r c**4/4 + c**3/2 - 7*c**2/4 - 5*c - 3.
(c - 3)*(c + 1)*(c + 2)**2/4
Let -18*r**4 + 94*r**3 - 20*r**2 = 0. What is r?
0, 2/9, 5
Find p, given that p**4/2 - 7*p**3 - 147*p**2/2 = 0.
-7, 0, 21
Factor -y**2/10 - 213*y/10 - 106/5.
-(y + 1)*(y + 212)/10
Solve v**4/4 - 17*v**3/8 + 43*v**2/8 - 43*v/8 + 15/8 = 0 for v.
1, 3/2, 5
Find c such that -4*c**3 - 32*c**2 + 316*c + 728 = 0.
-13, -2, 7
Let 2*x**2/7 - 6*x/7 = 0. Calculate x.
0, 3
Find s, given that 4*s**3 - 2792*s**2 + 11120*s - 11104 = 0.
2, 694
Factor -c**3 + 480*c**2 - 1433*c + 954.
-(c - 477)*(c - 2)*(c - 1)
Factor 2*o**3/5 - 278*o**2/5 - 56*o.
2*o*(o - 140)*(o + 1)/5
Suppose -w**4 - 9*w**3 - 15*w**2 - 7*w = 0. Calculate w.
-7, -1, 0
Factor -2*c**5/7 - 16*c**4/7 - 32*c**3/7.
-2*c**3*(c + 4)**2/7
Factor -h**4 - 48*h**3 - 138*h**2 - 136*h - 45.
-(h + 1)**3*(h + 45)
Suppose -f**4/4 - 145*f**3 + 1163*f**2/4 - 291*f/2 = 0. What is f?
-582, 0, 1
Factor -2*l**2/5 - 3338*l/5 - 3336/5.
-2*(l + 1)*(l + 1668)/5
Factor 37*w**3 + 45*w**2 + 8*w.
w*(w + 1)*(37*w + 8)
Determine l, given that -7*l**5 + 5*l**4 + 93*l**3 - 149*l**2 + 34*l + 24 = 0.
-4, -2/7, 1, 3
Factor 2*p**4/7 + 4*p**3/7 - 58*p**2/7 + 12*p.
2*p*(p - 3)*(p - 2)*(p + 7)/7
Factor 5*t**3 - 3735*t**2 + 695640*t + 699380.
5*(t - 374)**2*(t + 1)
Determine s so that 2*s**3/17 - 60*s**2/17 - 2*s/17 + 60/17 = 0.
-1, 1, 30
Let -3*v**5 - 15*v**4 - 3*v**3 + 39*v**2 + 6*v - 24 = 0. What is v?
-4, -2, -1, 1
Factor 3*i**3 + 756*i**2 + 2988*i + 2976.
3*(i + 2)**2*(i + 248)
Find h, given that -h**4 + 17*h**2 - 36*h + 20 = 0.
-5, 1, 2
Determine t, given that 3*t**3 + 6*t**2 - 9*t = 0.
-3, 0, 1
Factor s**5/4 - 7*s**4/4 + 5*s**3/2 + 9*s**2/2 - 27*s/4 - 27/4.
(s - 3)**3*(s + 1)**2/4
Solve -4*z**4 - 120*z**3 + 128*z**2 + 120*z - 124 = 0 for z.
-31, -1, 1
Factor -3*g**2 - 1722*g - 247107.
-3*(g + 287)**2
Factor -r**4/2 + 4*r**2 - 8.
-(r - 2)**2*(r + 2)**2/2
Determine p so that 12*p**4 + 340*p**3 + 2356*p**2 + 748*p = 0.
-17, -11, -1/3, 0
Factor -3*w**3 - 287*w**2/2 - 1704*w + 288.
-(w + 24)**2*(6*w - 1)/2
What is z in z**3/3 + 16*z**2/3 - z/3 - 16/3 = 0?
-16, -1, 1
Factor -f**4/3 + 2*f**3 + 11*f**2/3 - 20*f - 100/3.
-(f - 5)**2*(f + 2)**2/3
Suppose -2*k**4/7 + 2*k**3/7 + 4*k**2/7 = 0. What is k?
-1, 0, 2
Determine i, given that -5*i**3 + 35*i**2 + 150*i = 0.
-3, 0, 10
What is p in -2*p**3 + 12*p**2 + 176*p - 384 = 0?
-8, 2, 12
Suppose -5*g**4 - 140*g**3 - 980*g**2 = 0. What is g?
-14, 0
Solve -s**3/2 + 5*s**2 - 16*s + 16 = 0 for s.
2, 4
Factor -5*r**5 - 5*r**4 + 10*r**3 + 10*r**2 - 5*r - 5.
-5*(r - 1)**2*(r + 1)**3
Factor -24*p**2/11 + 322*p/11 + 82/11.
-2*(3*p - 41)*(4*p + 1)/11
Solve -8*t**5/5 - 4*t**4 + 8*t**3/5 + 4*t**2 = 0 for t.
-5/2, -1, 0, 1
Solve 2*w**3/3 - 304*w**2/3 + 1192*w/3 - 1184/3 = 0 for w.
