e the first derivative of p**6/40 + p**5/10 + p**4/8 - 5*p**2/2 + 1. Let o(w) be the second derivative of x(w). Factor o(s).
3*s*(s + 1)**2
Let h(t) be the second derivative of -7*t**6/165 - 9*t**5/110 + 5*t**4/66 + 3*t**3/11 + 2*t**2/11 + 8*t. Determine n, given that h(n) = 0.
-1, -2/7, 1
Let j(d) be the second derivative of d**8/3360 + d**7/3780 - d**6/540 + d**4/6 + d. Let w(f) be the third derivative of j(f). Solve w(u) = 0 for u.
-1, 0, 2/3
Let y(g) be the third derivative of -g**8/2352 - g**7/735 + g**5/210 + g**4/168 - 4*g**2. Suppose y(j) = 0. What is j?
-1, 0, 1
Let y(k) be the second derivative of k**5/5 - 5*k**4/3 - 2*k**3/3 + 10*k**2 + 14*k. Let y(h) = 0. Calculate h.
-1, 1, 5
Let u(p) be the first derivative of -4/3*p**2 + 2/3*p - 2/3*p**4 + 4/3*p**3 - 2 + 2/15*p**5. Suppose u(m) = 0. What is m?
1
What is t in 2/3*t**5 + 2/3*t**3 - 4/3*t**4 + 0*t + 0 + 0*t**2 = 0?
0, 1
Let h(v) = -v**3 - 24*v**2 - 22*v + 27. Let k be h(-23). Determine p so that -1/4*p + 0 - 2*p**3 + 7/4*p**2 - 4*p**k = 0.
-1, 0, 1/4
Let g = 764/1173 + 6/391. Factor 10/3*d**3 + 4/3 + g*d**4 + 14/3*d + 6*d**2.
2*(d + 1)**3*(d + 2)/3
Let y(j) = 10*j**2 - 6*j - 22. Let o(m) = -m**2 + 7*m - 3. Let t be o(5). Let n(h) = -11*h**2 + 5*h + 23. Let i(g) = t*y(g) + 6*n(g). Factor i(q).
4*(q - 4)*(q + 1)
Let h be 0 + (6/(-4))/(-3). Suppose -81*a + 36 = -72*a. Determine b, given that -3/2*b**2 - 1/2*b**a + 0 + h*b + 3/2*b**3 = 0.
0, 1
Let m be (2 - -2) + -2 - 17. Let q be (m - -15)/(2*1). Factor 4/3*b**2 + 2/3*b + q.
2*b*(2*b + 1)/3
Let n be 1279/(-36) + (-1)/4. Let p = n + 36. Factor -p*w**2 - 8/9 - 8/9*w.
-2*(w + 2)**2/9
Determine n, given that -96*n**2 + 59 + 136*n - 392*n + 3*n**4 - 16*n**3 - 4*n**4 - 315 = 0.
-4
Let d(f) be the third derivative of 1/96*f**4 + 0*f - f**2 + 1/24*f**3 - 1/480*f**6 + 0 - 1/240*f**5. Let d(u) = 0. Calculate u.
-1, 1
Let x be 11/(-2)*(-2 + -2). Let f be 4/x - (-84)/22. Factor 6*c**2 - 18*c**2 - 16*c**2 - 22*c - f.
-2*(2*c + 1)*(7*c + 2)
Let n(b) be the first derivative of 2*b**5/15 + 7*b**4/24 + b**3/6 + 53. Solve n(g) = 0.
-1, -3/4, 0
Let g(d) be the first derivative of 1/24*d**4 - 1/36*d**6 - 1/30*d**5 + 1/18*d**3 + 0*d + 0*d**2 - 1. Solve g(i) = 0 for i.
-1, 0, 1
Let r(h) = h**5 - h - 1. Let x(n) = -4*n**5 + 3*n**4 - 3*n**3 + n**2 + 3*n + 3. Let u(t) = 3*r(t) + x(t). Find l, given that u(l) = 0.
0, 1
Let v(q) be the first derivative of -q**5/30 + q**4/12 + 9. Find m, given that v(m) = 0.
0, 2
Let h = 0 - 2. Let n = h - -19. Factor p**3 + 17*p**2 - n*p**2.
p**3
Suppose -7*d - d + 2*d = 0. Let j(k) be the second derivative of -k**3 + d - k + 0*k**2 + 7/4*k**4. Solve j(s) = 0.
0, 2/7
Let r be 54/10 - (-8)/(-20). Let i(f) be the third derivative of 0 + 0*f**3 + 1/48*f**4 + 0*f - f**2 + 1/120*f**r. Let i(k) = 0. What is k?
