4
Determine r so that -2*r**2/9 + 4250*r/9 = 0.
0, 2125
Suppose 4*v**3/7 - 16*v/7 = 0. What is v?
-2, 0, 2
Factor -d**2/2 + 5*d - 9/2.
-(d - 9)*(d - 1)/2
Solve 2*b**2/7 + 16*b/7 + 24/7 = 0 for b.
-6, -2
Factor 3*k**2 + 1332*k + 147852.
3*(k + 222)**2
Solve g**4 + g**3 - 4*g**2 - 4*g = 0 for g.
-2, -1, 0, 2
Factor -4*p**2 + 32*p - 64.
-4*(p - 4)**2
Factor -3*s**2/7 + 6072*s/7 - 3072432/7.
-3*(s - 1012)**2/7
Determine u, given that 1080*u**3 + 8636*u**2 - 32*u = 0.
-8, 0, 1/270
Factor -5*h**3 + 145*h**2 - 140*h.
-5*h*(h - 28)*(h - 1)
Factor -a**3/3 + 4*a**2/3 - 4*a/3.
-a*(a - 2)**2/3
Factor 3*d**3/7 - 78*d**2/7 + 213*d/7 - 138/7.
3*(d - 23)*(d - 2)*(d - 1)/7
Factor 5*x**2/4 - 75*x/4 + 55.
5*(x - 11)*(x - 4)/4
Let 5*j**5/4 - 15*j**4/4 + 5*j**3/2 + 5*j**2/2 - 15*j/4 + 5/4 = 0. What is j?
-1, 1
What is c in 16*c**4 - 242*c**3 - 226*c**2 + 32*c = 0?
-1, 0, 1/8, 16
Factor 5*o**2 - 35*o.
5*o*(o - 7)
Determine a so that a**3 + 244*a**2 + 3269*a + 11270 = 0.
-230, -7
Suppose 6*d**2/5 - 7452*d/5 + 2313846/5 = 0. Calculate d.
621
Let y**5 + 195*y**4 + 14210*y**3 + 456190*y**2 + 5294205*y - 5764801 = 0. Calculate y.
-49, 1
What is c in -2*c**5/7 - 340*c**4/7 - 14104*c**3/7 + 29584*c**2/7 = 0?
-86, 0, 2
Let -20*v**5 + 155*v**4 - 180*v**3 - 215*v**2 + 200*v + 60 = 0. Calculate v.
-1, -1/4, 1, 2, 6
Factor -3*k**2 + 558*k - 25947.
-3*(k - 93)**2
Factor -2*k**3/15 - 4*k**2/3 - 6*k/5.
-2*k*(k + 1)*(k + 9)/15
Factor -2*k**3/3 + 4*k**2 + 74*k/3 + 20.
-2*(k - 10)*(k + 1)*(k + 3)/3
Suppose -z**3/10 - z**2/10 = 0. What is z?
-1, 0
Solve -d**4/8 - 3*d**3/8 = 0.
-3, 0
Factor 20*v**3 + 15*v**2 - 45*v + 10.
5*(v - 1)*(v + 2)*(4*v - 1)
Factor 4*q**4 - 256*q**3.
4*q**3*(q - 64)
Find y such that -4*y**2 + 196*y - 1440 = 0.
9, 40
Find m, given that -2*m**3/9 + 8*m**2 + 50*m/3 + 76/9 = 0.
-1, 38
Find c, given that -2*c**3 + 80*c**2 - 154*c + 76 = 0.
1, 38
Determine o, given that -2*o**4/9 - 158*o**3/9 - 1840*o**2/9 + 55016*o/9 = 0.
-46, 0, 13
Solve -p**2 + 150*p - 5625 = 0.
75
Factor -p**3/4 - 3*p**2/2 + 25*p/4 - 9/2.
-(p - 2)*(p - 1)*(p + 9)/4
Let 99*z**2 - 2*z = 0. Calculate z.
