olve -2*z**4 + 12*z**3 + 16*z**2 - 12*z - 14 = 0.
-1, 1, 7
Factor a**2 + 69*a.
a*(a + 69)
Factor 2*h**3/3 + 88*h**2/9 + 158*h/9 + 76/9.
2*(h + 1)**2*(3*h + 38)/9
Factor 4*f**4 - 12*f**3 - 40*f**2.
4*f**2*(f - 5)*(f + 2)
Factor 2*l**2/3 + 2*l/3 - 4/3.
2*(l - 1)*(l + 2)/3
Factor -112*a**3 - 452*a**2 - 352*a - 12.
-4*(a + 1)*(a + 3)*(28*a + 1)
Factor b**2/11 + 7*b/11 + 12/11.
(b + 3)*(b + 4)/11
Determine d, given that d**4 + 3*d**3 - 3*d**2 - 7*d + 6 = 0.
-3, -2, 1
Suppose -2*u**2/3 + 56*u/3 - 392/3 = 0. What is u?
14
Determine i, given that 294*i**3 - 3430*i**2 + 3056*i - 600 = 0.
2/7, 2/3, 75/7
Factor b**2 - 6*b - 16.
(b - 8)*(b + 2)
Factor -2*z**2/7 + 50*z/7 - 92/7.
-2*(z - 23)*(z - 2)/7
Let -k**2 - 950*k - 225625 = 0. Calculate k.
-475
Factor 4*m**3 + 64*m**2 - 740*m + 672.
4*(m - 7)*(m - 1)*(m + 24)
Determine v, given that 2*v**3/13 + 116*v**2/13 - 622*v/13 + 504/13 = 0.
-63, 1, 4
Factor -20*d**3 - 108*d**2 - 120*d - 32.
-4*(d + 1)*(d + 4)*(5*d + 2)
Factor -2*u**2 + 30*u.
-2*u*(u - 15)
Let 3*q**5 - 30*q**4 + 108*q**3 - 174*q**2 + 129*q - 36 = 0. Calculate q.
1, 3, 4
Factor -v**4/8 + 37*v**3/4 - 283*v**2/8 + 105*v/4.
-v*(v - 70)*(v - 3)*(v - 1)/8
Factor 4*q**2 - 184*q + 2116.
4*(q - 23)**2
Solve 6*b**4/5 + 292*b**3 + 264986*b**2/15 - 35624*b/3 + 29768/15 = 0 for b.
-122, 1/3
Factor k**4 + 111*k**3 - 455*k**2 + 573*k - 230.
(k - 2)*(k - 1)**2*(k + 115)
Factor -2*t**4/11 - 46*t**3/11 - 32*t**2 - 896*t/11.
-2*t*(t + 7)*(t + 8)**2/11
Suppose -2*x**4/3 + 18*x**3 - 220*x**2/3 = 0. What is x?
0, 5, 22
Factor -j**5 + 29*j**4 - 224*j**3 + 196*j**2.
-j**2*(j - 14)**2*(j - 1)
Factor 3*t**3 + 7*t**2 - 4.
(t + 1)*(t + 2)*(3*t - 2)
Solve g**3 + 91*g**2 - 92*g = 0 for g.
-92, 0, 1
Let 17*q**4/2 + 42*q**3 + 97*q**2/2 - 3*q = 0. What is q?
-3, -2, 0, 1/17
Factor 3125*d**5/2 + 9500*d**4 + 1505*d**3/2 + 15*d**2.
5*d**2*(d + 6)*(25*d + 1)**2/2
What is j in -3*j**5 + 54*j**4 - 15*j**3 - 696*j**2 + 1476*j - 816 = 0?
-4, 1, 2, 17
Find t, given that 35*t**2 + 955*t + 270 = 0.
-27, -2/7
Factor -4*r**3 + 196*r**2 + 404*r + 204.
-4*(r - 51)*(r + 1)**2
Factor -r**3/6 + 7*r/6 + 1.
-(r - 3)*(r + 1)*(r + 2)/6
Factor 5*x**4 + 10225*x**3.
5*x**3*(x + 2045)
Factor -2*k**4/19 - 14*k**3/19 + 34*k**2/19 - 18*k/19.
-2*k*(k - 1)**2*(k + 9)/19
What is p in -2*p**3/15 - 8*p**2/15 + 122*p/3 - 40 = 0?
-20, 1, 15
Suppose 2*l**5 - 28*l**4 - 62*l**3 - 32*l**2 = 0. Calculate l.
-1, 0, 16
Find n, given that -5*n**3/2 + 155*n**2/2 + 2905*n/2 + 11025/2 = 0.
-7, 45
Suppose -j**2/3 - 124*j/3 - 3844/3 = 0. Calculate j.
-62
Determine w, given that -w**5/2 + 11*w**4 + 73*w**3/2 + 25*w**2 = 0.
-2, -1, 0, 25
Suppose 2*t**2 - 14*t + 12 = 0. Calculate t.
1, 6
Find l such that -4*l**3/5 - 12*l**2 - 152*l/5 - 96/5 = 0.
