1)
Factor 2*k**4/9 - 32*k**3/9 - 2*k**2/9 + 32*k/9.
2*k*(k - 16)*(k - 1)*(k + 1)/9
Suppose -48*n**5 + 972*n**4 - 5913*n**3 + 40905*n**2/4 - 13851*n/2 + 6561/4 = 0. What is n?
3/4, 9
Factor 3*l**2 + 126*l + 123.
3*(l + 1)*(l + 41)
Factor j**5/2 + 11*j**4/2 + 7*j**3/2 - 35*j**2/2 - 26*j - 10.
(j - 2)*(j + 1)**3*(j + 10)/2
Find s such that -2*s**3/5 - 4*s**2 + 46*s/5 - 24/5 = 0.
-12, 1
Suppose 10086*c**4 + 29930*c**3 + 57572*c**2/3 - 648*c + 16/3 = 0. Calculate c.
-2, -1, 2/123
Find g, given that 604*g**4 + 612*g**3 - 596*g**2 - 612*g - 8 = 0.
-1, -2/151, 1
Suppose -4*l**2/3 + 3416*l/3 = 0. What is l?
0, 854
Solve 4*a**2/5 + 1988*a/5 + 1968 = 0 for a.
-492, -5
Solve -40*t**4 + 270*t**3 - 545*t**2 + 300*t - 45 = 0 for t.
1/4, 1/2, 3
Let 12*n**4 - 404*n**3 + 4620*n**2 - 18876*n + 10648 = 0. What is n?
2/3, 11
Find u such that 5*u**5 - 65*u**4 + 275*u**3 - 375*u**2 = 0.
0, 3, 5
Factor 4*c**5 - 52*c**4 + 192*c**3 + 128*c**2 - 2048*c + 3072.
4*(c - 4)**4*(c + 3)
Factor -4*z**3/7 - 23*z**2/7 - 4*z.
-z*(z + 4)*(4*z + 7)/7
Let 5*m**4 + 16150*m**3 + 16140*m**2 - 16150*m - 16145 = 0. What is m?
-3229, -1, 1
Solve -8*f**4/13 + 194*f**3/13 - 400*f**2/13 + 88*f/13 = 0.
0, 1/4, 2, 22
Find d such that -2*d**2/5 + 22*d/5 + 24/5 = 0.
-1, 12
What is v in 63*v**4/5 - 96*v**3/5 + 6*v**2/5 + 24*v/5 + 3/5 = 0?
-1/3, -1/7, 1
Determine i so that -2*i**3/9 + 14*i**2/3 - 4*i - 80/9 = 0.
-1, 2, 20
Factor 4827*s**3 - 19314*s**2 + 14505*s - 18.
3*(s - 3)*(s - 1)*(1609*s - 2)
Determine y so that y**2/7 - 402*y/7 + 40401/7 = 0.
201
Suppose -5*l**4 + 685*l**3 - 2025*l**2 + 2015*l - 670 = 0. Calculate l.
1, 134
Factor -5*a**2 - 470*a - 11045.
-5*(a + 47)**2
Suppose 27*h**3 - 42*h**2 + 17*h - 2 = 0. What is h?
2/9, 1/3, 1
Factor -3*s**3 + 1062*s**2 - 95040*s + 185856.
-3*(s - 176)**2*(s - 2)
Solve 2*b**2/3 + 1948*b/3 + 474338/3 = 0.
-487
Let 2*k**5/23 - 200*k**4/23 + 4182*k**3/23 - 33808*k**2/23 + 106624*k/23 - 76800/23 = 0. Calculate k.
1, 8, 75
Find k such that k**5 - 27*k**4 + 23*k**3 + 79*k**2 - 24*k - 52 = 0.
-1, 1, 2, 26
Factor r**5/4 - 3*r**4/4 + r**2.
r**2*(r - 2)**2*(r + 1)/4
Find g, given that -g**3 + 155*g**2/3 + 376*g/3 + 36 = 0.
-2, -1/3, 54
Factor 2*k**4 - 32*k**3 - 208*k**2 + 2688*k + 14112.
2*(k - 14)**2*(k + 6)**2
What is a in 20*a**4/3 - 44*a**3/3 - 172*a**2/3 + 132*a - 24 = 0?
-3, 1/5, 2, 3
Factor -3*a**3 + 1890*a**2 + 1893*a.
-3*a*(a - 631)*(a + 1)
Factor 2*l**2 - 320*l + 4088.
2*(l - 146)*(l - 14)
Find l, given that -2*l**4 - 65*l**3 + 104*l**2 + 68*l = 0.
-34, -1/2, 0, 2
Let f**2/7 + 1544*f/7 - 1545/7 = 0. Calculate f.
-1545, 1
Factor -32*g**2/17 - 378*g/17 + 72/17.
-2*(g + 12)*(16*g - 3)/17
Suppose -5*j**5 - 14225*j**4 - 16188050*j**3 - 9211000450*j**2 - 2620529628025*j - 298216271669245 = 0. What is j?
