uch that -35*j**5 - 4085*j**4 + 13665*j**3 - 16135*j**2 + 7790*j - 1200 = 0.
-120, 2/7, 1
Factor 2*t**4/11 + 74*t**3/11 + 936*t**2/11 + 4320*t/11 + 3456/11.
2*(t + 1)*(t + 12)**3/11
Let 3*b**2 - 219*b = 0. Calculate b.
0, 73
Factor 5*f**2 - 600*f.
5*f*(f - 120)
Factor j**5 + 7*j**4 + 18*j**3 + 22*j**2 + 13*j + 3.
(j + 1)**4*(j + 3)
Factor -6*k**3 + 152*k**2 - 50*k.
-2*k*(k - 25)*(3*k - 1)
Solve w**5/2 + 3*w**4 + w**3/2 - 12*w**2 + 8*w = 0 for w.
-4, 0, 1
Factor -2*b**2/7 + 88*b/7 + 384/7.
-2*(b - 48)*(b + 4)/7
Factor -o**4 - 22*o**3/3 - 20*o**2/3 + 8*o.
-o*(o + 2)*(o + 6)*(3*o - 2)/3
Suppose 35*a**3/3 + 25*a**2/3 - 10*a/3 = 0. What is a?
-1, 0, 2/7
Solve -324*z**5/7 + 2448*z**4/7 + 7292*z**3/7 + 872*z**2 + 1744*z/7 + 160/7 = 0 for z.
-1, -2/9, 10
Factor -2*v**3 - 1660*v**2 - 16450*v - 41000.
-2*(v + 5)**2*(v + 820)
Determine k so that 4*k**3/7 - 244*k**2/7 = 0.
0, 61
Determine n, given that 3*n**3/8 - 3*n**2/2 - 15*n/8 = 0.
-1, 0, 5
Factor d**3/4 + 14*d**2 - 363*d/4 + 279/2.
(d - 3)**2*(d + 62)/4
Suppose -2304*s**4 - 4416*s**3 + 7292*s**2 - 584*s + 12 = 0. Calculate s.
-3, 1/24, 1
Suppose -27*x**5/4 - 357*x**4/4 - 330*x**3 - 150*x**2 + 468*x + 108 = 0. Calculate x.
-6, -2, -2/9, 1
Solve -v**3/4 - 57*v**2/4 - 651*v/4 + 4805/4 = 0 for v.
-31, 5
Suppose -2*b**5/17 - 94*b**4/17 - 432*b**3/17 - 496*b**2/17 + 352*b/17 + 672/17 = 0. What is b?
-42, -2, 1
Factor -2*i**3/9 + 28*i**2/9 - 70*i/9 + 44/9.
-2*(i - 11)*(i - 2)*(i - 1)/9
Factor -2*t**5/3 + 10*t**4/3 - 16*t**3/3 + 8*t**2/3.
-2*t**2*(t - 2)**2*(t - 1)/3
Factor 6*n**2/5 + 5772*n + 6940830.
6*(n + 2405)**2/5
Factor -2*l**3/3 - 4*l**2 + 6*l + 28/3.
-2*(l - 2)*(l + 1)*(l + 7)/3
Find x, given that x**3/3 + 1018*x**2/3 + 2033*x/3 + 1016/3 = 0.
-1016, -1
Factor -2*n**5 + 24*n**4 + 120*n**3 + 128*n**2.
-2*n**2*(n - 16)*(n + 2)**2
Factor 5*d**2 + 50*d + 105.
5*(d + 3)*(d + 7)
Factor -2*h**2/9 + 4*h.
-2*h*(h - 18)/9
What is w in 3*w**2/5 + 2106*w/5 + 369603/5 = 0?
-351
Solve -h**4/2 + 77*h**3/2 + 159*h**2/2 - 77*h/2 - 79 = 0.
-2, -1, 1, 79
Suppose f**4 - 156*f**3 - 802*f**2 - 492*f + 1449 = 0. What is f?
-3, 1, 161
Suppose -2*v**4 + 12*v**3 - 18*v**2 = 0. Calculate v.
0, 3
Factor 2*a**2/7 - 2/7.
2*(a - 1)*(a + 1)/7
Solve -7*i**3/2 - 6*i**2 + 7*i/2 + 6 = 0.
-12/7, -1, 1
Factor -t**3/4 - 2*t**2 - 17*t/4 - 5/2.
-(t + 1)*(t + 2)*(t + 5)/4
Factor -6*l**3 - 20*l**2 - 8*l + 16.
-2*(l + 2)**2*(3*l - 2)
Suppose 5*s**2 - 32980*s + 54384020 = 0. What is s?
3298
Factor i**2/2 + 15*i + 100.
(i + 10)*(i + 20)/2
Factor 3*l**2/4 - 633*l/2 - 3825/4.
3*(l - 425)*(l + 3)/4
Solve -2*o**5/11 + 14*o**4/11 - 14*o**3/11 - 38*o**2/11 + 32*o/11 + 40/11 = 0 for o.
-1, 2, 5
Factor -2*x**4/11 - 16*x**3/11.
-2*x**3*(x + 8)/11
Factor 752*b**2 + 60*b - 32.