0, 2/99
Factor 3*p**4/5 - 18*p**3/5 - 36*p**2/5 + 114*p/5 - 63/5.
3*(p - 7)*(p - 1)**2*(p + 3)/5
Factor 9*g**3 + 12*g**2 - 51*g - 18.
3*(g - 2)*(g + 3)*(3*g + 1)
Factor -3*i**3/7 + 216*i**2/7 - 621*i/7.
-3*i*(i - 69)*(i - 3)/7
Factor -5*r**4 + 1200*r**3 - 73190*r**2 + 142800*r - 70805.
-5*(r - 119)**2*(r - 1)**2
Let -5*n**5/4 - 55*n**4/4 + 465*n**3/2 - 1205*n**2/2 + 2275*n/4 - 735/4 = 0. Calculate n.
-21, 1, 7
Suppose -5*d**5 + 55*d**4 - 190*d**3 + 260*d**2 - 120*d = 0. What is d?
0, 1, 2, 6
Find c such that 5*c**3 - 85*c**2 + 70*c + 160 = 0.
-1, 2, 16
Let 4*o**3 - 4296*o**2 + 4292*o = 0. Calculate o.
0, 1, 1073
Factor y**2/4 + 207*y/4 - 209/2.
(y - 2)*(y + 209)/4
Suppose -5*g**3 + 15*g**2 + 5*g - 15 = 0. Calculate g.
-1, 1, 3
Factor -5*i**4 + 75*i**3 - 130*i**2.
-5*i**2*(i - 13)*(i - 2)
What is o in 4*o**5 + 44*o**4 + 132*o**3 + 36*o**2 - 216*o = 0?
-6, -3, 0, 1
Factor -2*v**5/9 - 638*v**4/9 - 22684*v**3/3 - 2449448*v**2/9 - 2382032*v/9.
-2*v*(v + 1)*(v + 106)**3/9
Solve -5*w**4 - 25*w**3 - 25*w**2 + 25*w + 30 = 0.
-3, -2, -1, 1
Solve -5*z**4 - 45*z**3 = 0 for z.
-9, 0
Determine a so that 2*a**2 - 42*a - 464 = 0.
-8, 29
Factor -3*n**4 + 30*n**3 - 57*n**2 - 90*n.
-3*n*(n - 6)*(n - 5)*(n + 1)
Factor -3*y**4/8 + 51*y**3/8 - 30*y**2 + 24*y.
-3*y*(y - 8)**2*(y - 1)/8
Suppose 2*a**4/5 + 3*a**3/2 - 5*a/2 + 3/5 = 0. What is a?
-3, -2, 1/4, 1
Let 2*u**2/7 - 1688*u/7 + 356168/7 = 0. Calculate u.
422
Determine p, given that -2*p**2 + 122*p + 252 = 0.
-2, 63
Let 9*l**5/5 - 69*l**4/5 + 33*l**3 - 27*l**2 + 6*l/5 + 24/5 = 0. What is l?
-1/3, 1, 2, 4
Factor -44*o**2 + 55228*o - 10040.
-4*(o - 1255)*(11*o - 2)
Factor 5*r**4 + 260*r**3 + 3630*r**2 + 6500*r + 3125.
5*(r + 1)**2*(r + 25)**2
Factor 4*o**5 - 4*o**4 - 12*o**3 + 4*o**2 + 8*o.
4*o*(o - 2)*(o - 1)*(o + 1)**2
Suppose d**5/4 - 317*d**4/4 + 23991*d**3/4 + 178857*d**2/4 + 97686*d + 59049 = 0. Calculate d.
-3, -1, 162
Factor 3*u**2 + 402*u + 13467.
3*(u + 67)**2
Factor -18*h**3/5 + 219*h**2/5 - 684*h/5 + 108/5.
