8/n. Determine k so that f + 3 - 4 + 8*k + 3*k**2 - 14*k = 0.
1
Let u(w) be the first derivative of -5/9*w**2 - 2/9*w - 4/45*w**5 - 23 - 7/18*w**4 - 2/3*w**3. Determine k so that u(k) = 0.
-1, -1/2
Let b(o) = -4. Let d(v) = 9. Let s(i) = 7*b(i) + 3*d(i). Let u(k) = k**2 - 2. Let m(n) = -2*s(n) - u(n). Factor m(y).
-(y - 2)*(y + 2)
Let s(w) be the first derivative of 0*w**2 + 1/36*w**6 + 0*w**3 + 1/10*w**5 + 1/12*w**4 + 0*w - 10. Factor s(f).
f**3*(f + 1)*(f + 2)/6
Let g(b) be the second derivative of b**6/195 + 2*b**5/65 - 11*b**4/78 + 2*b**3/13 - 14*b + 4. What is h in g(h) = 0?
-6, 0, 1
Suppose g + 2*g - 63 = 0. Suppose g = 6*d - 3*d. Determine z so that -23*z**2 - d*z**2 - 32*z - 47*z**3 + 51*z**3 - 8 + 10*z**4 = 0.
-1, -2/5, 2
Let w(o) be the third derivative of -o**5/30 + 3*o**4/2 - 17*o**3/3 - 56*o**2. Solve w(r) = 0 for r.
1, 17
Let u(k) = 31*k - 53. Let p be u(2). Let o(c) be the first derivative of 1/5*c**5 - 1/2*c**4 + 0*c + 0*c**2 + 1/3*c**3 - p. Let o(b) = 0. Calculate b.
0, 1
Let q(a) be the first derivative of -1/10*a**2 + 18 - 4/5*a + 4/15*a**3 + 1/20*a**4. Factor q(b).
(b - 1)*(b + 1)*(b + 4)/5
Let d(q) = -5*q**4 + 19*q**3 - 60*q**2 + 74*q - 28. Let h(c) = 4*c**4 - 20*c**3 + 62*c**2 - 74*c + 28. Let v(j) = 2*d(j) + 3*h(j). Find w such that v(w) = 0.
1, 2, 7
Let y(n) be the third derivative of 5*n**8/336 + n**7/7 + n**6/24 - 2*n**5 + 10*n**4/3 - 124*n**2. Factor y(u).
5*u*(u - 1)**2*(u + 4)**2
Factor -18*t**3 - 29*t + 62*t**2 - 117 + 89*t - 15 + 7*t**2 + 21*t**3.
3*(t - 1)*(t + 2)*(t + 22)
Factor -2*f**4 + 6*f**2 - 14783*f**3 + 2*f**4 + 14784*f**3 - f**4.
-f**2*(f - 3)*(f + 2)
Let o(l) be the second derivative of l**7/504 + l**6/48 + l**5/12 + 5*l**4/12 + 3*l. Let u(n) be the third derivative of o(n). Determine w, given that u(w) = 0.
-2, -1
Let t = 2 - -10. Suppose -t*w**2 - 4*w**3 + 14*w - 4*w**3 + 12*w**4 - 6*w = 0. Calculate w.
-1, 0, 2/3, 1
Let f(m) be the third derivative of 0 + 0*m**3 + 2*m**2 + 0*m**4 + 1/6*m**5 + 0*m - 1/60*m**6. Factor f(n).
-2*n**2*(n - 5)
Let i(u) be the second derivative of -u**6/30 + u**5/5 + 5*u**4/12 + u + 8. Factor i(d).
-d**2*(d - 5)*(d + 1)
Let m(f) = 190*f**3 + 170*f**2 + 35*f + 35. Let a(j) = 21*j**3 + 19*j**2 + 4*j + 4. Let s(b) = -35*a(b) + 4*m(b). Factor s(t).
5*t**2*(5*t + 3)
Let f(q) be the first derivative of -2*q**3/21 - 9*q**2/7 + 72*q/7 + 268. Suppose f(h) = 0. Calculate h.
-12, 3
Let w(m) = -14*m + 45. Let k be w(3). Let -8/3*r - 8/3*r**2 - 2/3*r**k + 0 = 0. Calculate r.
-2, 0
Factor -45771*o - 6393*o + 535*o**2 - 3*o**3 - 26244 - 263*o**2 + o**3 + 375*o**2.
-(o - 162)**2*(2*o + 1)
Let c be 4/(-55)*(-2 - 12/24). Factor 8/11 + 10/11*o + c*o**2.
2*(o + 1)*(o + 4)/11
Factor 0 + 0*g + 9/2*g**3 - 1/4*g**4 - 81/4*g**2.