4*(4*b + 1)*(47*b - 8)
Factor 5*w**2 - 555*w - 560.
5*(w - 112)*(w + 1)
Determine n so that 2*n**3 + 164*n**2/7 + 442*n/7 - 20 = 0.
-7, -5, 2/7
What is m in 4*m**4 + 6*m**3 - 32*m**2 + 30*m - 8 = 0?
-4, 1/2, 1
Factor 3*n**3 - 84*n**2 + 147*n + 234.
3*(n - 26)*(n - 3)*(n + 1)
Factor 5*i**3 + 765*i**2 - 1565*i - 2325.
5*(i - 3)*(i + 1)*(i + 155)
Let 2*m**5/11 - 2*m**4/11 - 100*m**3/11 + 100*m**2/11 + 98*m/11 - 98/11 = 0. Calculate m.
-7, -1, 1, 7
Suppose 5*l**2/3 + 160*l/3 - 55 = 0. What is l?
-33, 1
Factor -3*l**4 - 126*l**3 + 537*l**2 - 684*l + 276.
-3*(l - 2)*(l - 1)**2*(l + 46)
Factor 2*d**5/5 - 12*d**3/5 - 16*d**2/5 - 6*d/5.
2*d*(d - 3)*(d + 1)**3/5
Factor 5*r**5 - 30*r**4 - 90*r**3 + 1080*r**2 - 2835*r + 2430.
5*(r - 3)**4*(r + 6)
Find o such that 2*o**2/9 - 172*o/3 + 514/9 = 0.
1, 257
Suppose 24*r**3 + 3150*r**2 + 6291*r/8 + 393/8 = 0. What is r?
-131, -1/8
Factor o**2/7 - 1/7.
(o - 1)*(o + 1)/7
Determine t, given that 12*t**5 - 8*t**4 - 116*t**3/3 - 8*t**2/3 + 80*t/3 + 32/3 = 0.
-1, -2/3, 1, 2
Find r, given that 3*r**5/5 + 12*r**4/5 + 18*r**3/5 + 12*r**2/5 + 3*r/5 = 0.
-1, 0
Determine f so that -5*f**3 + 105*f**2 - 735*f + 1715 = 0.
7
Let 2*q**4/9 + 2*q**3/3 - 2*q**2/3 - 22*q/9 - 4/3 = 0. Calculate q.
-3, -1, 2
Let 3*q**2 + 30*q - 225 = 0. What is q?
-15, 5
Solve 3*t**3 + 16*t**2 + 12*t - 16 = 0 for t.
-4, -2, 2/3
Suppose 3*r**4/7 + 48*r**3/7 + 258*r**2/7 + 528*r/7 + 45 = 0. Calculate r.
-7, -5, -3, -1
Let b**2 - 70*b + 1225 = 0. Calculate b.
35
Factor 5*y**2/2 - 2680*y + 718240.
5*(y - 536)**2/2
Let -3*s**4 - 114*s**3 - 324*s**2 - 318*s - 105 = 0. Calculate s.
-35, -1
Suppose u**5 - u**4 - 9*u**3 + 13*u**2 + 8*u - 12 = 0. Calculate u.
-3, -1, 1, 2
Let 5*i**5 - 10*i**4 - 20*i**3 + 10*i**2 + 15*i = 0. What is i?
-1, 0, 1, 3
Factor -c**4/6 - c**3 - 3*c**2/2 + 2*c/3 + 2.
-(c - 1)*(c + 2)**2*(c + 3)/6
Suppose 36*b**3 + 172*b**2 - 40*b = 0. Calculate b.
-5, 0, 2/9
Suppose g**2 + 613*g = 0. What is g?
-613, 0
Find i such that -5*i**5 - 35*i**4 - 90*i**3 - 100*i**2 - 40*i = 0.
-2, -1, 0
Suppose 5*c**2 - 3570*c - 3575 = 0. Calculate c.
-1, 715
Factor -5*s**2 - 740*s.
-5*s*(s + 148)
Factor -2*w**4 - 20*w**3 - 64*w**2 - 76*w - 30.
-2*(w + 1)**2*(w + 3)*(w + 5)
Let 5*s**4 + 15*s**3 - 545*s**2 - 15*s + 540 = 0. Calculate s.
-12, -1, 1, 9
Solve -2*y**3/9 - 454*y**2/9 - 4390*y/9 - 10850/9 = 0.
-217, -5
Factor -2*p**2/7 - 536*p/7.
-2*p*(p + 268)/7
Find y, given that -4*y**4 - 124*y**3 + 132*y**2 + 124*y - 128 = 0.
-32, -1, 1
Factor -15*r**2 - 6950*r + 4640.
-5*(r + 464)*(3*r - 2)
Let 3*m**2 - 123*m + 120 = 0. Calculate m.
1, 40
Factor -2*i**2 - 20*i - 18.
-2*(i + 1)*(i + 9)
Let 2*h**3 - 15*h**2/2 + 4*h + 3/2 = 0. What is h?
-1/4, 1, 3
Let 2*g**2/3 + 56*g/3 - 58/3 = 0. What is g?
