1)
Determine f, given that f**5 + f**4 - 3*f**3 - f**2 + 2*f = 0.
-2, -1, 0, 1
Solve -i**5/4 + 3*i**3/2 + 2*i**2 + 3*i/4 = 0 for i.
-1, 0, 3
Let 4*s**2 + 312*s - 2380 = 0. What is s?
-85, 7
Find q, given that 2*q**4 - 11*q**3 - 29*q**2 + 59*q - 21 = 0.
-3, 1/2, 1, 7
Find q, given that q**2/3 + 271*q + 812/3 = 0.
-812, -1
Factor b**4/3 - 2*b**3/3 - 8*b**2/3.
b**2*(b - 4)*(b + 2)/3
Factor -4*q**4 - 8*q**3 - 4*q**2.
-4*q**2*(q + 1)**2
Factor -3*m**3 - 27*m**2 + 36*m + 60.
-3*(m - 2)*(m + 1)*(m + 10)
Factor 57*c**3/4 + 519*c**2/4 + 213*c + 21.
3*(c + 2)*(c + 7)*(19*c + 2)/4
Solve -j**3/6 - 5*j**2 - 51*j/2 + 578/3 = 0 for j.
-17, 4
Factor 15*q**5 - 35*q**4 + 10*q**3 + 30*q**2 - 25*q + 5.
5*(q - 1)**3*(q + 1)*(3*q - 1)
Determine a so that 2*a**3 - 10*a**2 + 16*a - 8 = 0.
1, 2
Suppose -4*f**4 + 120*f**3 - 112*f**2 - 120*f + 116 = 0. What is f?
-1, 1, 29
Factor 2*s**4 - 2*s**2.
2*s**2*(s - 1)*(s + 1)
Let u**5/4 + 2*u**4 + 5*u**3 + 5*u**2/2 - 21*u/4 - 9/2 = 0. Calculate u.
-3, -2, -1, 1
Let 3*u**2/7 - 141*u/7 + 936/7 = 0. Calculate u.
8, 39
Suppose -3*a**2/4 - 237*a/4 + 594 = 0. Calculate a.
-88, 9
Factor -3*p**2 - 86*p - 56.
-(p + 28)*(3*p + 2)
Suppose -f**2 + 1414*f - 499849 = 0. What is f?
707
Factor -5*i**3/2 + 60*i**2 - 225*i/2 + 55.
-5*(i - 22)*(i - 1)**2/2
Find n, given that -5*n**2 - 3380*n - 571220 = 0.
-338
Let -9*n**4/5 - 1988*n**3/5 - 110659*n**2/5 - 19316*n + 2420 = 0. What is n?
-110, -1, 1/9
Suppose 3*m**2 + 516*m + 513 = 0. What is m?
-171, -1
Factor -2*q**3/13 + 1088*q**2/13 - 11298*q - 22932.
-2*(q - 273)**2*(q + 2)/13
Solve 5*q**3 - 90*q**2 + 85*q = 0.
0, 1, 17
Let 8*j**5/3 - 2*j**4 - 128*j**3/3 - 146*j**2/3 + 40*j + 152/3 = 0. Calculate j.
-2, -1, 1, 19/4
Factor d**2 + 2808*d + 1971216.
(d + 1404)**2
Factor m**5/3 + 11*m**4/3 + 38*m**3/3 + 52*m**2/3 + 8*m.
m*(m + 1)*(m + 2)**2*(m + 6)/3
Factor -2*h**5/17 - 2*h**4 - 32*h**3/17.
-2*h**3*(h + 1)*(h + 16)/17
Let -3*u**3 + 30*u**2 + 156*u + 168 = 0. Calculate u.
-2, 14
Find g such that -2*g**4/5 + 18*g**3/5 - 38*g**2/5 - 18*g/5 + 8 = 0.
-1, 1, 4, 5
Suppose 4*b**2 - 48*b + 108 = 0. What is b?
3, 9
Factor -r**3/8 + 5*r**2/8 - 7*r/8 + 3/8.
-(r - 3)*(r - 1)**2/8
Factor 2*i**2/5.
2*i**2/5
Let 2*u**2/21 + 188*u/21 + 26 = 0. Calculate u.
-91, -3
Factor -p**3/3 + 77*p**2/3 + 158*p/3.
-p*(p - 79)*(p + 2)/3
Factor -3*t**2 + 78*t - 144.
-3*(t - 24)*(t - 2)
Solve 12*r**3 - 31960*r**2 + 21269376*r + 14193792 = 0.
-2/3, 1332
Factor -h**4/7 + 4*h**3/7 - 4*h**2/7.
-h**2*(h - 2)**2/7
Factor 2*t**3 - 26*t**2 - 136*t.
2*t*(t - 17)*(t + 4)
What is n in 3*n**4 + 18*n**3 - 153*n**2 + 132*n = 0?
-11, 0, 1, 4
Factor -2*d**2/11 - 74*d/11 + 1560/11.
-2*(d - 15)*(d + 52)/11
Find r such that -2*r**3 + 16*r**2 + 38*r + 20 = 0.
