**2 + 1/27*n**i + 2/3*n. Factor q(t).
2*(t + 1)**4*(t + 3)/9
Suppose -w - 32 = -5*w. Let o(c) = c**3 - 9*c**2 + 10*c - 14. Let y be o(w). Determine u, given that -70*u**2 + 74*u**y - 6*u - 2*u = 0.
0, 2
Let g = -1755 + 1755. Let x = 87/56 + -9/8. Find c, given that g*c**4 + 4/7*c**3 - x*c - 2/7 - 1/7*c**5 + 2/7*c**2 = 0.
-1, 1, 2
Suppose -2*p + 12 = 2*r, -1762 = -p + 3*r - 1768. Let 80/3*m + 20/3*m**4 + 16 - 32/3*m**p - 116/3*m**2 = 0. What is m?
-2, -2/5, 1, 3
Let t be 26/2 - 1*153/12. Find w such that -9/2 + 35/4*w - 4*w**2 - t*w**3 = 0.
-18, 1
Let q = -82975/8 - -10372. Factor -1/4*p + 3/8 - q*p**2.
-(p - 1)*(p + 3)/8
Let i = 654 + -653. Let u be i - ((-3)/1 + (3 - -1)). Factor -1/2*n**2 + 0*n - 1/2*n**4 - n**3 + u.
-n**2*(n + 1)**2/2
Suppose 5*b - 6*x - 205 = -3*x, 170 = 5*b + 4*x. Suppose -7*o - b*o - 50*o**2 - 13*o**3 - 7*o**3 + 5*o**3 - 10 = 0. What is o?
-2, -1, -1/3
Let l(c) be the first derivative of -1/12*c**2 + 1/18*c**3 + 1/24*c**4 - 206 - 1/6*c. Factor l(p).
(p - 1)*(p + 1)**2/6
Suppose 5*c - 48 = -4*k, 4*c - 33 = -5*k + 27. Suppose -k*v = -21 - 3. Let 2*a**5 + 10*a + 358*a**4 + 5 + 1 - 360*a**4 - 4*a**v - 12*a**3 = 0. What is a?
-1, 1, 3
Let q(n) be the third derivative of -n**5/12 - 15*n**4/2 + 195*n**3/2 - 1410*n**2. Let q(k) = 0. What is k?
-39, 3
Let q(l) be the second derivative of l**6/75 + 13*l**5/25 - 49*l**4/10 + 244*l**3/15 - 124*l**2/5 - 13*l - 10. Solve q(z) = 0.
-31, 1, 2
Let j(h) be the second derivative of 0*h**2 - 7/36*h**4 + 1/126*h**7 + 3/20*h**5 + 2 + 174*h - 1/18*h**6 + 1/9*h**3. Determine k so that j(k) = 0.
0, 1, 2
Solve 21 + 158855*q**2 + 37 - 57 + 55514*q**2 + 926*q = 0 for q.
-1/463
Let p(d) = -581*d - 31953. Let z be p(-55). Factor -4/19*y**z + 16/19 + 2/19*y**3 - 8/19*y.
2*(y - 2)**2*(y + 2)/19
Let f be (-970)/(-2385) - (1704/(-212) + 8). Let q(n) = n**2 - 6*n + 2. Let k be q(6). Factor 0 - f*o**4 - 2/9*o**5 + 4/9*o**k + 2/9*o + 0*o**3.
-2*o*(o - 1)*(o + 1)**3/9
Let w(a) be the third derivative of -a**6/480 - 7*a**5/80 - 5*a**4/4 - 26*a**3/3 + 301*a**2. Solve w(h) = 0 for h.
-13, -4
Let w(p) be the third derivative of p**9/3024 + p**8/336 + p**7/120 + p**6/120 + 11*p**3/3 + p**2 - 15. Let y(m) be the first derivative of w(m). Factor y(d).
d**2*(d + 1)**2*(d + 3)
Let o(z) be the second derivative of -z**4/20 + 54*z**3/5 + 2*z + 1088. Factor o(q).
-3*q*(q - 108)/5
Factor -10/7*n - 2/7*n**2 + 76.
-2*(n - 14)*(n + 19)/7
Suppose 1/6*h**2 + 1666374 + 1054*h = 0. Calculate h.
-3162
Factor -13/2*f + 11/6*f**2 + 15/2 - 1/6*f**3.
-(f - 5)*(f - 3)**2/6
Let -7*r**5 - 7*r**5 - 149*r**2 - 84*r + 10782 - 10762 + 57*r**4 + 23*r**3 + 3*r**5 = 0. What is r?
-1, 2/11, 2, 5
Let u(x) be the first derivative of -x**4/36 - 7*x**3/27 + x**2/2 + 7*x - 582. Solve u(p) = 0.
