148*z/3.
2*z*(z - 37)*(z + 2)/3
Let 4*n**3 - 27*n**2 + 17*n + 6 = 0. Calculate n.
-1/4, 1, 6
Determine a so that -4*a**2 + 28*a + 680 = 0.
-10, 17
Factor 5*z**2/3 - 5980*z/3 - 1995.
5*(z - 1197)*(z + 1)/3
Suppose -2*c**4/9 + 32*c**3/9 + 34*c**2/9 = 0. What is c?
-1, 0, 17
Suppose -i**4/11 - 179*i**3/11 - 8445*i**2/11 - 38889*i/11 - 45414/11 = 0. What is i?
-87, -3, -2
Suppose -4*g**2/3 + 32*g/3 - 16 = 0. What is g?
2, 6
Factor -j**2 + 2*j + 3.
-(j - 3)*(j + 1)
Factor 9*f**4/2 + 11*f**3/2 + f**2.
f**2*(f + 1)*(9*f + 2)/2
Determine h, given that 33*h**5 + 108*h**4 + 211*h**3/3 - 146*h**2/3 - 124*h/3 + 8/3 = 0.
-2, -1, 2/33, 2/3
Determine y so that -10*y**2/9 + 1366*y/9 + 548/9 = 0.
-2/5, 137
Factor -p**4/11 + 7*p**2/11 - 6*p/11.
-p*(p - 2)*(p - 1)*(p + 3)/11
Factor 2*x**5 + 16*x**4 + 34*x**3 + 20*x**2.
2*x**2*(x + 1)*(x + 2)*(x + 5)
Factor 10*c**3/11 + 24*c**2/11 - 72*c/11 - 32/11.
2*(c - 2)*(c + 4)*(5*c + 2)/11
Factor a**2 - 82*a + 1681.
(a - 41)**2
Factor 5*g**3 + 650*g**2 - 5*g - 650.
5*(g - 1)*(g + 1)*(g + 130)
Solve 4*j**2 - 4*j - 24 = 0.
-2, 3
Solve 55*g**5 - 430*g**4 + 1260*g**3 - 1640*g**2 + 800*g = 0 for g.
0, 20/11, 2
Determine r, given that 4*r**4 + 20*r**3 = 0.
-5, 0
Let -5*s**5/2 - 35*s**4/2 - 15*s**3 + 80*s**2 + 80*s = 0. Calculate s.
-4, -1, 0, 2
Factor 22*v**2/15 + 4*v/15.
2*v*(11*v + 2)/15
Factor 2*r**5/3 - 10*r**4/3 + 6*r**3 - 14*r**2/3 + 4*r/3.
2*r*(r - 2)*(r - 1)**3/3
Find a, given that 3*a**4 - 45*a**3 + 240*a**2 - 540*a + 432 = 0.
2, 3, 4, 6
Factor 24*q**2/5 + 51*q - 99/5.
3*(q + 11)*(8*q - 3)/5
Factor -4*i**3/5 + 304*i**2/5 + 124*i + 312/5.
-4*(i - 78)*(i + 1)**2/5
Factor 2*w**2/9 + 16*w/3.
2*w*(w + 24)/9
Find o such that -40*o**5/7 + 604*o**4/7 + 180*o**3 + 548*o**2/7 - 68*o/7 = 0.
-1, 0, 1/10, 17
Determine j so that 3*j**2 - 69*j = 0.
0, 23
Factor -4*h**3 - 148*h**2 + 308*h - 156.
-4*(h - 1)**2*(h + 39)
Factor 2*p**2 - 2376*p - 7146.
2*(p - 1191)*(p + 3)
Find k such that k**4/3 + 55*k**3/3 + 50*k**2/3 - 220*k/3 - 72 = 0.
-54, -2, -1, 2
Factor 2*u**4/17 + 2*u**3/17 - 8*u**2/17 - 8*u/17.
2*u*(u - 2)*(u + 1)*(u + 2)/17
Factor -g**4/4 - 5*g**3/4 + 11*g**2/4 + 33*g/4 + 9/2.
-(g - 3)*(g + 1)**2*(g + 6)/4
Factor -69*j**2/7 - 9*j + 6/7.
-3*(j + 1)*(23*j - 2)/7
Factor -125*k**3 + 276100*k**2 - 220820*k + 44160.
-5*(k - 2208)*(5*k - 2)**2
Factor -15*o**3 - 297*o**2 + 375*o - 63.
-3*(o - 1)*(o + 21)*(5*o - 1)
Let 3*w**4 - 441*w**3 + 2154*w**2 - 3420*w + 1704 = 0. What is w?
1, 2, 142
Factor -5*c**2 - 7590*c - 2880405.
-5*(c + 759)**2
Factor -2*z**3/7 - 58*z**2/7 + 2*z/7 + 58/7.
-2*(z - 1)*(z + 1)*(z + 29)/7
Factor -3*l**4 + 27*l**3 + 273*l**2 - 2727*l + 2430.
-3*(l - 9)**2*(l - 1)*(l + 10)
Determine z, given that -2*z**2/15 - 3392*z/15 - 1438208/15 = 0.
