2
Factor 5*a**3/2 + 125*a**2 - 535*a/2 - 390.
5*(a - 3)*(a + 1)*(a + 52)/2
Suppose -q**3 + 281*q**2 - 19880*q + 19600 = 0. Calculate q.
1, 140
Factor 5*h**4 + 230*h**3 + 1585*h**2 + 2500*h + 1140.
5*(h + 1)**2*(h + 6)*(h + 38)
Determine b, given that b**2 + 168*b + 7056 = 0.
-84
Determine u so that -12*u**3/5 + 22*u**2/5 + 12*u/5 - 22/5 = 0.
-1, 1, 11/6
Factor -2*n**4/5 + 278*n**3/5 + 2044*n**2/5.
-2*n**2*(n - 146)*(n + 7)/5
Let -81*h**5/2 + 25515*h**4/2 - 1011015*h**3 + 1002525*h**2 - 666465*h/2 + 73947/2 = 0. Calculate h.
1/3, 157
Solve -2*x**3/13 - 620*x**2/13 - 55096*x/13 - 80656 = 0 for x.
-142, -26
Solve -12*u**2 + 16*u + 16 = 0.
-2/3, 2
Let k**2 - 56*k + 159 = 0. Calculate k.
3, 53
Factor -2*n**4 + 12*n**3 + 96*n**2 + 148*n + 66.
-2*(n - 11)*(n + 1)**2*(n + 3)
Solve -2*g**5/7 + 52*g**4/7 - 146*g**3/7 - 2504*g**2/7 - 4352*g/7 - 2048/7 = 0.
-4, -1, 16
Factor -51809805*x**2 + 64380*x - 20.
-5*(3219*x - 2)**2
Suppose -5*h**3/2 + 3*h**2 + 18*h - 28 = 0. Calculate h.
-14/5, 2
Solve -99*b**5 - 229*b**4 + 233*b**3 + 89*b**2 + 6*b = 0 for b.
-3, -2/9, -1/11, 0, 1
What is a in 2*a**2/11 + 804*a/11 + 80802/11 = 0?
-201
Factor v**2 - 37*v.
v*(v - 37)
Let 50*y**5 - 40*y**4 - 46*y**3 + 76*y**2/5 + 88*y/5 + 16/5 = 0. What is y?
-2/5, 1
Let 512*l**4/5 - 192*l**2/5 + 64*l/5 - 6/5 = 0. What is l?
-3/4, 1/4
Let 3*y**4 + 24*y**3 + 45*y**2 - 24*y - 48 = 0. Calculate y.
-4, -1, 1
Determine k so that -5*k**2 - 135*k = 0.
-27, 0
What is h in 4*h**4 + 76*h**3 + 132*h**2 - 76*h - 136 = 0?
-17, -2, -1, 1
Determine z so that -4*z**2/9 - 140*z/3 + 424/9 = 0.
-106, 1
Factor h**2/3 - 106*h/3 - 109.
(h - 109)*(h + 3)/3
Determine d, given that d**5 + 3*d**4/2 - 17*d**3/2 - 27*d**2/2 - 9*d/2 = 0.
-3, -1, -1/2, 0, 3
Determine o so that -5*o**3 + 55*o**2 + 90*o - 360 = 0.
-3, 2, 12
Determine z, given that 5*z**3 - 25*z**2 + 40*z - 20 = 0.
1, 2
Let 2*f**5 - 148*f**4 + 1094*f**3 - 2532*f**2 + 1584*f = 0. Calculate f.
0, 1, 3, 4, 66
Suppose 3*s**3 - 69*s**2 - 507*s - 435 = 0. What is s?
-5, -1, 29
Let 2*t**2/3 - 2*t = 0. What is t?
0, 3
Factor t**2 - 2564*t + 1643524.
(t - 1282)**2
Suppose -29380*s**2 - 7285*s + 15 = 0. What is s?
-1/4, 3/1469
Let -2*n**2/5 + 2906*n/5 + 2908/5 = 0. What is n?
-1, 1454
Factor -2*h**3 - 34*h**2/5 + 28*h/5 + 16/5.
-2*(h - 1)*(h + 4)*(5*h + 2)/5
Find b such that -555*b**2/7 + 549*b/7 + 6/7 = 0.
-2/185, 1
Factor 19*z**2/9 + 98*z/9 + 5/3.
(z + 5)*(19*z + 3)/9
Let -3*q**3/7 - 1221*q**2/7 - 1212*q/7 + 348 = 0. What is q?
-406, -2, 1
Solve 4*v**3 + 44*v**2 + 124*v + 84 = 0 for v.
-7, -3, -1
Factor -4*l**3/3 + 1428*l**2 - 2852*l + 4276/3.
-4*(l - 1069)*(l - 1)**2/3
Factor -9*x**3/5 + 51*x**2/5 - 15*x + 33/5.
-3*(x - 1)**2*(3*x - 11)/5
Factor 5*p**5 - 105*p**4 - 125*p**3 + 305*p**2 + 540*p + 220.
