
Factor i**3/12 + 985*i**2/12 + 242063*i/12 - 243049/12.
(i - 1)*(i + 493)**2/12
Solve -l**3 + 120*l**2 - 4212*l + 34992 = 0.
12, 54
Solve 3*s**5 - 33*s**4 + 51*s**3 + 33*s**2 - 54*s = 0 for s.
-1, 0, 1, 2, 9
Find v, given that -v**3/2 - 3*v**2/2 + 3*v + 4 = 0.
-4, -1, 2
Factor r**2/9 + 182*r/9 - 61/3.
(r - 1)*(r + 183)/9
Let -2*f**4/9 + 46*f**3/9 - 94*f**2/3 + 74*f - 60 = 0. What is f?
2, 3, 15
Find k such that -9*k**4 + 15*k**3 + 69*k**2 + 57*k + 12 = 0.
-1, -1/3, 4
Factor 4*q**2/7 + 384*q/7 - 1024.
4*(q - 16)*(q + 112)/7
Determine t, given that 30*t**4 - 85*t**3 + 85*t**2 - 35*t + 5 = 0.
1/3, 1/2, 1
Factor 2*t**2/3 - 1862*t/3 + 620.
2*(t - 930)*(t - 1)/3
Factor -4*v**3/9 - 128*v**2/3 - 2516*v/9 - 712/3.
-4*(v + 1)*(v + 6)*(v + 89)/9
Factor -x**3 + 390*x**2 - 38025*x.
-x*(x - 195)**2
Find d, given that -2*d**2/13 - 15684*d/13 - 30748482/13 = 0.
-3921
Find d such that -2*d**3/9 + 56*d**2 - 3528*d = 0.
0, 126
Factor y**2 + 434*y + 433.
(y + 1)*(y + 433)
Factor -3*f**3/2 - 63*f**2/2 + 36*f + 66.
-3*(f - 2)*(f + 1)*(f + 22)/2
Determine z so that 3*z**2/2 - 15*z/2 = 0.
0, 5
What is w in w**3/4 + 21*w**2/4 + 71*w/4 + 51/4 = 0?
-17, -3, -1
Factor -2*a**2 - 12*a - 10.
-2*(a + 1)*(a + 5)
Solve 9*g**3 - 123*g**2 + 78*g = 0.
0, 2/3, 13
Suppose -48*y**5 + 216*y**4 + 1845*y**3 + 879*y**2 + 108*y = 0. Calculate y.
-4, -1/4, 0, 9
Determine z, given that 4*z**3 - 212*z**2 = 0.
0, 53
Find o, given that -7*o**2/5 + 19*o/5 + 6/5 = 0.
-2/7, 3
Factor -2*i**3 + 50*i**2.
-2*i**2*(i - 25)
Let -3*b**4 - 6*b**3 + 36*b**2 - 42*b + 15 = 0. What is b?
-5, 1
Factor -q**2 + 21*q.
-q*(q - 21)
What is f in 3*f**5/8 - 3*f**4/2 - 3*f**3/8 + 3*f**2/2 = 0?
-1, 0, 1, 4
Find l, given that -l**4/5 - 3*l**3 + 76*l**2/5 = 0.
-19, 0, 4
Factor 2*l**3/9 - 40*l**2/9 + 136*l/9 - 128/9.
2*(l - 16)*(l - 2)**2/9
Factor 3*g**3 + 246*g**2.
3*g**2*(g + 82)
Factor -5*n**5 - 15*n**4 - 10*n**3.
-5*n**3*(n + 1)*(n + 2)
Factor 4*z**2 + 9228*z + 9224.
4*(z + 1)*(z + 2306)
Factor -2*q**3 - 30*q**2 - 46*q + 462.
-2*(q - 3)*(q + 7)*(q + 11)
Factor 8*m**4 + 2*m**3 - 32*m**2 - 8*m.
