derivative of -y**6/900 + y**5/300 - 13*y**3/6 + 5*y. Let g(u) be the second derivative of v(u). Suppose g(t) = 0. Calculate t.
0, 1
Let z(y) be the second derivative of y**5/20 - 29*y**4/6 + 841*y**3/6 + 39*y. Factor z(k).
k*(k - 29)**2
Let q(v) be the first derivative of 1/9*v**3 - 5/3*v**2 + 25/3*v + 14. Let q(x) = 0. Calculate x.
5
Let d(v) = 66*v**2 + 66*v + 6. Let c(z) = -200*z**2 - 272*z + 74*z - 17 - 2. Let h(n) = -2*c(n) - 7*d(n). Find p such that h(p) = 0.
-1, -2/31
Let f(q) be the second derivative of -13/20*q**5 + 5/4*q**4 + 1/2*q**2 - 10*q + 2/15*q**6 - 7/6*q**3 + 0. Factor f(d).
(d - 1)**3*(4*d - 1)
Let m(k) be the third derivative of k**10/302400 + k**9/60480 - k**8/13440 - k**5/6 - 22*k**2. Let n(c) be the third derivative of m(c). Factor n(r).
r**2*(r - 1)*(r + 3)/2
Suppose -4*p + 5*q - 69 = 0, -3*p + 2*q = -q + 54. Let m = -12 - p. Factor m*h**2 + 7*h + 13*h + 12*h - 5*h + 27 + h**3.
(h + 3)**3
Let i(l) = 12*l + 4. Let s(g) = g**3 - g**2 + g + 1. Let n(v) = v - 4. Let m be n(8). Let z(x) = m*s(x) - i(x). Factor z(o).
4*o*(o - 2)*(o + 1)
Suppose 2*d = -5*a - 15 + 21, -4*a + 3*d + 14 = 0. Suppose 1/7*t**3 + 0 + 1/7*t**a + 0*t = 0. What is t?
-1, 0
Factor -286/3*t - 1/6*t**3 - 484/3 - 23/3*t**2.
-(t + 2)*(t + 22)**2/6
Let a(j) be the second derivative of j**8/40320 - j**6/4320 - j**4/12 - 34*j. Let z(r) be the third derivative of a(r). Let z(m) = 0. What is m?
-1, 0, 1
Suppose 5*n = 4 + 1. Suppose -5*b + 9 = -n. Factor r**2 + b*r - r**2 - 4 - 14*r + 12*r**3 + 4*r**2.
4*(r - 1)*(r + 1)*(3*r + 1)
Let p(z) be the second derivative of 1/4*z**4 + 3 + 0*z**3 + z - 1/20*z**6 + 3/40*z**5 + 0*z**2. Determine n, given that p(n) = 0.
-1, 0, 2
Suppose 0 = -3*d - 5*u + 29, 15 = 2*d + u - 2. Let i be 4 - 64/(-60)*(-18)/d. Factor -2/5*z + 0 + i*z**2.
2*z*(4*z - 1)/5
Let w(l) be the first derivative of -3*l**4/4 - 5*l**3 + 9*l**2 - 86. Factor w(z).
-3*z*(z - 1)*(z + 6)
Let w(j) be the third derivative of -1/60*j**5 + 13*j**2 + 0 + 0*j**3 + 0*j + 0*j**4. Solve w(z) = 0 for z.
0
Let a be (-1)/2*2*-15. Factor -2*g**2 - a*g - 4 + 18*g - 9*g.
-2*(g + 1)*(g + 2)
Let q(h) be the third derivative of h**8/56 - 53*h**7/315 + 17*h**6/30 - 2*h**5/3 - 2*h**4/9 - 5*h**2 + 25. Factor q(o).
2*o*(o - 2)**3*(9*o + 1)/3
Let g = 22725/2 + -11361. Factor -g*q + 3/2*q**2 - 3.
3*(q - 2)*(q + 1)/2
Let -7*n**2 - 3*n**2 + 644*n - 3*n**3 + 4*n**2 - 644*n = 0. What is n?
-2, 0
Suppose 0 = -m + 5*h + 35, -4*h - 26 = -2*m + 20. What is f in m*f**2 + 10/3 + 25/3*f**3 + 5/3*f**4 + 35/3*f = 0?
-2, -1
Suppose -y + 3 = 4*m - 1, m = -4*y + 1. Let l(c) be the second derivative of y*c**2 + 3*c + 0 + 1/18*c**4 + 1/9*c**3. Factor l(s).
2*s*(s + 1)/3
Suppose 2*h - 20 = -2*j, -2578*j + 2573*j = 4*h - 42. Factor -27/2 - 3*a - 1/6*a**j.
