e g.
-1, 29
Suppose -8*t**5 - 74*t**4 - 234*t**3 - 270*t**2 - 54*t = 0. What is t?
-3, -1/4, 0
Suppose 2*p**5 - p**4 - 31*p**3 - 61*p**2 - 43*p - 10 = 0. Calculate p.
-2, -1, -1/2, 5
Factor -r**4/4 - 9*r**3 + 189*r**2/2 - 297*r + 1215/4.
-(r - 3)**3*(r + 45)/4
Suppose -4*o**5 + 8*o**4 + 8*o**3 - 32*o**2 + 28*o - 8 = 0. What is o?
-2, 1
Find j, given that 3*j**2 - 28*j + 9 = 0.
1/3, 9
Suppose 4*x**2 - 160*x + 1200 = 0. What is x?
10, 30
Determine v, given that -v**2 + 618*v = 0.
0, 618
Factor 98*k**3/3 - 2030*k**2/3 - 5024*k/3 - 2944/3.
2*(k - 23)*(7*k + 8)**2/3
Solve 3*d**3 - 201*d**2 - 414*d = 0.
-2, 0, 69
Let -a**3/3 - 14*a**2/3 - 65*a/3 - 100/3 = 0. What is a?
-5, -4
Factor -2*q**3/5 - 2862*q**2/5 - 1365174*q/5 - 217062666/5.
-2*(q + 477)**3/5
Factor -4*o**3 - 20*o**2 + 16*o + 80.
-4*(o - 2)*(o + 2)*(o + 5)
Let 8*p**4/3 - p**3 - 11*p**2/3 = 0. What is p?
-1, 0, 11/8
Determine v so that -4*v**4 - 360*v**3 + 12*v**2 + 1088*v + 720 = 0.
-90, -1, 2
Suppose -3*b**2 + 21*b/2 - 15/2 = 0. Calculate b.
1, 5/2
Factor q**2/4 - 825*q/2 + 680625/4.
(q - 825)**2/4
Factor -5*d**3 + 45*d.
-5*d*(d - 3)*(d + 3)
Solve -7*f**5/10 + 37*f**4/10 - 9*f**3/2 - 5*f**2/2 + 26*f/5 - 6/5 = 0.
-1, 2/7, 1, 2, 3
Determine f, given that 3*f**3/4 + 6*f**2 + 45*f/4 = 0.
-5, -3, 0
Factor 3*p**2/2 + 33*p/2 - 39.
3*(p - 2)*(p + 13)/2
What is g in 2*g**4/3 - 76*g**3/15 + 56*g**2/5 - 16*g/3 - 64/15 = 0?
-2/5, 2, 4
Let -c**4/4 + 5*c**3/2 - 27*c**2/4 + 9*c/2 = 0. Calculate c.
0, 1, 3, 6
Find l such that 2*l**5/3 + 46*l**4/3 + 284*l**3/3 + 196*l**2/3 - 286*l/3 - 242/3 = 0.
-11, -1, 1
Find y, given that 12*y**5 + 297*y**4 + 2001*y**3 + 2781*y**2 + 687*y - 378 = 0.
-14, -9, -1, 1/4
Solve l**5/2 + 11*l**4/2 + 13*l**3 - 37*l**2 - 315*l/2 - 225/2 = 0 for l.
-5, -3, -1, 3
Let c**2/2 - 14*c + 171/2 = 0. What is c?
9, 19
Determine w so that 3*w**2/2 + 81*w/2 - 87 = 0.
-29, 2
Suppose 4*b**2 - 4 = 0. Calculate b.
-1, 1
Find l such that -l**5/5 - 9*l**4/5 - 27*l**3/5 - 23*l**2/5 + 24*l/5 + 36/5 = 0.
-3, -2, 1
Factor -5*z**3 - 70*z**2 + 20*z + 280.
-5*(z - 2)*(z + 2)*(z + 14)
Factor 11*d**4/2 + 30*d**3 + 48*d**2 + 8*d - 24.
(d + 2)**3*(11*d - 6)/2
Factor 2*d**4/5 + 44*d**3/5 + 158*d**2/5 - 204*d/5.
2*d*(d - 1)*(d + 6)*(d + 17)/5
Find d, given that -3*d**2 - 1944*d - 314928 = 0.
-324
Factor -h**2/3 + 54*h.
-h*(h - 162)/3
Determine s so that -2*s**3/5 - 568*s**2/5 - 39168*s/5 + 165888/5 = 0.
-144, 4
Factor -y**3/3 + 9*y**2 + 28*y/3.
-y*(y - 28)*(y + 1)/3
Factor -g**4 + g**3 + g**2 - g.
-g*(g - 1)**2*(g + 1)
Factor -21*m**2/2 - 509*m/2 - 60.
-(m + 24)*(21*m + 5)/2
Suppose 5*u**2 + 167*u - 102 = 0. Calculate u.
-34, 3/5
Solve -245*s**4/2 - 3045*s**3/2 + 900*s**2 - 130*s = 0.
-13, 0, 2/7
Let 5*a**2 - 2605*a + 2600 = 0. Calculate a.
