, 3
Factor -y**2/2 - 37*y/2.
-y*(y + 37)/2
Factor -4*f**4 + 216*f**3 + 672*f**2 + 680*f + 228.
-4*(f - 57)*(f + 1)**3
Let 2*i**4 + 4*i**3 - 14*i**2 + 8*i = 0. Calculate i.
-4, 0, 1
Determine o, given that -8*o**4 - 56*o**3 - 90*o**2 + 56*o + 98 = 0.
-7/2, -1, 1
Factor -4*a**2 + 32*a - 28.
-4*(a - 7)*(a - 1)
Factor c**3 + 29*c**2 + 180*c.
c*(c + 9)*(c + 20)
Solve -2*u**2/19 - 534*u/19 - 28 = 0 for u.
-266, -1
Suppose m**2/5 + 17*m - 264/5 = 0. What is m?
-88, 3
Let 4*g**4/5 - 212*g**3/5 - 348*g**2/5 + 1476*g - 13608/5 = 0. Calculate g.
-7, 3, 54
Solve q**3/9 - 409*q**2/9 + 42427*q/9 - 41209/3 = 0.
3, 203
Solve -2*d**3/7 + 12*d**2 + 86*d/7 = 0 for d.
-1, 0, 43
Factor -2*n**2/17 + 2386*n/17 + 4780/17.
-2*(n - 1195)*(n + 2)/17
Factor -2*o**4/11 + 2*o**3/11 + 12*o**2/11.
-2*o**2*(o - 3)*(o + 2)/11
Suppose 9*s**4 + 24*s**3 + 21*s**2 + 6*s = 0. What is s?
-1, -2/3, 0
Factor -p**3 - 140*p**2 - 5293*p - 26934.
-(p + 6)*(p + 67)**2
Determine j so that -j**2 - 75*j + 76 = 0.
-76, 1
Let 3*j**3 + 45*j**2 - 3*j - 45 = 0. What is j?
-15, -1, 1
Factor 5*n**2 + 50*n + 125.
5*(n + 5)**2
Solve -25*g**5/2 - 445*g**4/2 - 1919*g**3/2 + 697*g**2/2 + 684*g + 162 = 0 for g.
-9, -2/5, 1
Factor -2025*d**4/2 + 735*d**3 - 102*d**2 - 12*d.
-3*d*(5*d - 2)**2*(27*d + 2)/2
Find x such that 2*x**3/11 + 20*x**2/11 - 104*x/11 + 112/11 = 0.
-14, 2
Factor 16*h**4 + 12*h**3 - 84*h**2 + 68*h - 12.
4*(h - 1)**2*(h + 3)*(4*h - 1)
Let 2*f**5 - 36*f**4 + 116*f**3 - 48*f**2 - 118*f + 84 = 0. What is f?
-1, 1, 3, 14
Find f, given that -3*f**4 - 180*f**3 + 9*f**2 + 534*f - 360 = 0.
-60, -2, 1
Let -4*p**3/3 + 4*p**2 - 4*p + 4/3 = 0. What is p?
1
Determine r, given that r**3/2 + 40*r**2 - 83*r/2 - 81 = 0.
-81, -1, 2
Solve 2*u**2/7 + 10*u/7 - 72/7 = 0.
-9, 4
Factor 20*f**5/3 + 816*f**4 + 25132*f**3 + 29768*f**2/3.
4*f**2*(f + 61)**2*(5*f + 2)/3
Solve 12*t**5 - 38*t**4 + 30*t**3 - 4*t**2 = 0.
0, 1/6, 1, 2
Suppose -3*s**2 - 72*s + 243 = 0. What is s?
-27, 3
Determine n so that 2*n**2/9 - 4*n/3 - 6 = 0.
-3, 9
Factor 2*i**5/3 - 2*i**4/3 - 2*i**3 + 10*i**2/3 - 4*i/3.
2*i*(i - 1)**3*(i + 2)/3
Factor c**4/2 - 93*c**3/2 + 2115*c**2/2 + 2209*c/2.
c*(c - 47)**2*(c + 1)/2
Determine u so that 10*u**2/3 + 4*u/9 = 0.
-2/15, 0
Factor 2*t**3 - 196*t**2 + 3586*t - 18392.
2*(t - 76)*(t - 11)**2
Let 2*y**2/9 + 572*y/9 + 40898/9 = 0. Calculate y.
-143
Let -4*i**2 + 132*i - 864 = 0. What is i?
9, 24
Let -2*c**5 + 8*c**4 - 2*c**3 - 20*c**2 + 8*c + 16 = 0. What is c?
-1, 2
Factor -2*w**2 - 156*w + 158.
-2*(w - 1)*(w + 79)
Suppose -10*n**5/3 - 68*n**4/9 + 22*n**3/9 + 28*n**2/3 + 8*n/9 - 16/9 = 0. What is n?
-2, -1, -2/3, 2/5, 1
Factor -y**4/4 + 2*y**3 - 23*y**2/4 + 7*y - 3.
-(y - 3)*(y - 2)**2*(y - 1)/4
Determine p so that -2*p**4 + 244*p**3 - 7194*p**2 - 15128*p - 7688 = 0.
