given that -4*n**3 - 180*n**2 + 372*n - 188 = 0.
-47, 1
Factor -2*s**2 + 24*s + 26.
-2*(s - 13)*(s + 1)
Determine z, given that 5*z**5/3 - 35*z**4 + 730*z**3/3 - 1610*z**2/3 - 245*z + 1715/3 = 0.
-1, 1, 7
Solve y**5/2 - 9*y**4/2 + 10*y**3 - 6*y**2 = 0.
0, 1, 2, 6
Factor -4*f**3/3 - 24*f**2.
-4*f**2*(f + 18)/3
Suppose -7*j**2/10 - 1489*j/10 + 213/5 = 0. Calculate j.
-213, 2/7
Suppose o**2/5 - 23*o/5 + 132/5 = 0. Calculate o.
11, 12
Factor 15*k**2 + 183*k + 198.
3*(k + 11)*(5*k + 6)
Solve 2*h**5 - 32*h**3 + 76*h**2 - 66*h + 20 = 0 for h.
-5, 1, 2
Factor -p**2 + 3*p - 2.
-(p - 2)*(p - 1)
Solve 2*w**2/5 - 259*w/5 + 129/5 = 0.
1/2, 129
Determine d, given that d**2/3 + 14*d/3 + 49/3 = 0.
-7
Factor -3*c**4/7 + 66*c**3/7 - 324*c**2/7 + 600*c/7 - 384/7.
-3*(c - 16)*(c - 2)**3/7
Find d, given that d**2 + 34*d - 195 = 0.
-39, 5
Suppose -2*c**3/3 + 8*c**2/3 - 2*c/3 - 4 = 0. What is c?
-1, 2, 3
Factor -2*k**3/13 - 84*k**2/13 + 86*k/13.
-2*k*(k - 1)*(k + 43)/13
Find i, given that 3*i**3 - 81*i**2 + 150*i = 0.
0, 2, 25
What is q in -q**5/7 + 16*q**4/7 - 48*q**3/7 - 82*q**2/7 + 7*q + 66/7 = 0?
-1, 1, 6, 11
Find l, given that 3*l**4/8 - 9*l**3/8 - 27*l**2/4 = 0.
-3, 0, 6
Factor -2*c**3 - 24*c**2/7 + 120*c/7 - 32/7.
-2*(c - 2)*(c + 4)*(7*c - 2)/7
Suppose 2*x**2/17 - 2796*x/17 + 977202/17 = 0. Calculate x.
699
Factor f**5 + 6*f**4 + 12*f**3 + 8*f**2.
f**2*(f + 2)**3
Factor 3*t**4/5 + 18*t**3/5 + 12*t**2/5 - 18*t/5 - 3.
3*(t - 1)*(t + 1)**2*(t + 5)/5
Solve -m**2/3 + 5*m - 14/3 = 0.
1, 14
Factor 15*s**3 + 970*s**2 + 1585*s + 630.
5*(s + 1)*(s + 63)*(3*s + 2)
Suppose -8281*g**4/8 + 91*g**3/2 - g**2/2 = 0. What is g?
0, 2/91
Factor -3*t**3/5 + 34*t**2/5 + 24*t/5.
-t*(t - 12)*(3*t + 2)/5
Factor -z**2 - 56*z + 57.
-(z - 1)*(z + 57)
Find c such that 4*c**3 - 332*c**2 + 652*c - 324 = 0.
1, 81
Determine h so that 6*h**2 + 1089*h/2 - 273/2 = 0.
-91, 1/4
Factor -v**5 - 14*v**4 - 48*v**3 + 14*v**2 + 49*v.
-v*(v - 1)*(v + 1)*(v + 7)**2
Suppose -i**4 + 9*i**3/2 + 49*i**2/2 + 27*i + 8 = 0. What is i?
-2, -1, -1/2, 8
Factor 3*u**4 + 18*u**3 + 24*u**2 - 18*u - 27.
3*(u - 1)*(u + 1)*(u + 3)**2
Factor -m**2/8 + 119*m/4 + 239/8.
-(m - 239)*(m + 1)/8
Find b, given that -2*b**3/3 + 206*b**2/3 - 2518*b/3 + 2314/3 = 0.
1, 13, 89
Factor 2*f**4 + 204*f**3 + 5402*f**2 + 10200*f + 5000.
2*(f + 1)**2*(f + 50)**2
Suppose 2*z**3/5 + 2*z**2 - 1052*z/5 + 208 = 0. What is z?
-26, 1, 20
Solve 10*d**5/3 + 76*d**4/3 + 6*d**3 - 160*d**2/3 + 56*d/3 = 0 for d.
-7, -2, 0, 2/5, 1
Find w, given that -w**2 + 24*w - 23 = 0.
1, 23
Factor -3*y**4 + 9*y**3 + 18*y**2 - 24*y.
-3*y*(y - 4)*(y - 1)*(y + 2)
Find z, given that -3*z**5/5 + 12*z**4/5 - 6*z**3/5 - 12*z**2/5 + 9*z/5 = 0.
-1, 0, 1, 3
Determine o, given that -5*o**4 + 55*o**3 - 210*o**2 + 340*o - 200 = 0.
