1)
Determine r, given that -r**2/4 - 21*r/2 - 54 = 0.
-36, -6
Factor -50*n**3/13 - 630*n**2/13 - 912*n/13 - 352/13.
-2*(n + 11)*(5*n + 4)**2/13
Factor 2*l**3/5 - 642*l**2 + 343470*l - 61252150.
2*(l - 535)**3/5
Find t, given that 6*t**2/11 + 4*t - 50/11 = 0.
-25/3, 1
Factor -3*t**4 - 39*t**3 - 117*t**2 - 81*t.
-3*t*(t + 1)*(t + 3)*(t + 9)
Factor -4*h**2 + 84*h + 88.
-4*(h - 22)*(h + 1)
What is f in 2*f**2 - 22*f + 36 = 0?
2, 9
What is r in -4*r**3 - 16*r**2 + 84*r = 0?
-7, 0, 3
Suppose -4*v**2 + 648*v + 2656 = 0. What is v?
-4, 166
Find u, given that 5*u**2 + 135*u - 290 = 0.
-29, 2
Suppose 81*g**5 - 522*g**4 + 447*g**3 + 774*g**2 - 396*g - 120 = 0. Calculate g.
-1, -2/9, 2/3, 2, 5
Solve -4*u**3 - 40*u**2 - 112*u - 96 = 0.
-6, -2
What is u in -4*u**2/5 - 484*u/5 + 488/5 = 0?
-122, 1
What is w in -5*w**3 + 2545*w**2/4 + 4525*w/4 - 645/2 = 0?
-2, 1/4, 129
Let p**3/3 - 59*p**2 + 232*p - 692/3 = 0. What is p?
2, 173
Find n, given that -8*n**4/7 - 684*n**3/7 - 14444*n**2/7 + 7740*n/7 + 7396/7 = 0.
-43, -1/2, 1
Factor 28*q**3 - 20*q**2 - 28*q + 20.
4*(q - 1)*(q + 1)*(7*q - 5)
Solve -q**3/7 + 376*q**2/7 - 2589*q/7 + 2214/7 = 0 for q.
1, 6, 369
Let 180*l**5 + 10335*l**4 + 14345*l**3 + 3625*l**2 - 845*l - 280 = 0. Calculate l.
-56, -1, -1/3, 1/4
Factor -9*m**3/4 - 43*m**2/4 - 13*m/2 + 2.
-(m + 1)*(m + 4)*(9*m - 2)/4
Factor 4*c**3/9 + 2156*c**2/9 + 2152*c/9.
4*c*(c + 1)*(c + 538)/9
Factor 5*t**4 - 55*t**3 + 50*t**2.
5*t**2*(t - 10)*(t - 1)
Factor -5*g**4 + 40*g**3 - 105*g**2 + 90*g.
-5*g*(g - 3)**2*(g - 2)
Solve -3*u**2/4 - 63*u/2 - 1323/4 = 0 for u.
-21
Solve -2*x**2/3 + 2110*x/3 + 4228/3 = 0.
-2, 1057
Let -5*d**3 + 35*d**2 + 5*d - 35 = 0. Calculate d.
-1, 1, 7
Factor -5*y**2 + 4730*y - 1118645.
-5*(y - 473)**2
Factor -3*p**3/4 - 459*p**2/2 + 462*p.
-3*p*(p - 2)*(p + 308)/4
Find m such that 2*m**4/11 - 50*m**3/11 + 244*m**2/11 - 304*m/11 = 0.
0, 2, 4, 19
Let 2*n**5/3 - 4*n**4/3 + 4*n**2/3 - 2*n/3 = 0. Calculate n.
-1, 0, 1
Factor t**2 - 396*t + 395.
(t - 395)*(t - 1)
Find h such that -h**3 + 88*h**2 + 273*h = 0.
-3, 0, 91
Factor 2*z**5 - 18*z**4 + 40*z**3 - 24*z**2.
2*z**2*(z - 6)*(z - 2)*(z - 1)
Find l such that 670*l**3 - 4022*l**2/3 + 2014*l/3 - 2/3 = 0.
1/1005, 1
Factor -8*r**5/5 - 14*r**4/5 + 4*r**3/5.
-2*r**3*(r + 2)*(4*r - 1)/5
Factor 3*n**2/2 + 2046*n + 697686.
3*(n + 682)**2/2
Find g such that 3*g**3 + 51*g**2 + 264*g + 432 = 0.
-9, -4
Find h such that 8*h**5 - 122*h**4 - 234*h**3 - 70*h**2 + 34*h = 0.
-1, 0, 1/4, 17
Factor -z**2/2 - 419*z/2 + 210.
-(z - 1)*(z + 420)/2
Solve 2*p**3 + 20*p**2 - 2*p - 20 = 0 for p.
-10, -1, 1
What is z in -2*z**4/11 + 16*z**3/11 - 36*z**2/11 + 32*z/11 - 10/11 = 0?
1, 5
Factor -3*q**2/4 - 711*q/2.
-3*q*(q + 474)/4
What is t in -t**4/9 + 7*t**3 - 61*t**2/3 + 181*t/9 - 20/3 = 0?