-848
Suppose x**2/3 + 4*x/3 + 1 = 0. Calculate x.
-3, -1
Solve 5*x**2 - 380*x - 2025 = 0 for x.
-5, 81
Suppose -8*c**3 - 20*c**2 - 16*c - 4 = 0. Calculate c.
-1, -1/2
Factor y**2 + 98*y + 465.
(y + 5)*(y + 93)
Factor -25*l**4 - 210*l**3 - 255*l**2 - 70*l.
-5*l*(l + 1)*(l + 7)*(5*l + 2)
Factor y**4/8 - 5*y**3/8 - 8*y**2 + 35*y/2.
y*(y - 10)*(y - 2)*(y + 7)/8
Find u, given that -2*u**4/11 + 24*u**3/11 - 58*u**2/11 + 36*u/11 = 0.
0, 1, 2, 9
Suppose 2*m**5 + 132*m**4 + 2176*m**3 - 132*m**2 - 2178*m = 0. Calculate m.
-33, -1, 0, 1
Factor -5*z**2 - 4495*z + 4500.
-5*(z - 1)*(z + 900)
Factor -94*k**2/9 + 23*k/3 + 25/9.
-(k - 1)*(94*k + 25)/9
Factor 3*w**3/5 + 39*w**2/5 - 87*w/5 + 9.
3*(w - 1)**2*(w + 15)/5
Let -72*x**4/7 - 1992*x**3/7 - 6242*x**2/7 + 2248*x/7 - 192/7 = 0. Calculate x.
-24, -4, 1/6
Let 2*y**5/3 - 4*y**4/3 - 2*y**3/3 + 4*y**2/3 = 0. What is y?
-1, 0, 1, 2
Determine y so that -13*y**2 - 81*y - 126 = 0.
-42/13, -3
Factor p**3/6 + 175*p**2/6 - 266*p/3 + 178/3.
(p - 2)*(p - 1)*(p + 178)/6
Determine a so that 3*a**5/5 - 27*a**4 + 477*a**3 - 4137*a**2 + 17640*a - 148176/5 = 0.
7, 12
Factor -122*m**4/5 - 248*m**3/5 - 26*m**2 - 4*m/5.
-2*m*(m + 1)**2*(61*m + 2)/5
Factor u**5 + 2*u**4 - 28*u**3 + 46*u**2 - 21*u.
u*(u - 3)*(u - 1)**2*(u + 7)
Solve 3*f**2/2 - 27*f/2 - 33 = 0.
-2, 11
Factor -5*x**3 + 7090*x**2 - 14165*x + 7080.
-5*(x - 1416)*(x - 1)**2
Let -4*l**3/7 + 12*l**2/7 - 16/7 = 0. What is l?
-1, 2
Suppose d**4/2 + 73*d**3 - 147*d**2/2 = 0. Calculate d.
-147, 0, 1
Factor -4*c**4 + 4*c**3 + 68*c**2 + 60*c.
-4*c*(c - 5)*(c + 1)*(c + 3)
Suppose -12*d**2/11 + 34*d/11 - 20/11 = 0. Calculate d.
5/6, 2
Find u such that -196*u**5 - 4620*u**4 + 7208*u**3 + 5232*u**2 + 800*u = 0.
-25, -2/7, 0, 2
Determine a so that -4*a**3/7 + 52*a/7 + 48/7 = 0.
-3, -1, 4
Factor -2*u**4/13 - 14*u**3/13 + 36*u**2/13.
-2*u**2*(u - 2)*(u + 9)/13
Factor 4*y**4/9 + 248*y**3/9 - 1040*y**2/9 + 352*y/3.
4*y*(y - 2)**2*(y + 66)/9
Factor 6*k**3 - 32*k**2/3 + 10*k/3 + 4/3.
2*(k - 1)**2*(9*k + 2)/3
Suppose -8*t**3 + 34*t**2 - 40*t + 8 = 0. What is t?
1/4, 2
Factor -g**3/5 - 46*g**2/5 + 49*g/5 + 94/5.
-(g - 2)*(g + 1)*(g + 47)/5
Factor 11*d**2/5 + 82*d/5.
d*(11*d + 82)/5
Factor 5*d**2 + 27020*d + 36504020.
5*(d + 2702)**2
Suppose -2*q**3/11 + 12*q**2/11 + 2*q/11 - 12/11 = 0. What is q?
-1, 1, 6
Suppose 4*n**4 - 12*n**3 - 8*n**2 + 48*n - 32 = 0. What is n?
-2, 1, 2
Factor 3*n**2 - 201*n + 1980.
3*(n - 55)*(n - 12)
Factor -18*c**2/11 + 1822*c/11 - 404/11.
-2*(c - 101)*(9*c - 2)/11
Let -w**4/3 + 71*w**3 + 293*w**2 - 2393*w/3 + 434 = 0. What is w?
-6, 1, 217
Let 3*j**5 - 24*j**4 - 24*j**3 + 288*j**2 + 432*j = 0. Calculate j.
-2, 0, 6
Factor 4*d**3 + 6852*d**2 + 3912492*d + 744677644.
