, 28
Factor -1/4*k**2 + 42 + 41/2*k.
-(k - 84)*(k + 2)/4
Suppose 0 = -4011*w + 3537*w. Factor -122/7*f**3 - 2/7*f**5 - 200/7*f - 36/7*f**4 + w + 360/7*f**2.
-2*f*(f - 1)**2*(f + 10)**2/7
Let l = 1846 + -1835. Let b(v) be the second derivative of 0 - 1/9*v**4 + 0*v**3 + l*v + 2/3*v**2. Factor b(n).
-4*(n - 1)*(n + 1)/3
Let p(w) be the second derivative of -w**7/3780 + w**6/54 - 5*w**5/9 - 43*w**4/12 + 7*w - 4. Let o(f) be the third derivative of p(f). Factor o(g).
-2*(g - 10)**2/3
Let m = -17776/27 + 71833/108. What is v in -81/8*v + 3/8*v**5 + 81/8 + 39/4*v**3 - m*v**2 - 27/8*v**4 = 0?
-1, 1, 3
Solve 324/11 - 6*s + 2/11*s**2 = 0.
6, 27
Let r(q) be the third derivative of -289*q**6/200 - 17119*q**5/100 - 502*q**4/5 - 118*q**3/5 - 121*q**2 - 2. Let r(t) = 0. Calculate t.
-59, -2/17
Let j(g) be the second derivative of 0 - 1/273*g**7 + 8993/78*g**4 + 67/195*g**6 - 207*g - 1449/130*g**5 + 0*g**2 + 24334/39*g**3. Factor j(w).
-2*w*(w - 23)**3*(w + 2)/13
Let f be (-50)/(-8) + 0 + (-3)/(-4). Suppose 74 = f*i + 11. Determine p, given that -13 + 7*p**5 - 42*p**4 + 54*p**3 - 52*p**5 - i*p + 7 + 48*p**2 = 0.
-1, -1/3, 2/5, 1
Suppose -2/7*a**2 - 24/7*a + 170/7 = 0. What is a?
-17, 5
Let u(f) be the second derivative of -f**2 + 1/10*f**3 - 12*f + 1/60*f**4 + 6. Factor u(o).
(o - 2)*(o + 5)/5
Let i(b) be the first derivative of -1/180*b**6 - 4*b**3 - 21 + 0*b**2 + 0*b**4 + 0*b + 0*b**5. Let z(f) be the third derivative of i(f). Factor z(h).
-2*h**2
Let f(c) = c**3 + 2*c**2 - 446*c - 447. Let d(w) = -w**2 + 2*w + 3. Let t(k) = 42*d(k) + 2*f(k). What is h in t(h) = 0?
-12, -1, 32
Let x(w) be the first derivative of 3*w**4 + 280*w**3/3 - 106*w**2 - 480*w - 1255. Factor x(l).
4*(l + 1)*(l + 24)*(3*l - 5)
Let k(a) be the first derivative of -a**4/22 + 46*a**3/33 - 95*a**2/11 - 238*a/11 + 3898. Determine f, given that k(f) = 0.
-1, 7, 17
Let a(o) be the third derivative of 126*o**2 + 1/90*o**5 + 2809/9*o**3 + 0*o + 0 + 53/18*o**4. Solve a(l) = 0.
-53
Suppose a = 2*i + 133 - 41, -3*a + 5*i = -272. Factor 25 - 145 - 5*w**2 + 34*w - a*w.
-5*(w + 4)*(w + 6)
Let v(d) = 5*d**3 - 231*d**2 - 238*d + 466. Let k(j) = -12*j**3 + 462*j**2 + 478*j - 933. Let z(h) = 2*k(h) + 5*v(h). Solve z(c) = 0.
-2, 1, 232
Factor -1359 + 0*c**2 + 1666*c + 968 - 2537 - 4*c**2 + 1266*c.
-4*(c - 732)*(c - 1)
Let r = -3/4687 - 8141313/9374. Let x = r + 881. Factor -8*c**2 - x + 20*c.
-(4*c - 5)**2/2
Factor 0*g + 27*g**4 - 3072/7*g**2 + 0 - 3/7*g**5 - 2880/7*g**3.
-3*g**2*(g - 32)**2*(g + 1)/7
Let o be 4*(0 + 27/14 - 5/(-70)). Factor o*h + 3*h**2 + 1/3*h**3 + 16/3.
(h + 1)*(h + 4)**2/3
Factor -21/2*w + 0*w**2 + 9 + 3/2*w**3.
3*(w - 2)*(w - 1)*(w + 3)/2
Suppose 8*a + 4*j + 20 = 0, 6*a + 254 = -5*j + 217. Find h, given that -9/8*h**a + 15/8*h**2 - 27/8*h**4 - 3/8*h + 0 = 0.