5*(p - 22)*(p - 2)*(p + 1)**3
Factor 2*s**3/23 + 108*s**2/23 + 1080*s/23 - 10800/23.
2*(s - 6)*(s + 30)**2/23
Solve 2*v**2/11 - 48*v/11 + 8 = 0.
2, 22
Suppose -5*v**2 - 5560*v - 5555 = 0. What is v?
-1111, -1
Factor j**2/7 + 18*j/7 + 65/7.
(j + 5)*(j + 13)/7
Find o, given that -2*o**3 + 256*o**2 - 7930*o - 16900 = 0.
-2, 65
Factor -4*q**3 - 284*q**2 - 2044*q - 1764.
-4*(q + 1)*(q + 7)*(q + 63)
Factor -c**2 - 632*c - 99856.
-(c + 316)**2
Let -2*o**5/21 - 40*o**4/21 - 44*o**3/3 - 160*o**2/3 - 1850*o/21 - 1000/21 = 0. What is o?
-5, -4, -1
Let -i**5/6 - i**4/2 + 11*i**3/6 + 9*i**2/2 - 5*i/3 - 4 = 0. What is i?
-4, -2, -1, 1, 3
Find y, given that y**5 + 10*y**4 - 12*y**3 - 10*y**2 + 11*y = 0.
-11, -1, 0, 1
Factor 3*j**2 + 48*j + 117.
3*(j + 3)*(j + 13)
Factor 2*q**2 - 6*q - 836.
2*(q - 22)*(q + 19)
What is b in -b**3/7 + 10*b**2/7 - 32*b/7 + 32/7 = 0?
2, 4
Suppose 11*w**2 + 53*w + 36 = 0. Calculate w.
-4, -9/11
Factor -5*x**3 - 265*x**2 - 3555*x - 14175.
-5*(x + 9)**2*(x + 35)
What is l in -6*l**2/11 + 282*l/11 - 276/11 = 0?
1, 46
Factor 2*y**3 - 4*y**2 - 22*y + 24.
2*(y - 4)*(y - 1)*(y + 3)
Factor -2*v**3/7 + 144*v**2/7 - 282*v/7 + 20.
-2*(v - 70)*(v - 1)**2/7
Determine b so that -3*b**5 + 273*b**4 - 525*b**3 - 825*b**2 + 2148*b - 1068 = 0.
-2, 1, 2, 89
Determine r so that -3*r**3 - 54*r**2 - 288*r - 480 = 0.
-10, -4
Factor b**5/2 - 9*b**4/2 + 15*b**3 - 22*b**2 + 12*b.
b*(b - 3)*(b - 2)**3/2
Solve -i**4/4 - 85*i**3/4 + 22*i**2 + 43*i = 0 for i.
-86, -1, 0, 2
Let -3*d**3/5 - 42*d**2/5 + 528*d/5 = 0. What is d?
-22, 0, 8
Factor 12*g**4 - 36*g**3 + 15*g**2 + 36*g - 27.
3*(g - 1)*(g + 1)*(2*g - 3)**2
Factor -t**3/5 + 48*t**2/5 - 576*t/5.
-t*(t - 24)**2/5
Factor 3*p**4/8 - 21*p**3/8 + 9*p**2/2.
3*p**2*(p - 4)*(p - 3)/8
Factor -64*m**5 + 5472*m**4 - 2724*m**3 + 340*m**2.
-4*m**2*(m - 85)*(4*m - 1)**2
Let -q**2/3 + 14*q/3 - 13/3 = 0. Calculate q.
1, 13
Find x, given that 2*x**2 - 84*x - 368 = 0.
-4, 46
Solve 3*h**3 + 147*h**2 + 1725*h - 1875 = 0.
-25, 1
Let 3*b**3/5 - 3*b**2/5 - 12*b/5 + 12/5 = 0. What is b?
-2, 1, 2
Factor 2*m**3/9 - 14*m**2/3.
2*m**2*(m - 21)/9
Suppose 115*i**3 + 90*i**2 - 25*i = 0. What is i?
-1, 0, 5/23
Suppose 27*q**3 + 21*q**2 - 60*q + 12 = 0. Calculate q.
-2, 2/9, 1
Factor -5*h**3 - 20*h**2 + 55*h - 30.
-5*(h - 1)**2*(h + 6)
Factor 4*m**2 + 912*m - 916.
4*(m - 1)*(m + 229)
Let -5968*a**3 + 26824*a**2 - 30069*a - 162 = 0. What is a?
-2/373, 9/4
Determine q, given that -5*q**3 - 7290*q**2 + 14595*q - 7300 = 0.
-1460, 1
Factor 3*q**4 - 51*q**3 - 309*q**2 - 453*q - 198.
3*(q - 22)*(q + 1)**2*(q + 3)
Determine d, given that -5*d**3 - 25*d**2 - 40*d - 20 = 0.
-2, -1
Find b such that -b**4 + 11*b**3 + 14*b**2 - 24*b = 0.
-2, 0, 1, 12
Factor -2*r**2/5 + 62*r/5 - 116/5.