4*(d + 571)**3
Suppose -p**3/2 + p**2 = 0. What is p?
0, 2
Factor 5*d**2 - 95*d + 170.
5*(d - 17)*(d - 2)
Let 315*q**2 + 305*q - 10 = 0. Calculate q.
-1, 2/63
Factor 54*b**3/5 + 114*b**2/5 - 84*b - 48/5.
6*(b - 2)*(b + 4)*(9*b + 1)/5
Let -4*h**5 + 176*h**4 - 168*h**3 - 176*h**2 + 172*h = 0. Calculate h.
-1, 0, 1, 43
Factor -2*j**4 - 504*j**3 - 32250*j**2 - 62500*j.
-2*j*(j + 2)*(j + 125)**2
Factor -x**3 - 182*x**2 - 6080*x - 56800.
-(x + 20)**2*(x + 142)
Solve -2*s**3/5 - 236*s**2/5 + 238*s/5 = 0 for s.
-119, 0, 1
Find m such that -m**2/5 - 41*m/5 = 0.
-41, 0
What is i in -2*i**5/17 - 4*i**4/17 + 52*i**3/17 - 112*i**2/17 + 94*i/17 - 28/17 = 0?
-7, 1, 2
Suppose -3*x**3/7 + 76*x**2/7 + 19*x + 54/7 = 0. What is x?
-1, -2/3, 27
Determine q so that -41*q**2/4 + 64*q - 15 = 0.
10/41, 6
Factor -5*a**2 + 160*a.
-5*a*(a - 32)
Suppose -y**2/2 - 2*y + 16 = 0. What is y?
-8, 4
Factor -l**3 - 51*l**2 + 162*l.
-l*(l - 3)*(l + 54)
Factor -10*t**3/11 + 10924*t**2/11 - 4368*t/11.
-2*t*(t - 1092)*(5*t - 2)/11
Find j such that 5*j**4/7 + 16*j**3/7 + 13*j**2/7 + 2*j/7 = 0.
-2, -1, -1/5, 0
Determine d so that 18*d**3 - 273*d**2 + 837*d - 132 = 0.
1/6, 4, 11
Determine w, given that w**2/6 - 3*w/2 - 200/3 = 0.
-16, 25
Factor 9*z**4 + 30*z**3 - 404*z**2 - 568*z - 192.
(z - 6)*(z + 8)*(3*z + 2)**2
Solve -5*t**2 + 70*t - 240 = 0 for t.
6, 8
Solve -4*y**3 + 772*y**2 - 37632*y + 36864 = 0 for y.
1, 96
Factor -2*s**3 + 610*s**2 + 1226*s + 614.
-2*(s - 307)*(s + 1)**2
Let -3*s**2 - 33*s - 54 = 0. Calculate s.
-9, -2
Factor 2*s**5/3 - 4240*s**4 + 20237516*s**3/3 - 13478960*s**2 + 20212082*s/3.
2*s*(s - 3179)**2*(s - 1)**2/3
Factor 4*x**3 - 220*x**2 + 216*x.
4*x*(x - 54)*(x - 1)
Find f such that -16*f**5/9 + 340*f**4/9 - 692*f**3/9 + 152*f**2/9 = 0.
0, 1/4, 2, 19
Determine g, given that -10*g**4/7 + 8*g**3/7 + 212*g**2/7 - 408*g/7 - 90/7 = 0.
-5, -1/5, 3
Factor 4*z**4/5 - 36*z**3/5 + 72*z**2/5.
4*z**2*(z - 6)*(z - 3)/5
Suppose 2*c**5/5 - 2*c**4/5 - 6*c**3/5 + 2*c**2 - 4*c/5 = 0. Calculate c.
-2, 0, 1
Find z, given that 3*z**3/4 + 51*z**2/4 + 33*z/4 - 1815/4 = 0.
-11, 5
Factor 5*t**3 + 30*t**2 + 55*t + 30.
5*(t + 1)*(t + 2)*(t + 3)
Determine b so that -b**4 + 39*b**3 - 158*b**2 - 4512*b - 8064 = 0.
-7, -2, 24
Find b such that -3*b**5/2 + 315*b**4/8 - 1479*b**3/4 + 1434*b**2 - 1872*b + 384 = 0.
1/4, 2, 8
Suppose n**3 + 23*n**2 - 24*n = 0. Calculate n.
-24, 0, 1
Find w, given that 4*w**2 - 1912*w - 1916 = 0.
-1, 479
Let l**3/6 - 55*l**2/6 - 241*l/6 + 295/6 = 0. What is l?
-5, 1, 59
Factor 2*u**2 - 1128*u + 159048.
2*(u - 282)**2
Determine t so that -t**2/3 + 71*t/3 - 1240/3 = 0.
31, 40
Let -125*u**5 + 225*u**4 + 130*u**3 - 180*u**2 + 40*u = 0. What is u?
-1, 0, 2/5, 2
Suppose 2*m**5/13 - 18*m**4/13 + 14*m**3/13 + 186*m**2/13 - 160*m/13 - 600/13 = 0. Calculate m.
-2, 3, 5