-1, 0
Let c(i) = 4*i**4 - 8*i**3 + 4*i**2 - 12*i - 12. Let s(g) = g + 1. Let l(f) = -c(f) - 12*s(f). Suppose l(w) = 0. Calculate w.
0, 1
Factor -4/3*m**3 + 2 + 2/3*m**4 - 8/3*m**2 + 4/3*m.
2*(m - 3)*(m - 1)*(m + 1)**2/3
Suppose 4 = 4*p - 12. Factor 5*z**2 + 5*z - 3*z**2 - 4*z + 0*z**4 - 2*z**p - z**5.
-z*(z - 1)*(z + 1)**3
Let b(h) be the second derivative of -h**6/50 + h**5/50 + h**4/20 - h**3/15 - 4*h. Find m such that b(m) = 0.
-1, 0, 2/3, 1
Suppose -4*n + 12 = -0*n, -4*q + 3*n + 63 = 0. Let i = -18 + q. Determine w, given that -2/5*w**3 + i - 2/5*w**2 + 0*w = 0.
-1, 0
Let s(a) be the third derivative of 0*a + 1/210*a**5 - 9*a**2 - 1/210*a**6 + 0*a**3 + 0*a**4 + 1/735*a**7 + 0. Let s(q) = 0. What is q?
0, 1
Factor 28 + n**2 + n**2 - 4*n - 34.
2*(n - 3)*(n + 1)
Let w be 3/5*(-9)/(-3). Let n(a) be the second derivative of a**3 + w*a**5 - 11/4*a**4 + 0*a**2 + 0 - 2*a. Solve n(l) = 0 for l.
0, 1/4, 2/3
Let m(o) be the first derivative of 2/3*o**3 - 8/5*o**5 + 5 + 0*o**2 + 3/2*o**4 + 0*o. Solve m(x) = 0.
-1/4, 0, 1
Let m(l) be the first derivative of l**3/24 - 3*l**2/16 + l/4 - 47. Factor m(d).
(d - 2)*(d - 1)/8
Let h be (6/8 - 1)*-12. Let c(r) be the first derivative of -2 - 2/7*r - 2/21*r**h + 2/7*r**2. Solve c(j) = 0.
1
Suppose -2*s + 2*j = s - 12, s - 4*j - 14 = 0. Suppose s*i = -i + 36. Find c such that 2*c**2 - i*c**3 + 10*c - 10*c + 18*c**4 - 8*c**5 = 0.
0, 1/4, 1
Suppose -3*x - 2*o = -28, -5*x + 45 = -4*o + 7*o. Suppose -b = -x*b. Suppose n - 4/3*n**3 + 1/3 + b*n**2 = 0. Calculate n.
-1/2, 1
Let y(v) be the third derivative of 2*v**7/945 - v**6/90 + v**5/135 + v**4/18 - 4*v**3/27 + 12*v**2. Suppose y(u) = 0. Calculate u.
-1, 1, 2
Suppose 0*r = -x - 3*r + 8, -5*r = -3*x - 4. Determine t, given that 0*t**x - 2/5*t**4 + 0*t**3 + 0 + 0*t = 0.
0
Let w(h) be the first derivative of 10*h**3/3 - 4*h**2 + 14*h - 8. Let r(f) = f**2 - 1 - 2*f**2 + 0. Let b(y) = -8*r(y) - w(y). Find m, given that b(m) = 0.
1, 3
Let v(f) be the first derivative of -2/3*f**3 - 1/2*f**2 - 1/4*f**4 - 7 + 0*f. Factor v(q).
-q*(q + 1)**2
Suppose -2*o - 7*o + 3*o = 0. Let d(b) be the second derivative of -1/30*b**4 - 1/5*b**2 - b - 2/15*b**3 + o. Solve d(m) = 0 for m.
-1
Let l = 225 + -2039/9. Let v = l - -37/18. Factor 1/2*n**4 + 0 + 3/2*n**2 - 3/2*n**3 - v*n.
n*(n - 1)**3/2
Let k = -2 + 23. Let x = k - 62/3. Suppose 1/3*s**5 + 0 + 0*s - s**4 + s**3 - x*s**2 = 0. What is s?
0, 1
Let i be 5/((-70)/(-788)) + 1. Let o = -57 + i. Factor 0*x + 4/7*x**3 - 2/7*x**4 - o*x**2 + 0.
-2*x**2*(x - 1)**2/7
Let v(s) be the third derivative of s**7/42 + s**6/8 - s**5/12 - 5*s**4/8 + 47*s**2. Solve v(g) = 0.
