-a**3 + 7*a**2/4 - a/2 - 1/4.
-(a - 1)**2*(4*a + 1)/4
Factor -a**5/9 + 5*a**4/9 - 7*a**3/9 + a**2/3.
-a**2*(a - 3)*(a - 1)**2/9
Determine a so that 3*a**5 + 699*a**4 + 39654*a**3 - 123900*a**2 + 83544*a = 0.
-118, 0, 1, 2
Determine c, given that c**4/2 + 2*c**3 - 13*c**2/2 - 2*c + 6 = 0.
-6, -1, 1, 2
Factor -5*g**4 + 185*g**3 - 1725*g**2 + 5895*g - 6750.
-5*(g - 25)*(g - 6)*(g - 3)**2
Suppose -w**4/4 + 18*w**3 - 71*w**2/4 = 0. What is w?
0, 1, 71
Let 76*z**3/7 - 144*z**2/7 - 16*z/7 = 0. Calculate z.
-2/19, 0, 2
Let p**4 - 150*p**3 + 7033*p**2 - 105600*p + 495616 = 0. What is p?
11, 64
Factor -3*r**4 - 45*r**3 - 171*r**2 + 105*r + 882.
-3*(r - 2)*(r + 3)*(r + 7)**2
Factor -4*r**4 + 428*r**3 - 10788*r**2 - 35420*r - 24200.
-4*(r - 55)**2*(r + 1)*(r + 2)
Factor 4*d**2 + 2056*d - 2060.
4*(d - 1)*(d + 515)
Suppose 2*m**2 - 784*m + 76832 = 0. Calculate m.
196
Factor 2*p**3 - 40*p**2 + 234*p - 324.
2*(p - 9)**2*(p - 2)
Factor z**2/4 - 35*z/4 + 33/2.
(z - 33)*(z - 2)/4
Let -3*y**2/5 + 36*y/5 - 108/5 = 0. Calculate y.
6
Factor 5*d**2 + 25*d - 630.
5*(d - 9)*(d + 14)
Solve 3*y**2 + 48*y + 192 = 0 for y.
-8
Factor -32*s**4/7 - 16*s**3 + 62*s**2/7 - 8*s/7.
-2*s*(s + 4)*(4*s - 1)**2/7
Determine l, given that -2*l**3/3 + 4*l**2/3 + 58*l/3 + 28 = 0.
-3, -2, 7
Find w, given that 3*w**5 - 3*w**4 - 18*w**3 = 0.
-2, 0, 3
Factor v**4/5 - 9*v**3/5.
v**3*(v - 9)/5
Let -9*l**4/2 - 11*l**3/2 - l**2 = 0. What is l?
-1, -2/9, 0
Suppose -r**4 + 35*r**3 + 804*r**2 + 4096*r + 3328 = 0. Calculate r.
-8, -1, 52
Factor 3*z**3 + 2142*z**2 - 6447*z + 4302.
3*(z - 2)*(z - 1)*(z + 717)
Factor 92*l**2 + 33*l - 14.
(4*l - 1)*(23*l + 14)
Determine j, given that j**2/3 + 29*j/3 - 114 = 0.
-38, 9
Factor 2*t**3/19 - 11496*t**2/19 + 22026336*t/19 - 14067486592/19.
2*(t - 1916)**3/19
Solve -2*j**5/11 + 16*j**4/11 - 32*j**3/11 + 4*j**2/11 + 34*j/11 - 20/11 = 0.
-1, 1, 2, 5
Factor j**5 + 7*j**4 + 18*j**3 + 22*j**2 + 13*j + 3.
(j + 1)**4*(j + 3)
Factor -5*a**5 + 85*a**4 - 575*a**3 + 1935*a**2 - 3240*a + 2160.
-5*(a - 4)**2*(a - 3)**3
Solve -5*i**3/2 + 26*i**2 - 145*i/2 + 25 = 0.
2/5, 5
Factor 12*v**3 + 4*v**2 - 76*v + 60.
4*(v - 1)*(v + 3)*(3*v - 5)
Factor -2*i**2/7 + 20*i/7 + 192/7.
-2*(i - 16)*(i + 6)/7
Suppose -4*p**2 - 176*p + 2420 = 0. Calculate p.
-55, 11
Find d, given that 3*d**3 - 177*d**2 - 390*d + 1464 = 0.
-4, 2, 61
Factor v**5/7 + 2*v**4/7 - 8*v**3/7.
v**3*(v - 2)*(v + 4)/7
Suppose 3*g**5 + 6*g**4 - 57*g**3 - 60*g**2 = 0. Calculate g.
-5, -1, 0, 4
Find p, given that -3*p**5 + 3*p**4 + 9*p**3 - 15*p**2 + 6*p = 0.
-2, 0, 1
Solve 2*p**2/9 + 136*p/3 + 134 = 0.
-201, -3
Factor j**2/4 - 23*j/2.
j*(j - 46)/4
Factor g**2 + 692*g + 691.
(g + 1)*(g + 691)
Factor y**4/7 + 2*y**3/7 - 179*y**2/7 - 180*y/7 + 8100/7.
