, 1/4
Factor 2*t**2/11 + 36*t + 1782.
2*(t + 99)**2/11
Factor -2*h**2/5 - 6*h - 28/5.
-2*(h + 1)*(h + 14)/5
Factor 5*l**2 + 105*l - 360.
5*(l - 3)*(l + 24)
Let 5*d**3 + 90*d**2 + 300*d + 280 = 0. What is d?
-14, -2
Find u, given that 16*u**3 - 36*u**2 + 8*u = 0.
0, 1/4, 2
Find a such that 3*a**3/5 + 141*a**2/5 - 3*a/5 - 141/5 = 0.
-47, -1, 1
Factor 3*a**4/2 - 33*a**3 - 69*a**2/2.
3*a**2*(a - 23)*(a + 1)/2
Determine a, given that 2*a**3 + 62*a**2 + 624*a + 2016 = 0.
-12, -7
Factor -2*q**3/13 + 46*q**2/13.
-2*q**2*(q - 23)/13
Factor p**3/2 - 3*p**2/2 + 3*p/2 - 1/2.
(p - 1)**3/2
Solve -j**3/7 + 37*j**2/7 + 302*j/7 + 264/7 = 0.
-6, -1, 44
Determine y so that y**2/2 + 26*y - 1005/2 = 0.
-67, 15
Suppose -3*s**3 + 9*s**2 + 3*s - 9 = 0. What is s?
-1, 1, 3
Determine c so that 2*c**5/21 - 26*c**3/21 + 32*c**2/21 + 8*c/7 - 32/21 = 0.
-4, -1, 1, 2
Suppose r**3 + 1065*r**2 + 378075*r + 44738875 = 0. Calculate r.
-355
Find t such that -5*t**5 + 70*t**4 + 435*t**3 + 740*t**2 + 380*t = 0.
-2, -1, 0, 19
Factor a**2 + 72*a + 71.
(a + 1)*(a + 71)
What is l in -5*l**5 + 15*l**4 + 230*l**3 - 730*l**2 + 735*l - 245 = 0?
-7, 1, 7
Factor r**2/4 - 67*r - 269/4.
(r - 269)*(r + 1)/4
Factor 3*y**5 + 16*y**4 + 3*y**3 - 10*y**2.
y**2*(y + 1)*(y + 5)*(3*y - 2)
Determine d, given that d**2 - 18*d - 63 = 0.
-3, 21
Suppose -3*y**3 - 483*y**2 + 1968*y - 1980 = 0. What is y?
-165, 2
Let -18*q**3 - 32*q**2 + 278*q - 60 = 0. What is q?
-5, 2/9, 3
Solve 5*j**5 - 10075*j**4 + 6763680*j**3 - 1510548480*j**2 - 1517322240*j = 0.
-1, 0, 672
Factor 44*w**2 + 4044*w - 368.
4*(w + 92)*(11*w - 1)
What is w in 4*w**3 - 1112*w**2 + 78384*w - 152352 = 0?
2, 138
Solve -y**2/8 - 15*y/4 - 225/8 = 0 for y.
-15
Let 5*i**2 + 5570*i + 1551245 = 0. What is i?
-557
Find f, given that 2*f**2/5 + 1682*f/5 + 3356/5 = 0.
-839, -2
Find u such that -5*u**4/3 - 10*u**3 + 5*u**2 + 100*u/3 + 20 = 0.
-6, -1, 2
Suppose 45*r**4 + 2640*r**3 - 910*r**2 - 1480*r - 295 = 0. Calculate r.
-59, -1/3, 1
Find o such that -2*o**3/21 + 26*o**2/21 - 52*o/21 - 80/21 = 0.
-1, 4, 10
Factor -3*r**5 - 18*r**4 - 39*r**3 - 36*r**2 - 12*r.
-3*r*(r + 1)**2*(r + 2)**2
Factor 20*y**3 - 132*y**2 + 144*y + 80.
4*(y - 5)*(y - 2)*(5*y + 2)
Factor 3*g**4/4 - 9*g**3/4 - 27*g**2/4 - 15*g/4.
3*g*(g - 5)*(g + 1)**2/4
Factor 72*a**4/11 + 96*a**3/11 - 70*a**2/11 - 98*a/11.
2*a*(a - 1)*(6*a + 7)**2/11
Solve 2*y**4/11 + 10*y**3/11 = 0.
-5, 0
Factor -2*v**3/3 + 34*v**2/3 - 118*v/3 - 154/3.
-2*(v - 11)*(v - 7)*(v + 1)/3
Let 5*y**3 - 5*y**2 - 10*y = 0. What is y?
-1, 0, 2
Factor -13*s**2 + 622*s + 96.
-(s - 48)*(13*s + 2)
Find r such that -288*r**3 + 584*r**2/3 - 49*r/2 - 3 = 0.
-2/27, 3/8
Factor -3*r**4/2 + 4*r**3 - 3*r**2/2 - r.
-r*(r - 2)*(r - 1)*(3*r + 1)/2
Factor -20*o**3 + 292*o**2 - 160*o - 112.