-(a + 9)**2/6
Let b(r) be the first derivative of -r**3/12 + 91*r**2/8 - 89*r/2 + 157. Determine x, given that b(x) = 0.
2, 89
Factor -14*u**2 + 4*u + 4*u**2 + 0*u - 6 + 12*u**2.
2*(u - 1)*(u + 3)
Solve 109/12*m**2 - 11/3*m + 1/3 - 2*m**3 - 15/4*m**4 = 0 for m.
-2, 2/15, 1/3, 1
Let l(d) be the third derivative of d**7/840 + d**6/240 - d**5/80 - d**4/12 - d**3/6 + 136*d**2. Factor l(y).
(y - 2)*(y + 1)**2*(y + 2)/4
Let l(b) be the first derivative of b**6/10 + 9*b**5/20 + 8*b - 8. Let z(m) be the first derivative of l(m). Determine t, given that z(t) = 0.
-3, 0
Let r(m) = 6*m**3 + 46*m**2 + 2*m - 2. Let f(d) = 7*d**3 + 47*d**2 + 3*d - 3. Let a(o) = -2*f(o) + 3*r(o). Suppose a(n) = 0. Calculate n.
-11, 0
Factor -323*f - 3*f**2 - 157*f + 8*f**2 - 3*f**2 - 14400 - 6*f**2.
-4*(f + 60)**2
Let b(s) be the second derivative of 0 - 38*s + 2*s**2 - 8/3*s**3 - 3/4*s**4. Solve b(a) = 0 for a.
-2, 2/9
Let r(m) = m - 1. Let h(g) = -2*g**2 - 6 + 8*g - 3*g + g. Let b(v) = -h(v) - 2*r(v). Factor b(u).
2*(u - 2)**2
Let y(c) be the first derivative of -25*c**4/4 - 5*c**3/3 + 10*c**2 - 66. Factor y(b).
-5*b*(b + 1)*(5*b - 4)
Let a be ((-12)/(-2) + -7)/(-9). Let z(j) be the first derivative of 1/15*j**5 - a*j**3 + 4 + 1/6*j**4 - 1/3*j**2 + 0*j. Factor z(f).
f*(f - 1)*(f + 1)*(f + 2)/3
Let g(v) = -70*v + 32*v - v**3 + 9 + 8*v**2 + 30*v. Let o be g(7). Factor 2/3*u**o - 2 + 4/3*u.
2*(u - 1)*(u + 3)/3
Let a be (130/60 + -2)/((-3)/(-6)). Find m, given that 1/3 - 2*m**2 - a*m = 0.
-1/2, 1/3
Let c(g) be the third derivative of 0*g**3 + 0*g + 0*g**4 - 1/420*g**6 - 16*g**2 + 0 + 1/735*g**7 + 0*g**5. Factor c(n).
2*n**3*(n - 1)/7
Suppose -4/7*l**3 - 2/7*l**4 + 0*l + 0 + 0*l**2 = 0. Calculate l.
-2, 0
Let w(p) be the second derivative of -p**5/90 + 7*p**4/54 + 8*p**3/27 - 92*p. Factor w(h).
-2*h*(h - 8)*(h + 1)/9
Let t = -13/4 + 19/4. Let u be (30/8)/(1105/442). Find j such that 0*j**2 - u*j**3 + t*j + 0 = 0.
-1, 0, 1
Let c be -5*(3 + 35/(-25)). Let x(u) = -u**3 - 7*u**2 + 10*u + 18. Let m be x(c). Factor 4*r**4 - r**4 - 15*r**4 - 6*r**m + 15*r**3 + 3*r**5.
3*r**2*(r - 2)*(r - 1)**2
Let j(a) be the second derivative of a**10/20160 - a**8/2240 + a**6/480 - 13*a**4/6 - 25*a. Let u(c) be the third derivative of j(c). Factor u(l).
3*l*(l - 1)**2*(l + 1)**2/2
Let c be (-74)/(-518) - (0 + (-41)/7). Let a(t) be the second derivative of 1/2*t**3 - c*t - 1/4*t**4 + 0 + 0*t**2. What is r in a(r) = 0?
0, 1
Solve -2*a**2 - 5 - 3 + 10 = 0 for a.
-1, 1
Let 160 - 2*r**2 + 269*r - 642*r + 297*r = 0. What is r?
-40, 2
Let n(x) be the first derivative of -x**8/5880 - x**7/735 - x**6/252 - x**5/210 - 2*x**3 + 28. Let q(a) be the third derivative of n(a). Factor q(o).
-2*o*(o + 1)**2*(o + 2)/7
Suppose -3*c - u = -5*c + 7, -4*u - 2 = 5*c. Suppose c*a + 5*r = 21, -5*a = -0*r + r - 18. Factor -4*j**4 - 4*j + j**a + 51*j**2 - 47*j**2 + 3*j**3.