(y - 9)**2*(y + 10)**2/7
Determine t, given that 2*t**2 - 46*t + 84 = 0.
2, 21
Find d, given that d**4/2 + 11*d**3/2 + 18*d**2 + 8*d - 32 = 0.
-4, 1
Solve -2*j**4/17 - 22*j**3/17 + 186*j**2/17 - 18*j = 0.
-17, 0, 3
Solve -3*s**4/4 + 21*s**3/4 - 39*s**2/4 - 9*s/4 + 27/2 = 0.
-1, 2, 3
Find d, given that -9*d**3/2 - 548*d**2 - 845*d/2 + 121 = 0.
-121, -1, 2/9
Factor 2*d**2/5 + 26*d/5.
2*d*(d + 13)/5
Suppose 4*o**4 + 16*o**3 - 64*o**2 - 64*o + 192 = 0. What is o?
-6, -2, 2
Factor -5*b**2/4 - 215*b.
-5*b*(b + 172)/4
Factor 24*j**2 + 8*j + 2/3.
2*(6*j + 1)**2/3
Determine r, given that r**2/2 + 522*r + 136242 = 0.
-522
Factor 4*u**4 - 156*u**3 - 492*u**2 - 500*u - 168.
4*(u - 42)*(u + 1)**3
Factor -26*f**2/11 + 23*f/11 + 3/11.
-(f - 1)*(26*f + 3)/11
Factor -25*v**4 - 665*v**3 + 270*v**2.
-5*v**2*(v + 27)*(5*v - 2)
Find q such that -3*q**4/4 - 9*q**3/2 - 6*q**2 = 0.
-4, -2, 0
Factor -b**3 - 22*b**2 + 175*b + 196.
-(b - 7)*(b + 1)*(b + 28)
Factor 3*h**3 + 18*h**2 - 27*h - 42.
3*(h - 2)*(h + 1)*(h + 7)
Determine g, given that -6*g**2/5 + 30*g + 324/5 = 0.
-2, 27
Find c, given that c**4/2 + 23*c**3 + 300*c**2 + 400*c - 8000 = 0.
-20, -10, 4
Solve -2*g**4/15 + 2*g**3/5 + 10*g**2/3 + 14*g/5 = 0.
-3, -1, 0, 7
Let -k**2 - 128*k - 732 = 0. Calculate k.
-122, -6
Suppose 16*k**5/5 - 4*k**4 - 464*k**3/5 - 1112*k**2/5 - 992*k/5 - 308/5 = 0. Calculate k.
-11/4, -1, 7
Factor -f**4/2 + 125*f**3 - 10458*f**2 + 296227*f - 571787/2.
-(f - 83)**3*(f - 1)/2
Find w such that 2*w**5 - 3050*w**4 = 0.
0, 1525
Factor -86*a**2/11 + 184*a/11 - 24/11.
-2*(a - 2)*(43*a - 6)/11
Find n, given that 2*n**3/11 + 26*n**2/11 - 28*n/11 = 0.
-14, 0, 1
What is w in -2*w**3/11 + 26*w**2/11 + 240*w/11 - 288 = 0?
-11, 12
Let q**2/2 + 18*q - 37/2 = 0. Calculate q.
-37, 1
Suppose b**3/5 + 9*b**2/5 + 26*b/5 + 24/5 = 0. Calculate b.
-4, -3, -2
Factor -3*r**2 - 5823*r/4 - 1455/4.
-3*(r + 485)*(4*r + 1)/4
Factor 3*c**2 + 201*c - 414.
3*(c - 2)*(c + 69)
Factor 4*t**4 - 24*t**3 + 48*t**2 - 32*t.
4*t*(t - 2)**3
Factor k**2/3 - 27*k - 82/3.
(k - 82)*(k + 1)/3
Factor -3*w**2/4 - 285*w/4.
-3*w*(w + 95)/4
Solve 841*j**2/4 - 174*j + 36 = 0.
12/29
Factor 2*w**5 + 16*w**4 - 2*w**3 - 16*w**2.
2*w**2*(w - 1)*(w + 1)*(w + 8)
Factor 2*a**4 - 32*a**3 + 144*a**2 - 256*a + 160.
2*(a - 10)*(a - 2)**3
Determine j so that j**3/10 - 3*j**2/10 - 23*j/5 - 36/5 = 0.
-4, -2, 9
What is i in i**2 + 81*i + 158 = 0?
-79, -2
Factor -465*o**3 + 170*o**2 - 5*o.
-5*o*(3*o - 1)*(31*o - 1)
Factor -t**3/4 - 3*t**2/4 + 10*t + 21.
-(t - 6)*(t + 2)*(t + 7)/4
Suppose 5*d**4 + 15*d**3 - 340*d**2 + 1020*d - 880 = 0. Calculate d.
-11, 2, 4
Factor t**4/2 - 51*t**3 + 2601*t**2/2.
t**2*(t - 51)**2/2
Factor -3*c**3 - 6819*c**2 - 3871485*c + 3878307.
-3*(c - 1)*(c + 1137)**2
Determine a so that 3*a**4 - 39*a**3 - 162*a**2 + 264*a + 384 = 0.
