be the first derivative of x**5 + 45*x**4/2 - 100*x**3 + 155*x**2 - 105*x - 20. Determine z so that c(z) = 0.
-21, 1
Let f(q) be the second derivative of 0*q**3 + 0*q**2 - 1/98*q**7 + 2*q + 3/70*q**6 + 1/28*q**4 - 9/140*q**5 + 0. Suppose f(d) = 0. What is d?
0, 1
Let s(m) = -m**3 + 7*m**2 - 2*m + 15. Let x be s(7). Let y be (-6)/(-9) - x - 21/(-36). Let 1/4*p**4 + 1/4*p - 3/4*p**2 + 1/2 - y*p**3 = 0. Calculate p.
-1, 1, 2
Let t(z) be the second derivative of 12*z + 0*z**2 - 1/2*z**4 + 0*z**3 + 3/4*z**6 + 0 + 1/7*z**7 + 9/10*z**5. Determine g, given that t(g) = 0.
-2, 0, 1/4
Let k(w) be the third derivative of w**5/210 - 13*w**4/42 + 44*w**2 - 2. Let k(b) = 0. Calculate b.
0, 26
Let y(c) be the third derivative of -1/20*c**5 + 1/4*c**4 + 0 + 0*c - 11*c**2 + 3/2*c**3. Factor y(q).
-3*(q - 3)*(q + 1)
Let f be 8/20 - (-126)/10. Suppose -2*s + f = -5. Factor -5*x**4 + 8*x**4 + s*x**2 - 12*x**2.
3*x**2*(x - 1)*(x + 1)
Let x(h) = -6*h**2 + 6*h + 16. Let y(s) = s**2 + s. Let c(u) = -5*u**2 - u + 5. Let z(q) = c(q) + 3*y(q). Let r(p) = 5*x(p) - 16*z(p). Factor r(a).
2*a*(a - 1)
Let q(a) be the second derivative of a**6/10 - 183*a**5/20 + 315*a**4 - 4600*a**3 + 12000*a**2 - a. Suppose q(y) = 0. Calculate y.
1, 20
Let j(v) = -v**3 - 35*v**2 - 88*v + 258. Let k be j(-32). Find a, given that -2/7*a - 3/7*a**3 + 9/7*a**k + 0 - 4/7*a**4 = 0.
-2, 0, 1/4, 1
Let s(c) be the first derivative of -30 - 2/13*c - 2/13*c**3 + 3/13*c**2 + 1/26*c**4. Factor s(g).
2*(g - 1)**3/13
Let b(a) be the third derivative of a**6/30 - 27*a**5/5 + 729*a**4/2 - 13122*a**3 + 71*a**2. Solve b(u) = 0 for u.
27
Let t = 1549/6 - 258. Let c(i) be the second derivative of 4*i + 1/3*i**3 - t*i**4 + 0 + 0*i**2. Factor c(v).
-2*v*(v - 1)
Let q(t) = 3*t**3 - 24*t**2 - 96*t - 123. Let d = -53 + 43. Let p(w) = -w**3 - 1. Let b(a) = d*p(a) - 2*q(a). Find z, given that b(z) = 0.
-4
Factor 16*q**2 - 18*q**3 + 1 - 5*q**2 - 9*q - 21*q + 25*q**2 + 3*q**4 + 8.
3*(q - 3)*(q - 1)**3
Let u(f) be the second derivative of f**6/30 - f**5/2 + 17*f**4/12 - 4*f**3/3 - 19*f + 5. Factor u(b).
b*(b - 8)*(b - 1)**2
Solve 39/5*c**4 + 0*c + 33/5*c**3 - 6/5*c**2 + 0 = 0.
-1, 0, 2/13
Let a be 27/162 + (-86)/(-60). Let g = 1 + -3/5. Factor g*w**2 + 8/5*w + a.
2*(w + 2)**2/5
Let r(h) = -13*h**2 - 70*h + 51. Let l be r(-6). Factor 16/13 + 76/13*q + 50/13*q**2 + 8/13*q**l.
2*(q + 2)*(q + 4)*(4*q + 1)/13
Let m(f) be the third derivative of -f**8/448 - 3*f**7/140 - 3*f**6/40 - f**5/8 - 3*f**4/32 - 36*f**2. Let m(a) = 0. What is a?
-3, -1, 0
Let r(o) = 2*o**2. Let m(l) = 4*l**2 - 8*l + 64. Let x(g) = -m(g) + 3*r(g). Factor x(n).
2*(n - 4)*(n + 8)
Let s(b) be the third derivative of 0 + 1/28*b**4 - 3/280*b**6 + 1/28*b**5 + 0*b - 8*b**2 + 0*b**3. Find x, given that s(x) = 0.
-1/3, 0, 2
Suppose -6*i + 8 = -22. Factor -7*y**5 - y**5 + 4*y**i - 4*y - 6*y**4 - 4 + 8*y**3 + 8*y**2 + 2*y**4.