-1, 0, 1/3
Let j(d) be the second derivative of -26*d - 3/20*d**5 - 2*d**4 + 3 - 15*d**2 - 17/2*d**3. Factor j(w).
-3*(w + 1)*(w + 2)*(w + 5)
Let a(b) be the first derivative of -b**6/6 - 31*b**5/10 - 271*b**4/16 - 103*b**3/8 + 315*b**2/4 + 1323*b/8 - 339. Solve a(s) = 0 for s.
-7, -3/2, 3/2
Let a be (-2)/19 - (-80)/38. Suppose -27 = -a*v - 7*v. Factor -v*j**3 - 3 + j + 2*j + 4*j**2 + 3*j**2 - 4*j**2.
-3*(j - 1)**2*(j + 1)
Let k(b) be the first derivative of 2*b**5/5 + 492*b**4 - 2402. Suppose k(d) = 0. Calculate d.
-984, 0
Suppose 140*v + 702 = 218*v. Let i(d) be the first derivative of v*d**2 - 4*d**3 - 9/2*d**4 + 1 - 3*d + 3*d**5. Factor i(f).
3*(f - 1)**2*(f + 1)*(5*f - 1)
Factor 11*k**2 + 1/2*k**3 + 165 - 353/2*k.
(k - 10)*(k - 1)*(k + 33)/2
Factor -2125/2*k - 1815/4 - 35/4*k**2.
-5*(k + 121)*(7*k + 3)/4
Let h(n) = -9*n**3 - 108*n**2 - 816*n + 3. Let a(f) = -43*f**3 - 541*f**2 - 4078*f + 14. Let t(w) = -3*a(w) + 14*h(w). Factor t(i).
3*i*(i + 10)*(i + 27)
Factor 171 - 123*j + 10*j**2 + 358*j - 56.
5*(j + 23)*(2*j + 1)
Let u = 624856 - 624854. Solve -232/5 + 4/5*c**u - 228/5*c = 0.
-1, 58
Let y be 242/(-4477) - (-6212)/(-74). Let z be y/108*4*(-12)/112. Factor -1331/3 + z*q**4 - 32/3*q**3 + 110*q**2 - 968/3*q.
(q - 11)**3*(q + 1)/3
Suppose 1413*r**5 + 39*r - 9*r**4 + 96 - 717*r**5 + 32*r**2 - 698*r**5 - 5*r**4 + 89*r - 24*r**3 = 0. What is r?
-3, -2, 2
Determine q so that -776/15*q**3 + 1431126/5 + 6708*q**2 + 2/15*q**4 - 1464408/5*q = 0.
1, 129
Let z = 142 - 135. Suppose 78 = 33*n - z*n. Factor 0 + 2/11*g**2 - 4/11*g + 2/11*g**n.
2*g*(g - 1)*(g + 2)/11
Suppose 0 = 4*u + 20, 11 = -2*t - 5*u + 2*u. Solve -2 + 13*n + 8*n + 9*n + t*n**2 + n**3 - 31*n = 0 for n.
-2, -1, 1
Let z be 240645/39450 - (1/2 - 1). Factor -8*x + z*x**2 + 16/5 - 2*x**3 + 1/5*x**4.
(x - 4)**2*(x - 1)**2/5
Suppose 23 = -3*i + 26. Let v be (-2 + i)/(4/(-344)). Solve v*f**4 + 3*f**5 - f**5 - 88*f**4 = 0 for f.
0, 1
Factor -214/5*f - 128/3 - 2/15*f**2.
-2*(f + 1)*(f + 320)/15
Factor -357/2*q**3 + 3/2*q**4 + 1053/2*q**2 - 1047/2*q + 174.
3*(q - 116)*(q - 1)**3/2
Let i(y) = y**2 - y - 2. Let v(x) = -3*x**2 + 2317*x + 668178. Let s(r) = 5*i(r) + v(r). Factor s(u).
2*(u + 578)**2
Let w(p) be the second derivative of 0 + 4*p - 6*p**3 + 162*p**2 + 1/12*p**4. Determine d so that w(d) = 0.
18
Factor 268 + 56 + 6*l**3 + 21676*l - 651*l**2 - 21355*l.
3*(l - 108)*(l - 1)*(2*l + 1)
What is r in -120/11 + 2/11*r**5 - 70/11*r**2 + 54/11*r**3 + 2*r**4 - 224/11*r = 0?
-6, -5, -1, 2
Determine z so that z + 5/4*z**2 + 0 - 11/2*z**3 + 13/4*z**4 = 0.
-4/13, 0, 1
Suppose 12 = 3*z, 0 = 3*n - 5*z + 330 - 322. Let a(f) be the first derivative of -16/3*f**3 + 22*f**2 - f**n - 24*f + 7. Factor a(l).
