r -20*z**2 + 394*z + 414.
-2*(z + 1)*(10*z - 207)
Factor d**3/2 - 13*d**2/4 - 2*d + 7/4.
(d - 7)*(d + 1)*(2*d - 1)/4
Factor 2*w**4 - 2*w**3 - 50*w**2 + 50*w.
2*w*(w - 5)*(w - 1)*(w + 5)
Factor 21*v**3 + 219*v**2 + 279*v + 81.
3*(v + 1)*(v + 9)*(7*v + 3)
Solve -4*z**2/5 - 7048*z/5 - 3104644/5 = 0.
-881
Suppose k**3/2 + 69*k**2/2 + 720*k + 4050 = 0. What is k?
-30, -9
Factor -2*w**4/3 + 36*w**3 + 110*w**2/3.
-2*w**2*(w - 55)*(w + 1)/3
Solve 4*r**4/7 - 68*r**3/7 + 300*r**2/7 - 412*r/7 + 176/7 = 0 for r.
1, 4, 11
Factor -2*u**2 + 210*u - 208.
-2*(u - 104)*(u - 1)
Find r, given that -r**4/3 + 107*r**3/3 - 1260*r**2 + 14256*r + 15552 = 0.
-1, 36
Determine b so that -b**2/7 + 121*b - 846/7 = 0.
1, 846
Factor -2*b**2 + 4968*b - 3085128.
-2*(b - 1242)**2
Factor k**4/3 + 16*k**3/3 + 13*k**2 - 4*k/3 - 52/3.
(k - 1)*(k + 2)**2*(k + 13)/3
Let -162*l**4 + 46926*l**3 - 4515216*l**2 + 1285048960*l/9 + 1326109696/9 = 0. What is l?
-1, 872/9
Factor -2*k**3 + 112*k**2 - 218*k + 108.
-2*(k - 54)*(k - 1)**2
Let -5*f**3 + 15*f**2 + 45*f - 135 = 0. Calculate f.
-3, 3
Suppose -3*k**2/5 - 27*k + 1092/5 = 0. What is k?
-52, 7
Determine j, given that 2*j**4/9 + 38*j**3/9 + 214*j**2/9 + 322*j/9 + 16 = 0.
-9, -8, -1
Solve 3*d**5/2 + 63*d**4 - 9*d**3/2 - 186*d**2 + 126*d = 0.
-42, -2, 0, 1
Factor 2*s**3 - 20*s**2 + 32*s.
2*s*(s - 8)*(s - 2)
Solve -3*j**4/8 - 93*j**3/8 - 819*j**2/8 - 1851*j/8 - 561/4 = 0.
-17, -11, -2, -1
Factor -2*x**4 - 4*x**3 + 2*x**2 + 4*x.
-2*x*(x - 1)*(x + 1)*(x + 2)
Determine h so that 10*h**2 + 36*h + 18 = 0.
-3, -3/5
Factor -2*k**2 + 874*k + 3528.
-2*(k - 441)*(k + 4)
Factor -2*g**5/7 - 10*g**4/7 - 18*g**3/7 - 2*g**2 - 4*g/7.
-2*g*(g + 1)**3*(g + 2)/7
Factor s**5/7 + 95*s**4/7 + 2395*s**3/7 + 6625*s**2/7 + 920*s + 2116/7.
(s + 1)**3*(s + 46)**2/7
Factor 4*m**3 + 9972*m**2 - 9976*m.
4*m*(m - 1)*(m + 2494)
Factor 3*f**3/5 - 162*f**2/5 + 2187*f/5.
3*f*(f - 27)**2/5
Let -24*n**2/5 + 2*n + 4/5 = 0. What is n?
-1/4, 2/3
Factor -3*h**4 + 69*h**3 - 129*h**2 + 63*h.
-3*h*(h - 21)*(h - 1)**2
Solve -b**2/5 + 544*b/5 - 543/5 = 0 for b.
