18
Find q, given that q**3/5 - 141*q**2/5 + 1320*q - 20500 = 0.
41, 50
Determine u so that 256*u**4 + 4672*u**3 + 10756*u**2 - 96360*u + 108900 = 0.
-11, 15/8
Factor -h**4 - 20*h**3 - 83*h**2 - 124*h - 60.
-(h + 1)*(h + 2)**2*(h + 15)
Factor -3*r**5 + 12*r**4 - 3*r**3 - 30*r**2 + 12*r + 24.
-3*(r - 2)**3*(r + 1)**2
Factor 5*x**3/6 - 55*x**2/3 + 400*x/3 - 320.
5*(x - 8)**2*(x - 6)/6
Solve -2*k**3 + 308*k**2 + 2*k - 308 = 0 for k.
-1, 1, 154
Find m, given that -m**4/5 + 15*m**2 - 50*m = 0.
-10, 0, 5
Find u, given that u**4 - 6*u**3 + 32*u = 0.
-2, 0, 4
Factor 2*a**2/23 - 76*a/23 - 78/23.
2*(a - 39)*(a + 1)/23
Find k such that -4*k**4/3 - 16*k**3/3 + 40*k**2/3 + 112*k/3 + 20 = 0.
-5, -1, 3
Solve -7*k**3 + 506*k**2 - 144*k = 0.
0, 2/7, 72
Factor o**3 - 16*o**2 - 36*o.
o*(o - 18)*(o + 2)
Factor -t**2/2 + 47*t - 2209/2.
-(t - 47)**2/2
Factor -4*i**2 + 2120*i - 280900.
-4*(i - 265)**2
Find u such that -u**2/2 - 132*u - 783/2 = 0.
-261, -3
Factor c**3 - 28*c**2 - 29*c.
c*(c - 29)*(c + 1)
Solve 5*c**2 + 80*c + 320 = 0.
-8
Let 5*a**3 - 135*a**2 + 480*a - 460 = 0. What is a?
2, 23
Factor -5*l**2 - 60*l - 135.
-5*(l + 3)*(l + 9)
Factor q**4/4 - 5*q**3/2 - 3*q**2/4 + 7*q + 5.
(q - 10)*(q - 2)*(q + 1)**2/4
Let -2*t**4/3 + 106*t**3 - 6230*t**2 + 482650*t/3 - 1543500 = 0. Calculate t.
35, 54
Let -2*p**4/5 + 12*p**3 - 448*p**2/5 + 192*p = 0. What is p?
0, 4, 6, 20
Factor 4*y**2 - 192*y + 860.
4*(y - 43)*(y - 5)
Let 3*p**2/7 - 1740*p/7 + 3468/7 = 0. Calculate p.
2, 578
Let -2*o**2/7 - 8*o/7 + 6490/7 = 0. Calculate o.
-59, 55
Suppose -27*w**2 + 60*w - 12 = 0. What is w?
2/9, 2
Suppose -4*k**5 - 28*k**4 - 44*k**3 + 76*k**2 + 240*k + 144 = 0. What is k?
-3, -2, -1, 2
Factor j**3 + 24*j**2 - 108*j + 112.
(j - 2)**2*(j + 28)
Factor -2*r**2/5 + 8164*r/5 - 8331362/5.
-2*(r - 2041)**2/5
Suppose 8*m**3 + 30*m**2 + 28*m = 0. What is m?
-2, -7/4, 0
What is n in -2*n**2/3 + 10*n + 32/3 = 0?
-1, 16
Factor -2*k**3/15 + 58*k**2/5 + 536*k/15 + 24.
-2*(k - 90)*(k + 1)*(k + 2)/15
Let f**4/5 + 6*f**3 - 35*f**2 = 0. What is f?
-35, 0, 5
Solve 5*x**2 - 2530*x + 320045 = 0.
253
Suppose -10*r**4/13 - 314*r**3/13 - 1778*r**2/13 + 3482*r/13 - 1380/13 = 0. What is r?
-23, -10, 3/5, 1
Suppose 9*h**4 + 506*h**3 + 1084*h**2 + 216*h = 0. Calculate h.
-54, -2, -2/9, 0
Factor 5*a**4/4 - 5*a**3/4 - 10*a**2 + 15*a.
5*a*(a - 2)**2*(a + 3)/4
Solve -4*s**3 - 1688*s**2 - 181412*s - 698896 = 0 for s.
-209, -4
Let 80*w**5 + 440*w**4 - 275*w**3 - 215*w**2 - 30*w = 0. Calculate w.
-6, -1/4, 0, 1
Find y such that y**4 - 9*y**3 = 0.
0, 9
Factor i**3 + 24*i**2 + 84*i - 784.
(i - 4)*(i + 14)**2
Determine l, given that -2*l**4 - 374*l**3/9 - 206*l**2/3 - 62*l/3 + 76/9 = 0.
-19, -1, 2/9
Solve 4*l**3/5 + 383*l**2/5 + 1824*l - 2304/5 = 0 for l.
-48, 1/4
Factor w**2/4 - 22*w - 89/4.