-7, -3, 3
Let h be ((-4)/7)/(66/(-231)). Factor -11*t + t**h + 28*t - 14*t - 11*t.
t*(t - 8)
Let o(u) be the second derivative of 0*u**3 + 0 + 1/42*u**7 - 6*u**2 + u + 0*u**6 + 0*u**4 - 1/3*u**5. Let x(v) be the first derivative of o(v). Factor x(b).
5*b**2*(b - 2)*(b + 2)
Suppose -4*k + 5*t = -117, 25*k - 27*k + 63 = -t. Suppose -45 + k = -6*o. Solve -2/3*j**4 + 0 + 0*j**o + 0*j - 1/2*j**5 - 1/6*j**3 = 0 for j.
-1, -1/3, 0
Suppose -1783*v - 234 = -1822*v. Let 2/5*c**3 - v*c**2 - 26/5 + 54/5*c = 0. Calculate c.
1, 13
Suppose -5*t - 7891 + 320 = -4*h, -4*t - 9457 = -5*h. Let i = -1889 + h. Factor 2*q**2 - 1/2*q**3 - 3/2*q + i.
-q*(q - 3)*(q - 1)/2
Let i(l) = -2*l**3 + l - 1. Let c(y) = 8*y - 36. Let v be c(3). Let f(m) = -9*m**3 - 10*m**2 - 17*m - 4. Let q(g) = v*i(g) + 3*f(g). Factor q(z).
-3*z*(z + 3)*(z + 7)
Let d(j) = j**2 - 16*j - 73. Let c be d(-4). Suppose -v - c = -2*m - 15, 5*m = v - 17. Factor 8/7*b - 4/7*b**v + 0 - 12/7*b**3.
-4*b*(b + 1)*(3*b - 2)/7
Let i = -218 - -221. Factor -4*w**5 - 22*w**4 - 22*w**i + 70*w**4 - 62*w**3 + 40*w**2.
-4*w**2*(w - 10)*(w - 1)**2
Factor 61 - 49 + c**2 - 638*c + 645*c.
(c + 3)*(c + 4)
Let y = -15346 - -15349. What is h in -2/7*h**4 + 8/7*h - 9/7*h**y + 0 + 2/7*h**2 + 1/7*h**5 = 0?
-2, -1, 0, 1, 4
Suppose 0*g = 2*g - x + 8, -3*x + 12 = 0. Let v be -18*g/(-4)*-1. Factor 12*t - 5*t**2 + 15*t**2 + v*t - 7*t**2.
3*t*(t + 7)
Determine t, given that -3*t**3 + 85/2*t - 29*t**2 + 11/2*t**4 - 33/2 + 1/2*t**5 = 0.
-11, -3, 1
Let a be 16/(-24)*(17/(-16) + 1)/(149/596). Factor -a*n**3 + 0 - 4/3*n**2 - 2*n.
-n*(n + 2)*(n + 6)/6
Factor 262*b - 75 + 8*b**3 - 41*b**3 - 319*b**2 + 325*b**2 - 2*b**4 + 247 - 53*b**3.
-2*(b - 2)*(b + 1)**2*(b + 43)
Factor -802/5 - 160*s + 2/5*s**2.
2*(s - 401)*(s + 1)/5
Factor -528/5*u + 9/5*u**3 + 786/5*u**2 + 0.
3*u*(u + 88)*(3*u - 2)/5
Let m(v) be the first derivative of -4/3*v**3 - 196*v + 28*v**2 + 43. Factor m(c).
-4*(c - 7)**2
Let i(x) be the first derivative of 4*x**4 - 2/3*x**6 + 0*x**5 - 79 + 0*x**3 + 0*x + 0*x**2. Factor i(o).
-4*o**3*(o - 2)*(o + 2)
Let n be 0*(64 + 1358/(-21))*1/2. Let 95/4*d + n*d**2 + 75/2 - 5/4*d**3 = 0. What is d?
-3, -2, 5
Suppose 136890 + 2/5*p**2 + 468*p = 0. Calculate p.
-585
Suppose 0 = 51*i - 28*i + 123*i - 292. Factor -6*r**i + 4*r - 2/3 + 8/3*r**3.
2*(r - 1)**2*(4*r - 1)/3
Let o(x) = 4*x**5 + 4*x**3 - 4*x + 4. Let g(a) = 3*a**4 - 2*a**4 - a**3 - 71*a + 72*a - 1. Let p = -3 - 1. Let b(w) = p*g(w) - o(w). Factor b(k).
-4*k**4*(k + 1)
Suppose -3*z - 8 = -0*z + 4*l, -z - 3*l = 11. Solve 26*h**2 - 191*h**4 + 30*h**3 + 196*h**z + 30*h + 29*h**2 = 0 for h.