1, 543
Let -n**5/3 - 13*n**4/3 - 11*n**3 - 31*n**2/3 - 10*n/3 = 0. What is n?
-10, -1, 0
Determine n, given that -2*n**3/17 + 40*n**2/17 - 74*n/17 + 36/17 = 0.
1, 18
Factor i**4/6 + 2*i**3/3 - 19*i**2/6 + 7*i/3.
i*(i - 2)*(i - 1)*(i + 7)/6
What is n in n**5/4 - n**4/4 - 5*n**3/4 - 3*n**2/4 = 0?
-1, 0, 3
Let -2*p**2 - 64*p = 0. Calculate p.
-32, 0
Determine r so that -18*r**3/13 + 662*r**2/13 - 500*r/13 - 144/13 = 0.
-2/9, 1, 36
Factor 4*v**2 + 48*v + 144.
4*(v + 6)**2
Factor 5*k**4 - 70*k**3 - 880*k**2.
5*k**2*(k - 22)*(k + 8)
Factor -5*m**2 - 285*m - 3780.
-5*(m + 21)*(m + 36)
Factor 5*a**2 + 75*a + 130.
5*(a + 2)*(a + 13)
Find b, given that 4*b**3 + 620*b**2 + 23712*b - 24336 = 0.
-78, 1
Factor 10*g**2/7 - 88*g/7 + 18.
2*(g - 7)*(5*g - 9)/7
Suppose 5*s**5 + 5*s**4 - 45*s**3 - 5*s**2 + 100*s - 60 = 0. Calculate s.
-3, -2, 1, 2
Factor -5*k**5 + 45*k**4 - 75*k**3 + 35*k**2.
-5*k**2*(k - 7)*(k - 1)**2
Factor -n**4/3 - 160*n**3/3 - 6992*n**2/3 - 46208*n/3.
-n*(n + 8)*(n + 76)**2/3
What is k in 40*k**2 - 646*k + 96 = 0?
3/20, 16
Factor -2*w**4 - 26*w**3/3 - 34*w**2/3 - 14*w/3.
-2*w*(w + 1)**2*(3*w + 7)/3
Factor 2*x**3/5 - 26*x**2/5 + 46*x/5 - 22/5.
2*(x - 11)*(x - 1)**2/5
Solve 3*p**3/8 - 129*p**2/2 + 5547*p/2 = 0 for p.
0, 86
Let 5*v**3 + 55*v**2 - 145*v - 195 = 0. What is v?
-13, -1, 3
Factor -3*w**4 - 30*w**3 + 27*w**2 + 270*w.
-3*w*(w - 3)*(w + 3)*(w + 10)
Solve -3*m**5 - 168*m**4 + 3*m**3 + 168*m**2 = 0.
-56, -1, 0, 1
Solve 5*i**4 - 25*i**3 + 30*i**2 = 0 for i.
0, 2, 3
What is n in -n**3 + 38*n**2 + 45*n - 234 = 0?
-3, 2, 39
Factor b**2 + 86*b + 1849.
(b + 43)**2
What is m in -m**2/4 + 251*m/2 + 252 = 0?
-2, 504
Factor -2*o**3 + 48*o**2 + 552*o - 1280.
-2*(o - 32)*(o - 2)*(o + 10)
Factor 12*g**3/7 - 879*g**2/7 + 219*g/7.
3*g*(g - 73)*(4*g - 1)/7
Factor 2*r**3 + 200*r**2/7 + 8*r.
2*r*(r + 14)*(7*r + 2)/7
Factor 4*y**3/5 + 6112*y**2/5 + 2340884*y/5 + 4657352/5.
4*(y + 2)*(y + 763)**2/5
Find c, given that 15*c**4 + 156*c**3 - 855*c**2 - 1416*c - 420 = 0.
-14, -1, -2/5, 5
What is u in 2*u**3/3 + 98*u**2/3 + 496*u + 2400 = 0?
