s**5 + 4/3*s**3 - 5/24*s**4. Let m(k) = 0. Calculate k.
2, 8
Let t(a) be the third derivative of -a**5/60 + 17*a**4/24 - 35*a**3/3 + 11*a**2. Let x be t(8). What is w in 24*w**x - 48*w**2 + 26*w**2 + 2*w = 0?
-1, 0
Suppose -99/2*o + 189/2*o**2 - 93/2*o**3 + 3/2 = 0. What is o?
1/31, 1
Let u(n) = -n**2 + 75*n - 410. Let p be u(69). Let j(x) be the third derivative of 0*x**p - 3/20*x**5 + 2*x**3 - 1/40*x**6 + 14*x**2 + 0*x + 0. Factor j(r).
-3*(r - 1)*(r + 2)**2
Let -1708/9*g - 364658/9 - 2/9*g**2 = 0. What is g?
-427
Let a(l) = 5*l + 27. Let g be a(-11). Let z = -24 - g. Factor 13*n**3 - n**3 - 4*n**5 + 20*n**2 - 4*n**z - 9*n + 17*n.
-4*n*(n - 2)*(n + 1)**3
Suppose 4*t - 39 + 51 = 4*l, -3*l + 9 = t. What is y in 6*y**l - 3*y - 2*y + 5*y - 330*y**5 + 339*y**5 - 21*y**4 = 0?
0, 1/3, 2
Let d(l) be the first derivative of -1/6*l**4 - 17*l + 2/15*l**3 + 0*l**2 - 8. Let q(b) be the first derivative of d(b). Factor q(o).
-2*o*(5*o - 2)/5
Let m(p) be the third derivative of -1/30*p**6 - 26/15*p**5 + 0*p + 0*p**4 + 0*p**3 + 0 - 162*p**2. Suppose m(k) = 0. Calculate k.
-26, 0
Suppose 55*w + 329/2*w**3 + 989/6*w**2 + 109/2*w**4 - 1/6*w**5 + 0 = 0. What is w?
-1, 0, 330
Let v(f) = -7*f**2 - 30*f - 8. Let o = 21 + -18. Suppose 2*x = o*x - 5. Let h(t) = -5*t**2 - 20*t - 5. Let s(l) = x*v(l) - 8*h(l). Factor s(m).
5*m*(m + 2)
Let w(r) = 4*r**2 + 22*r + 4*r**2 - 18 - 2*r**2 - 7*r**2. Let k be w(21). Find o such that 2*o**2 + 3*o**2 - 3*o - 2*o**2 - 21 + k = 0.
-2, 3
Solve 0 + 35/3*o**2 + 77/6*o**3 + 4/3*o + 5/2*o**4 = 0 for o.
-4, -1, -2/15, 0
Let n = 625664 + -1876966/3. Suppose 2*p**2 - n*p - 10 + 2/3*p**3 = 0. What is p?
-5, -1, 3
Let j be 30/18*((-4590)/119)/(-9). Factor 0 + j*d**3 + 26/7*d**2 + 22/7*d**4 - 2/7*d**5 + 0*d.
-2*d**2*(d - 13)*(d + 1)**2/7
Let r(g) = 9160*g + 9216. Let x be r(-1). Factor 8*a + x + 2/7*a**2.
2*(a + 14)**2/7
Solve -2/3*u**2 - 514*u - 1540/3 = 0.
-770, -1
Suppose 6 = c + 11. Let i be -3 + (38/8 - c/20). Suppose -15/4*b - 3 - 3/4*b**i = 0. What is b?
-4, -1
Let b be 3/(-8) - 23650/9680 - -11. Factor -216/11 - 6/11*x**3 + b*x + 12/11*x**2.
-6*(x - 3)**2*(x + 4)/11
Let s(f) be the third derivative of -f**6/600 - f**5/75 - f**4/30 - 4829*f**2. Suppose s(u) = 0. Calculate u.
-2, 0
Let v = -169726 + 169730. Factor 8/9*c**2 + 0 + 0*c + 2/9*c**v + 8/9*c**3.
2*c**2*(c + 2)**2/9
What is t in -2/7*t**2 + 5/7*t**3 + 200/7 - 500/7*t = 0?
-10, 2/5, 10
Suppose 1/7*o**5 + 177/7*o**3 - 2160/7*o + 72/7*o**2 + 0 - 26/7*o**4 = 0. Calculate o.
-3, 0, 5, 12
Let h be 15180/(-1265) + 0 + 15. Factor 117/8*y - 81/4 - 5/2*y**2 + 1/8*y**h.
(y - 9)**2*(y - 2)/8
Let j(w) = -3*w**3 + 23*w**2 - 15*w + 8. Let n be j(7). Let y be (-5 + -2 + -5)*n/(-15). Factor -48/5*c**2 - y*c**3 - 192/5*c - 256/5.