1, 520
Solve -d**4/3 - 14*d**3 - 208*d**2 - 3968*d/3 - 3072 = 0.
-18, -8
Factor -q**2 - 1055*q + 1056.
-(q - 1)*(q + 1056)
Factor -y**3/3 + 1360*y**2/3 + 2729*y + 4098.
-(y - 1366)*(y + 3)**2/3
Find z, given that -2*z**3/11 - 84*z**2/11 - 1176*z/11 - 5488/11 = 0.
-14
Factor -v**5 + 129*v**4 - 5547*v**3 + 79507*v**2.
-v**2*(v - 43)**3
Suppose 28*y**2 + 8308*y - 2376 = 0. What is y?
-297, 2/7
Solve b**5/5 - b**3 + 4*b/5 = 0.
-2, -1, 0, 1, 2
Factor -l**2/3 - 229*l/3 - 76.
-(l + 1)*(l + 228)/3
Suppose 3*d**2 + 1419*d + 2826 = 0. What is d?
-471, -2
Suppose -2*l**5 - 224*l**4 + 1872*l**3 - 5696*l**2 + 7648*l - 3840 = 0. What is l?
-120, 2
Determine f so that 2*f**3/3 - 74*f**2/3 + 646*f/3 + 722/3 = 0.
-1, 19
Determine s so that -90*s**5 + 1236*s**4 - 9128*s**3/5 - 2768*s**2/5 - 192*s/5 = 0.
-2/15, 0, 2, 12
Determine p so that 3*p**4 + 78*p**3 - 360*p**2 = 0.
-30, 0, 4
Factor 2*n**2/19 + 222*n/19 + 2020/19.
2*(n + 10)*(n + 101)/19
Factor -2*h**2 + 20*h + 78.
-2*(h - 13)*(h + 3)
Find p, given that 2*p**4 - 1262*p**3 + 1260*p**2 = 0.
0, 1, 630
Find l such that -2*l**5/11 - 36*l**4/11 - 118*l**3/11 - 84*l**2/11 = 0.
-14, -3, -1, 0
Factor 2*r**2 - 90*r - 4712.
2*(r - 76)*(r + 31)
What is l in 2*l**2/7 + 22*l/7 + 36/7 = 0?
-9, -2
Factor -s**4/3 - s**3/3 + 2*s**2.
-s**2*(s - 2)*(s + 3)/3
Factor -5*x**3/4 - 181*x**2/2 - 2661*x/4 + 432.
-(x + 9)*(x + 64)*(5*x - 3)/4
Determine w, given that 2*w**3/11 - 14*w**2/11 - 20*w/11 + 32/11 = 0.
-2, 1, 8
Suppose -b**5/2 + 35*b**4 - 1285*b**3/2 + 920*b**2 + 3910*b + 2312 = 0. What is b?
-1, 4, 34
Factor 2*d**4/7 + 2*d**3/7 - 2*d**2/7 - 2*d/7.
2*d*(d - 1)*(d + 1)**2/7
Let d**3/10 + 15*d**2 - 156*d/5 - 608/5 = 0. What is d?
-152, -2, 4
Factor 5*c**2/2 - 575*c/2.
5*c*(c - 115)/2
Determine f so that 4*f**5 + 24*f**4 + 52*f**3 + 48*f**2 + 16*f = 0.
-2, -1, 0
Factor -25*y**3/2 - 2185*y**2/2 - 871*y/2 - 87/2.
-(y + 87)*(5*y + 1)**2/2
Factor 2*o**2/7 + 12*o/7 - 2.
2*(o - 1)*(o + 7)/7
Let -8*i**2/3 - 46*i/3 + 124/3 = 0. What is i?
-31/4, 2
What is w in -48*w**3/5 - 99*w**2/5 - 54*w/5 - 3/5 = 0?
-1, -1/16
What is o in -6*o**3/11 + 536*o**2/11 - 9538*o/11 + 3120/11 = 0?
1/3, 24, 65
Suppose 160*b**5/3 - 184*b**4/3 + 20*b**3/3 + 4*b**2/3 = 0. What is b?
-1/10, 0, 1/4, 1
Suppose 2*a**3/17 - 2120*a**2/17 + 32922*a + 1127844/17 = 0. Calculate a.
-2, 531
Factor -2*x**3/3 - 17*x**2/3 - 37*x/3 - 22/3.
-(x + 1)*(x + 2)*(2*x + 11)/3
Factor 2*m**3/7 - 90*m**2 + 9450*m - 330750.
2*(m - 105)**3/7
Let -765*c**4 - 8250*c**3 - 6145*c**2 - 1460*c - 100 = 0. What is c?
-10, -1/3, -2/17
Determine x so that -2*x**5 - 20*x**4 - 58*x**3 - 16*x**2 + 96*x = 0.
-4, -3, 0, 1
Factor -5*n**3/3 - 40*n**2/3 - 35*n/3.
-5*n*(n + 1)*(n + 7)/3
Solve -4*h**2 + 4864*h - 9712 = 0.