-25, -12
Factor -2*y**2/5 - 16*y - 792/5.
-2*(y + 18)*(y + 22)/5
Factor 2*k**4/3 + 22*k**3/3 + 28*k**2 + 128*k/3 + 64/3.
2*(k + 1)*(k + 2)*(k + 4)**2/3
Let 294*m**4 - 532*m**3 - 328*m**2/3 - 16*m/3 = 0. What is m?
-2/21, 0, 2
What is v in 3*v**2/2 + 57*v - 117/2 = 0?
-39, 1
Factor -4*v**2/5 - 12*v + 80.
-4*(v - 5)*(v + 20)/5
Factor 5*b**3 - 130*b**2 + 460*b - 440.
5*(b - 22)*(b - 2)**2
Factor -2*d**3/7 - 128*d**2/7 - 2048*d/7.
-2*d*(d + 32)**2/7
Factor -3*a**5 - 48*a**4 + 315*a**3.
-3*a**3*(a - 5)*(a + 21)
Determine j so that 14*j**5 + 18*j**4 - 52*j**3 - 72*j**2 - 16*j = 0.
-2, -1, -2/7, 0, 2
Factor -m**2/3 + 137*m/3 - 90.
-(m - 135)*(m - 2)/3
Solve 4*n**3 + 2220*n**2 = 0 for n.
-555, 0
Factor 3*j**3 + 21*j**2 - 15*j - 225.
3*(j - 3)*(j + 5)**2
Let -5*t**2 + 105*t + 110 = 0. Calculate t.
-1, 22
Factor d**4/4 - 107*d**3/2 + 635*d**2/4 - 211*d/2.
d*(d - 211)*(d - 2)*(d - 1)/4
Find d such that 38*d**4/5 + 104*d**3/5 - 258*d**2/5 - 244*d/5 + 16 = 0.
-4, -1, 5/19, 2
Find u such that 8*u**2/7 + 2*u + 6/7 = 0.
-1, -3/4
Solve -65*v**3/2 - 175*v**2/6 + 10*v/3 = 0 for v.
-1, 0, 4/39
Find f, given that 2*f**2 + 546*f/5 - 44 = 0.
-55, 2/5
Suppose 3*l**4/8 - 145*l**3/8 + 23*l**2/4 + 12*l = 0. What is l?
-2/3, 0, 1, 48
Factor w**3 + 84*w**2 + 2340*w + 21600.
(w + 24)*(w + 30)**2
Solve 8*h**4 - 28*h**3 + 24*h**2 + 4*h - 8 = 0 for h.
-1/2, 1, 2
Solve 2*c**5/5 - 222*c**3/5 + 44*c**2 = 0.
-11, 0, 1, 10
Determine y so that 62*y**2/5 + 582*y/5 + 216/5 = 0.
-9, -12/31
Find p such that -3*p**5 - 8*p**4 + 24*p**3 + 74*p**2 + 27*p - 18 = 0.
-3, -2, -1, 1/3, 3
Solve -3*k**2 + 19050*k - 30241875 = 0.
3175
Let 1458*a**4 - 1191672*a**3 - 794880*a**2 - 176672*a - 13088 = 0. What is a?
-2/9, 818
Factor -3*r**3 - 15*r**2 - 6*r + 24.
-3*(r - 1)*(r + 2)*(r + 4)
Solve 16*y**5 - 96*y**4 - 44*y**3 + 300*y**2 - 224*y + 48 = 0.
-2, 1/2, 1, 6
Solve j**3/5 - 31*j**2/5 = 0 for j.
0, 31
Factor 2007889*f**2/5 - 5668*f/5 + 4/5.
(1417*f - 2)**2/5
Factor -2*q**4/3 + 170*q**3/3 + 174*q**2 + 526*q/3 + 176/3.
-2*(q - 88)*(q + 1)**3/3
Factor 5*d**2/3 + 760*d/3 + 2960/3.
