derivative of n**9/37800 + n**8/8400 + n**4/4 + 2*n. Let y(q) be the third derivative of d(q). Determine l, given that y(l) = 0.
-2, 0
Let a(c) be the first derivative of 5*c**3/3 - 20*c - 4. Factor a(s).
5*(s - 2)*(s + 2)
Let y(i) be the second derivative of 0*i**3 + 0*i**5 + 0 - 1/10*i**6 + 0*i**2 - 5*i + 1/4*i**4. Factor y(p).
-3*p**2*(p - 1)*(p + 1)
Suppose 126*y - 123*y = 0. Let d(g) be the second derivative of -1/5*g**6 - 2*g + 0*g**2 + 1/10*g**5 + y*g**3 + 1/3*g**4 + 0. Suppose d(r) = 0. What is r?
-2/3, 0, 1
Let v = -431 + 299. Let q be (v/(-32) + -4)*4. Solve q*u**2 - 1/2*u - 1/2 + 1/2*u**3 = 0.
-1, 1
Let w(l) be the second derivative of 3*l**5/2 + 25*l**4/12 - 5*l**3/3 - 5*l**2/2 - 4*l. Let w(i) = 0. What is i?
-1, -1/3, 1/2
Let q(b) be the second derivative of b**9/21168 + b**8/5880 - b**6/1260 - b**5/840 + 2*b**3/3 - 2*b. Let v(s) be the second derivative of q(s). Factor v(d).
d*(d - 1)*(d + 1)**3/7
Let w(l) be the first derivative of -4*l**5/5 - 5*l**4 - 12*l**3 - 14*l**2 - 8*l + 3. Factor w(h).
-4*(h + 1)**3*(h + 2)
Let c(a) = a - 4. Let f(g) = -5*g**2 + g - 12. Let r(w) = -14*w**2 + 3*w - 35. Let s(q) = -11*f(q) + 4*r(q). Let j(v) = -14*c(v) + 6*s(v). Factor j(l).
-2*(l + 2)*(3*l - 2)
Let b(a) be the first derivative of a**3/12 + 27. Determine c so that b(c) = 0.
0
Suppose u = -0 + 3. Suppose -3 = -3*s + u. Determine l so that -2 + l**s + 0 + 2*l**2 + 7*l + 4 = 0.
-2, -1/3
Let b(k) be the first derivative of 4*k**3/3 + 4*k**2 - 12*k + 23. Factor b(d).
4*(d - 1)*(d + 3)
Suppose -48 = 2*n - f, 0 = -2*n - f + 5*f - 48. Let v = 27 + n. Suppose -v*s**3 + 3/2*s**2 + 0*s + 3/2*s**4 + 0 = 0. Calculate s.
0, 1
Let g(x) be the third derivative of -x**6/360 - x**5/120 - x**3/2 - 2*x**2. Let w(j) be the first derivative of g(j). Determine d so that w(d) = 0.
-1, 0
What is d in 0 + 2*d**3 - 1/3*d**5 + 8/3*d**2 + 0*d**4 + d = 0?
-1, 0, 3
Let a(r) = -23*r**2 - 29*r - 23. Let j(w) = 4*w**2 + 5*w + 4. Let b = -9 - -15. Let v(t) = b*a(t) + 34*j(t). Factor v(p).
-2*(p + 1)**2
Let m be 7/(-1)*(-4)/14. Suppose 0*u - 3*u - u**2 + 9 - 3*u - m*u**2 = 0. Calculate u.
-3, 1
Suppose 0 = -2*f + 3*d - 27, 0 = 2*d - 4*d + 6. Let h be 4/(-18) - 38/f. Let -v**2 + v**2 + h*v + 2 + 2*v**2 = 0. What is v?
-1
Let h(t) = -21*t**2 - 90*t - 27. Let q(r) = r**2 - 1. Let g(v) = -9*v**2 - 13*v + 2. Let a(p) = g(p) + 6*q(p). Let f(o) = -27*a(o) + 4*h(o). Factor f(x).
-3*x*(x + 3)
Let a(d) be the second derivative of 0*d**2 - 2*d - 1/6*d**3 + 0 + 1/12*d**4. Find x such that a(x) = 0.
0, 1
Suppose 11*k + 6 = 13*k. Let o(t) be the first derivative of -1/5*t**2 + 2/15*t**k + 0*t + 3. Find w such that o(w) = 0.
0, 1
Let x = -8 + 10. Let d(f) be the second derivative of 0*f**x + 2/75*f**6 + 0 + 2*f - 1/15*f**4 - 1/15*f**3 + 1/105*f**7 + 0*f**5. Solve d(a) = 0 for a.
