(w + 11)*(w + 54)/7
Let i(p) be the first derivative of p**6/2 + 6*p**5/5 - 6*p**4 - 18*p**3 - 27*p**2/2 + 1742. Determine q, given that i(q) = 0.
-3, -1, 0, 3
Let z(j) be the third derivative of -j**6/180 + j**5/30 + 11*j**4/12 - 35*j**3/9 + 24*j**2 - 11*j. Suppose z(s) = 0. Calculate s.
-5, 1, 7
Let n(d) = -d**3 - 13*d**2 + 3*d + 41. Let w be n(-13). Factor 8*t - 18*t**3 + 6*t**4 - 4821*t**2 + 4797*t**w + 8*t**4.
2*t*(t - 2)*(t + 1)*(7*t - 2)
Let v(n) be the third derivative of -n**7/42 + 7*n**6/3 - 244*n**5/3 + 1120*n**4 - 7680*n**3 - n**2 - 375*n + 4. Suppose v(k) = 0. What is k?
4, 24
Let h(m) be the first derivative of -m**5/390 + 2*m**4/39 - 7*m**3/39 - 3*m**2/2 + 22*m + 22. Let f(p) be the second derivative of h(p). Factor f(v).
-2*(v - 7)*(v - 1)/13
Let k(t) be the first derivative of t**4/30 + t**3/5 - 4*t**2/5 - 139*t - 122. Let g(r) be the first derivative of k(r). Determine z so that g(z) = 0.
-4, 1
Let y = 168 - 165. Factor -y*n**4 + 5*n**3 + 9*n**3 + 4*n**3 + 3*n**3.
-3*n**3*(n - 7)
Let r(y) = 18*y**3 + 3849*y**2 - 22383*y - 26511. Let z(v) = v**3 + 241*v**2 - 1399*v - 1657. Let b(j) = -2*r(j) + 33*z(j). Suppose b(o) = 0. Calculate o.
-1, 7, 79
Let g = 39 + -31. Suppose 0 = g*u - 14 - 26. Factor u*z + 8*z - 2*z**4 + 2*z**2 + z**5 - 14*z.
z*(z - 1)**3*(z + 1)
Let l(p) be the third derivative of p**5/270 - 2203*p**4/54 + 4853209*p**3/27 + 4*p**2 + 355. Factor l(k).
2*(k - 2203)**2/9
Let g = 472 - 473. Let x be -3 + (-7)/2*g. Factor -1/8*s - 1/8*s**3 + x*s**2 - 3/4.
-(s - 3)*(s - 2)*(s + 1)/8
Suppose 88 - 109 = 38*p - 97. Factor 0 + 0*a - 1/4*a**3 - 3/2*a**p.
-a**2*(a + 6)/4
Let z(s) be the first derivative of -2*s**5/15 + 19*s**4/9 - 184*s**3/27 - 182*s**2/9 - 98*s/9 + 1624. Solve z(a) = 0 for a.
-1, -1/3, 7
Let q(x) = 2*x**2 - 23*x + 60. Let z be q(8). Suppose -3*k + 3*t - 2*t + 4 = 0, 0 = 3*k + z*t - 14. Solve k*l - 15/2*l**2 + 2 + l**3 + 5/2*l**4 = 0.
-2, -2/5, 1
Let y(m) = m**3 + 10*m**2 + 26*m + 80. Suppose -3*n = 3*a + 27, 8*n + 23 = -3*a + 9*n. Let x be y(a). What is f in 2/5*f + 2/5*f**2 + x = 0?
-1, 0
Let z(i) be the first derivative of 81*i**4/14 + 768*i**3/7 + 253*i**2/7 + 4*i - 533. Let z(o) = 0. Calculate o.
-14, -1/9
Let o(d) = d**3 + 60*d**2 - 1216*d. Let s be o(-76). Factor 14/17*g**3 - 12/17*g + s + 38/17*g**2.
2*g*(g + 3)*(7*g - 2)/17
Suppose 5*s + 2 - 21 = -4*h, 5*s - 10 = 5*h. Let x be (h - -3 - 5) + 4. Factor 5*w**2 + 12*w**3 + w**2 - w**3 - 3*w**4 - 8*w**x.
-3*w**2*(w - 2)*(w + 1)
Suppose -10*u + 188 = 160 - 872. Factor -u + 40*y + 5/2*y**2.
5*(y - 2)*(y + 18)/2
Let h be (8 - 12) + (-327)/(-66). Let a(b) be the first derivative of 8/55*b**5 + 74/33*b**3 + 8/11*b - 1 + h*b**4 + 24/11*b**2. What is z in a(z) = 0?
-2, -1, -1/4
Let s(k) = k**2 + 143*k + 468. Let t(x) = 2*x**2 + 281*x + 937. Let q(n) = -7*s(n) + 3*t(n). Solve q(u) = 0.