-1, 10
Find j such that 5*j**3 - 3020*j**2 - 6060*j = 0.
-2, 0, 606
Determine r so that 4*r**4/7 - 40*r**3/7 - 52*r**2/7 + 88*r/7 = 0.
-2, 0, 1, 11
Factor h**3/4 + 11*h**2/4 - 7*h/2 - 6.
(h - 2)*(h + 1)*(h + 12)/4
Factor -c**3/3 + 13*c**2 - 25*c + 37/3.
-(c - 37)*(c - 1)**2/3
Suppose -5*q**5 - 185*q**4 - 655*q**3 + 185*q**2 + 660*q = 0. What is q?
-33, -4, -1, 0, 1
Suppose 15*r**3 + 21*r**2 - 138*r + 72 = 0. Calculate r.
-4, 3/5, 2
Factor 642978*l**4 - 353808*l**3 + 3312*l**2 + 12480*l + 800.
2*(21*l + 2)**2*(27*l - 10)**2
Factor -5*w**5 + 995*w**4 - 65330*w**3 + 1370150*w**2 + 2940295*w + 1503815.
-5*(w - 67)**3*(w + 1)**2
What is v in 90*v**5 - 1300*v**4 + 14058*v**3/5 - 10512*v**2/5 + 520*v - 96/5 = 0?
2/45, 2/5, 1, 12
Suppose -2*x**5/3 - 6*x**4 + 144*x**3 - 504*x**2 = 0. What is x?
-21, 0, 6
Suppose 4*x**3 - 3144*x**2 + 823728*x - 71938912 = 0. Calculate x.
262
Solve 2*x**5/9 + 6*x**4 + 502*x**3/9 + 194*x**2 + 144*x = 0.
-9, -8, -1, 0
Find k, given that 14*k**5 - 60*k**4 - 68*k**3 + 80*k**2 + 54*k - 20 = 0.
-1, 2/7, 1, 5
Find y, given that y**2/2 - 295*y/2 = 0.
0, 295
Factor 21*r**5 - 60*r**4 + 54*r**3 - 12*r**2 - 3*r.
3*r*(r - 1)**3*(7*r + 1)
Let u**3/4 - 11*u**2 + 437*u/4 + 529/2 = 0. Calculate u.
-2, 23
Let 7*y**2/9 + 59*y/9 + 10 = 0. Calculate y.
-45/7, -2
Determine a so that -a**2/2 - 793*a/2 - 396 = 0.
-792, -1
Let 5*u**3 + 235*u**2 + 980*u - 2940 = 0. What is u?
-42, -7, 2
Solve 2*l**2/11 + 3524*l/11 + 1552322/11 = 0.
-881
Factor -3*f**5 - 18*f**4 + 165*f**3.
-3*f**3*(f - 5)*(f + 11)
Determine q so that q**4/5 - q**3 - 63*q**2/5 - 43*q/5 + 22 = 0.
-5, -2, 1, 11
Find c such that 4*c**3 - 1380*c**2 - 16*c + 5520 = 0.
-2, 2, 345
Find a, given that -2*a**3 - 32*a**2 + 152*a - 160 = 0.
-20, 2
Let 4*p**2/7 - 432*p/7 - 436/7 = 0. Calculate p.
-1, 109
Factor -b**4/4 - 15*b**3/2 - 157*b**2/4 + 255*b - 289.
-(b - 2)**2*(b + 17)**2/4
Factor -x**3 + 27*x**2 + 324*x.
-x*(x - 36)*(x + 9)
Factor 4*y**2 + 40*y + 100.
4*(y + 5)**2
Factor -2*s**2/3 - 1130*s/3 + 1132/3.
-2*(s - 1)*(s + 566)/3
Suppose 2*t**4 - 84*t**3 + 630*t**2 + 1612*t = 0. Calculate t.
-2, 0, 13, 31
Find s such that 2*s**4/17 + 26*s**3/17 + 22*s**2/17 - 26*s/17 - 24/17 = 0.
-12, -1, 1
Find l, given that -20*l**3 - 3845*l**2 - 8560*l - 1900 = 0.
-190, -2, -1/4
Factor 21*x**3 - 279*x**2 + 63*x + 195.
3*(x - 13)*(x - 1)*(7*x + 5)
Factor -2*w**2/7 + 330*w/7 + 332/7.
-2*(w - 166)*(w + 1)/7
Solve v**5 + 18*v**4 - 310*v**3 + 272*v**2 + 309*v - 290 = 0 for v.
-29, -1, 1, 10
Factor g**5 + 11*g**4 + 43*g**3 + 77*g**2 + 64*g + 20.
(g + 1)**2*(g + 2)**2*(g + 5)
Determine t, given that -2*t**2 + 9210*t = 0.
0, 4605
Factor -16*i**4/3 - 40*i**3/3 - 11*i**2 - 3*i.
-i*(i + 1)*(4*i + 3)**2/3
Find n, given that 10*n**5 - 12*n**4 - 18*n**3 + 4*n**2 = 0.
-1, 0, 1/5, 2
Determine x so that -x**2/3 + 90*x - 6075 = 0.