-g**2*(g - 9)**2/4
Suppose 34*s - 30 = 28 + 10. Find u such that -u**s - 3/4*u + 1/4*u**3 + 9/2 = 0.
-2, 3
Let m(h) = h + 7. Let t be m(-6). Suppose 0 = -6*a + 5*a + t. Suppose w**3 - 2*w - 7*w + 8*w - w**2 + a = 0. What is w?
-1, 1
Let j(x) = 13*x**2 - 973*x + 965. Let n(w) = 20*w**2 - 1460*w + 1448. Let q(p) = -8*j(p) + 5*n(p). Factor q(h).
-4*(h - 120)*(h - 1)
Let h(a) be the second derivative of -a**7/210 + a**6/80 + a**5/40 - 5*a**4/6 + 5*a. Let c(s) be the third derivative of h(s). Factor c(f).
-3*(f - 1)*(4*f + 1)
Let u(g) be the second derivative of -1/9*g**4 - 12*g - 1/120*g**5 + 0 - 7/12*g**3 - 3/2*g**2. Determine z, given that u(z) = 0.
-3, -2
Suppose -2/7*h**2 - 30/7*h - 52/7 = 0. Calculate h.
-13, -2
Let m(z) be the third derivative of 3*z**7/70 + z**6/8 - z**5/5 - z**4/2 - 10*z**2. Factor m(u).
3*u*(u - 1)*(u + 2)*(3*u + 2)
Let b = 104223/5 + -20837. Factor 40 - b*d**2 + 2/5*d**3 + 32*d.
2*(d - 10)**2*(d + 1)/5
Let a = -109/6 + 869/30. Let y = a - 9. Suppose y*l + 0 - 3/5*l**2 = 0. What is l?
0, 3
Factor -32/3*m**2 + 0 + 2/3*m.
-2*m*(16*m - 1)/3
Let g(a) be the second derivative of -a**7/5040 + a**6/720 - 7*a**4/12 - 7*a. Let v(s) be the third derivative of g(s). Factor v(b).
-b*(b - 2)/2
Let c(n) = -3*n**3 + 4*n**2 - n. Let z(s) = -5*s**3 + 7*s**2 - 2*s. Suppose m = -4*h + 13, 2*m + 5 = 4*h - 29. Let i(w) = m*c(w) + 4*z(w). Factor i(q).
q*(q - 1)*(q + 1)
Suppose 119*m = 85*m + 68. Let g(q) be the first derivative of q**3 + 6 - 1/5*q**5 + 0*q - q**m + 0*q**4. Suppose g(z) = 0. What is z?
-2, 0, 1
Let a be (23 - (-6928)/(-304))*19/2. Solve 34/5*r + 12/5 - 6/5*r**a = 0 for r.
-1/3, 6
Find s, given that -1/3*s**2 + 0 - 2/3*s**4 - 5/3*s**3 + 2/3*s = 0.
-2, -1, 0, 1/2
Let n = 4021/60 + -67. Let x(f) be the third derivative of 0*f + 2/3*f**3 - n*f**5 + 0 + 3*f**2 + 1/3*f**4 - 1/15*f**6 - 1/70*f**7. Solve x(d) = 0.
-2, -1, -2/3, 1
Let i(q) = -144*q - 16. Let f be i(-11). Solve -f*n**4 - 128*n**5 - 64*n - 1186*n**3 + 69*n**2 - 830*n**3 - 709*n**2 + 1500*n**5 = 0 for n.
-2/7, 0, 2
Factor 55/3*o**4 + 70/3*o + 130/3*o**2 + 40*o**3 + 5 + 10/3*o**5.
5*(o + 1)**4*(2*o + 3)/3
Let h be ((-438)/(-1065))/((-8)/(-10)). Let v = h + -1/71. Factor -1/2*r - 1 + v*r**2.
(r - 2)*(r + 1)/2
Let v(n) = n**2 - 39*n + 44. Let t(u) = 40*u - 44. Let l(g) = 6*t(g) + 4*v(g). Factor l(a).
4*(a - 1)*(a + 22)
Let k(i) = -10*i**5 - 45*i**4 - 16*i**3 + 23*i**2 + 4*i + 2. Let o(l) = l**5 - l**4 - l**3 - l + 1. Let t(y) = 2*k(y) - 4*o(y). Find c such that t(c) = 0.
-3, -1, -1/4, 0, 2/3
Let n(o) = 48*o**2 - 393*o - 27. Let d(w) = -7*w**2 + 56*w + 4. Let v(q) = -27*d(q) - 4*n(q). Solve v(f) = 0 for f.
0, 20
Let q(u) = -u**3 - 5*u**2 - 3*u + 4. Let l be q(-4). Suppose -4*y + 2*k + 3*k - 12 = l, -4*y = -2*k. Factor v + 2 + 5*v**2 - v**y - 5*v**2.