-155, -3
Let a be 39 - 11 - (-20 - -46). Factor -27/7 - 90/7*w - 75/7*w**a.
-3*(5*w + 3)**2/7
Let d(g) be the second derivative of 0*g**2 - 24*g + g**4 + 0 + 5/3*g**3 + 1/15*g**5 + 1/540*g**6. Let c(b) be the second derivative of d(b). Factor c(s).
2*(s + 6)**2/3
Let n be ((-52)/143)/((-2)/11). Factor 222*k**n - 2*k**3 + 6*k**3 - 227*k**2 - 3*k**3.
k**2*(k - 5)
Factor 248/3 + 136/9*l + 2/9*l**2.
2*(l + 6)*(l + 62)/9
Suppose -263*k = 300*k - 762 - 2616. Solve 1/4*l**5 + 0 - 3/2*l**3 + 3/4*l**4 - k*l - 7*l**2 = 0.
-2, 0, 3
Let x(p) be the second derivative of -5*p**4/12 + 14875*p**3/3 - 44253125*p**2/2 - 9*p + 29. Factor x(n).
-5*(n - 2975)**2
What is c in 1/6*c**4 + 0 - 22/3*c**2 - 1/6*c**3 - 16*c = 0?
-4, -3, 0, 8
Let v be (-9)/(-4) - 27/108. Suppose 0 = 3*r - 2 + 14, -2*g = -v*r - 12. Find t such that t**5 - 7 - t**3 + 2*t**4 + 7 - 4*t**2 + 2*t**g = 0.
-2, -1, 0, 1
Let j(c) = c**5 - 10*c**4 - 15*c**3 - 8*c**2 - 4*c. Let m(g) = -2*g**4 - 2*g**3. Let w(k) = 5*j(k) - 30*m(k). Factor w(i).
5*i*(i - 2)*(i + 1)**2*(i + 2)
What is g in -322*g - 5*g**2 + 2*g**2 + 184*g - 264 = 0?
-44, -2
Find w, given that 2/15*w**2 - 5392/5*w + 10902624/5 = 0.
4044
Suppose -24*s - 17082 = -17202. Factor -2/5*l**3 + 0*l**2 + 0*l**4 + 2/5*l**s + 0 + 0*l.
2*l**3*(l - 1)*(l + 1)/5
Find z such that 2*z**3 - 51*z + 25*z - 9 + 95 - 86*z**2 + 24*z = 0.
-1, 1, 43
Let c(o) be the third derivative of 0*o**4 - 11/60*o**5 + 0 + o**3 + 0*o - 20*o**2. Let q(g) = 32*g**2 - 17. Let i(k) = -17*c(k) - 6*q(k). Solve i(s) = 0 for s.
0
Let q(h) be the first derivative of -h**3/3 + 8*h**2 + 24*h - 42. Let i be q(17). Factor -i*z**4 + 10*z**4 + 2*z**2 - 5*z**4.
-2*z**2*(z - 1)*(z + 1)
Factor -2056/7*h**2 + 522/7*h - 2/7.
-2*(4*h - 1)*(257*h - 1)/7
Let r(s) be the third derivative of -2/5*s**5 + 8*s**3 + 5/6*s**4 + 2 - 43*s**2 + 1/30*s**6 + 0*s. Factor r(f).
4*(f - 4)*(f - 3)*(f + 1)
Let v(u) be the third derivative of -1/8*u**4 - 19 + 0*u**3 - 7/240*u**6 + 0*u + 1/672*u**8 + 13/120*u**5 - 3*u**2 - 1/420*u**7. Factor v(n).
n*(n - 2)*(n - 1)**2*(n + 3)/2
Let b = 17282 + -17279. Find v, given that -2*v**2 - b*v**3 + 1/2*v**4 + 0 + 1/2*v**5 + 4*v = 0.
-2, 0, 1, 2
Let l = -251 - 529. Let j = -2338/3 - l. Determine m, given that 0 + 8/3*m - j*m**2 = 0.
0, 4
Let l(z) be the first derivative of 5*z**6/6 + 9*z**5/5 - 43*z**4/2 - 332*z**3/3 - 204*z**2 - 160*z + 824. Factor l(n).
(n - 5)*(n + 2)**3*(5*n + 4)
Let c(o) = -o**3 + 8*o**2 - 48*o + 31. Let h(g) = 2*g**2 + g**2 + 1 - 2*g**2. Let u(j) = c(j) + 5*h(j). Find n such that u(n) = 0.
1, 6
Factor -1970*z**3 - 7250*z**2 + 116*z**4 - 1935 - 5*z**5 - 7705*z + 1066 - 1776 + 6*z**4 + 93*z**4.