135
Suppose -b**2/5 - 1112*b/5 - 309136/5 = 0. Calculate b.
-556
Factor -a**2/6 - 17*a/6 - 10.
-(a + 5)*(a + 12)/6
Factor -5*f**3 + 705*f**2 - 690*f - 1400.
-5*(f - 140)*(f - 2)*(f + 1)
Solve 84*b**3 + 764*b**2 + 744*b + 64 = 0.
-8, -1, -2/21
Let -3*d**5 + 51*d**4 - 126*d**3 = 0. Calculate d.
0, 3, 14
Factor -2*n**3/9 - 310*n**2/9 - 12166*n/9 - 11858/9.
-2*(n + 1)*(n + 77)**2/9
Find z, given that -7*z**5 - 31*z**4 - 44*z**3 - 20*z**2 = 0.
-2, -10/7, -1, 0
Factor -2*r**2/13 + 8352*r/13 - 8719488/13.
-2*(r - 2088)**2/13
Solve -2*d**2/5 - 8*d/5 + 18 = 0 for d.
-9, 5
Factor -h**3/4 + 715*h**2/4 - 1069*h/2 + 356.
-(h - 712)*(h - 2)*(h - 1)/4
Factor -2*b**3/13 + 198*b**2/13 - 30*b + 194/13.
-2*(b - 97)*(b - 1)**2/13
Factor -2*k**3 - 348*k**2 - 1360*k.
-2*k*(k + 4)*(k + 170)
Factor -2*f**3 - 12*f**2 + 30*f + 200.
-2*(f - 4)*(f + 5)**2
Let -2*n**4 + 282*n**3 + 300*n**2 - 2248*n - 3408 = 0. What is n?
-2, 3, 142
Determine o so that 4*o**4 + 24*o**3 - 28*o**2 - 144*o + 144 = 0.
-6, -3, 1, 2
Factor -5*s**3 - 330*s**2 - 1555*s - 1830.
-5*(s + 2)*(s + 3)*(s + 61)
Let -3*d**3 - 4722*d**2 - 1858107*d = 0. What is d?
-787, 0
Find v such that 54*v**4 + 2952*v**3/5 - 3432*v**2/5 + 64*v + 384/5 = 0.
-12, -4/15, 2/3
Let -5*o**5 - 75*o**4 - 305*o**3 - 105*o**2 + 490*o = 0. What is o?
-7, -2, 0, 1
Find v such that v**3 - 155*v**2 - 3400*v - 17500 = 0.
-10, 175
Solve -8*j**3 - 386*j**2 - 832*j - 184 = 0.
-46, -2, -1/4
Solve -x**4/4 - 11*x**3/4 - 5*x**2/2 = 0 for x.
-10, -1, 0
Factor -2*v**3 - 8*v**2 + 2*v + 8.
-2*(v - 1)*(v + 1)*(v + 4)
Suppose -4*p**2/7 - 334*p/7 - 166/7 = 0. Calculate p.
-83, -1/2
Factor 32*z**3/3 + 670*z**2/9 - 782*z/9 + 16/9.
2*(z - 1)*(z + 8)*(48*z - 1)/9
Suppose -2*v**3 + 4*v**2 + 48*v = 0. What is v?
-4, 0, 6
Factor -4*j**4 - 68*j**3 + 276*j**2 + 740*j + 400.
-4*(j - 5)*(j + 1)**2*(j + 20)
Factor 5*o**3 + 35*o**2 + 55*o + 25.
5*(o + 1)**2*(o + 5)
Determine h so that -5*h**5 + 20*h**4 + 210*h**3 + 160*h**2 - 205*h - 180 = 0.
-4, -1, 1, 9
Factor z**4 - 181*z**3 + 8274*z**2 - 7020*z - 48600.
(z - 90)**2*(z - 3)*(z + 2)
Let 2*s**4/3 + 20*s**3/3 + 24*s**2 + 36*s + 18 = 0. Calculate s.
-3, -1
Suppose 5*v**4 - 60*v**3 - 75*v**2 + 130*v = 0. What is v?
-2, 0, 1, 13
Factor -2*a**2/7 + 104*a/7 - 42.
-2*(a - 49)*(a - 3)/7
Determine f so that f**2/4 + 31*f/4 - 33/2 = 0.
-33, 2
Factor -f**3/3 - 16*f**2/3 - 76*f/3 - 32.
-(f + 2)*(f + 6)*(f + 8)/3
Factor 2*z**4/13 - 28*z**3/13 + 138*z**2/13 - 280*z/13 + 200/13.
2*(z - 5)**2*(z - 2)**2/13
Factor 2*m**2/13 - 292*m/13 + 576/13.
2*(m - 144)*(m - 2)/13
Solve 2*c**2/9 + 106*c/9 - 112/3 = 0 for c.
-56, 3
Let -2*y**2 + 22*y/3 - 4 = 0. What is y?
2/3, 3
Factor 2*o**3/9 + 28*o**2/9 + 26*o/9.
2*o*(o + 1)*(o + 13)