-4*(y - 1)**2*(y + 1)**3
Suppose -5*a = -3*u + 29, 5*u + 3*a - 37 = 34. Determine j so that -22*j**4 + 4*j**2 + 32*j + 2*j**4 - u*j**3 + 0*j + 16 - 15*j**3 - 4*j**5 = 0.
-2, -1, 1
Let l(b) = -6*b**2 - 28 - 2*b - 6*b**4 + 28 + 7*b**4. Let d(t) = -4*t**4 + 25*t**2 + 9*t. Let g(x) = -4*d(x) - 18*l(x). Determine u so that g(u) = 0.
-2, 0, 2
Let s = 0 - 8. Let y be s/(-6)*(-9)/(-2). Suppose -5*h**3 + 4*h**2 + y*h**3 + 0*h + 0*h = 0. Calculate h.
-4, 0
Let b be 14/70*30 - 6*1. Factor b*h + 2/5*h**2 - 2/5.
2*(h - 1)*(h + 1)/5
Let x(c) = 2*c**4 + 14*c**3 - 64*c**2 + 48*c. Let i(s) = 3*s**4 + 29*s**3 - 128*s**2 + 96*s. Let t(v) = -2*i(v) + 5*x(v). Factor t(q).
4*q*(q - 2)*(q - 1)*(q + 6)
Let l(u) = u**3 - 35*u**2 - 119*u + 190. Let o be l(38). Determine f, given that -1/3*f**3 - 5/3*f**2 - 4/3*f + o = 0.
-4, -1, 0
Let s(d) be the first derivative of -d**3/2 + 12*d**2 - 42*d + 55. Factor s(i).
-3*(i - 14)*(i - 2)/2
Let c be ((-28)/126)/((-9)/162). Find h, given that 16*h**3 - h - 2/3 + 16/3*h**c + 31/3*h**2 = 0.
-2, -1, -1/4, 1/4
Let n(b) be the first derivative of b**6/240 - b**5/16 - 11*b**3/3 + 9. Let o(a) be the third derivative of n(a). Factor o(g).
3*g*(g - 5)/2
Let q = 388/327 - 93/109. Let u = 25/3 + -8. Factor q*c**2 - u*c + 0.
c*(c - 1)/3
Let p(u) = u**5 + u**4 + u**3 - u**2. Let g(x) = -5*x**5 - 12*x**4 + 11*x**3 - 73*x**2 - 27*x**3 + 99*x**2 - 11*x + 2. Let s(t) = 5*g(t) + 40*p(t). Factor s(b).
5*(b - 1)**3*(b + 2)*(3*b - 1)
Let 12800/11*u**2 - 320/11*u + 2/11 = 0. Calculate u.
1/80
Suppose 0*o = 2*o + 10. Let z be 180/o*4/(-66). Suppose 28/11*q**5 - 90/11*q**4 - 8/11 + 56/11*q**3 + 38/11*q**2 - z*q = 0. Calculate q.
-1/2, -2/7, 1, 2
Let j(k) be the first derivative of -k**3/3 - 13*k**2/2 - 22*k - 134. Let j(o) = 0. What is o?
-11, -2
Let c(t) be the third derivative of 1/3*t**3 + 1/840*t**7 - 12 - 7/480*t**6 + 3/40*t**5 + t**2 + 0*t - 5/24*t**4. Factor c(k).
(k - 2)**3*(k - 1)/4
Let w(r) be the first derivative of 4 - 1/18*r**2 + 1/27*r**3 + 0*r. Determine i, given that w(i) = 0.
0, 1
Let w(y) = -6*y**5 + 6*y**4 + y**3 - 6*y**2 + 5*y + 5. Let r(d) = 3*d**5 - 3*d**4 + 3*d**2 - 3*d - 3. Let v(g) = -5*r(g) - 3*w(g). Find a such that v(a) = 0.
-1, 0, 1
Let k(d) be the second derivative of 50*d**4/21 + 60*d**3/7 + 81*d**2/7 - 143*d. Factor k(t).
2*(10*t + 9)**2/7
Let h = -19/36 + 3/4. Let k(o) = 4*o - 30. Let y be k(8). Suppose -4/9*t**y + 4/9 - h*t + 2/9*t**3 = 0. What is t?
-1, 1, 2
Solve 81/2*k - 18*k**2 - 21 - 3/2*k**3 = 0.
-14, 1
Let j(o) = -o**3 + 8*o**2 - 14*o + 53. Let s be j(7). Find c, given that 0*c**2 + 3/5*c**5 + 0*c - 6/5*c**s + 0 + 3/5*c**3 = 0.
0, 1
Let g(d) be the second derivative of -1/5*d**5 + 6*d - 1/3*d**4 + 0 + 2/3*d**3 + 0*d**2 + 2/15*d**6. Solve g(s) = 0.