5*(d + 4)*(d + 148)/3
Factor -3*w**2/5 - 72*w/5 - 81.
-3*(w + 9)*(w + 15)/5
Factor -7*c**5 - 19*c**4 + 6*c**3.
-c**3*(c + 3)*(7*c - 2)
Factor z**2/4 - 15*z/4 - 19.
(z - 19)*(z + 4)/4
Let -t**3 - 2*t**2 + 7*t - 4 = 0. What is t?
-4, 1
Find u such that 5*u**5 - 20*u**4 - 80*u**3 + 320*u**2 = 0.
-4, 0, 4
What is x in 2*x**3/13 + 14*x**2/13 + 20*x/13 = 0?
-5, -2, 0
Factor -40*r**2/3 - 412*r + 124/3.
-4*(r + 31)*(10*r - 1)/3
Factor -m**4 + 286*m**3 + 1155*m**2 + 1448*m + 580.
-(m - 290)*(m + 1)**2*(m + 2)
Suppose -2*u**5/7 + 34*u**4/7 - 134*u**3/7 - 14*u**2 + 352*u/7 + 40 = 0. What is u?
-1, 2, 7, 10
Solve -66*m**4/17 + 202*m**3/17 + 174*m**2 + 5166*m/17 - 324/17 = 0.
-3, 2/33, 9
Factor -5*n**2/4 + 15*n - 55/4.
-5*(n - 11)*(n - 1)/4
Find d such that 5*d**2 - 2565*d - 5150 = 0.
-2, 515
Factor h**2/6 + h/6 - 1.
(h - 2)*(h + 3)/6
Solve -m**5/4 + 11*m**4/2 + 111*m**3 + 522*m**2 + 648*m = 0.
-6, -2, 0, 36
Factor -g**2/5 + 8*g/5.
-g*(g - 8)/5
Let -g**4/10 - g**3/10 + 9*g**2/10 - 11*g/10 + 2/5 = 0. Calculate g.
-4, 1
What is i in -2*i**5/3 + 8*i**4 + 18*i**3 + 28*i**2/3 = 0?
-1, 0, 14
Factor -f**2 + 7*f + 18.
-(f - 9)*(f + 2)
Factor -j**3/4 + j**2 + 20*j + 48.
-(j - 12)*(j + 4)**2/4
Find w, given that 2*w**5 + 56*w**4 - 2*w**3 - 56*w**2 = 0.
-28, -1, 0, 1
Solve 2*z**5/9 - 2*z**4/3 - 4*z**3/3 + 16*z**2/9 = 0.
-2, 0, 1, 4
Find t such that 2*t**3/15 - 1114*t**2/15 = 0.
0, 557
Factor -5*g**4 + 1250*g**3 - 74285*g**2 - 480000*g - 737280.
-5*(g - 128)**2*(g + 3)**2
Factor 2*j**2/15 - 208*j/3 + 2072/15.
2*(j - 518)*(j - 2)/15
Let -4*i**2/3 - 776*i/3 = 0. Calculate i.
-194, 0
Suppose -q**5/2 - 77*q**4 - 2435*q**3 + 43582*q**2 + 188327*q/2 + 48223 = 0. What is q?
-83, -1, 14
Suppose 26*c**4 - 74*c**3 + 40*c**2 + 8*c = 0. What is c?
-2/13, 0, 1, 2
Find h, given that h**2/2 + 39*h/2 + 54 = 0.
-36, -3
Factor -m**4 + 3*m**3 + 19*m**2 - 87*m + 90.
-(m - 3)**2*(m - 2)*(m + 5)
Factor 2*v**2/5 - 196*v/5.
2*v*(v - 98)/5
Find o, given that 9*o**4/4 - 51*o**3/4 - 27*o**2/4 + 51*o/4 + 9/2 = 0.
-1, -1/3, 1, 6
Determine m 