-3*(h - 6)**2*(6*h - 1)/5
Factor -2*d**4/15 - 82*d**3/5 - 742*d**2 - 43610*d/3 - 102900.
-2*(d + 18)*(d + 35)**3/15
Factor -5*j**2 + 25*j + 180.
-5*(j - 9)*(j + 4)
Factor 7*s**4 + 2348*s**3 + 1373572*s**2/7 - 112704*s + 16128.
(s + 168)**2*(7*s - 2)**2/7
Factor 2*n**2/7 + 2*n - 36/7.
2*(n - 2)*(n + 9)/7
Determine h so that 5*h**3/9 + 23*h**2 - 128*h/9 - 28/3 = 0.
-42, -2/5, 1
Factor n**2/4 + 89*n/4 - 235/2.
(n - 5)*(n + 94)/4
Factor -2*q**2/15 + 224*q/5 - 18816/5.
-2*(q - 168)**2/15
Find j, given that -6*j**2/13 + 212*j/13 - 400/13 = 0.
2, 100/3
Factor 3*p**3/5 - 99*p**2/5 + 96*p/5.
3*p*(p - 32)*(p - 1)/5
Factor j**2/4 - 5*j/4 + 1.
(j - 4)*(j - 1)/4
Suppose -u**4/4 - 23*u**3/4 + 81*u**2/2 - 85*u + 58 = 0. Calculate u.
-29, 2
Let -4*g**3 - 64*g**2 - 80*g + 448 = 0. What is g?
-14, -4, 2
Factor 3*u**2 - 12*u - 15.
3*(u - 5)*(u + 1)
Determine h, given that 9*h**5 + 24*h**4 + 3*h**3 - 24*h**2 - 12*h = 0.
-2, -1, -2/3, 0, 1
Factor -n**3/5 - 4*n**2/5 + n/5 + 4/5.
-(n - 1)*(n + 1)*(n + 4)/5
Let 2*c**5/5 - 2*c**4/5 - 12*c**3/5 = 0. Calculate c.
-2, 0, 3
Factor -t**2/6 + t/2 + 65/3.
-(t - 13)*(t + 10)/6
Factor 12*w**2 - 51*w + 12.
3*(w - 4)*(4*w - 1)
Determine x so that 4*x**5 + 52*x**4 + 92*x**3 + 44*x**2 = 0.
-11, -1, 0
Let -5*x**5 + 110*x**4 + 10*x**3 - 220*x**2 - 5*x + 110 = 0. Calculate x.
-1, 1, 22
Factor -20*d**5 - 95*d**4 - 180*d**3 - 170*d**2 - 80*d - 15.
-5*(d + 1)**4*(4*d + 3)
Suppose x**2 - 24*x + 44 = 0. Calculate x.
2, 22
Suppose -a**3/2 + 5*a**2/2 + 22*a + 30 = 0. Calculate a.
-3, -2, 10
Let x**5 - 4*x**4 + 5*x**3 - 2*x**2 = 0. Calculate x.
0, 1, 2
Factor 2*r**4/3 + 2*r**3/3.
2*r**3*(r + 1)/3
Suppose 18*i**3 - 291*i**2/4 + 75*i - 3 = 0. What is i?
1/24, 2
Factor -9*i**4/4 - 30*i**3 - 357*i**2/4 + 147*i/2.
-3*i*(i + 7)**2*(3*i - 2)/4
Determine q so that 4*q**4/3 - 8*q**3 - 48*q**2 + 288*q = 0.
-6, 0, 6
Factor g**2 - 14*g + 24.
(g - 12)*(g - 2)
Factor -8*n**2/3 - 86*n/3.
-2*n*(4*n + 43)/3
Factor -j**4/5 + 8*j**3/5 + 94*j**2/5 + 32*j + 15.
-(j - 15)*(j + 1)**2*(j + 5)/5
Let 2*l**3/7 - 846*l**2/7 + 119286*l/7 - 5606442/7 = 0. What is l?
