2
Let -2*z**2/5 + 48*z/5 - 126/5 = 0. What is z?
3, 21
Factor c**3/8 + 95*c**2/4 + 187*c/8 - 189/4.
(c - 1)*(c + 2)*(c + 189)/8
Factor -d**4/5 - 3*d**3/5 + 3*d**2/5 + 7*d/5 - 6/5.
-(d - 1)**2*(d + 2)*(d + 3)/5
Solve g**5/2 - g**4 - 12*g**3 + 16*g**2 + 64*g = 0.
-4, -2, 0, 4
Factor -g**5 + 9*g**4 - 8*g**3.
-g**3*(g - 8)*(g - 1)
Suppose -2*f**5 + 4*f**4 + 1056*f**3 = 0. Calculate f.
-22, 0, 24
Find h, given that -10*h**4/11 + 48*h**3/11 - 82*h**2/11 + 60*h/11 - 16/11 = 0.
4/5, 1, 2
Factor -2*x**2/3 + 1706*x/3 - 568.
-2*(x - 852)*(x - 1)/3
Find r, given that -26*r**4 - 282*r**3 - 736*r**2 + 120*r = 0.
-6, -5, 0, 2/13
Suppose -w**4/4 - 2*w**3 - 9*w**2/2 + 27/4 = 0. What is w?
-3, 1
Factor -y**2 + 72*y + 640.
-(y - 80)*(y + 8)
Suppose 2*g**5 - 6*g**3 - 4*g**2 = 0. Calculate g.
-1, 0, 2
Factor 3*x**2 + 18*x.
3*x*(x + 6)
Let 4*j**2 + 36*j - 88 = 0. What is j?
-11, 2
Let 3*w**4/4 + 49*w**3/2 + 57*w**2/4 - 111*w/2 + 16 = 0. Calculate w.
-32, -2, 1/3, 1
Suppose j**4/3 - 5*j**3 + 77*j**2/3 - 55*j + 42 = 0. What is j?
2, 3, 7
Factor 5*t**4 - 90*t**3 - 5*t**2 + 90*t.
5*t*(t - 18)*(t - 1)*(t + 1)
Determine q, given that 2*q**5/7 - 50*q**4/7 + 362*q**3/7 - 446*q**2/7 - 1804*q/7 + 1936/7 = 0.
-2, 1, 4, 11
What is c in 4*c**2/3 - 38*c/3 - 20/3 = 0?
-1/2, 10
Let 5*u**4/6 + 146*u**3/3 + 4321*u**2/6 + 841*u/3 = 0. Calculate u.
-29, -2/5, 0
Factor -3*l**2/4 + 213*l/2 - 15123/4.
-3*(l - 71)**2/4
Factor -14*p**2 + 31630*p - 9036.
-2*(p - 2259)*(7*p - 2)
Solve 4*m**5 - 36*m**4 + 104*m**3 - 96*m**2 = 0.
0, 2, 3, 4
Solve -3*r**3 + 18*r**2 - 33*r + 18 = 0 for r.
1, 2, 3
Solve h**5 - 17*h**4 - 7*h**3 + 113*h**2 + 102*h = 0.
-2, -1, 0, 3, 17
Suppose -3*z**5/8 + 45*z**4/4 - 63*z**3/2 + 123*z**2/4 - 81*z/8 = 0. Calculate z.
0, 1, 27
Find a, given that 4*a**4/5 + 24*a**3/5 + 12*a**2/5 - 8*a = 0.
-5, -2, 0, 1
Find x such that -x**4/2 + 3*x**3 + 12*x**2 + 13*x + 9/2 = 0.
-1, 9
Let -2*j**2 + 80*j/7 + 24/7 = 0. Calculate j.
-2/7, 6
Factor x**3/5 - 32*x**2 + 159*x/5.
x*(x - 159)*(x - 1)/5
Suppose 3*v**5 - 12*v**4 + 3*v**3 + 18*v**2 = 0. Calculate v.