1, 60
Factor -4*q**2 - 40*q - 84.
-4*(q + 3)*(q + 7)
Let 2*q**2 - 28*q + 96 = 0. What is q?
6, 8
Factor -o**4/5 - o**3 + 111*o**2/5 - 47*o - 70.
-(o - 5)**2*(o + 1)*(o + 14)/5
Factor o**4 - 14*o**3 + 52*o**2 + 24*o - 288.
(o - 6)**2*(o - 4)*(o + 2)
Factor 64*l**3/5 + 32*l**2/5 - 12*l - 36/5.
4*(l - 1)*(4*l + 3)**2/5
Find m such that 9*m**5 - 87*m**4 - 522*m**3 - 372*m**2 + 504*m = 0.
-3, -2, 0, 2/3, 14
Factor 2*s**2/13 + 118*s/13 - 120/13.
2*(s - 1)*(s + 60)/13
Suppose -2*a**2/7 + 930*a/7 = 0. What is a?
0, 465
Factor w**3/5 - 22*w**2 + 3417*w/5 - 20808/5.
(w - 51)**2*(w - 8)/5
Factor -5*y**3 - 5*y**2 + 45*y + 45.
-5*(y - 3)*(y + 1)*(y + 3)
Let 5*k**2 - 2370*k + 280845 = 0. Calculate k.
237
Solve o**2/6 + 67*o/3 + 280 = 0.
-120, -14
Factor -11*h**4/3 + 7*h**3 + 2*h**2/3.
-h**2*(h - 2)*(11*h + 1)/3
Factor -2*o**3/3 - 30*o**2 - 352*o - 968/3.
-2*(o + 1)*(o + 22)**2/3
Solve -3*l**5/4 - 249*l**4/4 - 945*l**3/4 + 249*l**2/4 + 237*l = 0.
-79, -4, -1, 0, 1
Factor c**3/3 - 62*c**2 + 2820*c + 17672/3.
(c - 94)**2*(c + 2)/3
Factor -m**2/10 - 284*m/5 - 40328/5.
-(m + 284)**2/10
Factor 69*u**2/2 - 411*u/2 - 9.
3*(u - 6)*(23*u + 1)/2
Find u such that u**3/3 - 1444*u**2/3 - 2891*u/3 - 482 = 0.
-1, 1446
Factor -4*i**3 - 4*i**2 + 80*i.
-4*i*(i - 4)*(i + 5)
Factor -2*n**2/3 + 950*n/3 - 316.
-2*(n - 474)*(n - 1)/3
Solve -2*h**5 - 2*h**4 + 262*h**3 + 1882*h**2 + 4420*h + 2800 = 0.
-5, -4, -1, 14
Factor -3*r**3 + 18*r**2 - 36*r + 24.
-3*(r - 2)**3
Factor -3*c**3/7 - 3*c**2/7 + 3*c/7 + 3/7.
-3*(c - 1)*(c + 1)**2/7
Factor -g**3 - 1335*g**2 - 594075*g - 88121125.
-(g + 445)**3
Let -294*x**5 - 98*x**4 + 220*x**3 + 8*x**2 - 16*x = 0. What is x?
-1, -2/7, 0, 2/7, 2/3
Factor -q**5/7 + q**4 + 8*q**3/7.
-q**3*(q - 8)*(q + 1)/7
Let -3*s**2 + 294*s - 7203 = 0. Calculate s.
49
What is s in 3*s**4 - 306*s**3 + 8091*s**2 - 14100*s - 22500 = 0?
-1, 3, 50
Solve 2*m**3/19 - 492*m**2/19 - 1994*m/19 - 1500/19 = 0 for m.
-3, -1, 250
Factor -m**5 - m**4 + 6*m**3 + 4*m**2 - 8*m.
-m*(m - 2)*(m - 1)*(m + 2)**2
Let v**3 - 513*v**2 - 1029*v - 515 = 0. Calculate v.
-1, 515
Suppose -9*k**5 + 33*k**4 + 120*k**3 + 36*k**2 = 0. What is k?
-2, -1/3, 0, 6
Factor 2*l**2/13 - 58*l/13 - 420/13.
2*(l - 35)*(l + 6)/13
Let 6*m**4 - 447*m**3 - 690*m**2 + 456*m = 0. Calculate m.
-2, 0, 1/2, 76
Factor -3*v**4 - 180*v**3 - 2874*v**2 - 5220*v - 2523.
-3*(v + 1)**2*(v + 29)**2
Let 2*l**5/13 - 70*l**4/13 - 82*l**3/13 + 366*l**2/13 - 216*l/13 = 0. What is l?
-3, 0, 1, 36
Factor r**4 - 16*r**3 - 23*r**2 + 102*r.
r*(r - 17)*(r - 2)*(r + 3)
Find f such that -f**4 - 46*f**3 - 181*f**2 + 8004*f - 30276 = 0.
-29, 6
Find y such that -5*y**2 + 3955*y + 7930 = 0.
-2, 793
Determine p so that -2*p**4 + 22*p**3 + 180*p**2 + 392*p + 272 = 0.