-4, -1, 2, 16
Factor -2*p**2 + 30*p - 28.
-2*(p - 14)*(p - 1)
Find o such that 3*o**5/5 + 24*o**4/5 - 30*o**3 - 1536*o**2/5 - 2541*o/5 - 1176/5 = 0.
-7, -1, 8
Factor s**5 - 17*s**3 - 36*s**2 - 20*s.
s*(s - 5)*(s + 1)*(s + 2)**2
Solve 4*m**5 - 32*m**4 + 48*m**3 + 8*m**2 - 52*m + 24 = 0 for m.
-1, 1, 6
Suppose r**2 - 166*r + 165 = 0. What is r?
1, 165
Factor -d**2/4 + 1253*d/2 - 1570009/4.
-(d - 1253)**2/4
Factor 2*r**2/3 - 28*r/3 - 64/3.
2*(r - 16)*(r + 2)/3
Solve x**5 + 10*x**4 - 23*x**3 - 240*x**2 + 576*x = 0.
-8, 0, 3
Let t**3/2 + 7*t**2/2 - t/2 - 7/2 = 0. Calculate t.
-7, -1, 1
Let -c**5/4 - c**4/4 + 5*c**3/4 + c**2/4 - 2*c + 1 = 0. What is c?
-2, 1
Factor 2*q**3/9 + 4*q**2/3 + 2*q/3 - 20/9.
2*(q - 1)*(q + 2)*(q + 5)/9
Suppose 2*q**4 + 24*q**3 + 42*q**2 + 20*q = 0. Calculate q.
-10, -1, 0
Find l, given that -5*l**4 - 35*l**3 + 95*l**2 + 35*l - 90 = 0.
-9, -1, 1, 2
Solve 2*w**3 + 1164*w**2 + 225816*w + 14602768 = 0.
-194
Find f, given that -4*f**5/7 - 40*f**4/7 - 144*f**3/7 - 216*f**2/7 - 108*f/7 = 0.
-3, -1, 0
Solve -4*y**3 + 50*y**2/3 - 44*y/3 + 2 = 0.
1/6, 1, 3
Find f, given that 2304*f**5 + 13952*f**4/3 + 9760*f**3/3 + 2768*f**2/3 + 97*f + 3/2 = 0.
-3/4, -1/4, -1/54
Solve 20*g**3 - 275*g**2 + 190*g + 65 = 0 for g.
-1/4, 1, 13
Factor -2*o**3/3 + 18*o - 36.
-2*(o - 3)**2*(o + 6)/3
What is c in -3*c**5 - 27*c**4 - 54*c**3 + 66*c**2 + 153*c - 135 = 0?
-5, -3, 1
Solve -4*f**4 + 720*f**3 - 1420*f**2 - 720*f + 1424 = 0.
-1, 1, 2, 178
Let x**5 + 13*x**4 - 3*x**3 - 37*x**2 + 26*x = 0. Calculate x.
-13, -2, 0, 1
Suppose -12*n**3 - 111*n**2 + 93*n + 30 = 0. Calculate n.
-10, -1/4, 1
Find u such that 2*u**5/23 + 40*u**4/23 - 348*u**3/23 + 792*u**2/23 - 486*u/23 = 0.
-27, 0, 1, 3
Factor m**2/4 + 3*m/4 - 189/2.
(m - 18)*(m + 21)/4
Solve 4*n**5/7 + 110*n**4/7 + 250*n**3/7 - 10*n**2/7 - 254*n/7 - 100/7 = 0 for n.
-25, -2, -1, -1/2, 1
Factor 5*p**2 + 390*p + 385.
5*(p + 1)*(p + 77)
What is u in -955*u**2/2 + 15*u/2 = 0?
0, 3/191
Factor 2*v**3 + 240*v**2 - 1496*v + 2016.
2*(v - 4)*(v - 2)*(v + 126)
Factor 21*z**3 + 211*z**2 + 498*z - 160.
(z + 5)*(3*z + 16)*(7*z - 2)
Factor 4*r**2 - 16*r + 16.
4*(r - 2)**2
Factor 3*v**5 + 69*v**4 + 429*v**3 + 363*v**2.
3*v**2*(v + 1)*(v + 11)**2
Factor -v**2 + 533*v + 534.
-(v - 534)*(v + 1)
Suppose b**2/4 + 418*b - 1673/4 = 0. What is b?
-1673, 1
Find w, given that w**3/7 - 12*w/7 + 16/7 = 0.
-4, 2
Suppose 9*m**4 - 1032*m**3 - 350*m**2 + 576*m - 115 = 0. Calculate m.
-1, 1/3, 115
Suppose 27*p**3/5 - 144*p**2/5 - 21*p - 18/5 = 0. Calculate p.
-1/3, 6
Factor -2*q**4/11 - 598*q**3/11 + 600*q**2/11.
-2*q**2*(q - 1)*(q + 300)/11
Factor 4*m**5 - 44*m**4 + 108*m**3 - 100*m**2 + 32*m.
4*m*(m - 8)*(m - 1)**3
Factor -5*w**2 - 2