-29, 1
Factor -v**2 + 20*v - 64.
-(v - 16)*(v - 4)
Factor -5*l**2 + 470*l + 475.
-5*(l - 95)*(l + 1)
What is u in 4*u**2 + 1376*u + 17212 = 0?
-331, -13
Let 2*c**3/9 + 10*c**2/9 + 4*c/3 = 0. Calculate c.
-3, -2, 0
Suppose 4*p**5/5 - 32*p**4/5 - 96*p**3/5 + 152*p**2/5 + 92*p/5 - 24 = 0. Calculate p.
-3, -1, 1, 10
Let 2*b**5/11 - 314*b**4/11 + 614*b**3/11 + 938*b**2/11 - 112*b - 1240/11 = 0. What is b?
-1, 2, 155
Find g such that -2*g**4 - 18*g**3 - 28*g**2 + 48*g = 0.
-6, -4, 0, 1
Factor 2*k**3/3 + 228*k**2 + 25992*k + 987696.
2*(k + 114)**3/3
Find y, given that -y**4/6 + 5*y**3/2 - 14*y**2 + 104*y/3 - 32 = 0.
3, 4
Let 4*u**3/5 - 57*u**2 + 2087*u/5 - 504/5 = 0. What is u?
1/4, 8, 63
Factor -2*f**3/11 - 11820*f**2/11 - 23285400*f/11 - 15290746000/11.
-2*(f + 1970)**3/11
Factor -n**3/5 - 2*n**2/5 + 7*n/5 - 4/5.
-(n - 1)**2*(n + 4)/5
Factor 5*z**3 - 230*z**2 - 475*z - 240.
5*(z - 48)*(z + 1)**2
Let -2*i**2/5 + 89*i + 223/5 = 0. Calculate i.
-1/2, 223
Suppose 3*w**4 + 42*w**3 - 399*w**2 + 858*w - 504 = 0. Calculate w.
-21, 1, 2, 4
Suppose 2*b**3 + 85*b**2/2 + 88*b + 95/2 = 0. What is b?
-19, -5/4, -1
Factor m**4 + 7*m**3 + 15*m**2 + 9*m.
m*(m + 1)*(m + 3)**2
Factor -5*y**3 + 25*y**2 + 110*y + 80.
-5*(y - 8)*(y + 1)*(y + 2)
Factor 3*o**2 - 465*o + 9750.
3*(o - 130)*(o - 25)
Factor -2*a**3/7 + 16*a**2/7 + 86*a/7 - 220/7.
-2*(a - 11)*(a - 2)*(a + 5)/7
Factor 2*o**4/5 + 8*o**3/5 - 12*o**2/5 - 72*o/5 - 54/5.
2*(o - 3)*(o + 1)*(o + 3)**2/5
Factor 5*m**2 - 995*m + 990.
5*(m - 198)*(m - 1)
Factor -y**4/3 + 32*y**3/3 - 139*y**2/3 + 36*y.
-y*(y - 27)*(y - 4)*(y - 1)/3
Find t, given that 14*t**2 - 18*t - 20 = 0.
-5/7, 2
Factor 2*k**3 + 30*k**2 + 100*k.
2*k*(k + 5)*(k + 10)
Factor 4*p**2/7 - 2888*p/7 + 521284/7.
4*(p - 361)**2/7
Determine p, given that p**4/4 - 19*p**3/4 + 17*p**2/4 + 19*p/4 - 9/2 = 0.
-1, 1, 18
Determine i so that -2*i**4/7 - 18*i**3/7 + 46*i**2/7 + 18*i/7 - 44/7 = 0.
-11, -1, 1, 2
Suppose p**4 + 12*p**3 + 7*p**2 - 48*p - 44 = 0. What is p?
-11, -2, -1, 2
Suppose d**5/7 + 4*d**4/7 - 12*d**3/7 - 34*d**2/7 + 11*d/7 + 30/7 = 0. Calculate d.
-5, -2, -1, 1, 3
Solve 4*z**4 - 1596*z**3 + 4752*z**2 + 16*z - 6336 = 0 for z.
-1, 2, 396
Factor 5*x**5 - 15*x**4 + 20*x**2.
5*x**2*(x - 2)**2*(x + 1)
Factor -g**3 + 1717*g**2 + 3437*g + 1719.
-(g - 1719)*(g + 1)**2
Suppose -4*l**2 - 456*l - 12996 = 0. What is l?
-57
Determine g so that -g**2 + 114*g = 0.
0, 114
Let 2*k**4 - 2072*k**3 + 540776*k**2 - 2138304*k + 2130048 = 0. Calculate k.
2, 516
Factor -h**2/3 + 16*h/3 - 20.
-(h - 10)*(h - 6)/3
Suppose -2*g**4/9 + 242*g**3/9 - 104*g**2 = 0. What is g?
0, 4, 117
Determine a so that 3*a**3 - 6*a**2 - 15*a + 18 = 0.
-2, 1, 3
Factor -i**2/3 + 988*i/3 + 989/3.
-(i - 989)*(i + 1)/3
Find q such that -2*q**2 + 6586*q = 0.
0, 3293
Factor 