-12, -2, -1
Factor t**3 - 135*t**2 + 6075*t - 91125.
(t - 45)**3
Suppose 9*o**5 + 75*o**4 - 246*o**3 + 198*o**2 - 3*o - 33 = 0. What is o?
-11, -1/3, 1
Factor 3*b**3/2 + 9*b**2 - 3*b/2 - 9.
3*(b - 1)*(b + 1)*(b + 6)/2
Find v, given that 2*v**3/3 + 370*v**2/3 + 1456*v/3 + 1448/3 = 0.
-181, -2
Solve d**5 - 4*d**4 - 54*d**3 + 432*d**2 - 1107*d + 972 = 0 for d.
-9, 3, 4
Determine r, given that -2*r**5 + 6*r**4 + 20*r**3 - 48*r**2 = 0.
-3, 0, 2, 4
Factor -2*r**2/5 - 608*r/5 - 46208/5.
-2*(r + 152)**2/5
Factor -3*i**2/2 - 24*i + 630.
-3*(i - 14)*(i + 30)/2
Suppose p**2/6 - 9*p + 52/3 = 0. Calculate p.
2, 52
Let 8*l**2 - 510*l + 378 = 0. What is l?
3/4, 63
Factor 16*t**2 + 20*t - 36.
4*(t - 1)*(4*t + 9)
Factor -h**5/4 + 3*h**4/4 + 7*h**3 + 4*h**2 - 24*h - 28.
-(h - 7)*(h - 2)*(h + 2)**3/4
What is i in -2*i**2 + 40*i - 38 = 0?
1, 19
Solve 6*z**5/11 + 114*z**4/11 + 474*z**3/11 - 810*z**2/11 - 5400*z/11 = 0 for z.
-12, -5, 0, 3
Let 3*u**5 + 6*u**4 - 3*u**3 - 6*u**2 = 0. Calculate u.
-2, -1, 0, 1
Determine i, given that -4*i**4 - 3540*i**3 + 4*i**2 + 3540*i = 0.
-885, -1, 0, 1
Suppose -845*d**3/2 - 195*d**2 - 45*d/2 = 0. Calculate d.
-3/13, 0
Factor -j**2 + 502*j - 63001.
-(j - 251)**2
Solve -2*d**3/3 + 540*d**2 - 109350*d = 0.
0, 405
Factor z**3/4 + 27*z**2 + 729*z.
z*(z + 54)**2/4
Solve -2*l**5/7 + 22*l**3/7 + 12*l**2/7 - 8*l - 48/7 = 0.
-2, -1, 2, 3
Solve 2*t**3/7 - 256*t**2/7 + 998*t/7 - 744/7 = 0.
1, 3, 124
Factor 11*o**4 - 32*o**3 - 15*o**2 + 36*o.
o*(o - 3)*(o - 1)*(11*o + 12)
Solve -4*i**4 - 12*i**3 - 8*i**2 = 0 for i.
-2, -1, 0
Factor 2*i**4 + 28*i**3 + 48*i**2 - 188*i + 110.
2*(i - 1)**2*(i + 5)*(i + 11)
Suppose q**3 - 5*q**2 - 22*q - 16 = 0. Calculate q.
-2, -1, 8
Find f, given that -f**4/6 - 7*f**3/6 - 11*f**2/6 - 5*f/6 = 0.
-5, -1, 0
Factor d**5/4 - d**4/2.
d**4*(d - 2)/4
Let 4*z**4/11 - 146*z**3/11 + 332*z**2/11 + 278*z/11 - 204/11 = 0. What is z?
-1, 1/2, 3, 34
Suppose -5*w**2/4 + 905*w/4 + 925 = 0. What is w?
-4, 185
Factor 3*g**2 + 6810*g + 3864675.
3*(g + 1135)**2
What is p in -12*p**4/5 - 51*p**3/5 + 48*p**2/5 + 3*p = 0?
-5, -1/4, 0, 1
Determine i so that -5*i**3 + 220*i**2 - 2420*i = 0.
0, 22
Factor 14*b**3 + 24*b**2 + 6*b - 4.
2*(b + 1)**2*(7*b - 2)
Let 3*b**5/2 - 459*b**4/8 + 1983*b**3/4 + 8157*b**2/8 + 315*b - 150 = 0. What is b?
-1, 1/4, 20
Solve 2*i**5/11 + 2*i**4 + 84*i**3/11 + 136*i**2/11 + 80*i/11 = 0 for i.
-5, -2, 0
Find r such that 5*r**5 - 20*r**4 = 0.
0, 4
Suppose 5*h**5 + 10*h**4 - 130*h**3 - 540*h**2 - 675*h - 270 = 0. Calculate h.
-3, -1, 6
Factor -t**2/5 - 1126*t/5 - 316969/5.
-(t + 563)**2/5
Determine d so that -d**4/2 - 3*d**3/2 + 2*d = 0.
-2, 0, 1
Suppose -44*n**4 - 52*n**3 + 36*n**2 + 52*n + 8 = 0. Calculate n.
-1, -2/11, 1
Factor -2*h**5/5 + 26*h**4/5 - 46*h**3/5 + 22*h**2/5.
