)
Factor -a**2 - 22*a - 72.
-(a + 4)*(a + 18)
What is h in -22*h**2/5 + 468*h/5 - 112 = 0?
14/11, 20
What is c in 3*c**2/2 + 186*c + 5766 = 0?
-62
Factor m**4 + 86*m**3 + 1932*m**2 + 3528*m.
m*(m + 2)*(m + 42)**2
Let 138*p**2 + 333*p - 30 = 0. What is p?
-5/2, 2/23
Determine l, given that -18*l**4/7 - 15*l**3/7 + 3*l**2 + 15*l/7 - 3/7 = 0.
-1, 1/6, 1
Factor 4*k**2 - 892*k.
4*k*(k - 223)
What is p in -3*p**4 - 101*p**3 + 270*p**2 + 656*p + 288 = 0?
-36, -1, -2/3, 4
Suppose -2*r**3/5 + 258*r**2/5 - 508*r/5 = 0. Calculate r.
0, 2, 127
Factor -2*c**3/15 - 86*c**2/15 + 3584*c/15 - 27832/15.
-2*(c - 14)**2*(c + 71)/15
Factor -2*c**4/15 - 14*c**3/15 - 2*c**2 - 6*c/5.
-2*c*(c + 1)*(c + 3)**2/15
Determine u so that 4*u**4/7 + 24*u**3/7 - 16*u**2 - 24*u/7 + 108/7 = 0.
-9, -1, 1, 3
Solve -5*a**5 + 8*a**4 + 9*a**3 - 8*a**2 - 4*a = 0.
-1, -2/5, 0, 1, 2
Find o such that 5*o**3/2 - 16635*o**2/2 + 6913920*o + 6922240 = 0.
-1, 1664
Factor 2*t**2/19 + 2556*t/19 - 2558/19.
2*(t - 1)*(t + 1279)/19
Determine t so that 3*t**4 + 39*t**3 + 141*t**2 + 105*t = 0.
-7, -5, -1, 0
Factor -k**2/4 + 2610*k - 6812100.
-(k - 5220)**2/4
Factor a**2/6 + 3*a/2 + 3.
(a + 3)*(a + 6)/6
Find s, given that -2*s**5/7 - 8*s**4/7 + 6*s**3 + 200*s**2/7 + 200*s/7 = 0.
-5, -2, 0, 5
Suppose -j**2 - 13*j - 12 = 0. Calculate j.
-12, -1
Find z such that -4*z**4/3 + 56*z**3/3 - 140*z**2/3 + 88*z/3 = 0.
0, 1, 2, 11
What is t in -3*t**5/5 + 48*t**4/5 - 15*t**3 - 126*t**2/5 = 0?
-1, 0, 3, 14
Suppose 5*f**4 - 10*f**3 - 55*f**2 + 60*f + 180 = 0. Calculate f.
-2, 3
Determine y so that -y**4 - y**3 + 8*y**2 + 12*y = 0.
-2, 0, 3
Factor -k**4 + 15*k**3 - 23*k**2 - 39*k.
-k*(k - 13)*(k - 3)*(k + 1)
Find n such that -4*n**3/3 + 8*n**2/3 + 32*n = 0.
-4, 0, 6
Factor 119*j**3/2 + 733*j**2/4 + 43*j/4 - 21/2.
(j + 3)*(7*j + 2)*(34*j - 7)/4
Suppose 12*v**5 - 93*v**4 + 228*v**3 - 153*v**2 - 54*v = 0. What is v?
-1/4, 0, 2, 3
Factor 4*b**2 - 5680*b + 2016400.
4*(b - 710)**2
Suppose -2*f**2/17 + 260*f/17 + 1072/17 = 0. What is f?
-4, 134
Let -3*z**2 + 408*z - 13872 = 0. What is z?
68
Suppose 4*q**2 + 2080*q + 270400 = 0. What is q?
-260
Factor 4*s**2 + 616*s - 1248.
4*(s - 2)*(s + 156)
Let 2*v**4/9 - 14*v**3/9 + 4*v**2 - 40*v/9 + 16/9 = 0. What is v?
1, 2
Factor -m**4/2 + 11*m**3/2 - 33*m**2/2 + 37*m/2 - 7.
-(m - 7)*(m - 2)*(m - 1)**2/2
Determine m, given that 3*m**2 + 549*m = 0.
-183, 0
Find r such that 3*r**5 - 45*r**4 - 54*r**3 + 96*r**2 = 0.
-2, 0, 1, 16
What is m in 11*m**2 + 123*m + 22 = 0?
-11, -2/11
Factor -2*o**2 - 9172*o - 10515698.
-2*(o + 2293)**2
Factor -2*d**3/13 - 8*d**2/13 - 2*d/13 + 12/13.
-2*(d - 1)*(d + 2)*(d + 3)/13
Determine c so that c**4 - 3776*c**3 + 5346816*c**2 - 3364929536*c + 794123370496 = 0.
944
Factor -p**5 + 11*p**4 - 27*p**3 - 67*p**2 + 320*p - 300.