(w - 89)*(w + 1)/4
Suppose -4*n**4 + 31*n**3 + 203*n**2 + 24*n - 144 = 0. What is n?
-4, -1, 3/4, 12
Factor -b**4/3 + 44*b**3/3 - 43*b**2/3.
-b**2*(b - 43)*(b - 1)/3
Factor -4*m**2 - 260*m + 1400.
-4*(m - 5)*(m + 70)
Factor 3*i**3 - 15*i**2 + 21*i - 9.
3*(i - 3)*(i - 1)**2
Determine b so that 2*b**5 - 42*b**4 + 146*b**3 - 174*b**2 + 68*b = 0.
0, 1, 2, 17
Determine x so that 10*x**3/9 + 442*x**2/9 + 4928*x/9 + 968/9 = 0.
-22, -1/5
Factor a**3/9 - 392*a**2/3 + 38416*a.
a*(a - 588)**2/9
Determine r so that -2*r**3 + 18*r = 0.
-3, 0, 3
Factor -5*z**3 + 355*z**2 - 3895*z - 92455.
-5*(z - 41)**2*(z + 11)
Factor -2*p**2/21 + 4*p/21 + 16/21.
-2*(p - 4)*(p + 2)/21
Factor d**4 - 3*d**3/2 - 3*d**2/2 + d.
d*(d - 2)*(d + 1)*(2*d - 1)/2
Factor 2*g**2/11 + 24*g/11 + 70/11.
2*(g + 5)*(g + 7)/11
Solve p**3/4 - 26*p**2 + 499*p/4 - 99 = 0.
1, 4, 99
Factor -3*l**3 + 195*l**2 - 3069*l - 3267.
-3*(l - 33)**2*(l + 1)
Determine p so that -4*p**3/7 - 512*p**2/7 - 2480*p - 61504/7 = 0.
-62, -4
Factor -2*n**2/7 - 3212*n/7 - 1289618/7.
-2*(n + 803)**2/7
Solve t**4 - 5*t**3 + 5*t**2 + 5*t - 6 = 0 for t.
-1, 1, 2, 3
Factor i**5/8 - 7*i**4/8 + 5*i**3/8 + 7*i**2/8 - 3*i/4.
i*(i - 6)*(i - 1)**2*(i + 1)/8
Factor -r**3 - 84*r**2 - 1764*r.
-r*(r + 42)**2
Determine m so that -2*m**4 - 48*m**3 - 288*m**2 + 512*m + 6144 = 0.
-12, -8, 4
Factor o**3/2 + 21*o**2 - o/2 - 21.
(o - 1)*(o + 1)*(o + 42)/2
Let j**5 - 70*j**4 + 1548*j**3 - 11016*j**2 = 0. Calculate j.
0, 18, 34
Let -2*n**5/5 + 38*n**4/5 + 268*n**3 - 2740*n**2 - 59250*n - 56250 = 0. Calculate n.
-15, -1, 25
Find i, given that -2*i**5/7 + 12*i**4/7 + 256*i**3/7 + 960*i**2/7 + 1024*i/7 = 0.
-4, -2, 0, 16
Find b, given that 4*b**2 - 11928*b = 0.
0, 2982
Factor k**4/2 + 17*k**3 + 205*k**2/2 + 222*k + 162.
(k + 2)**2*(k + 3)*(k + 27)/2
Solve 14*z**4 + 802*z**3/9 + 1414*z**2/9 + 146*z/3 + 4 = 0 for z.
-3, -2/9, -1/7
Suppose 4*v**3/21 + 10*v**2/21 - 22*v/21 + 8/21 = 0. Calculate v.
-4, 1/2, 1
Factor 2*t**2 - 12*t - 270.
2*(t - 15)*(t + 9)
Factor 2*w**3/9 + 16*w**2/9 + 40*w/9 + 32/9.
2*(w + 2)**2*(w + 4)/9
Suppose 10*u**2/3 + 4*u + 6/5 = 0. Calculate u.
-3/5
Factor 4*u**2 - 4.
4*(u - 1)*(u + 1)
What is i in 3*i**2/2 - 195*i/2 - 99 = 0?
-1, 66
Factor 2*s**2/15 + 66*s/5 + 196/15.
2*(s + 1)*(s + 98)/15
Factor 50*a**3/3 - 830*a**2/3 - 338*a/3 - 34/3.
2*(a - 17)*(5*a + 1)**2/3
Find f such that -2*f**5/7 + 20*f**4/7 - 8*f**3 + 12*f**2/7 + 90*f/7 = 0.
-1, 0, 3, 5
Let -2*a**2 - 20*a - 18 = 0. Calculate a.
-9, -1
Factor -2*q**3/11 - 4262*q**2/11 + 8530*q/11 - 4266/11.
-2*(q - 1)**2*(q + 2133)/11
Determine m so that -3*m**2 + 480*m - 19200 = 0.
80
Factor 2*v**3/15 + 4*v**2/5 - 8*v/15 - 16/5.
2*(v - 2)*(v + 2)*(v + 6)/15
Factor 51*l**2/5 + 114*l/5 + 24/5.