-1, 0, 1
Let n = 45984/5 + -9347. Let d = 151 + n. Find r, given that 6/5*r**4 - 2/5 - d*r**2 + 8/5*r - 8/5*r**3 = 0.
-1, 1/3, 1
Let o = -1613/1050 - -54/35. Let c(y) be the third derivative of 0*y + 1/20*y**4 + y**2 + o*y**5 + 0*y**3 + 0. Solve c(k) = 0.
-3, 0
What is n in -3/4*n**5 + 0 - 1/2*n**4 + 9/4*n**3 - n + 0*n**2 = 0?
-2, -2/3, 0, 1
Let t(f) = -f**3 - 4*f**2 - 4*f - 12. Let n be t(-4). Suppose -4*j + n*v + 16 = 0, 5*j + 6*v - v = 10. Solve -4/5*p**2 + 0*p - 6/5*p**4 + 0 + 2*p**j = 0.
0, 2/3, 1
Let v(q) = -4*q**3 - 14*q**2 - 49*q - 39. Let i(g) = 2*g**3 + 6*g**2 + 24*g + 20. Let p(z) = 11*i(z) + 6*v(z). Solve p(f) = 0.
-7, -1
Let n(u) be the third derivative of 1/12*u**3 + 0 - 1/48*u**4 - 2*u**2 + 0*u + 1/240*u**6 - 1/120*u**5. Factor n(z).
(z - 1)**2*(z + 1)/2
Let g(h) be the third derivative of -h**5/75 - 2*h**4/3 - 24*h**3/5 + 302*h**2. Factor g(k).
-4*(k + 2)*(k + 18)/5
Let 2*l - 7*l**2 + 42 + 25*l + 12*l**2 - 2*l**2 = 0. What is l?
-7, -2
Let g be ((-2)/(-6) + -1)/(6/(-45)). Suppose g*x + u + 6 = 1, -u = -5*x + 5. Factor 9/5*h**4 - 3/5*h**5 + 0 + x*h**3 - 12/5*h**2 + 0*h.
-3*h**2*(h - 2)**2*(h + 1)/5
Let g(z) be the first derivative of -z**4/10 + 14*z**3/3 - 352*z**2/5 + 1536*z/5 + 211. Factor g(n).
-2*(n - 16)**2*(n - 3)/5
Let f(u) be the second derivative of -1/24*u**4 - 1/2*u**2 - 1/120*u**6 + 0 + 0*u**3 - 1/30*u**5 + 4*u. Let h(v) be the first derivative of f(v). Factor h(o).
-o*(o + 1)**2
Let t be (2 - 9)/21*1/(-4). Let v(k) be the second derivative of 4*k + 0*k**2 + 0*k**3 + 0 + 7/40*k**5 - 1/12*k**4 - t*k**6. Factor v(y).
-y**2*(y - 1)*(5*y - 2)/2
Suppose 53*z = 58*z + 2*c + 2, z - 3*c - 3 = 0. What is r in z + 4*r**2 - 4/3*r**3 - 8/3*r = 0?
0, 1, 2
Let v = 18/4103 - -16286/28721. Factor 2/7*p**5 + 0*p - v*p**3 + 0 + 0*p**2 + 2/7*p**4.
2*p**3*(p - 1)*(p + 2)/7
Factor 2*c**3 + 3*c**2 - 4 - 6 - 25*c - 2*c**3 - 23*c**2 - 5*c**3.
-5*(c + 1)**2*(c + 2)
Suppose 246 = 4*o - 2*w, 3*w - 96 = -o - 24. Factor 2*a**3 - 6 + 23*a + 30*a - o*a - 2*a**2.
2*(a - 3)*(a + 1)**2
Let c(u) = u**3 + 12*u**2 + 3*u + 35. Let k be c(-12). Let l(f) = -2*f**3 - 9*f**2 - 7*f. Let m(p) = p**2 + p. Let t(a) = k*l(a) - 3*m(a). Solve t(i) = 0.
-2, -1, 0
Let r = -9/523 + 2171/65375. Let s = 1129/250 - r. Factor 3*n + 0 + 3/2*n**3 + s*n**2.
3*n*(n + 1)*(n + 2)/2
Let p(m) = -m**2 + 12*m + 225. Let c be p(22). Let t be (-2)/(-2)*1 + -1. Factor t*k**2 - 4/3*k**c + 0 + 0*k + 2/3*k**3 - 7/3*k**4.
-k**3*(k + 2)*(4*k - 1)/3
Let g = 13 + -5. Suppose 4*d**2 + d - d + 4*d**4 - g*d**4 = 0. Calculate d.
-1, 0, 1
Let u(w) be the second derivative of -w**8/23520 + w**6/840 - w**5/210 + 7*w**4/4 