-(p - 5)**2*(p - 2)**2*(p + 3)
Suppose -21*i**3/4 - 10*i**2 + i = 0. Calculate i.
-2, 0, 2/21
Factor -4*d**2/3 + 40*d/3.
-4*d*(d - 10)/3
Factor -2*f**5 - 492*f**4 - 40344*f**3 - 1102736*f**2.
-2*f**2*(f + 82)**3
What is g in -578*g**2/9 + 34952*g/9 - 528392/9 = 0?
514/17
Factor 5*c**2 + 45*c + 70.
5*(c + 2)*(c + 7)
Solve 9*o**4 - 15*o**3 - 15*o**2 + 15*o + 6 = 0 for o.
-1, -1/3, 1, 2
Determine n so that -3*n**2 - 4644*n + 9300 = 0.
-1550, 2
Suppose 4*o**5 + 160*o**4 + 452*o**3 + 296*o**2 = 0. What is o?
-37, -2, -1, 0
Let 4*o**4 + 212*o**3/3 + 328*o**2/3 + 128*o/3 = 0. What is o?
-16, -1, -2/3, 0
Factor 4*f**2 + 2880*f.
4*f*(f + 720)
Factor 2*d**4/7 + 28*d**3 + 4602*d**2/7 - 1400*d + 5000/7.
2*(d - 1)**2*(d + 50)**2/7
Factor o**4 - 39*o**3 + 399*o**2 - 361*o.
o*(o - 19)**2*(o - 1)
Suppose 4*d**4 + 16*d**3 - 4*d**2 - 16*d = 0. What is d?
-4, -1, 0, 1
Find c, given that 22*c**2/13 - 42*c/13 = 0.
0, 21/11
Let 4*c**3/5 - 12*c**2 - 208*c/5 - 144/5 = 0. Calculate c.
-2, -1, 18
Determine d so that -d**3/3 + 24*d**2 - 176*d + 1024/3 = 0.
4, 64
Solve d**2/2 + 31*d/2 = 0.
-31, 0
Factor -5*v**2 - 5*v.
-5*v*(v + 1)
Factor -3*q**2 + 267*q - 1020.
-3*(q - 85)*(q - 4)
Factor u**3 - 28*u**2.
u**2*(u - 28)
Factor -h**2/9 + 38*h/9 + 13/3.
-(h - 39)*(h + 1)/9
Let -j**3/2 + 274*j**2 - 1637*j/2 + 545 = 0. Calculate j.
1, 2, 545
Factor -2*y**2 - 64*y - 270.
-2*(y + 5)*(y + 27)
Factor f**4/5 - 27*f**3 - 3*f**2/5 + 407*f/5 - 54.
(f - 135)*(f - 1)**2*(f + 2)/5
Suppose -3*q**4/5 + 6*q**3/5 + 12*q**2/5 - 6*q/5 - 9/5 = 0. What is q?
-1, 1, 3
Factor -5*t**3 - 50*t**2 + 205*t + 1650.
-5*(t - 6)*(t + 5)*(t + 11)
Determine p so that 21*p**3/4 + 31*p**2/2 - 21*p/4 - 31/2 = 0.
-62/21, -1, 1
Factor 2*r**3 + 10*r**2 + 6*r - 18.
2*(r - 1)*(r + 3)**2
What is d in 8*d**4/11 + 98*d**3/11 + 400*d**2/11 + 574*d/11 + 120/11 = 0?
-5, -4, -3, -1/4
Let 10*m**3 + 24*m**2 + 2*m - 12 = 0. What is m?
-2, -1, 3/5
Suppose 4*m**2 - 1288*m + 103684 = 0. Calculate m.
161
Solve 147*i**5/2 + 63*i**4/2 - 219*i**3/2 - 51*i**2/2 + 36*i - 6 = 0.
-1, 2/7, 1
Factor -2*c**3/3 - 2*c**2 - 4*c/3.
-2*c*(c + 1)*(c + 2)/3
Factor -2*o**3/9 + 20*o**2/9.
-2*o**2*(o - 10)/9
Factor -2*b**4 - 1174*b**3 + 2354*b**2 - 1178*b.
-2*b*(b - 1)**2*(b + 589)
Determine f so that 2*f**5 - 182*f**4/3 + 468*f**3 - 268*f**2/3 - 470*f + 150 = 0.
-1, 1/3, 1, 15
Factor -l**4/2 + 3*l**3 + 7*l**2/2.
-l**2*(l - 7)*(l + 1)/2
Factor i**2 + 32*i + 31.
(i + 1)*(i + 31)
What is n in -4*n**5 + 36*n**3 + 16*n**2 - 48*n = 0?
-2, 0, 1, 3
Solve 14*t**3/19 + 32*t**2/19 - 34*t/19 - 12/19 = 0.
-3, -2/7, 1
Factor -3*h**3 - 678*h**2 + 3*h + 678.
-3*(h - 1)*(h + 1)*(h + 226)
Suppose 22*h**3/3 - 103*h**2/3 + 53*h/3 + 28/3 = 0. Calculate h.