-(v - 2)*(v + 1)
Let t(k) be the second derivative of 0 + 1/11*k**4 - 2/11*k**2 - 1/33*k**3 + k. Determine j, given that t(j) = 0.
-1/2, 2/3
Let q be 0 + 585/(-60) - -12. Suppose 3/2*z - 3/4*z**5 - 3/4*z**3 + 0 + 9/4*z**4 - q*z**2 = 0. What is z?
-1, 0, 1, 2
Let s(d) be the third derivative of 0*d**4 + 1/8*d**8 + 2/25*d**5 + 0*d**6 + 0 + 0*d**3 - 39/175*d**7 - 14*d**2 + 0*d. Solve s(x) = 0.
-2/7, 0, 2/5, 1
Let f(i) be the first derivative of 0*i - 2/15*i**3 - 1/5*i**6 - 1/10*i**4 + 2/5*i**5 + 0*i**2 - 33. Factor f(u).
-2*u**2*(u - 1)**2*(3*u + 1)/5
What is f in 54/5*f + 3/5*f**3 + 0 - 33/5*f**2 = 0?
0, 2, 9
Let x = 438 - 1312/3. Let y(b) be the second derivative of 0*b**2 + 0 - 10*b - 1/6*b**3 - x*b**4 - 4/5*b**5. Factor y(m).
-m*(4*m + 1)**2
Factor -4/3*z**2 - 4/3*z**4 + 0*z - 8/3*z**3 + 0.
-4*z**2*(z + 1)**2/3
Suppose -10/17*r**2 - 26/17*r + 2/17*r**3 - 14/17 = 0. What is r?
-1, 7
Let d = -167/33 + 1357/308. Let r = -1/12 - d. Determine c, given that r - 6/7*c + 6/7*c**3 - 4/7*c**2 = 0.
-1, 2/3, 1
Let s(c) be the second derivative of -c**5/135 + c**4/27 - 2*c**3/27 + 13*c**2 - 20*c. Let g(d) be the first derivative of s(d). Find u, given that g(u) = 0.
1
Let h be (-537)/684 - -2*(-9)/(-24). Let r = 238/285 + h. Factor 2/5*y**4 - 2/5 - 4/5*y**3 + 0*y**2 + r*y.
2*(y - 1)**3*(y + 1)/5
Let j(y) be the second derivative of -y**4/24 - 11*y**3/24 - 9*y**2/8 + 171*y. Factor j(t).
-(t + 1)*(2*t + 9)/4
Let b(s) be the third derivative of s**6/60 + 2*s**5/15 + 5*s**4/12 + 2*s**3/3 + s**2 + 31. Factor b(m).
2*(m + 1)**2*(m + 2)
Factor 4/7*u**3 + 0*u + 4/7*u**4 - 4/7*u**5 - 4/7*u**2 + 0.
-4*u**2*(u - 1)**2*(u + 1)/7
Determine j, given that -8/3*j - 4*j**2 + 4/3*j**3 + 4/3*j**5 + 0 + 4*j**4 = 0.
-2, -1, 0, 1
Let k = 67/2 - -23/14. Let z = k + -795/28. Determine n, given that -z + 9/2*n - 3/4*n**2 = 0.
3
Let r(j) be the third derivative of j**8/2184 + 4*j**7/273 + 5*j**6/39 - 54*j**2. Factor r(d).
2*d**3*(d + 10)**2/13
Let f(v) = 15*v**3 + 1890*v**2 + 11815*v - 13775. Let u(j) = -j**3 - 135*j**2 - 844*j + 984. Let i(b) = -4*f(b) - 55*u(b). Let i(y) = 0. What is y?
-14, 1
Let p = 4 + 6. Let -8*r - 12*r - 5*r**2 - p + 5*r = 0. What is r?
-2, -1
Let h be ((-63)/(-2))/(9/18 + (-44)/(-8)). Factor -12 - 6*r - 3/4*r**3 + h*r**2.
-3*(r - 4)**2*(r + 1)/4
Let 14/13*j**3 + 16/13*j**2 + 0 + 2/13*j**4 - 32/13*j = 0. Calculate j.
-4, 0, 1
Let l(p) = 45*p**3 + 680*p**2 + 2160*p - 975. Let n(g) = -23*g**3 - 340*g**2 - 1081*g + 488. Let c(u) = 2*l(u) + 5*n(u). Factor c(b).
-5*(b + 7)**2*(5*b - 2)
Factor -2*n**4 - 11*n - 3*n**2 + 128 - 11*n**2 - 16*n**3 + 104 + 56 + 155*n.
-2*(n - 3)*(n + 3)*(n + 4)**2
Let y(n) be the first derivative of -1/30*n**3 + 5 - 1/60*n**4 + 1/150*n**6 - 11*n + 