-1, 62
Factor -3*l**2 + 1917*l - 1914.
-3*(l - 638)*(l - 1)
Let 2*j**4 - 14*j**3 + 10*j**2 + 14*j - 12 = 0. What is j?
-1, 1, 6
What is i in -2*i**2 + 576*i + 578 = 0?
-1, 289
Find g such that 2*g**2/7 - 34*g/7 - 36/7 = 0.
-1, 18
Factor 5*i**5 - 65*i**4 + 275*i**3 - 375*i**2.
5*i**2*(i - 5)**2*(i - 3)
Determine j so that -4*j**2 - 204*j - 752 = 0.
-47, -4
Suppose y**3/9 - 11*y**2/9 - 56*y/9 - 20/3 = 0. Calculate y.
-2, 15
Factor -u**3/2 + u/2.
-u*(u - 1)*(u + 1)/2
Factor 2*s**2/5 + 16*s/5.
2*s*(s + 8)/5
Factor 5*t**2/6 + 28*t - 34/3.
(t + 34)*(5*t - 2)/6
Determine s, given that -15*s**3 - 290*s**2 - 85*s + 190 = 0.
-19, -1, 2/3
Factor q**4/3 + 9*q**3 - 11*q**2 - 143*q/3 - 28.
(q - 3)*(q + 1)**2*(q + 28)/3
Factor 4*y**2 - 5036*y - 20208.
4*(y - 1263)*(y + 4)
Find d such that -3*d**3 + 288*d**2 - 7191*d + 13254 = 0.
2, 47
Solve -v**3/2 + 3*v**2/2 + 5*v - 12 = 0 for v.
-3, 2, 4
Solve 5*f**2 - 525*f = 0 for f.
0, 105
Factor 4*q**2 + 480*q + 476.
4*(q + 1)*(q + 119)
Suppose -2*w**2/5 + 6*w - 72/5 = 0. Calculate w.
3, 12
Factor -3*q**3/2 + 126*q**2 - 735*q/2 + 243.
-3*(q - 81)*(q - 2)*(q - 1)/2
Find t such that 4*t**5 - 21*t**4 + 13*t**3 + 30*t**2 - 8*t = 0.
-1, 0, 1/4, 2, 4
Determine l so that -5*l**2 - 2020*l - 204020 = 0.
-202
Factor 4*g**2 + 12*g - 160.
4*(g - 5)*(g + 8)
What is l in -2*l**3 - 506*l**2 - 32256*l - 31752 = 0?
-126, -1
What is m in -648*m**5/5 - 2268*m**4/5 + 2322*m**3 + 40983*m**2/5 - 51984*m/5 - 185193/5 = 0?
-19/6, 3
Factor -2*b**2/15 - 14*b/5 - 196/15.
-2*(b + 7)*(b + 14)/15
Find s such that -s**2 - 158*s - 6241 = 0.
-79
Find n, given that n**3/6 + 47*n**2/6 + 340*n/3 + 1400/3 = 0.
-20, -7
Solve 27*w**5/5 + 129*w**4/5 - 47*w**3/5 - 89*w**2/5 - 4*w = 0.
-5, -4/9, -1/3, 0, 1
Factor w**3/4 - w**2/2 - 3*w/4.
w*(w - 3)*(w + 1)/4
Determine l, given that 2*l**3/5 - 14*l**2/15 = 0.
0, 7/3
Let 2*c**3 - 122*c**2 + 2350*c - 13750 = 0. Calculate c.
11, 25
Suppose -s**5/9 - 931*s**4/9 - 1238*s**3/3 - 5566*s**2/9 - 3709*s/9 - 103 = 0. What is s?
-927, -1
Factor -4*o**4 - 136*o**3 - 1684*o**2 - 8976*o - 17424.
-4*(o + 6)**2*(o + 11)**2
Factor -5*r**4 + 20*r**3 + 90*r**2 + 100*r + 35.
-5*(r - 7)*(r + 1)**3
Let -6*d**2 - d/5 = 0. Calculate d.
-1/30, 0
Factor -b**5 + 236*b**4 - 13924*b**3.
-b**3*(b - 118)**2
Find q such that -2*q**2/23 + 144*q/23 - 670/23 = 0.
5, 67
Suppose -3*q**3 - 153*q**2/5 = 0. Calculate q.
-51/5, 0
Factor -4*x**4 + 8*x**3 + 240*x**2 + 736*x + 640.
-4*(x - 10)*(x + 2)**2*(x + 4)
Factor 16*f**3 + 60*f**2 - 352*f - 816.
4*(f + 2)*(f + 6)*(4*f - 17)
Find v such that -2*v**3 + 124*v**2 + 256*v = 0.
-2, 0, 64
Find r such that 147*r**4 - 378*r**3 - 14373*r**2 + 8292*r - 1188 = 0.
-9, 2/7, 11
Solve 3*b**5 - 12*b**4 + 15*b**3 - 6*b**2 = 0.
0, 1, 2
Let 5*i**2 - 15*i - 140 = 0. What is i?