2, 5
Find n such that -3*n**3 - 15*n**2 + 39*n - 21 = 0.
-7, 1
Determine l so that -3*l**4 + 21*l**3 + 300*l**2 + 852*l + 720 = 0.
-4, -2, 15
Factor k**3 - 299*k**2/4 + 537*k/2 - 639/4.
(k - 71)*(k - 3)*(4*k - 3)/4
Solve 2*q**4/19 + 104*q**3/19 + 1236*q**2/19 - 3240*q/19 - 4374/19 = 0 for q.
-27, -1, 3
Factor -70227*a**3 + 145044*a**2 - 9255*a + 150.
-3*(a - 2)*(153*a - 5)**2
Find u, given that -2*u**3/9 - 1902*u**2 - 5426406*u - 5160512106 = 0.
-2853
Find p such that -2*p**3 - 28*p**2 - 98*p - 72 = 0.
-9, -4, -1
Solve -c**4/10 - 108*c**3/5 - 2289*c**2/2 + 11881*c/5 = 0.
-109, 0, 2
Determine n so that 2*n**4 + 6*n**3 + 4*n**2 = 0.
-2, -1, 0
Factor -2*f**2 + 554*f + 556.
-2*(f - 278)*(f + 1)
Let -4*t**2 + 624*t - 24336 = 0. Calculate t.
78
Let -4*p**2/5 + 56*p - 804/5 = 0. What is p?
3, 67
Solve -h**2/8 + 5*h/2 = 0.
0, 20
What is j in -2*j**2 - 38*j - 36 = 0?
-18, -1
Determine x so that 14*x**4/11 - 18*x**3/11 - 24*x**2/11 + 8*x/11 = 0.
-1, 0, 2/7, 2
Suppose 2*b**5 + 48*b**4 + 328*b**3 + 436*b**2 - 330*b - 484 = 0. Calculate b.
-11, -2, -1, 1
Find x, given that -x**4/8 + 7*x**3/8 + 19*x**2/8 - 7*x/8 - 9/4 = 0.
-2, -1, 1, 9
Factor -m**2/4 - 7*m/4 + 2.
-(m - 1)*(m + 8)/4
Suppose 2*n**3 - 108*n**2 - 8*n + 432 = 0. Calculate n.
-2, 2, 54
Solve 26*x**3/5 + 56*x**2/5 + 34*x/5 + 4/5 = 0.
-1, -2/13
Factor 2*b**2/7 + 2*b/7.
2*b*(b + 1)/7
Factor -r**4/7 + r**3 - 17*r**2/7 + 17*r/7 - 6/7.
-(r - 3)*(r - 2)*(r - 1)**2/7
Factor 5*v**2 - 35*v + 30.
5*(v - 6)*(v - 1)
Determine u, given that -u**2/2 + 3*u/2 + 27 = 0.
-6, 9
Determine m so that 9*m**3 - 50*m**2 - 87*m - 28 = 0.
-1, -4/9, 7
Factor 29*k**2/3 + 34*k/3 - 16.
(k + 2)*(29*k - 24)/3
Let -2*i**5/17 - 20*i**4/17 + 6*i**3/17 + 280*i**2/17 - 392*i/17 = 0. What is i?
-7, 0, 2
Solve t**2/10 + 44*t/5 + 968/5 = 0.
-44
Let 4*p**2 + 960*p + 956 = 0. Calculate p.
-239, -1
Let 5*s**3/4 - 25*s**2/2 - 135*s/4 + 45 = 0. What is s?
-3, 1, 12
Suppose 2*q**3 + 418*q**2 + 21630*q - 22050 = 0. What is q?
-105, 1
Factor -2*n**2/3 - 8*n - 22/3.
-2*(n + 1)*(n + 11)/3
Find q, given that -2*q**5/13 - 16*q**4/13 - 36*q**3/13 + 54*q/13 = 0.
-3, 0, 1
Solve -4*y**3 + 28*y**2 - 28*y - 60 = 0.
-1, 3, 5
Let -2*h**4/3 - 74*h**3/3 - 270*h**2 - 450*h + 4500 = 0. What is h?
-15, -10, 3
Factor -j**4/2 + 21*j**3/2.
-j**3*(j - 21)/2
Let -21*z**4 - 68*z**3 + 75*z**2 + 38*z - 24 = 0. Calculate z.
-4, -2/3, 3/7, 1
Determine m so that -4*m**3 + 348*m**2 - 1344*m + 1328 = 0.
2, 83
Let 4*n**3/5 - 112*n**2/5 + 208*n - 640 = 0. Calculate n.
8, 10
Solve -n**4 + 33*n**3 + 69*n**2 + 35*n = 0.
-1, 0, 35
Factor y**2 - 23*y + 130.
(y - 13)*(y - 10)
Factor -4*g**3 - 196*g**2 - 380*g - 188.
-4*(g + 1)**2*(g + 47)
Determine n, given that 3*n**5/2 + 6*n**4 + 3*n**3/2 - 21*n**2 - 30*n - 12 = 0.