-4*(l - 1)**2*(l + 6)
Let k(b) = b**2 + 14*b + 24. Suppose -29*r + 16*r + 26 = 0. Let f(z) = 4*z**2 + 56*z + 96. Let o(n) = r*f(n) - 9*k(n). Factor o(a).
-(a + 2)*(a + 12)
Let y(q) = 12*q**2 + 108*q - 105. Let i(v) = 10*v**2 + 108*v - 106. Let l(k) = -5*i(k) + 4*y(k). Find x, given that l(x) = 0.
-55, 1
Let o(a) be the first derivative of 64*a**3 + 46/3*a**4 - 64/15*a**5 + 54*a**2 + 11 + 0*a + 2/9*a**6. Solve o(l) = 0 for l.
-1, 0, 9
Factor -1/4*c**4 - 65/4*c**2 + 0 + 4*c**3 + 25/2*c.
-c*(c - 10)*(c - 5)*(c - 1)/4
Solve 93 - 281/2*y + 48*y**2 - 1/2*y**3 = 0 for y.
1, 2, 93
Suppose 170*f - 164*f + 1464 = 0. Let b = 244 + f. Determine g so that -10/11*g**5 - 4/11*g**4 + b*g + 0 + 10/11*g**3 + 4/11*g**2 = 0.
-1, -2/5, 0, 1
Let c = -3530 + 1983. Let j = c - -10849/7. Suppose 6/7 + 2*n**2 - j*n = 0. Calculate n.
3/7, 1
Suppose -3*p - 98 = -2*p + 5*t, 0 = -2*p + 2*t - 172. Let r be 16/p - (-48)/22. What is z in 44 + 2*z**r - 4*z**2 - 2*z - 44 = 0?
-1, 0
Suppose -2*i + 14 = 0, 4*m = -2*i + 233 - 211. Determine b, given that 1/2*b + 0 - 1/2*b**m = 0.
0, 1
Let j(l) be the second derivative of -l**4/6 - 46*l**3 + 297*l + 4. Factor j(x).
-2*x*(x + 138)
Let z(w) be the third derivative of w**6/240 - 19*w**5/120 - 13*w**4/48 + 1183*w**3/12 + 2*w**2 - 6*w + 3. Solve z(x) = 0 for x.
-7, 13
Suppose -3 = -u, 2*k + 22 = 3*u + 17. Factor 77 - 20 + 3075*o**2 - 60*o + 6*o**3 + 54*o**3 - 3*o**4 - 3129*o**k.
-3*(o - 19)*(o - 1)**2*(o + 1)
Let r be 45 + (3/6 - (-4)/(-8)). Suppose 61 - 241 = -r*u. Factor 0 - 6/5*l**3 + 1/5*l**5 + 4/5*l**2 - 1/5*l**u + 8/5*l.
l*(l - 2)**2*(l + 1)*(l + 2)/5
Suppose -139 + 19 + 642 - 1600*k + 95*k**2 - 3455*k + 538 = 0. What is k?
4/19, 53
Let v be (-16 - -21)*6*(-2)/(-10). Let n be 0 + 3*(7 - v). Suppose 0*h**2 + 0 + 2/15*h**4 - 4/15*h**n + 2/15*h**5 + 0*h = 0. What is h?
-2, 0, 1
Let a(q) = -4*q**3 + 9*q**2 - 27*q + 30. Let l(x) = 2*x**2 + 5*x + 8. Let v be l(-2). Let z(s) = -2 + 0 + v - 3 - s**3. Let c(m) = a(m) - 3*z(m). Factor c(n).
-(n - 3)**3
Factor 3/8*g**3 - 1521/8*g + 0 + 249/4*g**2.
3*g*(g - 3)*(g + 169)/8
Let i(x) be the second derivative of x**4/4 - 229*x**3/2 - 693*x**2 - 78*x. Let i(r) = 0. What is r?
-2, 231
Let h(b) be the second derivative of -b**8/560 + b**6/120 + 155*b**3/6 + 7*b + 20. Let f(r) be the second derivative of h(r). Factor f(k).
-3*k**2*(k - 1)*(k + 1)
Solve 3/4*v**2 + 531*v + 93987 = 0 for v.
-354
Let k(d) be the first derivative of d**5/5 - 3*d**4 + 35*d**3/3 - 12*d**2 + 419. Solve k(g) = 0 for g.
0, 1, 3, 8
Let v = 509554 + -509554. Determine u so that v - 2/11*u**4 + 12/11*u - 8/11*u**3 - 2/11*u**2 = 0.
-3, -2, 0, 1
Let m(t) be the second derivative of -t**7/210 - 146*t**6/25 - 63948*t**5/25 - 6224272*t**4/15 - 2782*t. Factor m(h).
-h**2*(h + 