2, 148
Factor -2*s**2/13 - 3556*s/13 - 1580642/13.
-2*(s + 889)**2/13
Factor -2*m**4/5 - 6*m**3/5 + 810*m**2 - 13250*m.
-2*m*(m - 25)**2*(m + 53)/5
Suppose -2*y**4 - 88*y**3 - 1248*y**2 - 6048*y - 7776 = 0. What is y?
-18, -6, -2
Determine x, given that -25*x**2 + 20090*x + 8040 = 0.
-2/5, 804
Factor b**3/9 - 11*b**2/3 + 7*b - 31/9.
(b - 31)*(b - 1)**2/9
Suppose y**3 - 360*y**2 + 717*y - 358 = 0. Calculate y.
1, 358
Factor l**4/3 - 16*l**3/3 + 13*l**2.
l**2*(l - 13)*(l - 3)/3
Factor -i**2 + 26*i - 169.
-(i - 13)**2
What is l in -3*l**4/5 + 18*l**3/5 - 9*l**2/5 - 6*l = 0?
-1, 0, 2, 5
Let -30*f**5 - 155*f**4 + 750*f**3 + 4000*f**2 - 3125 = 0. Calculate f.
-5, -1, 5/6, 5
Factor -d**4 - 37*d**3 - 325*d**2 - 1059*d - 1170.
-(d + 3)**2*(d + 5)*(d + 26)
Solve -a**2/3 - 4*a/3 - 4/3 = 0 for a.
-2
Let 5*f**2 + 220*f + 215 = 0. Calculate f.
-43, -1
Solve r**3 + 8*r**2 - 23*r - 30 = 0 for r.
-10, -1, 3
Suppose l**2 + 98*l + 2401 = 0. What is l?
-49
Factor -10*n**3 - 565*n**2 + 2075*n - 1500.
-5*(n - 1)*(n + 60)*(2*n - 5)
Determine k, given that 5*k**4 - 65*k**3 - 225*k**2 - 235*k - 80 = 0.
-1, 16
Factor 2*c**2/7 - 22*c/7 + 48/7.
2*(c - 8)*(c - 3)/7
Factor -114242*y**2/9 - 1912*y/9 - 8/9.
-2*(239*y + 2)**2/9
Factor -4*o**2/7 + 152*o + 2144/7.
-4*(o - 268)*(o + 2)/7
Suppose d**2 + 1405*d/3 + 156 = 0. What is d?
-468, -1/3
Let -f**5 - 1456*f**4 - 531438*f**3 - 1058512*f**2 - 528529*f = 0. What is f?
-727, -1, 0
Determine d, given that 2*d**2/21 - 470*d/3 + 1096/7 = 0.
1, 1644
Factor 3*l**3 - 19*l**2/2 + 3*l/2.
l*(l - 3)*(6*l - 1)/2
Determine k, given that 4*k**2/7 + 536*k + 3748/7 = 0.
-937, -1
Factor -3*k**3 + 18216*k**2 - 36869184*k + 24874409472.
-3*(k - 2024)**3
Solve 5*g**3 + 55*g**2 - 60*g = 0.
-12, 0, 1
Factor -3*t**3 - 18*t**2 + 45*t - 24.
-3*(t - 1)**2*(t + 8)
What is j in -2*j**3/3 + 34*j**2/3 + 616*j/3 = 0?
-11, 0, 28
Let r**3 - 101*r**2 + 2600*r - 2500 = 0. What is r?
1, 50
Determine n, given that -2*n**2 + 360*n - 16200 = 0.
90
Factor -2*x**3/3 - 38*x**2/3 - 128*x/3 - 40.
-2*(x + 2)**2*(x + 15)/3
Solve p**3/5 + 4*p**2/5 + 3*p/5 = 0.
-3, -1, 0
Factor -32*z**3 - 1008*z**2 - 10584*z - 37044.
-4*(2*z + 21)**3
Factor 20*c**3 + 508*c**2 + 1880*c + 672.
4*(c + 4)*(c + 21)*(5*c + 2)
Determine q so that q**3 + 561*q**2 + 78399*q - 78961 = 0.
-281, 1
Factor -x**2/9 + 116*x/9 - 185/3.
-(x - 111)*(x - 5)/9
Determine a so that 178*a**4/9 - 574*a**3 + 39988*a**2/9 - 3976*a + 784/9 = 0.
2/89, 1, 14
Factor 15*v**2/7 + 51*v/7 - 36/7.
3*(v + 4)*(5*v - 3)/7
Factor 2*c**2/5 - 716*c/5 + 64082/5.
2*(c - 179)**2/5
Let 48*u**4 - 496*u**3 + 5716*u**2/3 - 3224*u + 2028 = 0. What is u?
13/6, 3
Determine i, given that -2*i**4/5 + 1584*i**3/5 - 418176*i**2/5 + 36799488*i/5 = 0.
0, 264
Suppose -g**2/5 - 2448*g/5 - 1498176/5 = 0. What is g?
-1224
Factor -3*y**2 + 69*y + 72.