-3, -2, -1, 0
Let c(a) be the first derivative of -a**9/4536 - 11*a**8/2520 - a**7/36 - 5*a**6/108 + 17*a**3 + 30. Let s(o) be the third derivative of c(o). Factor s(k).
-2*k**2*(k + 1)*(k + 5)**2/3
Let j(k) be the third derivative of -k**5/150 + 2*k**4/15 + 51*k**3/5 - 6*k**2 + 2*k - 47. Suppose j(h) = 0. Calculate h.
-9, 17
Let n(q) be the second derivative of q**6/120 + 11*q**5/16 + 1021*q**4/48 + 2335*q**3/8 + 5175*q**2/4 - 3336*q. Factor n(b).
(b + 2)*(b + 15)**2*(b + 23)/4
Let a(v) = -16*v**3 + 3*v**2 - v + 14. Let r(o) = -9*o**3 + 2*o**2 - o + 8. Let m(t) = 4*a(t) - 7*r(t). Factor m(l).
-l*(l - 1)*(l + 3)
Let y(x) be the third derivative of x**5/120 - 403*x**4/24 + 162409*x**3/12 + 1181*x**2. Suppose y(w) = 0. What is w?
403
Let l(y) be the second derivative of -y**4/4 + 63*y**3/2 + 852*y**2 + 15*y - 29. Factor l(z).
-3*(z - 71)*(z + 8)
Let o = 79/380 + 23/95. Let u(g) be the second derivative of -5/4*g**4 + o*g**5 + 9*g + 6*g**2 - 2*g**3 + 0. Solve u(k) = 0.
-1, 2/3, 2
Suppose 0 = -7*m - 360 + 353. Let g be (m + 14/12)*(-60)/(-8). Let s**2 - g*s - 1/4*s**3 + 1/2 = 0. What is s?
1, 2
Solve 142/3*a**2 + 6962/15 + 21122/15*a + 2/5*a**3 = 0.
-59, -1/3
Let f = -287 - -290. Factor 11*m**2 - 41*m**2 + m**f - 3*m**3 - 24*m**2 - 58 + 114*m.
-2*(m - 1)**2*(m + 29)
Let m be ((-76626)/2835)/86 - (-6)/10. Factor 4/7*b**3 - 1/7*b**4 + 3/7 - 4/7*b - m*b**2.
-(b - 3)*(b - 1)**2*(b + 1)/7
Let j(q) be the third derivative of -q**7/1155 + 157*q**6/660 - 208*q**5/11 + 507*q**4/11 - 744*q**2. Factor j(c).
-2*c*(c - 78)**2*(c - 1)/11
Let g(r) be the second derivative of r**5/30 - 3715*r**4/18 + 3448448*r**3/9 + 3452164*r**2/3 - 1819*r. Determine j, given that g(j) = 0.
-1, 1858
Find h, given that -5*h**3 + 1408*h**2 + 1472*h**2 + 3134*h**2 + 1061*h**2 = 0.
0, 1415
Let g(p) be the first derivative of -5*p**3/3 - 985*p**2/2 - 980*p - 1506. Determine u so that g(u) = 0.
-196, -1
Suppose -p - 2*y = 2 - 1, -3*y - 3 = p. Let s(j) = j + 1. Let h be s(1). What is o in -p*o + 2*o**h + 15*o + o**2 + 9 = 0?
-3, -1
Let m(t) be the third derivative of -t**8/84 + 124*t**7/105 - 299*t**6/10 - 1984*t**5/15 - 512*t**4/3 + 1069*t**2. Factor m(i).
-4*i*(i - 32)**2*(i + 1)**2
Factor 4*r**2 + 12*r**2 - 28*r**2 + 554*r - 7 - 177 + 6*r**2.
-2*(r - 92)*(3*r - 1)
Let s(z) = 5*z - 63. Let x be s(13). Suppose 229*d**x + 375*d**4 + 2648*d**2 - 313*d**2 + 2116*d**2 + 1824*d + 4200*d**3 + 240 = 0. Calculate d.
-10, -2/5
Let m(b) = b**3 - 18*b**2 - 42*b + 44. Let c be m(20). Suppose -c*w + 24 = -24. Solve -944*i**3 + w*i**2 + 878*i**3 - 6 - 6*i**4 + 33*i + 30*i**5 + 3*i**5 = 0.
-1, 2/11, 1
Let j(h) be the first derivative of -h**4/8 + 481*h**3/6 - 57599*h**2/4 - 58081*h/2 + 96. Factor j(y).
-(y - 241)**2*(y + 1)/2
Let v(k) be the second derivative of -k**4/24 - 107*k**3/12 - 105*k**2/2 + 35*k + 3. Let v(c) = 0. Calculate c.
-105, -2
Let z(t) = 2*t**3 - 39*t