141
Find h, given that -75*h**5 + 295*h**4 - 430*h**3 + 270*h**2 - 55*h - 5 = 0.
-1/15, 1
Factor 2*g**4 + 18*g**3 - 20*g**2 - 336*g.
2*g*(g - 4)*(g + 6)*(g + 7)
Suppose -5*c**2 + 5*c = 0. Calculate c.
0, 1
Factor u**3/3 - 80*u**2/3.
u**2*(u - 80)/3
Find q, given that -5*q**3 + 5*q**2 + 45*q - 45 = 0.
-3, 1, 3
Find w such that w**2/2 + 109*w + 1065/2 = 0.
-213, -5
Let 18*i**4 - 94*i**3 + 74*i**2 + 150*i - 36 = 0. What is i?
-1, 2/9, 3
What is g in 5*g**4 + 525*g**3 - 2710*g**2 + 4380*g - 2200 = 0?
-110, 1, 2
Determine z so that z**4 + 277*z**3 + 19043*z**2 - 19321*z = 0.
-139, 0, 1
Let r**4/3 - 3*r**2 - 4*r/3 + 4 = 0. Calculate r.
-2, 1, 3
Find o, given that o**2/3 - 337*o/3 + 334 = 0.
3, 334
Suppose -2*k**2/15 - 44*k/5 - 256/15 = 0. What is k?
-64, -2
Factor -d**5 - 15*d**4 - 67*d**3 + 3*d**2 + 680*d + 1200.
-(d - 3)*(d + 4)**2*(d + 5)**2
Factor -2*z**4/7 - 4*z**3/7 + 2*z**2/7 + 4*z/7.
-2*z*(z - 1)*(z + 1)*(z + 2)/7
Solve -m**5/3 - 28*m**4/3 - 23*m**3/3 + 112*m**2/3 + 36*m = 0 for m.
-27, -2, -1, 0, 2
Solve 13*v**5/5 - 2*v**4/5 - 39*v**3/5 + 32*v**2/5 - 4*v/5 = 0.
-2, 0, 2/13, 1
Factor -3*c**4/2 - 45*c**3 - 759*c**2/2 - 630*c - 294.
-3*(c + 1)**2*(c + 14)**2/2
What is c in -2*c**2/25 + 84*c/25 - 32/5 = 0?
2, 40
Let 5*h**2 + 415*h + 810 = 0. What is h?
-81, -2
Solve 2*i**3/11 + 4*i**2/11 - 8*i/11 - 16/11 = 0 for i.
-2, 2
Factor -5*a**4 - 140*a**3 + 145*a**2.
-5*a**2*(a - 1)*(a + 29)
Factor c**5/8 - 7*c**4/8 + 7*c**3/4 - c**2.
c**2*(c - 4)*(c - 2)*(c - 1)/8
Factor -2*x**3 - 20*x**2 + 78*x.
-2*x*(x - 3)*(x + 13)
Factor -2*l**2 + 18760*l/9 - 4168/9.
-2*(l - 1042)*(9*l - 2)/9
Factor -4*u**4 + 2520*u**3 - 529200*u**2 + 37044000*u.
-4*u*(u - 210)**3
Factor -3*p**2/7 + 3*p - 18/7.
-3*(p - 6)*(p - 1)/7
Determine b so that -4*b**4 + 156*b**3 - 292*b**2 - 156*b + 296 = 0.
-1, 1, 2, 37
Solve -2*z**2/5 + 60*z - 592/5 = 0 for z.
2, 148
Find n, given that -5*n**3 + 6745*n**2 + 13505*n + 6755 = 0.
-1, 1351
Suppose 2*q**4/3 - 11*q**3/3 = 0. Calculate q.
0, 11/2
Factor -m**2/7 + 89*m/7 - 790/7.
-(m - 79)*(m - 10)/7
Let 5*m**3 - 175*m*