-1, 0, 2, 3
Find t such that 9*t**3/8 - 7*t**2 + 93*t/8 - 9/4 = 0.
2/9, 3
Factor i**3/6 + 8*i**2/3 - 55*i/6 + 19/3.
(i - 2)*(i - 1)*(i + 19)/6
Factor -10*p**3/9 - 68*p**2/9 - 46*p/9 + 4/3.
-2*(p + 1)*(p + 6)*(5*p - 1)/9
Factor -2*a**2 + 317*a/2.
-a*(4*a - 317)/2
Factor 2*m**4/3 + 46*m**3/3 - 100*m**2/3.
2*m**2*(m - 2)*(m + 25)/3
Factor -2*w**2/15 - 148*w - 41070.
-2*(w + 555)**2/15
Let -129*q**4/4 - 135*q**3/2 - 153*q**2/4 - 3*q = 0. Calculate q.
-1, -4/43, 0
Factor 2*j**2 - 114*j + 220.
2*(j - 55)*(j - 2)
Solve 2*y**5/3 - 12*y**4 + 26*y**3/3 + 48*y**2 - 136*y/3 = 0.
-2, 0, 1, 2, 17
What is o in -7*o**4 + 191*o**3 - 978*o**2 - 856*o + 320 = 0?
-1, 2/7, 8, 20
Let 20*i**3 - 48*i**2 + 36*i - 8 = 0. What is i?
2/5, 1
Factor -u**2/2 - 16*u - 30.
-(u + 2)*(u + 30)/2
Let -z**4/4 - 341*z**3 - 116960*z**2 - 462400*z = 0. What is z?
-680, -4, 0
What is v in 44*v**5 - 168*v**4 + 56*v**3 + 192*v**2 - 100*v - 24 = 0?
-1, -2/11, 1, 3
Factor -2*v**2 + 18*v + 20.
-2*(v - 10)*(v + 1)
What is k in 5*k**4 + 20*k**3 - 65*k**2 - 200*k + 240 = 0?
-4, 1, 3
Factor y**4/3 + 4*y**3/3 - 4*y**2.
y**2*(y - 2)*(y + 6)/3
Factor -2*a**5 + 12*a**4 - 10*a**3.
-2*a**3*(a - 5)*(a - 1)
Find b such that 9*b**4/2 - 58*b**3/5 - 39*b**2/2 - 17*b/5 = 0.
-1, -1/5, 0, 34/9
Factor 2*u**4/3 - 2*u**2/3.
2*u**2*(u - 1)*(u + 1)/3
Factor 21*b**5 + 366*b**4 + 1485*b**3 - 972*b**2.
3*b**2*(b + 9)**2*(7*b - 4)
Determine n, given that 48*n**5 - 264*n**4 - 764*n**3 + 45218*n**2/9 + 8464*n/3 - 24334 = 0.
-3, 23/6
Factor -2*j**3/7 - 20*j**2/7 + 86*j/7 + 104/7.
-2*(j - 4)*(j + 1)*(j + 13)/7
Let -f**2 - 67*f - 660 = 0. Calculate f.
-55, -12
Factor 2*s**2 - 74*s - 76.
2*(s - 38)*(s + 1)
Factor -12*w**4 - 232*w**3 - 229*w**2/3 - 19*w/3.
-w*(w + 19)*(6*w + 1)**2/3
Let -5*w**3 + 15*w**2 = 0. What is w?
0, 3
Factor 5*b**5 - 20*b**4 - 80*b**3 + 320*b**2.
5*b**2*(b - 4)**2*(b + 4)
Solve 2*x**2/7 - 134*x/7 = 0 for x.
0, 67
Suppose -x**3 - 13*x**2/3 - 10*x/3 = 0. What is x?
-10/3, -1, 0
Let -r**2/6 + r/3 = 0. What is r?
0, 2
Factor 4*a**5 + 92*a**4 + 168*a**3.