-3*(y - 24)*(y + 1)
Find h such that 3*h**4 + 57*h**3/4 + 33*h**2/4 - 3*h = 0.
-4, -1, 0, 1/4
Solve f**3/6 + 242*f**2/3 + 965*f/6 + 241/3 = 0 for f.
-482, -1
Suppose 2*x**3 - 120*x**2 + 232*x = 0. What is x?
0, 2, 58
Factor -3*y**4 - 2709*y**3 + 3*y**2 + 2709*y.
-3*y*(y - 1)*(y + 1)*(y + 903)
Factor -2*i**2/5 + 118*i/5 + 24.
-2*(i - 60)*(i + 1)/5
Solve -u**2 - 3*u + 28 = 0 for u.
-7, 4
Suppose 3*r**3/5 + 384*r**2/5 + 759*r/5 + 378/5 = 0. What is r?
-126, -1
Suppose -a**4/3 + 287*a**3/3 - 20735*a**2/3 + 20449*a/3 = 0. Calculate a.
0, 1, 143
Factor c**3/8 - 21*c**2/8 + 9*c - 17/2.
(c - 17)*(c - 2)**2/8
Find b such that 39*b**3 + 357*b**2 + 834*b + 120 = 0.
-5, -4, -2/13
Solve -4*r**5/5 + 108*r**4/5 - 536*r**3/5 - 2808*r**2/5 + 108*r + 540 = 0 for r.
-3, -1, 1, 15
Let i**4/4 + i**3/2 - i**2/4 - i/2 = 0. Calculate i.
-2, -1, 0, 1
Factor -2*l**3/11 + 216*l/11 - 864/11.
-2*(l - 6)**2*(l + 12)/11
Factor 2*a**3/11 + 16*a**2/11 + 10*a/11 - 28/11.
2*(a - 1)*(a + 2)*(a + 7)/11
Suppose -2*n**5/7 - 8*n**4/7 - 4*n**3/7 + 8*n**2/7 + 6*n/7 = 0. What is n?
-3, -1, 0, 1
Solve 3*v**2/7 - 60*v/7 - 288/7 = 0.
-4, 24
Factor n**2 + 310*n + 309.
(n + 1)*(n + 309)
Factor 30*g**4 + 27*g**3.
3*g**3*(10*g + 9)
Let 2*h**4 - 30*h**3 + 50*h**2 + 30*h - 52 = 0. What is h?
-1, 1, 2, 13
Factor 5*q**3 + 250*q**2 + 3965*q + 20280.
5*(q + 13)**2*(q + 24)
Factor 2*a**2/7 - 36*a + 1134.
2*(a - 63)**2/7
Determine k, given that -5*k**5 - 430*k**4 + 455*k**3 + 1720*k**2 - 1740*k = 0.
-87, -2, 0, 1, 2
Factor -2*q**3/7 + 10*q**2/7 + 44*q/7 + 32/7.
-2*(q - 8)*(q + 1)*(q + 2)/7
Let 4*p**5/5 - 32*p**4/5 + 48*p**3/5 + 8*p**2/5 - 52*p/5 + 24/5 = 0. What is p?
-1, 1, 6
Suppose -2*f**4 + 14*f**3 + 18*f**2 - 14*f - 16 = 0. Calculate f.
-1, 1, 8
Factor 4*q**2 - 2620*q - 2624.
4*(q - 656)*(q + 1)
Determine m, given that -2*m**3/7 + 6*m**2 - 144*m/7 - 864/7 = 0.
-3, 12
Solve -4*t**3 - 24*t**2 - 20*t + 48 = 0 for t.
-4, -3, 1
Factor -f**3/2 + f**2 + 7*f/2 + 2.
-(f - 4)*(f + 1)**2/2
Suppose l**3/3 + 167*l**2/3 - 704*l + 2148 = 0. What is l?
-179, 6
Factor -2*g**3/7 + 4*g**2/7 + 30*g/7.
-2*g*(g - 5)*(g + 3)/7
Factor i**2 + 336*i + 28224.
(i + 168)**2
Find o such that -8*o**5/5 - 4*o**4 - 8*o**3/5 = 0.
-2, -1/2, 0
What is p in -5*p**2 + 12450*p - 7750125 = 0?
1245
Find w, given that w**4/6 + 7*w**3/6 - 3*w**2/2 - 7*w/6 + 4/3 = 0.
-8, -1, 1
What is m in -2*m**2/9 - 7550*m/9 - 2516/3 = 0?
-3774, -1
Factor r**5 + 18*r**4 + 69*r**3 + 52*r**2.
r**2*(r + 1)*(r + 4)*(r + 13)
Solve y**3 - 91*y**2 = 0.
0, 91
Solve p**4 + 20*p**3 + 99*p**2 - 20*p - 100 = 0 for p.
-10, -1, 1
Solve -2*a**2/3 - 22*a/3 - 56/3 = 0.
-7, -4
Factor -g**5/4 + 15*g**4/4 - 75*g**3/4 + 145*g**2/4 - 30*g + 9.
-(g - 6