2*m*(m - 2)*(m + 2)*(4*m + 1)
What is k in k**2 + 12*k - 13 = 0?
-13, 1
Let 4*v**3/5 - 1244*v**2/5 + 19468*v - 19220 = 0. Calculate v.
1, 155
Solve -3*i**3/4 - 99*i**2/4 - 189*i/4 - 93/4 = 0.
-31, -1
Factor 8*l**2/5 - 1838*l/5 - 92.
2*(l - 230)*(4*l + 1)/5
Factor 16*d**2 - 76*d + 48.
4*(d - 4)*(4*d - 3)
Determine a so that -4*a**2 + 200*a - 564 = 0.
3, 47
Factor -r**2/3 + 104*r/3 - 2704/3.
-(r - 52)**2/3
Factor 2*a**2/5 + 6*a - 2132/5.
2*(a - 26)*(a + 41)/5
Let c**5/3 + c**4/3 - c**3 - c**2/3 + 2*c/3 = 0. Calculate c.
-2, -1, 0, 1
Factor 4*v**4 - 320*v**3 + 6712*v**2 - 12480*v + 6084.
4*(v - 39)**2*(v - 1)**2
Determine j so that 3*j**2 + 909*j + 906 = 0.
-302, -1
Factor -2*j**2/15 + 112*j/15 - 184/3.
-2*(j - 46)*(j - 10)/15
Determine t so that t**5 - 31*t**4 + 114*t**3 - 166*t**2 + 109*t - 27 = 0.
1, 27
Factor 2*n**3/3 - 4*n**2/3 - 22*n/3 + 8.
2*(n - 4)*(n - 1)*(n + 3)/3
Suppose -4*a**3 - 100*a**2 - 700*a - 1500 = 0. What is a?
-15, -5
Solve -3*r**5 - 51*r**4 - 87*r**3 + 51*r**2 + 90*r = 0 for r.
-15, -2, -1, 0, 1
Find a, given that -2*a**2 + 18*a + 44 = 0.
-2, 11
Factor 8*s**4 - 36*s**3 + 36*s**2 + 4*s - 12.
4*(s - 3)*(s - 1)**2*(2*s + 1)
Solve -95*f**2/2 + 50*f - 5/2 = 0 for f.
1/19, 1
Factor -2*q**2/3 - 80*q/3.
-2*q*(q + 40)/3
Factor 2*o**4/5 + 2416*o**3/5 + 727212*o**2/5 - 292336*o + 146410.
2*(o - 1)**2*(o + 605)**2/5
Factor -27*j**3/2 - 261*j**2/2 - 420*j - 450.
-3*(j + 3)*(3*j + 10)**2/2
Factor -2*s**3/7 + 114*s**2 - 1590*s/7 + 794/7.
-2*(s - 397)*(s - 1)**2/7
Determine c, given that c**3/4 + 15*c**2/4 + 75*c/4 + 125/4 = 0.
-5
Solve v**5/4 - 41*v**4/4 - 21*v**3/2 = 0.
-1, 0, 42
Solve l**2 + 962*l + 231361 = 0.
-481
Factor 8*r**3/3 - 590*r**2/3 + 10804*r/3 + 2738/3.
2*(r - 37)**2*(4*r + 1)/3
Factor -q**2/4 - 37*q/4 - 33.
-(q + 4)*(q + 33)/4
Suppose 15*c**4/7 + 36*c**3 + 27*c**2 - 48*c/7 = 0. Calculate c.
-16, -1, 0, 1/5
Factor -5*s**3 + 21590*s**2 - 23327980*s + 46569640.
-5*(s - 2158)**2*(s - 2)
Find m such that -3*m**4/2 + 15*m**2 - 27/2 = 0.
-3, -1, 1, 3
Factor -b**3/4 + b**2 + 21*b/4.