4*a**3*(a + 2)*(a + 21)
Suppose 2*s**3 - 18*s**2 - 224*s = 0. What is s?
-7, 0, 16
Let 2*h**4 + 2*h**3 - 94*h**2 - 162*h + 252 = 0. Calculate h.
-6, -3, 1, 7
Find d, given that -2*d**2/11 - 64*d/11 + 456/11 = 0.
-38, 6
Determine b so that -2*b**2/15 - 128*b - 30720 = 0.
-480
Find v such that 2*v**5 - 6*v**4 + 2*v**3 + 6*v**2 - 4*v = 0.
-1, 0, 1, 2
What is l in -l**5/3 - 7*l**4/3 + 3*l**3 + 59*l**2/3 - 40*l/3 - 28 = 0?
-7, -3, -1, 2
Factor 9*w**5 + 675*w**4 - 681*w**3 + 683*w**2/3 - 76*w/3.
w*(w + 76)*(3*w - 1)**3/3
Let n**4/5 + 4*n**3/5 - 21*n**2/5 + 4*n/5 + 28/5 = 0. What is n?
-7, -1, 2
Factor l**2/3 - 58*l + 2523.
(l - 87)**2/3
Factor 5*k**2 - 190*k + 1805.
5*(k - 19)**2
Solve 6*u**2/7 - 540*u/7 + 12150/7 = 0.
45
Factor -z**3/5 + 247*z**2/5 - 3075*z + 15129/5.
-(z - 123)**2*(z - 1)/5
Factor -4*c**2/7 + 206*c/7 + 428/7.
-2*(c + 2)*(2*c - 107)/7
Suppose -3*p**2/4 + 1839*p/4 = 0. What is p?
0, 613
Factor -10*k**3 - 35*k**2 - 30*k.
-5*k*(k + 2)*(2*k + 3)
Suppose 28*g**5 - 432*g**4 + 1032*g**3 + 4768*g**2 + 4572*g + 1296 = 0. What is g?
-1, -4/7, 9
Find o such that 3*o**2/5 + 15*o + 138/5 = 0.
-23, -2
Factor -4*o**3/5 - 12*o**2/5 + 16*o/5 + 48/5.
-4*(o - 2)*(o + 2)*(o + 3)/5
Factor b**4/4 - 21*b**3/4 + 19*b**2/4 + 21*b/4 - 5.
(b - 20)*(b - 1)**2*(b + 1)/4
Factor 3*m**3 - 9*m**2 + 6*m.
3*m*(m - 2)*(m - 1)
Find c such that -c**2/4 - 3739*c/4 = 0.
-3739, 0
Factor 15*j**4 - 276*j**3 + 1728*j**2 - 3888*j + 1296.
3*(j - 6)**3*(5*j - 2)
Factor -2*l**2/9 - 266*l.
-2*l*(l + 1197)/9
Factor -3*p**2 + 1008*p - 84672.
-3*(p - 168)**2
Factor u**3/5 + 23*u**2/5 - 53*u/5 - 15.
(u - 3)*(u + 1)*(u + 25)/5
Factor -4*t**2/9 + 2504*t/9 - 391876/9.
-4*(t - 313)**2/9
Solve 24*i**4/5 - 254*i**3/5 + 696*i**2/5 - 46*i/5 - 84 = 0 for i.
-2/3, 1, 5, 21/4
Find c such that 27*c**3 - 249*c**2 - 1350*c + 312 = 0.
-4, 2/9, 13
Solve -4*i**2 + 24*i - 32 = 0.
2, 4
Factor -14*v**2 + 32868*v + 9392.
-2*(v - 2348)*(7*v + 2)
Factor n**5/2 + 5*n**4 - 82*n**3 + 332*n**2 - 544*n + 320.
(n - 4)*(n - 2)**3*(n + 20)/2
Factor -7*t**3 - 61*t**2 - 122*t + 40.