-3, -1, 0, 1
Let u(f) be the second derivative of f**4/42 + 2*f**3/21 + f**2/7 - 19*f. Determine n, given that u(n) = 0.
-1
Let p(f) be the second derivative of -f**8/4480 - 5*f**4/12 + f. Let j(y) be the third derivative of p(y). Solve j(l) = 0 for l.
0
Suppose -4*n = q - 5, 3*q + 17 = 4*n - 0. Let p(w) be the first derivative of -1/3*w**6 + 0*w**3 + 1/2*w**4 + 0*w**5 + 0*w + 0*w**n + 1. Factor p(j).
-2*j**3*(j - 1)*(j + 1)
Let n(c) be the second derivative of c**7/1120 + c**6/160 + 3*c**5/160 + c**4/32 + c**3/2 + 3*c. Let x(q) be the second derivative of n(q). Factor x(a).
3*(a + 1)**3/4
Let t = 0 - 7. Let k(p) = 3*p**2 - 7*p - 7. Let f(u) = -u**2 + 2*u + 2. Let n(v) = t*f(v) - 2*k(v). Factor n(j).
j**2
Let k(x) be the third derivative of x**8/840 + 4*x**7/525 + x**6/60 + x**5/75 - x**2. Let k(v) = 0. What is v?
-2, -1, 0
Let q = -12 - -19. Factor 2*z**2 - 5*z**2 - 8*z - 2 + 5*z**4 + z + q*z**3.
(z - 1)*(z + 1)**2*(5*z + 2)
Let r(i) be the third derivative of -i**6/30 + 4*i**5/5 - 8*i**4 + 128*i**3/3 - 7*i**2. Suppose r(a) = 0. What is a?
4
Let r = 22 - 19. Factor 18*m + 3/2*m**r + 9*m**2 + 12.
3*(m + 2)**3/2
Let b(j) be the first derivative of j**5/30 - j**4/12 + j**2/6 - j/6 - 27. Solve b(h) = 0.
-1, 1
Let m(c) = -5*c**3 - 9*c**2 - 3*c + 5. Let k(t) = 3*t. Let i be k(-2). Let a(o) = -4*o**3 - 8*o**2 - 2*o + 4. Let n(s) = i*a(s) + 5*m(s). Factor n(u).
-(u - 1)**3
Suppose 0 = -h + 3 - 0. Let b be (h - 4)*1*-2. Suppose 1 - 4*q**2 + 0*q**2 + 3*q**b = 0. Calculate q.
-1, 1
Factor -1/3*l**3 + 5/3 + l**2 + 3*l.
-(l - 5)*(l + 1)**2/3
Let f be 3 + -1 + 0*(-3)/(-12). Let y(k) be the first derivative of -1/12*k**3 + 1 + 1/8*k**f + 1/2*k. Factor y(s).
-(s - 2)*(s + 1)/4
Let g(u) be the third derivative of -u**5/20 - u**4/8 + u**3 + 7*u**2. Find h such that g(h) = 0.
-2, 1
Let h(l) be the first derivative of -1/21*l**3 - 9/7*l + 3/7*l**2 - 1. Factor h(a).
-(a - 3)**2/7
Let s(p) be the second derivative of p**7/35 - p**6/15 - p**5/30 + p**4/6 - p**2 - 2*p. Let u(i) be the first derivative of s(i). Factor u(b).
2*b*(b - 1)**2*(3*b + 2)
Solve 26/7*b**2 - 4*b**5 - 22/7*b**4 - 4/7 + 38/7*b**3 - 10/7*b = 0.
-1, -2/7, 1/2, 1
Let o(c) be the second derivative of -c**6/420 - c**5/210 + c**4/84 + c**3/21 + 2*c**2 - 4*c. Let p(h) be the first derivative of o(h). What is u in p(u) = 0?
-1, 1
Let q be -2*(-4)/(-4)*-1. Let 2*n**2 + 2 - 18*n**2 + 5*n + 12*n**4 + q + 3*n - 8*n**3 = 0. What is n?
-1, -1/3, 1
Suppose k**3 - 18*k**2 + 14 + 28*k + 8*k + 2*k**3 - 38 = 0. Calculate k.
2
Let x(s) be the third derivative of 5*s**8/336 - s**7/7 + 3*s**6/8 - s**5/3 + 25*s**2. Determine a so that x(a) = 0.
0, 1, 4
Let c(z) be the second derivative of z**8/1680 + z**7/420 - 2*z**3/3 + 2*z. Let k(d) be the second derivative of c(d). Solve k(j) = 0.
-2, 0
Let g(s) be the second derivative of 0*s**3 - 1