-b*(b - 7)*(b + 3)/4
What is r in -2*r**5/13 - 28*r**4/13 - 72*r**3/13 - 68*r**2/13 - 22*r/13 = 0?
-11, -1, 0
Suppose -b**2 + 2*b = 0. Calculate b.
0, 2
Determine h, given that -h**3/6 - 44*h**2/3 - 173*h/6 - 43/3 = 0.
-86, -1
Factor -3*f**3 - 1626*f**2 - 1617*f + 3246.
-3*(f - 1)*(f + 2)*(f + 541)
Let -4*k**3 - 348*k**2 - 680*k = 0. What is k?
-85, -2, 0
Let -5*k**2 - 90*k + 200 = 0. What is k?
-20, 2
Factor 2*r**5/7 - 8*r**4/7 - 4*r**3 + 144*r**2/7 - 54*r/7 - 216/7.
2*(r - 3)**3*(r + 1)*(r + 4)/7
Factor 2*k**2/15 - 104*k/15.
2*k*(k - 52)/15
Find s such that s**4/2 - s**3 - 6*s**2 - 7*s - 5/2 = 0.
-1, 5
Suppose -3*o**2/7 + 75*o/7 + 348/7 = 0. Calculate o.
-4, 29
Factor 3062*n**2/5 - 612*n - 2/5.
2*(n - 1)*(1531*n + 1)/5
Factor 2*r**2/3 + 302*r/3 + 100.
2*(r + 1)*(r + 150)/3
Factor -u**4 - 29*u**3 - 160*u**2 + 768*u.
-u*(u - 3)*(u + 16)**2
Factor -w**3 + 261*w**2 - 22707*w + 658503.
-(w - 87)**3
Factor s**4/2 + 7*s**3/4 - s**2.
s**2*(s + 4)*(2*s - 1)/4
Suppose 3*b**5/4 - 15*b**4/4 - 3*b**3 + 15*b**2 = 0. Calculate b.
-2, 0, 2, 5
Factor p**4/2 + 7*p**3/4 + 7*p**2/4 + p/2.
p*(p + 1)*(p + 2)*(2*p + 1)/4
Find z such that -3*z**4/4 - 15*z**3/4 - 9*z**2/2 = 0.
-3, -2, 0
Let b**4 - 19*b**3 - 22*b**2 + 40*b = 0. Calculate b.
-2, 0, 1, 20
Find i such that i**2/5 - 7*i + 216/5 = 0.
8, 27
Solve -y**3/6 - 11*y**2/6 + y/6 + 11/6 = 0 for y.
-11, -1, 1
Suppose 2*u**4/7 - 140*u**3 + 1952*u**2/7 = 0. Calculate u.
0, 2, 488
Factor -2*a**5 - 40*a**4 - 74*a**3 - 36*a**2.
-2*a**2*(a + 1)**2*(a + 18)
Factor 4*t**2/3 - 1676*t/3 - 3368/3.
4*(t - 421)*(t + 2)/3
Factor 3*t**2 - 54*t + 51.
3*(t - 17)*(t - 1)
Factor l**5/5 - 18*l**4/5 + 14*l**3/5 + 56*l**2/5 - 87*l/5 + 34/5.
(l - 17)*(l - 1)**3*(l + 2)/5
Let -69*j**5/2 - 281*j**4/6 + 58*j**3 + 26*j**2 - 8*j/3 = 0. Calculate j.
-2, -4/9, 0, 2/23, 1
Let -2*x**4 + 104*x**3 + 106*x**2 = 0. What is x?
-1, 0, 53
Factor -4*s**2 + 84*s.
-4*s*(s - 21)
Factor -2*s**5 + 12*s**4 - 16*s**3 - 4*s**2 + 18*s - 8.
-2*(s - 4)*(s - 1)**3*(s + 1)
Factor -w**2 - 51*w + 52.
-(w - 1)*(w + 52)
Factor 3*q**2 + 216*q + 420.