-4*j*(j - 1)**2*(j + 1)
Let l(a) be the third derivative of a**6/180 - a**5/30 - a**4/6 + 8*a**3/9 - 101*a**2. Factor l(i).
2*(i - 4)*(i - 1)*(i + 2)/3
Suppose -m - n - 2 = -6, 0 = n - 2. Factor -2*z**5 + 6*z**3 + z**4 - 17*z + 3*z**4 + 9*z - 8*z**m.
-2*z*(z - 2)**2*(z + 1)**2
Let d be 1/(-4 - 236/(-60)). Let j = -10 - d. Find f, given that -29*f - 43*f**2 + j*f + 39*f**2 - 36 = 0.
-3
Suppose 0*m = -3*m. Suppose -82*n + 225 = -7*n. Factor m - 2/3*p**n - 2/3*p**2 + 4/3*p.
-2*p*(p - 1)*(p + 2)/3
Let j(q) = -4*q**3 - 37*q**2 - 11*q - 15. Let o be j(-9). Suppose 0 - 4/9*k**2 + 0*k + 2/9*k**o + 2/9*k**4 = 0. Calculate k.
-2, 0, 1
Let k(z) = 2*z**3 - 8 + 4*z + 3 + 0*z**3 - 5*z**2 - z**3. Let t(r) = 4*r**2 - 4*r + 4. Let c(b) = 4*k(b) + 5*t(b). Solve c(u) = 0 for u.
-1, 0, 1
Let o(b) = 17*b**2 + 33*b - 56. Let q(x) = -15*x**2 - 35*x + 55. Let m(n) = 5*o(n) + 6*q(n). Factor m(d).
-5*(d - 1)*(d + 10)
Let q(j) be the third derivative of j**6/180 + 16*j**5/45 + 61*j**4/36 + 10*j**3/3 + 49*j**2 + 2*j. Suppose q(w) = 0. Calculate w.
-30, -1
Suppose 15*y + 4 = 4. Suppose y = 2*n + l - 1, l = 2*n + 1 - 0. Suppose n - 1/5*o**2 + 1/5*o = 0. What is o?
0, 1
Suppose 5*j + 5*s - 7*s + 475 = 0, -3*j - 286 = -s. Let g = j + 293/3. Factor 2*y + g + 0*y**2 - 8/3*y**3.
-2*(y - 1)*(2*y + 1)**2/3
Let m(c) be the first derivative of c**4/10 + 4*c**3/5 - c**2/5 - 12*c/5 - 136. Let m(r) = 0. Calculate r.
-6, -1, 1
Let p(r) be the second derivative of r**5/120 - 10*r**2 + 14*r. Let t(a) be the first derivative of p(a). Factor t(b).
b**2/2
Factor -78/11*j**2 + 42/11*j + 36/11.
-6*(j - 1)*(13*j + 6)/11
Let d(q) be the third derivative of 0*q + 1/180*q**5 + 1/540*q**6 + 0*q**4 + 0 - 1/3*q**3 - 3*q**2. Let n(j) be the first derivative of d(j). Factor n(p).
2*p*(p + 1)/3
Let k be ((-1)/13)/((-2)/4). Let y = 899/13 - 69. Factor k*m**2 + y - 4/13*m.
2*(m - 1)**2/13
Let j = -36 - -29. Let m be 2/(-14) - 15/j. Determine p, given that 25*p**m + 6 - 19 + 18 - 30*p = 0.
1/5, 1
Let h(r) be the first derivative of -9 + 2*r**2 + 24/5*r - 4/15*r**3. Factor h(j).
-4*(j - 6)*(j + 1)/5
Factor -2 + 6*f + 3*f**2 - 8 + 1.
3*(f - 1)*(f + 3)
Let p(w) be the first derivative of 7*w**4/10 - 4*w**3/3 - 11*w**2/5 + 12*w/5 - 357. Factor p(y).
2*(y - 2)*(y + 1)*(7*y - 3)/5
Let j(b) = -4*b + 41. Let f be j(10). Let h be f + 2 - (-23)/115. Let -h + 16/5*v - 4/5*v**2 = 0. What is v?
2
Let y be 20/6 - 33/(99/(-2)). Let -1 + 4/3*n + 2/3*n**2 + 1/3*n**y - 4/3*n**3 = 0. What is n?
-1, 1, 3
Let q(p) be the second derivative of -p**4/6 + 5*p**3/3 + 6*p**2 - 23*p - 2. Factor q(n).
-2*(n - 6)*(n + 1)
Suppose 249*g - 82 = 416. Factor -2