-4*(c + 4)**3/5
Let i = -103 - -113. Suppose s - 4*s = 2*a - i, 3*a - 3*s = 0. Let 2*m**2 + 0*m**a - 3*m**2 + 5*m**2 = 0. What is m?
0
Let z = 226 - 217. Let m(d) be the second derivative of 23*d + 0 + 243/2*d**2 - z*d**3 + 1/4*d**4. Factor m(j).
3*(j - 9)**2
Let o = 332 - 323. Suppose 0 = o*q - 147 + 129. Suppose 1/3 + 1/3*a**q - 2/3*a = 0. What is a?
1
Let j(t) be the first derivative of 8/9*t**2 + 86 - 2/27*t**3 + 0*t. What is o in j(o) = 0?
0, 8
Suppose 20*g = 18*g + 176. Let k = g + -80. Solve 4*i**2 - 14*i**3 - 1 - 3 + 6*i + k*i = 0.
-1, 2/7, 1
Suppose -2*n - 8 = 3*i, 3*n - 14 = -1828*i + 1830*i. Factor -2/13*r**n - 60/13 + 62/13*r.
-2*(r - 30)*(r - 1)/13
Let j(g) be the second derivative of 49*g**5/100 + 7*g**4/30 + g**3/30 - 84*g + 32. Factor j(p).
p*(7*p + 1)**2/5
Let k be (18/3)/3 + (-369)/205. Let u(i) = -i**2 + 16*i - 63. Let d be u(7). Determine f, given that d + 2/5*f**2 - 2/5*f**4 - 1/5*f**5 + 0*f**3 + k*f = 0.
-1, 0, 1
Let l(m) = 6*m**4 + 21*m**3 + 20*m**2 - 40*m. Suppose 0 = -13*o - 131 - 155. Let a(t) = -t**4 - 4*t**3 - 4*t**2 + 8*t. Let n(z) = o*a(z) - 4*l(z). Factor n(p).
-2*p*(p - 2)**2*(p + 2)
Let o(f) be the first derivative of 5/8*f**6 - 3/2*f + 120 - 33/10*f**5 - 8*f**3 + 57/8*f**4 + 39/8*f**2. Factor o(w).
3*(w - 1)**4*(5*w - 2)/4
Factor 0 - 104/3*x - 1/3*x**3 + 10*x**2.
-x*(x - 26)*(x - 4)/3
Let q(b) = -12*b**3 + 1788*b**2 + 7371*b + 7359. Let o(t) = 3*t**3 - 447*t**2 - 1844*t - 1840. Let i(d) = -15*o(d) - 4*q(d). Factor i(v).
3*(v - 153)*(v + 2)**2
Factor 0 - 24*w**2 + 70/3*w + 2/3*w**3.
2*w*(w - 35)*(w - 1)/3
Solve 2/9*d**5 + 14/9*d**2 + 0 - 2/9*d**3 + 0*d - 14/9*d**4 = 0 for d.
-1, 0, 1, 7
Let i(y) be the third derivative of -y**11/997920 + y**10/453600 + y**5/60 - 83*y**3/6 - y**2 - 126*y. Let f(q) be the third derivative of i(q). Solve f(z) = 0.
0, 1
Suppose 575 = 13*t - 205. Suppose 2*x = 7*x - t. What is q in -4*q**2 - 2*q**2 - 25*q + x*q**2 - q**2 = 0?
0, 5
Find r, given that -26*r**3 + 20*r**2 + 9*r**5 + 9*r**4 + 1274 - 1306 - 10*r**5 + 24*r = 0.
-1, 2, 4
Let h(m) = -m**3 + 2*m**2 + 2*m + 12. Let x be h(0). Factor o**3 - 87*o - 11*o + 2*o**3 + 35*o + x*o**2.
3*o*(o - 3)*(o + 7)
Let s(x) be the third derivative of x**8/504 - 24*x**7/35 + 2627*x**6/30 - 40328*x**5/9 + 357911*x**4/12 - 958*x**2 - 4*x. Factor s(m).
2*m*(m - 71)**3*(m - 3)/3
Let w(x) = -x**3 + 5*x**2 + 6*x + 6. Suppose 0*f = 5*f + 5*h - 5, 2*f - 7 = -h. Let s be w(f). Factor 0*o**2 - 10*o + 2*o**2 + s*o + 0 + 2.
2*(o - 1)**2
Let r(k) be the first derivative of 5/3*k**3 + 100*k + 93 + 105/2*k**2. Suppose r(q) = 0. Calculate q.
-20, -1
Suppose -401*k - 96 = -425*k. Let y(t) be the second derivative of -1/2*t**k + 1/15*t**6 + 2/3*t**3 + 0 + 0*t**5 + 14*t + 0*t**2. Factor y(h).