-4*(o - 14)*(o - 1)*(5*o + 2)
Let -2*x**2/5 + 112*x/5 = 0. What is x?
0, 56
What is m in 2*m**4/7 - 2*m**3/7 - 234*m**2/7 - 414*m/7 + 648/7 = 0?
-9, -3, 1, 12
Find h such that h**4/6 - 2*h**3/3 - 49*h**2/2 - 45*h = 0.
-9, -2, 0, 15
Factor -5*b**2 + 110*b + 375.
-5*(b - 25)*(b + 3)
Let -2*g**2/9 - 58*g/9 + 124/9 = 0. What is g?
-31, 2
Factor -3*n**2/4 + 23*n/4 + 29/2.
-(n + 2)*(3*n - 29)/4
Factor 2*r**3/7 + 30*r**2/7 - 2*r/7 - 30/7.
2*(r - 1)*(r + 1)*(r + 15)/7
Determine q so that 5*q**3 + 20*q**2 + 25*q + 10 = 0.
-2, -1
Suppose v**4/4 + 37*v**3/4 - 159*v**2/4 + 203*v/4 - 41/2 = 0. What is v?
-41, 1, 2
Factor 5*c**3 + 265*c**2 + 2795*c + 2535.
5*(c + 1)*(c + 13)*(c + 39)
Factor -d**3/3 + 10*d**2/3 + 13*d/3 - 22/3.
-(d - 11)*(d - 1)*(d + 2)/3
Determine g, given that 45*g**2 + 5*g = 0.
-1/9, 0
Factor -3*m**2 - 156*m.
-3*m*(m + 52)
Let -25*u**4 + 1195*u**3 + 265*u**2 - 1195*u - 240 = 0. Calculate u.
-1, -1/5, 1, 48
Determine c so that c**2 - 1008*c - 1009 = 0.
-1, 1009
Factor 2*p**5 + 8*p**4 + 4*p**3 - 8*p**2 - 6*p.
2*p*(p - 1)*(p + 1)**2*(p + 3)
Let -p**5/3 - 4*p**4 + 7*p**3/3 + 26*p**2 - 24*p = 0. What is p?
-12, -3, 0, 1, 2
Factor n**4 - 5*n**3 - 13*n**2 - 7*n.
n*(n - 7)*(n + 1)**2
Factor -3*q**3 - 417*q**2 - 3192*q - 6288.
-3*(q + 4)**2*(q + 131)
Factor -5*m**5 - 790*m**4 - 42125*m**3 - 784940*m**2 - 1446640*m - 703040.
-5*(m + 1)**2*(m + 52)**3
Factor -2*f**3/7 - 8*f**2/7 + 2*f + 20/7.
-2*(f - 2)*(f + 1)*(f + 5)/7
Suppose b**3 + 819*b**2/2 - 205*b = 0. Calculate b.
-410, 0, 1/2
Find q such that q**4/6 + q**3/6 - q**2/3 = 0.
-2, 0, 1
Factor f**5 + 39*f**4 - 123*f**3 + 125*f**2 - 42*f.
f*(f - 1)**3*(f + 42)
Factor -3*j**2 + 156*j - 2028.
-3*(j - 26)**2
Factor 2*u**2/3 - 688*u + 177504.
2*(u - 516)**2/3
Determine s so that 75*s**4 - 430*s**3 - 315*s**2 + 190*s = 0.
-1, 0, 2/5, 19/3
Find w such that -5*w**4/4 - 435*w**3/4 - 10475*w**2/4 - 43665*w/4 - 8405 = 0.
-41, -4, -1
Factor -256*c**4/9 + 7744*c**3 - 17328*c**2 + 12972*c - 3240.
-4*(c - 270)*(4*c - 3)**3/9
Factor 3*w**4 + 12*w**3.
3*w**3*(w + 4)
Find g such that 8*g**5/3 + 424*g**4/3 + 5402*g**3/3 - 1908*g**2 + 486*g = 0.
-27, 0, 1/2
Find h, given that -h**2/2 - 27*h - 53/2 = 0.
-53, -1
Factor -2*f**3/9 - 4*f**2/9 + 26*f/9 - 20/9.
-2*(f - 2)*(f - 1)*(f + 5)/9
Solve -3*z**4 + 39*z**3 - 120*z**2 + 108*z = 0.
0, 2, 9
Factor 2*o**4/3 - 10*o**3/3 + 2*o**2/3 + 14*o - 12.
2*(o - 3)**2*(o - 1)*(o + 2)/3
Determine s, given that s**2/5 - 156*s/5 = 0.
0, 156
Determine i, given that 54*i**5 + 1026*i**4 + 6876*i**3 + 17476*i**2 + 4046*i - 29478 = 0.
-17/3, -3, 1
Factor 3*w**2/5 - 3*w - 30.
3*(w - 10)*(w + 5)/5
Factor -18*v**3 - 13254*v**2 + 8842*v - 1474.
-2*(v + 737)*(3*v - 1)**2
Factor -4*m**3 - 356*m**2 - 352*m.