-7/22, 1, 4
Let -3*v**3 + 57*v**2 - 168*v - 588 = 0. What is v?
-2, 7, 14
What is z in -2*z**2/7 + 158*z/7 = 0?
0, 79
Factor -j**3/5 - j**2 + j/5 + 1.
-(j - 1)*(j + 1)*(j + 5)/5
Let 2*z**2/3 + 186*z - 560/3 = 0. What is z?
-280, 1
Factor k**3 + 271*k**2 + 18495*k + 18225.
(k + 1)*(k + 135)**2
Find j, given that j**4 + 32*j**3 + 168*j**2 - 1728*j - 3888 = 0.
-18, -2, 6
Find f such that -2*f**2 - 448*f = 0.
-224, 0
Solve 3*c**4/4 - 228*c**3 + 2247*c**2/2 - 666*c - 8073/4 = 0 for c.
-1, 3, 299
Solve -4*s**5 - 32*s**4 - 40*s**3 + 240*s**2 + 684*s + 432 = 0.
-4, -3, -1, 3
Let -4*f**3 - 88*f**2 + 4*f + 88 = 0. What is f?
-22, -1, 1
Suppose 3*k**4 - 9*k**3 = 0. Calculate k.
0, 3
Factor 3*m**4/2 - 12*m**3 + 21*m**2/2.
3*m**2*(m - 7)*(m - 1)/2
Factor r**3/3 + 8*r**2/3.
r**2*(r + 8)/3
Factor v**4 - 4*v**3 - v**2 + 4*v.
v*(v - 4)*(v - 1)*(v + 1)
Let 3721*v**4 - 22082*v**3 + 28308*v**2 + 1928*v + 32 = 0. Calculate v.
-2/61, 2, 4
Factor w**2/6 - 7*w/6.
w*(w - 7)/6
Let 5*u**2 + 1660*u + 137780 = 0. What is u?
-166
Find m, given that -3*m**5 - 111*m**4 - 213*m**3 - 105*m**2 = 0.
-35, -1, 0
Let 2*h**4 - 22*h**3 + 52*h**2 - 32*h = 0. Calculate h.
0, 1, 2, 8
What is h in -49*h**5/3 - 1477*h**4/3 - 59*h**3 + 327*h**2 - 90*h = 0?
-30, -1, 0, 3/7
Factor -3*q**4 + 6*q**2 - 3.
-3*(q - 1)**2*(q + 1)**2
Suppose -m**3/5 - 2413*m**2/5 - 1456848*m/5 - 1454436/5 = 0. Calculate m.
-1206, -1
Determine j, given that 254*j**2 - 2*j = 0.
0, 1/127
Let 3*j**5/5 + 126*j**4/5 + 1608*j**3/5 + 7074*j**2/5 + 5589*j/5 = 0. Calculate j.
-23, -9, -1, 0
Determine l, given that 8*l**4 - 466*l**3 + 6844*l**2 - 1682*l = 0.
0, 1/4, 29
Factor l**4 - 87*l**3 - l**2 + 87*l.
l*(l - 87)*(l - 1)*(l + 1)
Solve -2*k**5/9 + 2*k**4/3 + 4*k**3/9 - 8*k**2/3 + 16*k/9 = 0.
-2, 0, 1, 2
Determine b so that -b**4 + 16*b**3 - 59*b**2 + 44*b = 0.
0, 1, 4, 11
Factor -3*r**2/4 - 981*r/2 - 320787/4.
-3*(r + 327)**2/4
Factor -c**2 + 690*c - 119025.
-(c - 345)**2
Factor -2*b**4 + 38*b**3 - 210*b**2 + 314*b - 140.
-2*(b - 10)*(b - 7)*(b - 1)**2
Let 10*u**3/7 + 132*u**2/7 + 326*u/7 + 60/7 = 0. What is u?
-10, -3, -1/5
Suppose -x**3 - 368*x**2 + 369*x = 0. Calculate x.
-369, 0, 1
Solve -3*f**4/5 - 6*f**3/5 + 9*f**2/5 + 12*f/5 - 12/5 = 0 for f.
-2, 1
Determine o so that o**2 + 11*o - 26 = 0.
-13, 2
Factor 5*o**2 + 1190*o + 70805.
5*(o + 119)**2
Suppose -2*w**4 + 8*w**3 - 4*w**2 - 8*w + 6 = 0. Calculate w.
-1, 1, 3
Factor 4*s**4 - 2519*s**3 + 396267*s**2 + 101115*s - 297675.
(s - 315)**2*(s + 1)*(4*s - 3)
Determine d so that 4*d**4/7 + 8*d**3/7 - 48*d**2/7 + 8*d - 20/7 = 0.
-5, 1
Suppose r**2 - 38*r + 360 = 0. Calculate r.
18, 20
Find c such that -8*c**4/3 - 286*c**3/9 - 244*c**2/3 + 208*c/9 + 128/3 = 0.
-8, -4, -2/3, 3/4
Factor -3*d**3/7 - 972*d**2/7 - 2895*d/7 - 1926/7.
-3*(d + 1)*(