2*h*(h - 1)**2*(h + 2)
Let x(j) be the second derivative of 0 + 0*j**2 - 2/3*j**4 + 74*j - 2/3*j**3 - 1/5*j**5. Solve x(u) = 0.
-1, 0
Let o be (-89784)/(-71595) - 14/259. Factor -22/5*d**3 + 28/5*d**2 + 0 - o*d.
-2*d*(d - 1)*(11*d - 3)/5
Let z = 144250/9 + -1007995/63. What is h in -6 - 3*h**4 + z*h**3 - 369/7*h**2 + 237/7*h = 0?
2/7, 1, 7
Suppose a = -5*z + 330, z - 3*a = -8*a + 90. Find t, given that z*t**2 - 3985*t - 7422*t + 271*t**2 - 4*t**3 + 87808 + 1999*t = 0.
28
Let r(k) be the first derivative of -5*k**2/2 + 2*k + 17. Let n be r(0). Let -10*a + a**2 + n*a + 4*a**4 - 13*a**2 + 0*a**2 = 0. Calculate a.
-1, 0, 2
Let x be (-22)/(-99) + (-25)/(-9). Suppose -2*d + 1912*d**2 - x*d - 1937*d**2 - 10*d = 0. Calculate d.
-3/5, 0
What is u in 13/11*u + 1/11*u**2 - 30/11 = 0?
-15, 2
Let f(h) be the second derivative of h**5/4 + 25*h**4 - 635*h**3/6 - 465*h**2 - h - 271. Factor f(b).
5*(b - 3)*(b + 1)*(b + 62)
Let k(g) = 2*g**3 - 119*g**2 + 1417*g + 90. Let y be k(43). Let 9/5 + 3*v**3 - 3*v + 24/5*v**y - 33/5*v**2 = 0. What is v?
-1, 3/8, 1
Let f(b) be the second derivative of 3*b**5/40 + 5*b**4/4 + 23*b**3/4 + 21*b**2/2 - 85*b - 2. Factor f(z).
3*(z + 1)*(z + 2)*(z + 7)/2
Let y(c) = 3*c**2 + c + 1. Let v(t) = -10*t**2 + 83*t - 408. Let g(j) = v(j) + 3*y(j). Factor g(n).
-(n - 81)*(n - 5)
Let x = 11646844/9 + -1294092. Factor -x - 4/9*u + 10/9*u**2 - 2/9*u**3.
-2*(u - 4)*(u - 2)*(u + 1)/9
Let v = 17558/13 - 1350. Suppose 10 = u + 5*t - 25, 0 = 5*u - 3*t + 21. Factor -2/13*a**4 + v*a**2 + u + 0*a**3 + 0*a.
-2*a**2*(a - 2)*(a + 2)/13
Suppose -8/15*a**2 - 196/15 - 42/5*a = 0. Calculate a.
-14, -7/4
Let t be (1/(-4) - 240/(-448))*140/6. Let p be (-16)/(-18) - (-2)/(-9). Factor 0 - 13/3*y**4 + 0*y + p*y**3 + 0*y**2 + t*y**5.
y**3*(4*y - 1)*(5*y - 2)/3
Let t(z) = 1035*z + 146970. Let x be t(-142). Factor 1/4*k**4 - 1/4*k**2 - 19/4*k + 19/4*k**3 + x.
k*(k - 1)*(k + 1)*(k + 19)/4
Determine a so that -21*a**2 - 1280 + 395848*a - 397288*a + 30*a**4 - 259*a**2 + 140*a**3 - 5*a**5 = 0.
-2, 4, 8
Let w be (220/120)/(-1*99/(-27)). Factor -1/4*r**2 + 3/4 + w*r.
-(r - 3)*(r + 1)/4
Let q(d) be the first derivative of -28 - 5*d**4 + 3*d**5 + 0*d + 0*d**2 + 5/3*d**3. Suppose q(o) = 0. What is o?
0, 1/3, 1
Suppose -4*s - 3*h = 33, 1519*s + 55 = 1514*s - 5*h. Factor -4/13*m + s + 6/13*m**2.
2*m*(3*m - 2)/13
Let v be ((-3)/(-6) - 31/54)/(51/(-459)). What is o in -757/3*o**3 + 336*o**2 - 108*o - v*o**5 + 25*o**4 + 0 = 0?
0, 1/2, 1, 18
Let f be (-2)/(-16) + 496/128. Solve 39*k**f + 61 + 63*k**3 - 98*k - 87*k**2 + 56*k - 90*k - 97 - 15*k**5 = 0.
-1, -2/5, 2, 3
Suppose -49*w = -57*w + 16. Factor -4*v + v**w - 12 + 15 - 8.
(v - 5)*(v + 1)
Let k(t) = -11*t + 149. Let r be k(13). Let o(d) be the first derivative of 0*d - 1/27*d**