-4*m*(m + 1)*(m + 88)
Find s, given that -4*s**2 - 48544*s - 147282496 = 0.
-6068
Suppose -14*z**4/11 + 12*z**3/11 + 130*z**2/11 + 168*z/11 + 64/11 = 0. What is z?
-8/7, -1, 4
Factor -c**4/3 + 22*c**3/3 - 181*c**2/3 + 220*c - 300.
-(c - 6)**2*(c - 5)**2/3
Solve -3*a**5 - 9*a**4 + 6*a**3 + 18*a**2 - 3*a - 9 = 0.
-3, -1, 1
Determine d so that -3*d**4/5 - 63*d**3/5 - 354*d**2/5 - 36*d + 120 = 0.
-10, -2, 1
Solve 3*z**5/5 + 6*z**4/5 - 6*z**3/5 - 12*z**2/5 + 3*z/5 + 6/5 = 0 for z.
-2, -1, 1
Determine o, given that o**5 - 26*o**4 + 141*o**3 + 364*o**2 + 196*o = 0.
-1, 0, 14
Find c such that -c**2 - 40*c - 39 = 0.
-39, -1
Factor -4*r**5/7 - 920*r**4/7 - 55600*r**3/7 - 311840*r**2/7 - 87040*r - 57344.
-4*(r + 2)**3*(r + 112)**2/7
What is g in 9*g**5 - 59*g**4 + 335*g**3/3 - 85*g**2 + 26*g - 8/3 = 0?
2/9, 1/3, 1, 4
Find f such that -2*f**2 - 5028*f - 3160098 = 0.
-1257
Suppose 3*f**4 + 66*f**3 + 387*f**2 + 324*f = 0. What is f?
-12, -9, -1, 0
Factor -z**2/11 + 8*z/11 - 15/11.
-(z - 5)*(z - 3)/11
Factor x**5/4 - x**4 + 3*x**3/2 - x**2 + x/4.
x*(x - 1)**4/4
Find n such that 2*n**2 - 1428*n + 254898 = 0.
357
Factor -r**2/3 + 3443*r/3.
-r*(r - 3443)/3
Factor -u**3 - 31*u**2 - 150*u.
-u*(u + 6)*(u + 25)
Let -200*z**3 + 330*z**2 + 135*z + 10 = 0. Calculate z.
-1/4, -1/10, 2
Factor a**3 + 11*a**2 - a - 11.
(a - 1)*(a + 1)*(a + 11)
Factor 5*a**2 - 1390*a + 96605.
5*(a - 139)**2
Find m, given that 18*m**3/7 + 1770*m**2/7 + 20478*m/7 + 6630/7 = 0.
-85, -13, -1/3
Factor 2*m**3 + 2*m**2 - 2*m - 2.
2*(m - 1)*(m + 1)**2
Suppose -2*x**4/11 - 28*x**3/11 + 136*x**2/11 - 144*x/11 = 0. Calculate x.
-18, 0, 2
Find i such that -i**2/7 - 4*i/7 - 4/7 = 0.
-2
Factor -3*m**2 + 63*m - 60.
-3*(m - 20)*(m - 1)
Factor -2*r**2/15 - 2*r/5 + 12/5.
-2*(r - 3)*(r + 6)/15
Factor 2*u**4/3 - 8*u**3/3 - 4*u**2/3 + 8*u + 6.
2*(u - 3)**2*(u + 1)**2/3
Suppose b**3 - 28*b**2 - b + 28 = 0. Calculate b.
-1, 1, 28
Factor -i**2/3 - 121*i/3.
-i*(i + 121)/3
What is h in -1715*h**5 - 13965*h**4 - 18060*h**3 + 22720*h**2 - 7200*h + 720 = 0?
-6, -3, 2/7
Factor -2*o**4/9 - 32*o**3/9 - 58*o**2/9 - 28*o/9.
-2*o*(o + 1)**2*(o + 14)/9
Factor -2*x**2 + 7540*x - 7106450.
-2*(x - 1885)**2
Determine q, given that q**2 + 25*q + 46 = 0.
-23, -2
Factor -2*i**2/7 + 148*i/7.
-2*i*(i - 74)/7
Let -5*v**5 + 320*v**4 + 1330*v**3 + 2020*v**2 + 1355*v + 340 = 0. What is v?
-1, 68
Factor 4*r**3 - 620*r**2 - 16*r + 2480.
4*(r - 155)*(r - 2)*(r + 2)
Determine p so that -p**2/5 - 119*p/5 - 784/5 = 0.
-112, -7
Factor -4*a**2 - 2472*a + 4960.
-4*(a - 2)*(a + 620)
Suppose y**3/2 - 383*y**2 - 767*y/2 = 0. What is y?
-1, 0, 767
Let -2*z**5/5 - 6*z**4/5 + 92*z**3/5 - 156*z**2/5 - 18*z + 162/5 = 0. What is z?
-9, -1, 1, 3
Suppose 4*j**2/5 + 2236*j/5 = 0. Calculate j.
-559, 0
Factor 4*p**2