-4, 7
Factor 2*c**3/7 + 2034*c**2/7 + 518160*c/7 + 516128/7.
2*(c + 1)*(c + 508)**2/7
Factor -3*f**2/2 + 30*f + 63/2.
-3*(f - 21)*(f + 1)/2
Determine j, given that 3*j**4 + 9*j**3 - 33*j**2 - 9*j + 30 = 0.
-5, -1, 1, 2
Find q, given that -26*q**2 - 5066*q/13 + 60/13 = 0.
-15, 2/169
Determine c so that -12*c**5 + 45*c**4 + 150*c**3 - 315*c**2 - 840*c - 432 = 0.
-9/4, -1, 4
Let -3*k**4 - 57*k**3 - 105*k**2 - 51*k = 0. What is k?
-17, -1, 0
Let 4*h**3/5 + 14*h**2/5 + 14*h/5 + 4/5 = 0. What is h?
-2, -1, -1/2
Let u**5 - 3*u**3 - 2*u**2 = 0. Calculate u.
-1, 0, 2
Determine o so that -o**5/6 - 11*o**4/6 + 13*o**3/3 = 0.
-13, 0, 2
Factor 3*f**2 + 1800*f + 270000.
3*(f + 300)**2
Factor -m**5 + 3*m**4 + 7*m**3 - 7*m**2 - 18*m - 8.
-(m - 4)*(m - 2)*(m + 1)**3
Factor -2*h**4/7 - 8*h**3/7 + 24*h**2/7 + 64*h/7 - 128/7.
-2*(h - 2)**2*(h + 4)**2/7
Factor -2*l**4 + 146*l**3 - 1656*l**2 + 5832*l - 4320.
-2*(l - 60)*(l - 6)**2*(l - 1)
Factor -f**2/4 - 268*f.
-f*(f + 1072)/4
Factor 2*s**4/5 + 1598*s**3/5 + 3188*s**2/5.
2*s**2*(s + 2)*(s + 797)/5
Factor 5*g**3 - 2115*g**2 + 224715*g - 222605.
5*(g - 211)**2*(g - 1)
Suppose 15*k**2 - 13*k - 2 = 0. What is k?
-2/15, 1
Factor -2*o**2 + 114*o + 116.
-2*(o - 58)*(o + 1)
Solve 4*i**5/11 + 14*i**4/11 + 4*i**3/11 - 6*i**2/11 = 0.
-3, -1, 0, 1/2
Factor -3*h**4 - 9*h**3 + 12*h.
-3*h*(h - 1)*(h + 2)**2
Find l, given that 2*l**4/9 - 44*l**3/9 + 50*l**2/3 - 12*l = 0.
0, 1, 3, 18
Find n, given that -n**4/2 + 211*n**3 - 22678*n**2 + 87989*n - 131043/2 = 0.
1, 3, 209
Factor z**2/5 - 38*z + 189/5.
(z - 189)*(z - 1)/5
Find f such that 60*f**5 + 428*f**4 + 552*f**3 - 768*f**2 + 128*f = 0.
-4, 0, 1/5, 2/3
Find t such that 2*t**2 + 92*t + 1058 = 0.
-23
Factor 2*o**2/3 + 932*o + 325734.
2*(o + 699)**2/3
Factor 3*v**4/2 - 84*v**3 + 1764*v**2 - 16464*v + 57624.
3*(v - 14)**4/2
Find g such that 2*g**5 + 24*g**4/5 - 72*g**3/5 - 212*g**2/5 - 162*g/5 - 36/5 = 0.
-3, -1, -2/5, 3
Factor q**2 - 44*q + 484.
(q - 22)**2
Factor 4*x**2 - 320*x - 656.
4*(x - 82)*(x + 2)
Factor -g**2/2 - 11*g/2 - 15.
-(g + 5)*(g + 6)/2
Suppose 7*p**4/6 - 64*p**3/3 + 89*p**2/2 - 89*p/3 + 16/3 = 0. Calculate p.
2/7, 1, 16
Determine t, given that -5*t**3 + 165*t**2 - 1395*t + 1235 = 0.
1, 13, 19
Solve 2*m**5/3 + 8*m**4/3 - 4*m**3/3 - 16*m**2/3 + 2*m/3 + 8/3 = 0.
-4, -1, 1
Factor -2*t**2/11 - 150*t/11 + 468/11.
-2*(t - 3)*(t + 78)/11
Factor -2*u**2/9 + 4*u/9 + 16/3.
-2*(u - 6)*(u + 4)/9
Factor -3*s**4 - 267*s**3 + 6240*s**2 - 32700*s.
-3*s*(s - 10)**2*(s + 109)
Let 3*v**3/4 + 105*v**2/4 + 93*v = 0. What is v?
-31, -4, 0
Let a**3 + 6*a**2 + 5*a - 12 = 0. Calculate a.
-4, -3, 1
Factor 2*b**2/9 - 4*b/9 - 2/3.
2*(b - 3)*(b + 1)/9
Factor 5*c**5 + 40*c**4 + 30*c**3 - 40*c**2 - 