-1, 0, 1
Let p(l) be the first derivative of l**6/9 - 4*l**5/3 + 37*l**4/6 - 128*l**3/9 + 52*l**2/3 - 32*l/3 - 4. What is g in p(g) = 0?
1, 2, 4
Let l(w) = w**2 + 32*w - 64. Let a(d) = 8*d + 0*d + 24*d - 22 - 42. Let p(i) = -5*a(i) + 4*l(i). Factor p(b).
4*(b - 4)**2
Let t(l) be the first derivative of -1 + l**2 - 2/3*l**3 + l. Let m(c) = c**2 - 2*c - 1. Let z(x) = -3*m(x) - 2*t(x). Factor z(g).
(g + 1)**2
Suppose -36 = -8*h + 4*h. Factor 9*z**3 - h*z**4 + 42*z - 42*z - 3*z**2 + 3*z**5.
3*z**2*(z - 1)**3
Let g(d) be the first derivative of -14*d**5/25 - 8*d**4/5 - 22*d**3/15 - 2*d**2/5 + 9. Factor g(v).
-2*v*(v + 1)**2*(7*v + 2)/5
Let x(z) be the third derivative of 1/270*z**5 + 1/6*z**3 + 1/108*z**4 + 2*z**2 - 1/540*z**6 + 0*z + 0. Let d(w) be the first derivative of x(w). Factor d(i).
-2*(i - 1)*(3*i + 1)/9
Let w(u) be the first derivative of -4*u**3/3 - 16*u**2 - 20. Factor w(f).
-4*f*(f + 8)
Let z(v) be the first derivative of -v**7/525 - v**6/150 + v**5/150 + v**4/30 - 2*v**2 - 7. Let s(g) be the second derivative of z(g). Factor s(c).
-2*c*(c - 1)*(c + 1)*(c + 2)/5
Factor -11/8*n - 15/8*n**2 - 1/4.
-(3*n + 1)*(5*n + 2)/8
Let x(b) be the first derivative of -b**7/840 - b**6/180 - b**3/3 + 1. Let u(w) be the third derivative of x(w). Let u(d) = 0. What is d?
-2, 0
Suppose -2*n - 4 = -14, -3*t = -n - 76. Find b such that -11*b + 13*b**4 + 9 + 38*b - 34*b**4 + 15*b**2 - t*b**3 - 3 = 0.
-1, -2/7, 1
Factor 2/13*m**3 + 4/13*m**2 + 0 + 2/13*m.
2*m*(m + 1)**2/13
Let k be (-6)/(-9)*2682/30. Let v = 60 - k. Factor -1/5*g**2 - v*g + 2/5*g**3 + 1/5*g**4 + 0.
g*(g - 1)*(g + 1)*(g + 2)/5
Determine a, given that -1/4*a + 1/4*a**2 + 0 = 0.
0, 1
Let v = 1666/45 + -184/5. Let g = 1/29 - -49/261. What is b in -g*b - v*b**2 + 0 = 0?
-1, 0
Let h(q) be the third derivative of q**5/30 - q**4/3 + q**3/3 + 3*q**2. Let z(w) = w**2 - w + 1. Let b(t) = -h(t) + 4*z(t). Factor b(y).
2*(y + 1)**2
Let a(q) be the first derivative of -q**5/60 + q**4/12 - 2*q**2 + 1. Let r(z) be the second derivative of a(z). Suppose r(b) = 0. Calculate b.
0, 2
Factor 3/4*l**2 - 9/2*l + 27/4.
3*(l - 3)**2/4
Let z(t) be the first derivative of t**6/660 + t**5/165 - t**2 - 1. Let l(c) be the second derivative of z(c). Factor l(u).
2*u**2*(u + 2)/11
Let h(r) be the second derivative of 2*r**6/15 - 2*r**4/3 + 2*r**2 - 10*r. Let h(g) = 0. Calculate g.
-1, 1
Let g be 16/6 + 4/(-6). Let r(x) be the first derivative of 2 + 1/4*x + 1/12*x**3 + 1/4*x**g. Factor r(z).
(z + 1)**2/4
Suppose 6*r = 9*r. Let w(s) be the second derivative of r - s - 1/15*s**4 - 1/5*s**2 - 1/5*s**3. Let w(x) = 0. Calculate x.
-1, -1/2
Solve -30*b**2 - 24 + 29*b**2 - 33*b**3 + 96*b**3 - 365*b**2 + 147*b**4 + 180*b = 0.
-2, 2/7, 1
Let b(i) be the third derivative of 1/6*i**4 + 0*i + 0*i**3 - 1/30*i**6 + 1/15*i**5 + 0 - 7*i**2 - 2/105*i**7. Factor b(m).