3*(q + 2)*(q + 70)
Suppose 4*f**2 - 48*f + 44 = 0. Calculate f.
1, 11
Factor -3*h**2 + 20148*h - 33828492.
-3*(h - 3358)**2
Factor -4*w**2 - 5800*w - 2102500.
-4*(w + 725)**2
Solve -2*a**4/9 - 10*a**3/9 + 20*a**2/9 + 40*a/9 - 16/3 = 0.
-6, -2, 1, 2
Factor z**3/4 - 7*z**2/2 - 31*z/4 - 4.
(z - 16)*(z + 1)**2/4
Solve n**3/2 + 31*n**2 + 439*n/2 + 189 = 0 for n.
-54, -7, -1
Find b, given that 2*b**5/15 - 2*b**4/15 - 34*b**3/15 + 106*b**2/15 - 112*b/15 + 8/3 = 0.
-5, 1, 2
Solve -z**2/3 - 23*z/3 + 8 = 0.
-24, 1
Factor 2*p**5/19 - 958*p**4/19 + 3812*p**3/19 - 5708*p**2/19 + 3802*p/19 - 50.
2*(p - 475)*(p - 1)**4/19
Factor 500*s**2 + 100*s + 5.
5*(10*s + 1)**2
Find r, given that 2*r**5/11 + 6*r**4 + 122*r**3/11 - 6*r**2 - 124*r/11 = 0.
-31, -2, -1, 0, 1
Factor 21*h**4 + 603*h**3 - 174*h**2.
3*h**2*(h + 29)*(7*h - 2)
What is g in -9*g**2 + 15*g = 0?
0, 5/3
Factor -44*b**2/15 + 922*b/15 + 14/5.
-2*(b - 21)*(22*b + 1)/15
Factor 8*p**3 - 26*p**2 - 26*p + 8.
2*(p - 4)*(p + 1)*(4*p - 1)
Solve u**3/3 + 11*u**2 + 32*u/3 = 0 for u.
-32, -1, 0
Factor 81*k**3/4 + 963*k**2 - 431*k + 48.
(k + 48)*(9*k - 2)**2/4
Factor -q**2 - 98*q - 2401.
-(q + 49)**2
What is d in 14*d**4/13 - 3138*d**3/13 - 5866*d**2/13 - 174*d + 452/13 = 0?
-1, 1/7, 226
What is a in a**2 + 67*a - 138 = 0?
-69, 2
Find u, given that -3*u**5/5 - 2*u**4/5 + 14*u**3/5 - 19*u/5 + 2 = 0.
-2, -5/3, 1
Factor -16*w**4 - 72*w**3 - 57*w**2 + 43*w - 6.
-(w + 2)*(w + 3)*(4*w - 1)**2
Find s, given that -4*s**5/13 - 10*s**4/13 + 50*s**3/13 - 10*s**2/13 - 46*s/13 + 20/13 = 0.
-5, -1, 1/2, 1, 2
Factor -2*h**2/5 - 174*h + 872/5.
-2*(h - 1)*(h + 436)/5
Solve 8*k**3/3 + 316*k**2/3 + 432*k + 420 = 0.
-35, -3, -3/2
Factor -l**2/7 + l/7 + 2/7.
-(l - 2)*(l + 1)/7
Solve -2*q**3/3 - 226*q**2/3 - 212*q/3 + 448 = 0 for q.
-112, -3, 2
Factor -f**4 + 5*f**3 + 22*f**2 + 16*f.
-f*(f - 8)*(f + 1)*(f + 2)
Let -36*s**3 - 496*s**2 - 1508*s + 360 = 0. Calculate s.
-9, -5, 2/9
Factor -2*v**2/19 + 2132*v/19 - 568178/19.
-2*(v - 533)**2/19
Factor -2*v**2/11 - 2*v/11 + 24/11.
-2*(v - 3)*(v + 4)/11
Factor 2*l*