-569
Factor g**2 + 41*g - 392.
(g - 8)*(g + 49)
Let 5*x**3 + 125*x**2 + 120*x = 0. What is x?
-24, -1, 0
Factor -2*z**5 - 16*z**4/5 + 8*z**3/5.
-2*z**3*(z + 2)*(5*z - 2)/5
Solve a**2 + 42*a + 441 = 0 for a.
-21
Suppose 4*t**3 + 68*t**2 + 56*t - 128 = 0. What is t?
-16, -2, 1
Find n such that -234*n**4/5 - 24*n**3/5 + 148*n**2/5 - 56*n/5 + 6/5 = 0.
-1, 3/13, 1/3
Factor -92*d**3/5 - 558*d**2/5 - 864*d/5 - 54/5.
-2*(d + 3)**2*(46*d + 3)/5
Factor 5*x**2 - 2135*x + 2130.
5*(x - 426)*(x - 1)
Suppose 5*z**5 + 100*z**4 + 370*z**3 - 1540*z**2 - 1815*z = 0. What is z?
-11, -1, 0, 3
Factor 33915*v**3 - 5*v**2.
5*v**2*(6783*v - 1)
What is t in 5*t**5 + 40*t**4 + 95*t**3 + 40*t**2 - 100*t - 80 = 0?
-4, -2, -1, 1
Factor 2*i**3/3 + 116*i**2/3 + 110*i/3 - 76.
2*(i - 1)*(i + 2)*(i + 57)/3
What is s in 5*s**2 + 12115*s = 0?
-2423, 0
Factor q**3 - 38*q**2 - 39*q.
q*(q - 39)*(q + 1)
Let -4*x**3 - 20*x**2 + 4*x + 20 = 0. What is x?
-5, -1, 1
Factor 4*v**2 + 36*v + 80.
4*(v + 4)*(v + 5)
Factor 4*c**4/5 - 6*c**3/5 + 2*c**2/5.
2*c**2*(c - 1)*(2*c - 1)/5
Find b, given that -2*b**3 + 66*b**2 - 124*b = 0.
0, 2, 31
Determine g so that -g**5/2 + 27*g**4/2 - 12*g**3 - 26*g**2 = 0.
-1, 0, 2, 26
Suppose -4*c**3 - 84*c**2 - 72*c + 160 = 0. What is c?
-20, -2, 1
Factor -4*i**4 + 4244*i**3 + 25560*i**2 + 51184*i + 34144.
-4*(i - 1067)*(i + 2)**3
Factor 16*k**2/3 + 5780*k/3 - 1448.
4*(k + 362)*(4*k - 3)/3
Suppose 5*b**5 + 120*b**4 - 1200*b**3 + 2560*b**2 = 0. Calculate b.
-32, 0, 4
Suppose 2*j**5 + 354*j**4 - 6*j**3 - 1058*j**2 + 708*j = 0. What is j?
-177, -2, 0, 1
Factor 4*h**5 + 20*h**4 - 16*h**3 - 80*h**2.
4*h**2*(h - 2)*(h + 2)*(h + 5)
Factor 4*t**3 + 38*t**2 - 200*t + 216.
2*(t - 2)**2*(2*t + 27)
Determine o so that -2*o**3/3 + 8*o**2/3 + 10*o/3 = 0.
-1, 0, 5
Find o, given that -o**4/3 - 274*o**3/3 - 18493*o**2/3 + 12604*o - 6348 = 0.
-138, 1
Factor -3*d**3 + 4908*d**2 - 2007372*d.
-3*d*(d - 818)**2
Determine c so that c**5/3 - 2*c**4/3 - 13*c**3/3 - 10*c**2/3 = 0.
-2, -1, 0, 5
Let 3*i**2/4 - 207*i/2 - 7905/4 = 0. What is i?
-17, 155
Determine w so that w**2/7 - 2*w/7 - 3/7 = 0.
-1, 3
Factor 2*w**3/5 - 16*w**2/5 + 38*w/5 - 24/5.
2*(w - 4)*(w - 3)*(w - 1)/5
Find k such that k**5/3 - 8*k**4/9 - 8*k**3/9 + 14*k**2/9 + 5*k/9 - 2/3 = 0.
-1, 2/3, 1, 3
Determine j so that -3*j**2 - 1950*j - 316875 = 0.
-325
Factor -4*d**4 + 348*d**3 + 1468*d**2 - 1020*d - 6552.
-4*(d - 91)*(d - 2)*(d + 3)**2
Factor 3*k**4 + 1818*k**3 + 10836*k**2 + 21624*k + 14400.
3*(k + 2)**3*(k + 600)
Find b, given that b**3 + 35*b**2 - 118*b - 152 = 0.
-38, -1, 4
Find f, given that -2*f**4/11 - 202*f**3/11 + 3220*f**2/11 = 0.
-115, 0, 14
Factor 5*l**4 + 60*l**3 + 180*l**2.
5*l**2*(l + 6)**2
Determine z so that -2*z**4 - 46*z**3 - 196*z**2 - 296*z - 144 = 0.