-2*(r - 29)*(r - 2)/5
Factor -2*z**2 + 12294*z.
-2*z*(z - 6147)
Suppose q**2/4 - 5*q/2 + 9/4 = 0. What is q?
1, 9
Suppose -6*k**4/5 - 2*k**3/5 + 34*k**2/5 + 2*k/5 - 28/5 = 0. What is k?
-7/3, -1, 1, 2
Find v, given that 2*v**2 + 2*v = 0.
-1, 0
Determine t, given that -7*t**4/6 + 13*t**3/3 + t**2/6 - 22*t/3 - 2 = 0.
-1, -2/7, 2, 3
Determine h so that 4*h**3/5 - 233*h**2/5 + 3422*h/5 - 841/5 = 0.
1/4, 29
Factor -2*a**3 + 8*a**2 + 10*a.
-2*a*(a - 5)*(a + 1)
Determine y, given that 8*y**2/7 + 2942*y/7 - 736/7 = 0.
-368, 1/4
Factor 4*g**2/5 - 808*g/5 + 40804/5.
4*(g - 101)**2/5
Factor -25*f**2 + 740*f - 5476.
-(5*f - 74)**2
Factor h**4/6 + 77*h**3/6 - 79*h**2/6 - 77*h/6 + 13.
(h - 1)**2*(h + 1)*(h + 78)/6
Determine t so that 3*t**4 - 321*t**3 + 294*t**2 + 2580*t - 3816 = 0.
-3, 2, 106
Factor a**3 - 36*a**2 + 69*a - 34.
(a - 34)*(a - 1)**2
Solve -s**4 - 405*s**3 = 0 for s.
-405, 0
What is d in 33*d**5 - 333*d**4 + 405*d**3 + 1941*d**2 + 1170*d = 0?
-1, 0, 5, 78/11
Let -4*i**4 - 208*i**3 + 216*i**2 + 208*i - 212 = 0. Calculate i.
-53, -1, 1
Determine w so that w**2/2 - 10*w + 19/2 = 0.
1, 19
Solve -n**3/8 + n**2/4 = 0 for n.
0, 2
Factor -5*v**3/4 + 845*v**2/4 - 9030*v + 8820.
-5*(v - 84)**2*(v - 1)/4
Determine v so that -v**2/4 + 19*v/4 - 15 = 0.
4, 15
Solve -10*q**5 + 35*q**4/3 + 305*q**3/3 + 60*q**2 - 140*q/3 - 80/3 = 0.
-2, -1, -1/2, 2/3, 4
Suppose 4*c**5 - 20*c**4 - 232*c**3 - 352*c**2 = 0. What is c?
-4, -2, 0, 11
Determine n so that n**3 + 30*n**2 - 117*n - 594 = 0.
-33, -3, 6
Factor -2*z**3/13 - 160*z**2/13 - 3496*z/13 - 11552/13.
-2*(z + 4)*(z + 38)**2/13
Find m such that -m**2/6 - 19*m/6 - 3 = 0.
-18, -1
Factor -4*d**3/7 - 40*d**2/7 - 48*d/7 + 288/7.
-4*(d - 2)*(d + 6)**2/7
Suppose 3*c**3 - 4692*c**2 = 0. What is c?
0, 1564
Let -5*y**2 + 100*y = 0. What is y?
0, 20
Factor 3*t**2/7 + 549*t/7 - 552/7.
3*(t - 1)*(t + 184)/7
Factor b**4/7 + 2*b**3 + 25*b**2/7 + 12*b/7.
b*(b + 1)**2*(b + 12)/7
Factor -4*m**2/7 - 172*m/7 - 160.
-4*(m + 8)*(m + 35)/7
Let -2*x**4 - 282*x**3 + 286*x**2 + 282*x - 284 = 0. What is x?
-142, -1, 1
Find i, given that 91875*i**3 - 90825*i**2 - 1047*i - 3 = 0.
-1/175, 1
Factor -3*a**3/2 + 12525*a**2/2 - 6533352*a - 6539616.
-3*(a - 2088)**2*(a + 1)/2
Factor 27*x**2/7 - 60*x/7 + 12/7.
3*(x - 2)*(9*x - 2)/7
Find f, given that -f**2/3 + 3*f - 14/3 = 0.
2, 7
Suppose p**4/8 - 13*p**3/8 + 9*p**2/4 + 20*p + 16 = 0. Calculate p.
-2, -1, 8
Solve 3*u**2 - 921*u - 3732 = 0.
-4, 311
Factor 3*f**4 - 22830*f**3 + 43456899*f**2 - 86845320*f + 43411248.
3*(f - 3804)**2*(f - 1)**2
Find g, given that 3*g**2/2 + 414*g + 825/2 = 0.
-275, -1
Factor 3*z**5 - 18*z**4 - 45*z**3 + 348*z**2 + 144*z - 1728.
3*(z - 4)**3*(z + 3)**2
Determine k, given that 14*k**5/9 - 34*k**4/3 + 224*k**3/9 - 