-2, 17
Solve -7*a**4 + 89*a**3 + 33*a**2 - 89*a - 26 = 0.
-1, -2/7, 1, 13
Factor 401956*f**2/9 - 17752*f/9 + 196/9.
4*(317*f - 7)**2/9
Factor 4*s**2 - 82*s - 392.
2*(s + 4)*(2*s - 49)
Factor -3*f**4/2 + 375*f**3 - 52491*f**2/2 + 351000*f - 1314144.
-3*(f - 117)**2*(f - 8)**2/2
Find l, given that -l**4/8 - 17*l**3/4 - 253*l**2/8 + 153*l/2 - 81/2 = 0.
-18, 1
Factor -2*i**4/21 - 8*i**3/21 + 32*i**2/7 - 32*i/3 + 160/21.
-2*(i - 2)**3*(i + 10)/21
Factor -l**3/6 + 19*l**2/3 - 238*l/3 + 980/3.
-(l - 14)**2*(l - 10)/6
Suppose -4*u**4 + 32*u**3 - 92*u**2 + 112*u - 48 = 0. Calculate u.
1, 2, 3
Solve -3*f**3 + 174*f**2 = 0.
0, 58
Factor 12*f**3 - 201*f**2 + 912*f - 576.
3*(f - 8)**2*(4*f - 3)
Solve 2*i**3 - 62*i**2 + 412*i - 352 = 0 for i.
1, 8, 22
Factor 3*r**4 - 9378*r**3 + 7338279*r**2 - 14648436*r + 7319532.
3*(r - 1562)**2*(r - 1)**2
Factor 5*r**2 + 85*r.
5*r*(r + 17)
Factor 490*k**2 + 28*k + 2/5.
2*(35*k + 1)**2/5
Factor 3*n**2 + 6*n - 9.
3*(n - 1)*(n + 3)
Factor 16*z**5 + 16*z**4 - 12*z**3 - 8*z**2 + 4*z.
4*z*(z + 1)**2*(2*z - 1)**2
Suppose -3*m**5 + 33*m**4 - 51*m**3 - 213*m**2 + 306*m + 432 = 0. Calculate m.
-2, -1, 3, 8
Determine w, given that -12*w**4/7 - 18*w**3 - 150*w**2/7 + 108*w/7 = 0.
-9, -2, 0, 1/2
Factor -4*i**2 + 708*i.
-4*i*(i - 177)
Factor -2*r**2 + 62*r.
-2*r*(r - 31)
Factor 2*v**4 - 85*v**3 + 1218*v**2 - 6076*v + 2744.
(v - 14)**3*(2*v - 1)
Solve -2*x**3/7 - 14*x**2 - 1558*x/7 - 7942/7 = 0 for x.
-19, -11
Factor -3*a**3/4 - 57*a**2/4 + 48*a - 33.
-3*(a - 2)*(a - 1)*(a + 22)/4
Find y, given that -5*y**3 + 1245*y**2 + 5040*y + 5060 = 0.
-2, 253
Suppose -3*a**5 - 6*a**4 + 6*a**2 + 3*a = 0. Calculate a.
-1, 0, 1
Suppose -2*r**3/15 + 76*r**2/15 + 866*r/5 + 168 = 0. What is r?
-21, -1, 60
Factor 2*g**4/3 + 256*g**3/3 - 518*g**2/3 + 260*g/3.
2*g*(g - 1)**2*(g + 130)/3
What is c in -56*c**3 - 236*c**2 + 212*c - 40 = 0?
-5, 2/7, 1/2
Solve -25*g**4 - 210*g**3 - 256*g**2 - 78*g - 7 = 0 for g.
-7, -1, -1/5
Factor t**4/2 + 9*t**3/2 - 21*t**2/2 + 11*t/2.
t*(t - 1)**2*(t + 11)/2
Solve 3*l**4/2 + 9*l**3/2 - 9*l**2/2 - 21*l/2 + 9 = 0.
-3, -2, 1
Factor -2*i**2/7 - 1812*i/7 - 410418/7.
-2*(i + 453)**2/7
Find r such that -5*r**3 + 60*r**2 + 135*r + 70 = 0.
-1, 14
Factor z**3 - 194*z**2 + 9409*z.
z*(z - 97)**2
What is g in 2*g**2/7 - 108*g/7 + 144 = 0?
12, 42
Factor z**2/2 - 32*z + 512.
(z - 32)**2/2
Factor 2*u**2/13 - 298*u/13 + 588/13.
2*(u - 147)*(u - 2)/13
Solve 3*b**3/5 + 18*b**2/5 - 57*b/5 - 252/5 = 0 for b.
-7, -3, 4
Find s such that -4*s**5 - 144*s**4 - 272*s**3 + 8*s**2 + 276*s + 136 = 0.
-34, -1, 1
Suppose -10*j**3 - 15*j**2 + 5 = 0. Calculate j.
-1, 1/2
Factor -h**5/2 + 197*h**4 - 37201*h**3/2 - 158388*h**2 - 323208*h.
-h*(h - 201)**2*(h + 4)**2/2
Factor 389017*c**5/2 - 373