2, 1214
Factor f**2/2 + 238*f - 1936.
(f - 8)*(f + 484)/2
Factor 2*x**2 - 14*x/3 - 40/3.
2*(x - 4)*(3*x + 5)/3
What is l in 3*l**2 + 378*l + 4704 = 0?
-112, -14
Factor h**2/9 - 148*h/9.
h*(h - 148)/9
Factor 5*p**2 + 580*p + 16820.
5*(p + 58)**2
Let -i**2 + 37*i - 132 = 0. What is i?
4, 33
Factor -2*j**4/17 + 116*j**3/17 - 1434*j**2/17 - 7192*j/17 - 7688/17.
-2*(j - 31)**2*(j + 2)**2/17
Let 133*t**3 - 796*t**2 + 1185*t + 18 = 0. What is t?
-2/133, 3
Find i such that -i**3/3 + 115*i**2/3 - 38*i = 0.
0, 1, 114
Determine o so that 3*o**3/5 - 2196*o**2/5 - 4401*o/5 - 2202/5 = 0.
-1, 734
Let -4*x**2 - 7360*x - 3385600 = 0. What is x?
-920
Factor y**4/2 + 47*y**3/2 - 805*y**2/2 + 2989*y/2.
y*(y - 7)**2*(y + 61)/2
Factor -960*x**3 + 369*x**2 + 6*x.
-3*x*(5*x - 2)*(64*x + 1)
Determine n so that -n**5 - 95*n**4 - 93*n**3 + 95*n**2 + 94*n = 0.
-94, -1, 0, 1
Let 3*h**3/2 + 5*h**2/2 + h = 0. Calculate h.
-1, -2/3, 0
Solve -s**2/3 - 30*s - 675 = 0.
-45
Factor -638*o**2/3 + 3184*o/3 + 10.
-2*(o - 5)*(319*o + 3)/3
Suppose 2*l**5/7 + 36*l**4/7 + 202*l**3/7 + 456*l**2/7 + 360*l/7 = 0. Calculate l.
-10, -3, -2, 0
Let 3*x**3 + 1269*x**2 + 132273*x - 408321 = 0. Calculate x.
-213, 3
Factor -t**2/4 + 7*t/4 + 15/2.
-(t - 10)*(t + 3)/4
Factor -5*f**4 - 25*f**3 - 40*f**2 - 20*f.
-5*f*(f + 1)*(f + 2)**2
Find t such that -t**4/4 + t**2/2 - 1/4 = 0.
-1, 1
Factor -4*q**3/7 + 4*q**2/7 + 4*q/7 - 4/7.
-4*(q - 1)**2*(q + 1)/7
Suppose 4*c**2 - 168*c + 1764 = 0. What is c?
21
Let 414*w**4 + 813*w**3 + 384*w**2 - 15*w = 0. What is w?
-1, 0, 5/138
Factor -3*v**5 - 3*v**4 + 27*v**3 - 33*v**2 + 12*v.
-3*v*(v - 1)**3*(v + 4)
Find r, given that 12*r**5 - 94*r**4 - 260*r**3 - 26*r**2 + 248*r + 120 = 0.
-3/2, -1, -2/3, 1, 10
Find p such that 2*p**5/13 - 66*p**4/13 + 334*p**3/13 - 270*p**2/13 = 0.
0, 1, 5, 27
Factor 2*z**2/15 + 262*z/15 + 52/3.
2*(z + 1)*(z + 130)/15
Factor 2*x**4/5 + 26*x**3/5 + 32*x**2/5 - 384*x/5.
2*x*(x - 3)*(x + 8)**2/5
Factor 2*r**2/9 + 8*r/9 + 8/9.
2*(r + 2)**2/9
Find m, given that 2*m**4/11 - 42*m**2/11 - 40*m/11 = 0.
-4, -1, 0, 5
Find j such that -4*j**2/3 - 64*j/3 = 0.
-16, 0
Let 15*b**2 - 1295*b + 430 = 0. Calculate b.
1/3, 86
Determine n, given that -3*n**5 - 12*n**4 + 9*n**3 + 54*n**2 = 0.
-3, 0, 2
Solve -21*p**5 - 159*p**4/2 + 144*p**3 + 57*p**2 - 123*p + 45/2 = 0 for p.
-5, -1, 3/14, 1
Factor -4*h**3/5 + 12*h**2 + 4*h/5 - 12.
-4*(h - 15)*(h - 1)*(h + 1)/5
Factor 2*a**2/11 - 16*a/11 - 6.
2*(a - 11)*(a + 3)/11
Determine c, given that -3*c**4 + 45*c**3 - 192*c**2 + 144*c + 384 = 0.
-1, 4, 8
Find q, given that q**4 - 487*q**3 - 985*q**2 + 3427*q - 1956 = 0.
-4, 1, 489
Factor l**4 + 11*l**3 + 9*l**2 - 11*l - 10.
(l - 1)*(l + 1)**2*(l + 10)
Solve -12*k**5 - 21*k**4 + 135*k**3 + 108*k**2 = 0 for k.
-4, -3/4, 0, 3
Find g such that 7