1)
Factor w**4/5 + 43*w**3/5 - 89*w**2/5 + 9*w.
w*(w - 1)**2*(w + 45)/5
Factor -6*d**3 + 4*d**2 + 24*d - 16.
-2*(d - 2)*(d + 2)*(3*d - 2)
Determine w, given that w**4/7 + 8*w**3/7 - 43*w**2/7 + 58*w/7 - 24/7 = 0.
-12, 1, 2
Factor -12*s**3/7 - 23*s**2/7 + 14*s - 8/7.
-(s - 2)*(s + 4)*(12*s - 1)/7
Factor j**3/2 + 4*j**2 + 8*j.
j*(j + 4)**2/2
Determine h, given that -2*h**2/11 + 382*h/11 - 2928/11 = 0.
8, 183
Solve d**4 - 3*d**3 - 222*d**2 + 224*d = 0 for d.
-14, 0, 1, 16
Suppose -4*i**3 + 156*i**2 + 1728*i = 0. What is i?
-9, 0, 48
Factor h**3 + 21*h**2 - 49*h - 69.
(h - 3)*(h + 1)*(h + 23)
Let -2*s**5/9 - 8*s**4/9 - 2*s**3/3 = 0. What is s?
-3, -1, 0
Find w such that -5*w**3/2 + 105*w/2 - 50 = 0.
-5, 1, 4
Factor -5*b**4 + 55*b**3 + 140*b**2 - 1060*b + 1200.
-5*(b - 12)*(b - 2)**2*(b + 5)
Let -h**3 - 1448*h**2 + h + 1448 = 0. Calculate h.
-1448, -1, 1
Determine x, given that 2*x**5 + 8*x**4 - 54*x**3 + 76*x**2 - 32*x = 0.
-8, 0, 1, 2
Factor o**2 - 14*o + 33.
(o - 11)*(o - 3)
Let 4*o**2 - 24*o - 64 = 0. Calculate o.
-2, 8
Solve -q**4/2 + 3*q**3 - 11*q - 15/2 = 0 for q.
-1, 3, 5
Factor 4*j**4 + 160*j**3 + 2400*j**2 + 16000*j + 40000.
4*(j + 10)**4
What is p in 2*p**2/11 - 92*p/11 - 864/11 = 0?
-8, 54
Suppose -2*m**5/11 + 8*m**4/11 + 56*m**3/11 + 64*m**2/11 = 0. Calculate m.
-2, 0, 8
Solve 30*m**5/7 + 738*m**4/7 + 4752*m**3/7 + 2592*m**2/7 = 0.
-12, -3/5, 0
Let 5*w**2 - 110*w - 375 = 0. Calculate w.
-3, 25
Let -2*s**2/9 + 2*s/3 + 24 = 0. What is s?
-9, 12
Find z, given that 31*z**3/2 + 2*z**2/3 - 31*z/2 - 2/3 = 0.
-1, -4/93, 1
Let 12*c**3/5 + 1588*c**2/5 - 21944*c/5 + 2784 = 0. Calculate c.
-145, 2/3, 12
Factor 2*w**4 + 34*w**3 - 82*w**2 - 114*w.
2*w*(w - 3)*(w + 1)*(w + 19)
Solve -3*q**5 - 6*q**4 + 6*q**3 + 24*q**2 + 21*q + 6 = 0 for q.
-1, 2
Solve 4*d**4 + 64*d**3 + 312*d**2 + 448*d + 196 = 0.
-7, -1
Factor -r**2/3 + 20*r/3 - 32.
-(r - 12)*(r - 8)/3
Factor x**5 - x**4 - 5*x**3 - 3*x**2.
x**2*(x - 3)*(x + 1)**2
Factor -l**4/12 + 11*l**3/4 + 12*l**2 + 37*l/3.
-l*(l - 37)*(l + 2)**2/12
Suppose -4*n**5 + 350*n**4 + 180*n**3 - 350*n**2 - 176*n = 0. Calculate n.
-1, -1/2, 0, 1, 88
Factor -3*m**2 - 7854*m - 5140443.
-3*(m + 1309)**2
Factor -2*t**3/7 - 624*t**2/7 - 352*t.
-2*t*(t + 4)*(t + 308)/7
Factor w**2 + 70*w + 1225.
(w + 35)**2
Factor 2*o**2/7 + 316*o/7 - 138.
2*(o - 3)*(o + 161)/7
Suppose m**2/3 - 29*m - 178/3 = 0. Calculate m.
-2, 89
Suppose 3*u**3/7 + 678*u**2/7 + 38307*u/7 = 0. Calculate u.
-113, 0
Factor -2*t**2/9 + 182*t - 3268/9.
-2*(t - 817)*(t - 2)/9
Factor p**5 - 47*p**4 + 739*p**3 - 4257*p**2 + 6480*p - 2916.
(p - 18)**2*(p - 9)*(p - 1)**2
Determine o, given that 3*o**4/2 + 9*o**3/2 - 9*o**2/2 - 21*o/2 + 9 = 0.