-2, -1, 2
Determine u, given that 4*u**2/3 + 548*u = 0.
-411, 0
Find k such that -17*k**4/6 + 121*k**3/6 - 67*k**2/2 + 107*k/6 - 5/3 = 0.
2/17, 1, 5
Determine x, given that -2*x**2 - 9*x + 5 = 0.
-5, 1/2
Factor a**3 + 216*a**2 + 15552*a + 373248.
(a + 72)**3
Factor -w**4/4 + w**3/2 - w**2/4.
-w**2*(w - 1)**2/4
What is l in 2*l**4/3 - 110*l**3/3 + 1664*l**2/3 - 1352*l = 0?
0, 3, 26
Solve -16*m**5 - 88*m**4 + 63*m**3 + 82*m**2 - 47*m + 6 = 0.
-6, -1, 1/4, 1
Suppose 5*w**2/2 + 2175*w/2 - 3285 = 0. What is w?
-438, 3
Factor -f**2/5 + 21*f/5 - 4.
-(f - 20)*(f - 1)/5
Factor d**3 - 2*d**2 - 9*d + 18.
(d - 3)*(d - 2)*(d + 3)
Factor -2*x**3/15 + 8*x**2/3 + 2*x/15 - 8/3.
-2*(x - 20)*(x - 1)*(x + 1)/15
Suppose -9*t**5/7 - 29*t**4/7 - 24*t**3/7 - 4*t**2/7 = 0. What is t?
-2, -1, -2/9, 0
Factor -64*a**4 - 144*a**3 + 132*a**2 - 35*a + 3.
-(a + 3)*(4*a - 1)**3
Find c, given that -3*c**4 + 12*c**3 - 9*c**2 = 0.
0, 1, 3
Find u, given that 2*u**5 - 2*u**4 - 18*u**3 + 10*u**2 + 32*u - 24 = 0.
-2, 1, 3
Factor -j**3/5 + 2*j**2 - 12*j/5 - 72/5.
-(j - 6)**2*(j + 2)/5
Factor 14*f**4 - 60*f**3 + 72*f**2 - 16*f.
2*f*(f - 2)**2*(7*f - 2)
Solve 3*c**5 + 19*c**4/5 - 28*c**3 + 92*c**2/5 - 16*c/5 = 0.
-4, 0, 1/3, 2/5, 2
Factor 5*r**5 + 60*r**4 + 240*r**3 + 410*r**2 + 315*r + 90.
5*(r + 1)**3*(r + 3)*(r + 6)
Suppose -3*g**5 + 36*g**4 - 60*g**3 - 330*g**2 + 63*g + 294 = 0. What is g?
-2, -1, 1, 7
Determine r so that r**5/3 + r**4/3 - 7*r**3 + 47*r**2/3 - 40*r/3 + 4 = 0.
-6, 1, 2
Suppose -a**5 - 109*a**4 - 2914*a**3 + 3134*a**2 + 2915*a - 3025 = 0. What is a?
-55, -1, 1
Solve 3*m**3 - 246*m**2 + 5043*m = 0 for m.
0, 41
What is o in o**3/6 + o**2 - 3*o/2 - 7/3 = 0?
-7, -1, 2
Factor y**4 - 127*y**3/3 + 602*y**2 - 2940*y + 2744/3.
(y - 14)**3*(3*y - 1)/3
Factor 2*i**4/3 - 19*i**3/3 - 32*i**2/3 - 11*i/3.
i*(i - 11)*(i + 1)*(2*i + 1)/3
Determine m, given that 65*m**5 + 6035*m**4 - 25825*m**3 + 35225*m**2 - 17440*m + 1940 = 0.
-97, 2/13, 1, 2
Determine f so that 9*f**3/8 + 69*f**2/4 - 99*f/8 - 6 = 0.
-16, -1/3, 1
Factor -49*p**4/5 - 6097*p**3/5 + 3496*p**2/5 - 100*p.
-p*(p + 125)*(7*p - 2)**2/5
Let d**2/5 - 202*d/5 + 10201/5 = 0. Calculate d.
101
Factor -6*g**4 - 15*g**3 - 3*g**2 + 6*g.
-3*g*(g + 1)*(g + 2)*(2*g - 1)
Find b such that 2*b**3/11 + 13206*b**2/11 + 29066406*b/11 + 21325053202/11 = 0.
-2201
Factor 2*p**2/13 - 92*p/13 + 90/13.
2*(p - 45)*(p - 1)/13
Factor q**4 + 27*q**3 + 236*q**2 + 672*q.
q*(q + 7)*(q + 8)*(q + 12)
Factor x**2/3 + 7*x + 18.
(x + 3)*(x + 18)/3
Factor -4*h**3/7 - 184*h**2/7 - 180*h/7.
-4*h*(h + 1)*(h + 45)/7
Determine r so that -r**5/5 - 17*r**4/5 - 17*r**3 - 159*r**2/5 - 18*r = 0.
-10, -3, -1, 0
Find w such that 4*w**3/3 - 20*w**2/3 - 32*w/3 + 64 = 0.
-3, 4
Solve p**4 - 62*p**3 + 119*p*