-2*h**2*(h - 11)*(h - 1)**2/5
Determine t so that 3*t**2 + 51*t = 0.
-17, 0
Solve 4*f**2 + 32*f - 36 = 0 for f.
-9, 1
What is v in -39*v**2/2 - 1119*v/2 + 174 = 0?
-29, 4/13
Factor -5*u**2 - 3790*u - 718205.
-5*(u + 379)**2
Factor 125*n**4 - 225*n**3 + 120*n**2 - 20*n.
5*n*(n - 1)*(5*n - 2)**2
Suppose -2*l**4 - 18*l**3 + 94*l**2 - 126*l + 52 = 0. What is l?
-13, 1, 2
Factor r**2 + 19*r + 90.
(r + 9)*(r + 10)
Factor u**5/5 + 16*u**4 + 75*u**3.
u**3*(u + 5)*(u + 75)/5
Factor n**3 + 26*n**2 + 71*n + 46.
(n + 1)*(n + 2)*(n + 23)
Factor -4*z**4/5 + 48*z**3/5 - 84*z**2/5 - 392*z/5.
-4*z*(z - 7)**2*(z + 2)/5
Determine x, given that 3*x**2 + 4530*x + 1710075 = 0.
-755
Factor -3*u**3 + 3*u**2 + 6*u.
-3*u*(u - 2)*(u + 1)
Solve 4*u**4 + 20*u**3 - 28*u**2 - 20*u + 24 = 0 for u.
-6, -1, 1
Let 45*m**5/2 + 129*m**4 - 819*m**3/2 + 12*m**2 + 198*m + 48 = 0. What is m?
-8, -2/5, -1/3, 1, 2
Determine i, given that 2*i**2/7 - 248*i/7 + 960/7 = 0.
4, 120
Factor m**3/3 + 103*m**2/3 - 1105*m/3 + 2825/3.
(m - 5)**2*(m + 113)/3
Let 8*z**3/11 - 6*z**2/11 = 0. Calculate z.
0, 3/4
Factor a**3 + 390*a**2 + 38412*a + 75272.
(a + 2)*(a + 194)**2
Factor 68*b**5 + 284*b**4 + 456*b**3 + 344*b**2 + 116*b + 12.
4*(b + 1)**4*(17*b + 3)
Suppose 3*f**2/2 - 5*f/2 - 1 = 0. What is f?
-1/3, 2
Factor 27*r**3 - 25*r**2 - 56*r - 4.
(r - 2)*(r + 1)*(27*r + 2)
Factor -2*q**5/19 - 36*q**4/19 - 112*q**3/19.
-2*q**3*(q + 4)*(q + 14)/19
Factor w**3/5 + 81*w**2/5 - 9*w/5 - 729/5.
(w - 3)*(w + 3)*(w + 81)/5
Factor -5*b**3 - 30*b**2 - 45*b.
-5*b*(b + 3)**2
Find s, given that -2*s**5/3 - 64*s**4/3 - 568*s**3/3 - 836*s**2/3 + 190*s + 300 = 0.
-15, -2, -1, 1
Solve -o**2/4 - 8889*o/2 - 79014321/4 = 0.
-8889
Factor 25*n**2/4 + 2245*n/2 - 4515/4.
5*(n - 1)*(5*n + 903)/4
Determine m, given that m**2/8 + m + 15/8 = 0.
-5, -3
Determine d so that 5*d**3 + 320*d**2 + 1220*d + 1200 = 0.
-60, -2
Determine n so that -n**5 - 43*n**4 + 269*n**3 + 25175*n**2 + 20000*n - 4000000 = 0.
-25, 16
Let 9*f**5 - 336*f**4 + 3012*f**3 + 2502*f**2 - 3021*f - 2166 = 0. Calculate f.
-1, -2/3, 1, 19
Find h, given that 4*h**2 - 144*h + 140 = 0.
1, 35
Let -a**2/6 - 83*a/6 - 27 = 0. Calculate a.
-81, -2
Factor -s**4 - 74*s**3 + 152*s**2.
-s**2*(s - 2)*(s + 76)
Find c such that 4*c**5 + 24*c**4 - 28*c**3 - 368*c**2 - 576*c - 256 = 0.
-4, -1, 4
Determine a so that 5*a**3 - 710*a**2 + 2035*a + 6950 = 0.
-2, 5, 139
Factor 4*n**4/5 + 12*n**3/5 - 16*n/5.
4*n*(n - 1)*(n + 2)**2/5
Factor -2*u**3 + 41*u**2 + 113*u + 46.
-(u - 23)*(u + 2)*(2*u + 1)
Factor -r**2 - 23*r + 24.
-(r - 1)*(r + 24)
Solve 3*z**3/2 + 19*z**2/2 + 21*z/2 + 5/2 = 0 for z.
-5, -1, -1/3
Factor 4*o**4 + 736*o**3 + 732*o**2.
4*o**2*(o + 1)*(o + 183)
What is p in p**4/3 - p**3/3 - 4*p**2/3 + 4*p/3 = 0?
-2, 0, 1