-3, -2, 1
Find u, given that -u**5/3 - 28*u**4 - 899*u**3/3 - 836*u**2 + 300*u + 864 = 0.
-72, -6, -1, 1
Factor 2*i**4 + 64*i**3 + 218*i**2 - 204*i - 1008.
2*(i - 2)*(i + 3)**2*(i + 28)
Find u, given that 196*u**3 + 1932*u**2 - 2400*u + 704 = 0.
-11, 4/7
Find i such that -3*i**5 + 12*i**4 - 12*i**3 = 0.
0, 2
Solve j**4/2 + 1467*j**3/2 + 359412*j**2 + 59178784*j + 174321408 = 0.
-488, -3
Factor 5*y**2 - 435*y + 4810.
5*(y - 74)*(y - 13)
Determine y, given that -2*y**2/7 - 1676*y/7 + 1678/7 = 0.
-839, 1
Factor 4*k**2/5 + 312*k/5 + 6084/5.
4*(k + 39)**2/5
Factor 4*c**3 - 336*c**2 + 7380*c - 13448.
4*(c - 41)**2*(c - 2)
Let 3*h**2 + 27*h = 0. What is h?
-9, 0
Factor t**2 + 13*t + 40.
(t + 5)*(t + 8)
Suppose 5*d**2 - 60*d - 225 = 0. Calculate d.
-3, 15
Suppose -2*g**4 - 74*g**3 - 786*g**2 - 1870*g - 1156 = 0. Calculate g.
-17, -2, -1
What is g in -g**4 + 6*g**3 + 16*g**2 - 96*g = 0?
-4, 0, 4, 6
Factor m**4/4 + 75*m**3/4 + 829*m**2/4 + 1437*m/4 + 341/2.
(m + 1)**2*(m + 11)*(m + 62)/4
Determine f, given that 4*f**2 - 2672*f - 8052 = 0.
-3, 671
Factor 2*h**5 + 28*h**4 - 62*h**3 + 32*h**2.
2*h**2*(h - 1)**2*(h + 16)
Determine o so that o**2/3 - 16*o/3 + 64/3 = 0.
8
Factor -3*i**3/7 - 6*i**2/7 + 9*i/7.
-3*i*(i - 1)*(i + 3)/7
Determine s, given that -2*s**5/3 + 14*s**4 + 2*s**3 - 130*s**2/3 + 28*s = 0.
-2, 0, 1, 21
Suppose -3*j**2 - 78*j - 75 = 0. Calculate j.
-25, -1
Factor -q**4/7 - 10*q**3 - 384*q**2/7 + 32*q/7 + 2048/7.
-(q - 2)*(q + 4)**2*(q + 64)/7
Suppose -q**3/6 - 53*q**2/6 + 109*q/6 - 55/6 = 0. Calculate q.
-55, 1
Find n, given that -n**4/3 - 2*n**3 + 55*n**2/3 + 84*n = 0.
-9, -4, 0, 7
Factor -3*n**4/4 - 3*n**3 - 3*n**2/4 + 9*n/2.
-3*n*(n - 1)*(n + 2)*(n + 3)/4
Factor -4*k**3 + 4608*k**2 - 1769472*k + 226492416.
-4*(k - 384)**3
Factor 2*i**3 - 50*i**2 + 228*i.
2*i*(i - 19)*(i - 6)
Find b, given that -14450*b**2/3 + 340*b/3 - 2/3 = 0.
1/85
Find m such that 2*m**3 + 172*m**2 - 2*m - 172 = 0.
-86, -1, 1
What is h in 3*h**5 - 390*h**4 + 18252*h**3 - 355914*h**2 + 2313441*h = 0?
0, 13, 39
Let 15*q**2 + 20*q = 0. Calculate q.
-4/3, 0
Factor 3*o**4 - 12*o**3 + 3*o**2 + 18*o.
3*o*(o - 3)*(o - 2)*(o + 1)
Find m such that m**5/7 - 185*m**4 + 418606*m**3/7 + 422496*m**2/7 - 839808*m/7 = 0.
-2, 0, 1, 648
Factor -t**4/5 + 8*t**3/5 - t**2 - 38*t/5 - 24/5.
-(t - 6)*(t - 4)*(t + 1)**2/5
Suppose 3*h**2 + 33*h - 78 = 0. Calculate h.
-13, 2
Find r such that -4*r**4 - 68*r**3 + 88*r**2 + 272*r - 288 = 0.
-18, -2, 1, 2
Solve -y**4 + 4*y**3 - 5*y**2 + 2*y = 0.
0, 1, 2
Factor -n**3/7 + 2*n**2/7 + 13*n/7 + 10/7.
-(n - 5)*(n + 1)*(n + 2)/7
What is d in 2*d**2/3 + 214*d/3 - 1120/3 = 0?
-112, 5
Factor 4*w**5 - 100*w**4 - 336*w**3.
4*w**3*(w - 28)*(w + 3)
Factor 25*f**3 - 14215*f**2 + 8510*f + 5680.
5*(f - 568)*(f - 1)*(5*f + 2)
What is i in i**2 - 862*i - 1728 = 0?
-2, 864
Find v, given that 4*v**2 - 1144*v + 81796 = 0.