3*(l + 2)*(17*l + 4)/5
Factor i**5 - 5*i**4 + 6*i**3 + 2*i**2 - 7*i + 3.
(i - 3)*(i - 1)**3*(i + 1)
Factor j**2 - 8*j + 12.
(j - 6)*(j - 2)
Find j, given that 5*j**5 + 970*j**4 - 10*j**3 - 1940*j**2 + 5*j + 970 = 0.
-194, -1, 1
What is f in -24*f**4 + 12*f**3 + 378*f**2 + 729*f + 405 = 0?
-3/2, 5
Suppose -9*m**4/2 - 6*m**3 + 39*m**2/2 - 9*m = 0. Calculate m.
-3, 0, 2/3, 1
Factor -z**2 + 3*z + 18.
-(z - 6)*(z + 3)
Solve 2*d**2/3 - 24*d + 136/3 = 0.
2, 34
Determine r so that 4*r**2 + 556*r + 552 = 0.
-138, -1
Factor t**5 - 5*t**4 - 17*t**3 + 49*t**2 + 160*t + 100.
(t - 5)**2*(t + 1)*(t + 2)**2
Factor -3*j**3 + 165*j**2 - 321*j + 159.
-3*(j - 53)*(j - 1)**2
Factor -2*s**3 + 188*s**2 - 1042*s - 1232.
-2*(s - 88)*(s - 7)*(s + 1)
Factor y**3 - 132*y**2 + 261*y - 130.
(y - 130)*(y - 1)**2
Factor 2*p**3/9 + 146*p**2/9 + 304*p + 288.
2*(p + 1)*(p + 36)**2/9
What is t in 10*t**3 - 775*t**2 - 1990*t - 800 = 0?
-2, -1/2, 80
Factor -d**2/7 + 20*d/7.
-d*(d - 20)/7
Factor -3*o**4 + 6*o**3 + 3*o**2 - 6*o.
-3*o*(o - 2)*(o - 1)*(o + 1)
Find o, given that 5*o**3/2 - 1483*o**2/2 + 443*o + 296 = 0.
-2/5, 1, 296
Find t such that -t**3 - 25*t**2 - 24*t = 0.
-24, -1, 0
Suppose 4*f**2/7 + 12*f + 216/7 = 0. Calculate f.
-18, -3
Factor -3*z**3 + 78*z**2 + 255*z + 174.
-3*(z - 29)*(z + 1)*(z + 2)
Solve -3*m**4/2 - 51*m**3/2 + 57*m**2 = 0 for m.
-19, 0, 2
Find i, given that -3*i**5 - 111*i**4 - 1347*i**3 - 6009*i**2 - 10170*i - 5400 = 0.
-15, -4, -2, -1
Suppose 4*a**3 - 36*a**2 + 80*a - 48 = 0. What is a?
1, 2, 6
Factor q**4 + 11*q**3 - 29*q**2 - 39*q.
q*(q - 3)*(q + 1)*(q + 13)
Factor -y**3/3 - 21*y**2 + y/3 + 21.
-(y - 1)*(y + 1)*(y + 63)/3
Let 14*k**5/3 - 148*k**4/15 - 62*k**3/15 + 164*k**2/15 - 8*k/15 - 16/15 = 0. Calculate k.
-1, -2/7, 2/5, 1, 2
Factor 5*j**5 - 45*j**4 + 120*j**3 - 80*j**2.
5*j**2*(j - 4)**2*(j - 1)
Let -10*y**5 - 64*y**4 - 54*y**3 + 88*y**2 + 40*y = 0. What is y?
-5, -2, -2/5, 0, 1
Determine x, given that 5*x**5/2 + 20*x**4 + 50*x**3 + 25*x**2 - 105*x/2 - 45 = 0.
-3, -2, -1, 1
Solve 2*n**4/21 - 226*n**3/21 + 2420*n**2/7 - 6656*n/3 - 54080/21 = 0.
-1, 10, 52
Factor 2*u**3/5 - 18*u**2/5 + 28*u/5 + 48/5.
2*(u - 6)*(u - 4)*(u + 1)/5
Factor 5*k**5 - 20*k**4 - 40*k**3 + 50*k**2 + 115*k + 50.
5*(k - 5)*(k - 2)*(k + 1)**3
Find l such that 2*l**3/5 + 6*l**2/5 - 8*l/5 = 0.
-4, 0, 1
Factor 2*g**3/5 - 908*g**2/5 - 1822*g/5 - 912/5.
2*(g - 456)*(g + 1)**2/5
Solve -4*z**4/3 + 58*z**3/3 - 8*z**2 - 58*z/3 + 28/3 = 0.
-1, 1/2, 1, 14
Solve 3*j**5 + 12*j**4 + 9*j**3 - 12*j**2 - 12*j = 0 for j.
-2, -1, 0, 1
What is g in -27*g**4/8 - 2073*g**3/8 - 2793*g**2/4 - 663*g/2 + 111 = 0?
-74, -2, -1, 2/9
Suppose 5*o**4 + 35*o**3 + 75*o**2 + 45*o = 0. What is o?
-3, -1, 0
Factor -5*n**3/2 - 43*n**2/4 - 33*n/4.
-n