-5*(z - 23)**2*(z + 1)**3
Let c(w) be the first derivative of -w**6/72 + 5*w**5/12 - 15*w**4/8 + 3*w**3 - w + 55. Let s(b) be the third derivative of c(b). Factor s(p).
-5*(p - 9)*(p - 1)
Let c(q) be the third derivative of -q**6/150 + 124*q**5/75 - 1496*q**4/15 - 36992*q**3/5 - 118*q**2 - 5*q. Factor c(p).
-4*(p - 68)**2*(p + 12)/5
Let w(q) be the third derivative of -2023/72*q**4 - 34/15*q**5 + 0 + 0*q - 64*q**2 - 5/72*q**6 + 4913/36*q**3 - 1/1260*q**7. Factor w(r).
-(r - 1)*(r + 17)**3/6
Solve 164/21*p + 10/7*p**4 + 0 - 176/3*p**3 + 26/7*p**2 = 0.
-1/3, 0, 2/5, 41
Find f, given that -192/7 + 28*f**2 + 330/7*f**3 - 64*f + 10/7*f**5 + 104/7*f**4 = 0.
-4, -3, -2/5, 1
Solve -460/7 + 2/7*n**3 + 226/7*n + 232/7*n**2 = 0 for n.
-115, -2, 1
Let c be -8*(-4 - -1)*1/6. Let i be 364/273 + (-2)/(-12). Find r, given that 0 + i*r**3 + 0*r**c - 3/4*r + 0*r**2 - 3/4*r**5 = 0.
-1, 0, 1
Let v = -538 - -763. Solve -30*r + 12*r**4 - 20*r - v*r**3 + 8*r**4 + 255*r**2 = 0.
0, 1/4, 1, 10
Let z(g) be the second derivative of -g**4/48 + 107*g**3/12 - 11449*g**2/8 + 3727*g. Find r such that z(r) = 0.
107
What is d in -27/2*d**2 + 473/2*d + 1/6*d**3 + 9245/6 = 0?
-5, 43
Let k = 464228 + -464223. Find c, given that 0 - 2/11*c**k - 36/11*c**3 - 40/11*c**2 - 14/11*c**4 - 16/11*c = 0.
-2, -1, 0
Let p(r) = -39*r**3 + 744*r**2 + 1497*r - 2290. Let v(y) = 21*y**3 - 372*y**2 - 747*y + 1146. Let z(i) = 6*p(i) + 11*v(i). Let z(m) = 0. Calculate m.
-3, 1, 126
Let n(k) = k**3 - 10*k**2 - 17*k + 71. Let o be n(11). Let a be ((3 - o) + 187/99)*-190. Determine l so that 8/9 - a*l**2 + 0*l - 88/9*l**4 + 30*l**3 = 0.
-2/11, 1/4, 1, 2
Find g, given that 9/4*g**5 - 2151/8*g**4 + 199*g - 183/2 - 2761/4*g**3 + 3891/8*g**2 = 0.
-3, -1/2, 1/3, 2/3, 122
Let b be (-5)/45 - 17540/90. Let u = 195 + b. Factor u + 2*h**2 + 0*h - 4*h**3 + 3/2*h**4.
h**2*(h - 2)*(3*h - 2)/2
Let u(q) = q**3 - q**2 - 9*q - 8. Let b be u(4). Suppose 18*f - 19*f - 3 = j, -4*j + b*f + 28 = 0. Determine c so that -6/5 - 13/5*c - 1/5*c**3 - 8/5*c**j = 0.
-6, -1
Let v(k) be the first derivative of -146/3*k**3 - 1/15*k**5 + 25 - 10/3*k**4 - 361/3*k - 380/3*k**2. Solve v(d) = 0.
-19, -1
Let t(z) be the third derivative of -70*z**2 + 0*z - 1/15*z**5 - 8/105*z**7 - 1/4*z**4 + 0*z**3 + 13/60*z**6 + 0. Factor t(u).
-2*u*(u - 1)**2*(8*u + 3)
Let p be 10/(-40) - (-18)/8. Determine l so that 76*l**p - 23*l**2 + 14*l - 51*l**2 = 0.
-7, 0
Let x be 16/(-24)*-417 - -6. Suppose -x*r + 4 = -282*r. Determine m so that -6/5*m + 9/5*m**3 + 9/5*m**r + 0 - 6/5*m**4 = 0.
-1, 0, 1/2, 2
Suppose 0 = -26*y - 64122 + 64174. Determine i so that 2/3*i**y + 486 - 36*i = 0.
27
Let v = 14/10301 - 16285937/41204. Let w = v - -396. Determine s, given that w*s**2 + 1 + 13/4*s = 0.
-4, -1/3
Let l = -230756 + 692