143
Let -5*n**4 - 10*n**3 - 25*n**2/4 - 5*n/4 = 0. Calculate n.
-1, -1/2, 0
Factor -5*g**3/2 + 8735*g**2 - 17465*g/2.
-5*g*(g - 3493)*(g - 1)/2
Solve -3*v**4/5 + 3*v**3/5 + 27*v**2/5 + 33*v/5 + 12/5 = 0.
-1, 4
Factor -28*m**5 - 40*m**4 - 12*m**3.
-4*m**3*(m + 1)*(7*m + 3)
Solve -3*l**2 + 180*l - 2700 = 0.
30
Factor 4*a**4/9 + 52*a**3/9 + 164*a**2/9 + 188*a/9 + 8.
4*(a + 1)**2*(a + 2)*(a + 9)/9
Factor -2*s**5/3 + 274*s**4/3 - 270*s**3 + 806*s**2/3 - 268*s/3.
-2*s*(s - 134)*(s - 1)**3/3
Let s**5 + 84*s**4 - 171*s**3 + 86*s**2 = 0. Calculate s.
-86, 0, 1
Factor 2*i**2/5 + 1504*i - 7522/5.
2*(i - 1)*(i + 3761)/5
Suppose 5*p**2 + 1110*p + 6480 = 0. Calculate p.
-216, -6
Factor -2*u**3/9 + 8*u**2/3 + 392*u/9 + 352/3.
-2*(u - 22)*(u + 4)*(u + 6)/9
Suppose -5*b**3/2 - 30*b**2 + 155*b/2 + 105 = 0. Calculate b.
-14, -1, 3
Solve 3*m**3 + 60*m**2 - 276*m + 288 = 0 for m.
-24, 2
Factor 4*l**3 + 486*l**2 - 244*l.
2*l*(l + 122)*(2*l - 1)
Factor -p**5/4 - 3*p**4 + 13*p**3/4.
-p**3*(p - 1)*(p + 13)/4
Let -9*n**5 - 93*n**4 + 177*n**3 - 39*n**2 - 36*n = 0. What is n?
-12, -1/3, 0, 1
Solve -25*a**4 + 290*a**3 - 780*a**2 + 440*a + 320 = 0.
-2/5, 2, 8
Determine x, given that -2*x**2/13 - 44*x/13 = 0.
-22, 0
Factor -2*i**5/7 + 66*i**4/7 - 438*i**3/7 - 1730*i**2/7 - 1872*i/7 - 648/7.
-2*(i - 18)**2*(i + 1)**3/7
Determine w so that 14*w**2 + 332*w - 96 = 0.
-24, 2/7
Suppose 11*o**3 + 292*o**2 + 1476*o + 720 = 0. Calculate o.
-20, -6, -6/11
Solve -2*w**5/3 - 8*w**4/3 - 8*w**3/3 = 0.
-2, 0
Factor -d**3/3 - 3*d**2 - 20*d/3 - 4.
-(d + 1)*(d + 2)*(d + 6)/3
Solve -500*i**3/3 + 21900*i**2 - 959220*i + 14004612 = 0.
219/5
Solve 10*b**5/11 - 94*b**4/11 + 310*b**3/11 - 378*b**2/11 + 216/11 = 0 for b.
-3/5, 2, 3
What is n in -n**4 - 18*n**3 + 3*n**2 + 52*n - 36 = 0?
-18, -2, 1
Suppose -c**3/3 - 15*c**2 - 218*c/3 + 208 = 0. Calculate c.
-39, -8, 2
Factor -2883*p**3/8 - 93*p**2/2 - 3*p/2.
-3*p*(31*p + 2)**2/8
Suppose 2*y**3/13 + 60*y**2/13 - 126*y/13 + 64/13 = 0. What is y?
-32, 1
Solve 55*h**4 + 30*h**3 - 55*h**2 - 30*h = 0 for h.
-1, -6/11, 0, 1
Factor -2*r**3/13 - 330*r**2/13 - 18150*r/13 - 332750/13.
-2*(r + 55)**3/13
Factor 3*t**2 - 8244*t + 5663628.
3*(t - 1374)**2
Find k such that 5*k**3 - 5*k**2 - 110*k + 200 = 0.
-5, 2, 4
Determine o so that 16*o**3 + 16*o**2 - 60*o - 72 = 0.
-3/2, 2
Factor -4*b**5/5 - 132*b**4/5 - 372*b**3/5 - 364*b**2/5 - 24*b.
-4*b*(b + 1)**3*(b + 30)/5
Solve -3*b**3 - 42*b**2 + 141*b + 720 = 0 for b.
-16, -3, 5
Factor -2*t**5 + 8*t**4 - 10*t**3 + 4*t**2.
-2*t**2*(t - 2)*(t - 1)**2
Determine n, given that 30*n**3 + 365*n**2 + 1140*n + 180 = 0.
-6, -1/6
Factor -2*t**3/7 - 956*t**2/7.
-2*t**2*(t + 478)/7
Factor 4*x**4 - 184*x**3 - 192*x**2 + 184*x 