-4*m*(m - 1)*(m + 1)**2
Suppose -4*m = -j + 4, -6*m + 4*m = -2*j + 2. Let l be (-7)/(-7) - m/(-2). Suppose -3/4*d**2 + 1/4*d + l = 0. What is d?
-2/3, 1
Let k(u) = -20*u**2 + 90*u - 420. Let g(j) = j**2 + 1. Let q(b) = -15*g(b) - k(b). Suppose q(s) = 0. Calculate s.
9
Factor -4/5 - 9/5*k**2 + 7/10*k**3 + 2*k - 1/10*k**4.
-(k - 2)**3*(k - 1)/10
Let y = -4 + 6. Let -o**4 - 1 + 3*o**3 - 1 - 9*o**y + 2*o**3 + 7*o = 0. Calculate o.
1, 2
Suppose 3*z**4 - 2/3*z**2 - 4*z**3 + 1/3 + 4/3*z = 0. Calculate z.
-1/3, 1
Let 14*q**3 + 47 - 23 - 13 - 23 + 26*q + 52*q**2 = 0. Calculate q.
-3, -1, 2/7
Let l be (1/(-9))/(7 + -8). Let x(t) be the third derivative of 1/45*t**5 + 0 + t**2 - l*t**3 + 0*t + 1/36*t**4. Let x(q) = 0. Calculate q.
-1, 1/2
Find o such that 6*o**3 + o**4 + 9*o**3 - 18*o**3 = 0.
0, 3
Factor 0*y + 0 - 2/3*y**2 - 2*y**3 - 2*y**4 - 2/3*y**5.
-2*y**2*(y + 1)**3/3
Suppose 2*q - 2*q = -q. Solve 0*i + q + 2/9*i**2 = 0 for i.
0
Factor 10*m**2 + 2*m**3 + 4 + 34/3*m - 2/3*m**4.
-2*(m - 6)*(m + 1)**3/3
Let i(t) be the third derivative of t**7/840 - t**5/240 + 3*t**2. Find k, given that i(k) = 0.
-1, 0, 1
Let r be -4*(-1 - (-4)/16). Let j(h) be the third derivative of 1/12*h**r - 1/240*h**5 + 0 + 0*h + 2*h**2 + 1/96*h**4. Factor j(k).
-(k - 2)*(k + 1)/4
Let q(i) be the first derivative of 2*i**3/11 - 15*i**2/11 + 24*i/11 - 5. Factor q(l).
6*(l - 4)*(l - 1)/11
Suppose 0 = 10*n - 8*n. Let t**3 + t + n*t - 1 - 2*t**3 + t**2 + 0*t**2 = 0. What is t?
-1, 1
Suppose 0*s = 2*s - 24. Factor 12*c**2 + s*c**3 + 16*c**4 + 0*c**2 + 0*c**3 - 12*c**4 + 4*c.
4*c*(c + 1)**3
Let s = 16 - 16. Factor -1/4*u**5 + s*u**4 - 1/4*u + 0*u**2 + 1/2*u**3 + 0.
-u*(u - 1)**2*(u + 1)**2/4
Let o = 165/4 - 41. Let r(f) be the second derivative of -1/3*f**2 + 1/12*f**5 - 5/18*f**3 + o*f**4 - 7/90*f**6 + 2*f + 0. Find x, given that r(x) = 0.
-1, -2/7, 1
Suppose -13 = 3*c - 4*d + 21, -2*d - 18 = 2*c. Let t = 14 + c. Factor -j**3 + 2*j**t + 2*j**2 - 4*j**3 + j**3.
2*j**2*(j - 1)**2
Let a(q) be the first derivative of -q**6/90 + q**5/15 + 2*q**3/3 + 5. Let l(o) be the third derivative of a(o). Factor l(w).
-4*w*(w - 2)
Let q(u) = 3*u**3 - 11*u**2 - u + 3*u - u + 2*u. Let s(j) = -j**2. Let i(n) = q(n) - 5*s(n). Find w, given that i(w) = 0.
0, 1
Solve -3 + 1 - 4*u**2 + 4*u + 5*u**2 - 3*u**2 = 0 for u.
1
Let t(x) = -5*x**4 - 30*x**3 - 66*x**2 - 50*x - 9. Let k(s) = 70*s**4 + 420*s**3 + 925*s**2 + 700*s + 125. Let m(c) = 6*k(c) + 85*t(c). Factor m(p).
-5*(p + 1)**3*(p + 3)
Suppose 4*q + 3*d + 4 = 6*q, 8 = 4*q - d. Suppose 0*b + q*b - 8 = 0. Factor 2/3*p - 2/3 + 4/3*p**2 + 2/3*p**5 - 2/3*p**b -