-(t + 4)*(t + 5)*(7*t - 2)
Factor -38*r**5 - 75*r**4 + 2*r**3 + 76*r**2 + 36*r - 1.
-(r - 1)*(r + 1)**3*(38*r - 1)
Factor -4*k**3/5 - 24*k**2/5 - 36*k/5 - 16/5.
-4*(k + 1)**2*(k + 4)/5
Determine n so that -2*n**2/7 - 62*n/7 + 132/7 = 0.
-33, 2
What is y in 24389*y**4/3 + 26912*y**3/3 + 870*y**2 + 88*y/3 + 1/3 = 0?
-1, -1/29
Factor -r**3/8 - 21*r**2/4 + 279*r/8 - 54.
-(r - 3)**2*(r + 48)/8
Factor 3*z**5 + 204*z**4 + 201*z**3.
3*z**3*(z + 1)*(z + 67)
Suppose 2*h**2 - 36*h - 80 = 0. Calculate h.
-2, 20
Solve -5*b**2 - 230*b - 1200 = 0 for b.
-40, -6
Factor -2*j**4 - 14*j**3 - 20*j**2.
-2*j**2*(j + 2)*(j + 5)
What is r in -r**5/5 + 3*r**4/5 + 17*r**3/5 + 9*r**2/5 - 16*r/5 - 12/5 = 0?
-2, -1, 1, 6
Determine q, given that -q**2 + 6*q + 352 = 0.
-16, 22
Factor -4*p**5 + 32*p**4 - 52*p**3 + 24*p**2.
-4*p**2*(p - 6)*(p - 1)**2
Factor 2*o**4/7 + 10*o**3/7 - 6*o**2/7 - 26*o/7 + 20/7.
2*(o - 1)**2*(o + 2)*(o + 5)/7
Let -9*t**4 + 60*t**3 - 108*t**2 + 48*t = 0. What is t?
0, 2/3, 2, 4
Suppose 2*n**5/5 - 98*n**4/5 + 1414*n**3/5 - 5086*n**2/5 + 2112*n/5 + 8712/5 = 0. Calculate n.
-1, 3, 22
Solve -2*k**4/3 - 5*k**3 - 32*k**2/3 - 4*k + 16/3 = 0 for k.
-4, -2, 1/2
Factor 2*u**2 + 3136*u + 3134.
2*(u + 1)*(u + 1567)
Suppose 3*r**4 - 48*r**3 + 276*r**2 - 672*r + 576 = 0. Calculate r.
2, 4, 6
Find v such that v**5/5 + 4*v**4/5 - 19*v**3/5 - 46*v**2/5 - 24*v/5 = 0.
-6, -1, 0, 4
Solve -2*g**5/3 - 146*g**4/3 + 298*g**3/3 - 50*g**2 = 0.
-75, 0, 1
Factor 2*i**4 - 10*i**3 - 2*i**2 + 10*i.
2*i*(i - 5)*(i - 1)*(i + 1)
Find q such that 2*q**5 + 124*q**4 - 6*q**3 - 376*q**2 - 248*q = 0.
-62, -1, 0, 2
Find f, given that 4*f**3 - 12360*f**2 + 24708*f - 12352 = 0.
1, 3088
Suppose 15*c**4/4 + 393*c**3/2 + 2613*c**2 + 1014*c = 0. What is c?
-26, -2/5, 0
Factor -o**5/2 - 494*o**4 - 123491*o**3 - 727662*o**2 - 2169729*o/2.
-o*(o + 3)**2*(o + 491)**2/2
Solve 169*u**5 + 1417*u**4 + 3136*u**3 + 352*u**2 - 1280*u + 256 = 0 for u.
-4, -1, 4/13
Factor -h**2/2 - 54*h - 1458.
-(h + 54)**2/2
Factor 2*u**3 - 24*u**2 + 512.
2*(u - 8)**2*(u + 4)
Solve 3*g**2/7 - 18*g/7 = 0 for g.
0, 6
