What is b?
-87
Find q such that q**3/4 - 1495*q**2/4 + 1492*q - 1491 = 0.
2, 1491
Factor 3*o**2 + 141*o - 144.
3*(o - 1)*(o + 48)
Solve -3*u**3/7 + 9*u/7 + 6/7 = 0.
-1, 2
Factor 3*u**2/7 - 21*u - 9180/7.
3*(u - 85)*(u + 36)/7
Factor 324*o**4 + 3708*o**3 + 7432*o**2 + 2768*o + 288.
4*(o + 2)*(o + 9)*(9*o + 2)**2
Find o such that -4*o**5/5 + 46*o**4/5 + 84*o**3 + 846*o**2/5 + 324*o/5 = 0.
-3, -1/2, 0, 18
Suppose g**4/3 - 3*g**3 + 8*g**2 - 16*g/3 = 0. What is g?
0, 1, 4
Factor 2*c**3/11 - 4*c**2/11 - 382*c/11 - 96.
2*(c - 16)*(c + 3)*(c + 11)/11
Let 2*t**5 - 34*t**4 + 188*t**3 - 380*t**2 + 322*t - 98 = 0. What is t?
1, 7
Factor n**3/9 + 4*n**2/9 - 11*n/9 + 2/3.
(n - 1)**2*(n + 6)/9
Find o, given that o**2/4 + 45*o/4 + 11 = 0.
-44, -1
Factor 2*g**3 - 4*g**2.
2*g**2*(g - 2)
Factor -3*d**2/8 - 333*d/4 - 36963/8.
-3*(d + 111)**2/8
Factor 2*r**2/9 - 56*r/3 + 392.
2*(r - 42)**2/9
What is k in 10*k**4 - 98*k**3 - 250*k**2 - 166*k - 24 = 0?
-1, -1/5, 12
Factor -h**4 + 19*h**3 - 95*h**2 + 137*h - 60.
-(h - 12)*(h - 5)*(h - 1)**2
Factor 2*t**2 - 30*t/7.
2*t*(7*t - 15)/7
Find r, given that -r**3/4 - 2*r**2 + 45*r/4 - 9 = 0.
-12, 1, 3
Factor b**3/4 - 65*b**2/2 + 257*b/4 - 32.
(b - 128)*(b - 1)**2/4
Let -4*m**5 + 312*m**4 + 4*m**3 - 312*m**2 = 0. Calculate m.
-1, 0, 1, 78
Solve 4*r**2 - 632*r + 24964 = 0 for r.
79
Solve b**3 + 7*b**2 - 17*b + 9 = 0 for b.
-9, 1
Solve 2*w**4 - 114*w**2 + 400*w - 288 = 0 for w.
-9, 1, 4
Factor -2*u**2 + 5608*u - 3931208.
-2*(u - 1402)**2
Suppose 4*x**5 + 96*x**4 - 4*x**3 - 96*x**2 = 0. What is x?
-24, -1, 0, 1
So