-18, -2, -1
Determine u so that -5*u**4 + 55*u**3 + 125*u**2 + 65*u = 0.
-1, 0, 13
Suppose -2*z**4/7 + 190*z**3/7 - 352*z**2 - 15232*z = 0. Calculate z.
-17, 0, 56
Factor 3*i**2 - 18*i + 15.
3*(i - 5)*(i - 1)
Find b, given that -10092*b**5 + 21315*b**4 - 12054*b**3 + 543*b**2 + 276*b + 12 = 0.
-2/29, 1/4, 1
Factor 5*p**2 - 420*p + 4900.
5*(p - 70)*(p - 14)
Factor -605*q**3/4 + 1485*q**2/2 - 2325*q/4 + 125.
-5*(q - 4)*(11*q - 5)**2/4
Factor -3*n**3/7 - 174*n**2/7 - 171*n/7.
-3*n*(n + 1)*(n + 57)/7
Let 39*w**4/5 - 1788*w**3/5 + 18444*w**2/5 + 47808*w/5 + 6912/5 = 0. What is w?
-2, -2/13, 24
Factor -2*s**2 - 6*s + 476.
-2*(s - 14)*(s + 17)
Solve 2*d**5 + 72*d**4 + 642*d**3 + 1012*d**2 = 0.
-23, -11, -2, 0
Find c such that -4*c**5/3 - 26*c**4/3 - 10*c**3 + 2*c**2/3 + 10*c/3 = 0.
-5, -1, 0, 1/2
Factor -x**5 - 17*x**4 - 16*x**3.
-x**3*(x + 1)*(x + 16)
Suppose -64*x**2/19 - 130*x/19 = 0. What is x?
-65/32, 0
Determine a, given that 20*a**5 + 218*a**4/3 + 298*a**3/3 + 62*a**2 + 50*a/3 + 4/3 = 0.
-1, -1/2, -2/15
Solve -2*q**2 + 1450*q = 0.
0, 725
Find z such that -z**4/3 + 5*z**3 + 4*z**2 - 196*z/3 + 80 = 0.
-4, 2, 15
Suppose -3*c**4/2 + 2694*c**3 - 8073*c**2 + 8070*c - 5379/2 = 0. What is c?
1, 1793
What is c in -20*c**5 + 178*c**4 - 222*c**3 - 904*c**2 + 872*c + 96 = 0?
-2, -1/10, 1, 4, 6
Solve 2*n**4/7 + 4*n**3 + 78*n**2/7 - 4*n - 80/7 = 0 for n.
-10, -4, -1, 1
Find p, given that -p**3/8 - 209*p**2/4 = 0.
-418, 0
Factor -5*h**3 + 240*h**2 - 2880*h.
-5*h*(h - 24)**2
Solve -2*r**2/11 + 14*r/11 - 20/11 = 0 for r.
2, 5
Solve -5*i**2/2 + 200*i + 405/2 = 0 for i.
-1, 81
Determine y, given that 8*y**5/7 - 230*y**4/7 - 82*y**3/7 + 674*y**2/7 + 634*y/7 + 116/7 = 0.
-1, -1/4, 2, 29
Find k such that -4*k**2 - 792*k + 3232 = 0.
-202, 4
Determine z, given that 4*z**5 - 4*z**4 - 12*z**3 + 20*z**2 - 8*z = 0.
-2, 0, 1
Find h, given that h**5 + 15*h**4 - 177*h**3 + 161*h**2 = 0.
-23, 0, 1, 7
Factor 15*h**3 + 170*h**2 + 420*h - 360.
5*(h + 6)**2*(3*h - 2)
Determine w so that -3*w**3/4 + 63*w**2/2 - 357*w/4 + 117/2 = 0.
1, 2, 39
What is a in -2*a**4/15 - 1186*a**3/15 + 2*a**2/15 + 1186*a/15 = 0?
-593, -1, 0, 1
Factor 5*u**2 - 15170*u + 11506445.
5*(u - 1517)**2
Factor -15*f**3 - 858*f**2 - 4071*f - 780.
-3*(f + 5)*(f + 52)*(5*f + 1)
Factor 5*o**2 + 115*o + 110.
5*(o + 1)*(o + 22)
Determine b so that b**3 + 394*b**2/7 + 800*b + 224 = 0.
-28, -2/7
Determine h, given that 3*h**2 - 396*h - 3807 = 0.
-9, 141
Factor -f**3/3 + 10*f**2/3 - 17*f/3 + 8/3.
-(f - 8)*(f - 1)**2/3
Solve 2*a**4/3 + 2*a**3/3 - 10*a**2 + 46*a/3 - 20/3 = 0.
-5, 1, 2
What is d in 2*d**4/3 + 38*d**3/3 + 34*d**2/3 - 38*d/3 - 12 = 0?
-18, -1, 1
Determine z, given that -2*z**3 + 6*z**2 + 12*z - 16 = 0.
-2, 1, 4
Factor -3*b**2 - 1