 derivative of m**9/90720 + m**8/40320 - m**7/7560 - m**4/24 - m**2. Let a(g) be the second derivative of l(g). Solve a(x) = 0 for x.
-2, 0, 1
Let y(k) = -k**3 + k**2 + k. Let h(x) = 6*x**4 - 14*x**3 + 8*x**2 + 2*x - 3. Let g(f) = -h(f) - y(f). What is t in g(t) = 0?
-1/2, 1
Let h be 8/(4/2) - (-68)/(-20). Let s(u) be the first derivative of 2/5*u**3 + h*u**2 + 2 + 1/10*u**4 + 2/5*u. Factor s(b).
2*(b + 1)**3/5
Suppose 5*p - p = -0*p. Factor 1/5*h**5 + p*h**2 + 0 - 2/5*h**3 + 0*h - 1/5*h**4.
h**3*(h - 2)*(h + 1)/5
Factor 2/5*t + 4/5*t**2 + 0 + 2/5*t**3.
2*t*(t + 1)**2/5
Factor b**5 + 16*b**3 + 8 - 5*b**5 - 12*b - 9*b**2 + b**2.
-4*(b - 1)**3*(b + 1)*(b + 2)
Suppose 2*k - 4*s = 20, k - 9*s = -6*s + 13. Factor 2/3*z**2 + 0 + 4/3*z**3 + 0*z + 2/3*z**k.
2*z**2*(z + 1)**2/3
Let v(l) be the first derivative of l**6/40 - 3*l**5/20 + 3*l**4/8 - l**3/2 - l**2/2 - 4. Let r(j) be the second derivative of v(j). Factor r(c).
3*(c - 1)**3
Let q(h) = -h**3 + 2*h**2 - h - 2. Let s be q(-1). Suppose -4*d = -1 - 3, 0 = -s*i - d + 5. Factor 9/2*b - 3/2*b**i - 3.
-3*(b - 2)*(b - 1)/2
Let a(t) = 4*t - 4*t - t**2 - t. Let y = -31 + 28. Let j(q) = -q**3 - 6*q + 1. Let h(g) = y*a(g) + j(g). Factor h(w).
-(w - 1)**3
Suppose -10 = -5*g - 3*k, -3*g + k + 10 = 2*g. Let a(z) be the first derivative of -g + 0*z - 2/9*z**3 - 1/6*z**2 + 1/18*z**6 + 2/15*z**5 + 0*z**4. Factor a(n).
n*(n - 1)*(n + 1)**3/3
Let a(k) = 2*k**2 - 4*k + 3. Let t be a(2). Let d = 57 + -55. Suppose -54/5*o**d - 14/5*o**4 - 4/5 + 26/5*o + 46/5*o**t = 0. What is o?
2/7, 1
Factor 0 - 3/2*k**3 + 3*k**2 - 3/2*k.
-3*k*(k - 1)**2/2
Let o(w) be the first derivative of -w**7/7 - 11*w**6/15 - 4*w**5/5 + 2*w**4/3 - 2*w + 6. Let j(i) be the first derivative of o(i). Find u such that j(u) = 0.
-2, 0, 1/3
Let n(h) = h**3 + 3*h**2 + 2*h + 24. Let v be n(-4). Factor 1/3*f - f**2 + v - 1/3*f**4 + f**3.
-f*(f - 1)**3/3
Suppose -8 = -4*q, -268 = a + 2*a - 2*q. Let t = -614/7 - a. Solve -2/7*o + t*o**2 + 0 = 0.
0, 1
Let p = 6 + -6. Factor 10*h**2 + 22*h**3 + h + 4*h**5 - 7*h**3 + p*h + 13*h**4 - 3*h**2.
h*(h + 1)**3*(4*h + 1)
Let c(g) be the first derivative of -g**5/5 + 3*g**4/2 - 13*g**3/3 + 6*g**2 - 4*g - 31. Find t such that c(t) = 0.
1, 2
Let u be (1 - (-11)/(-5))*5. Let v = 19/3 + u. Factor -1/3*y + 0 - v*y**2 + 1/3*y**3 + 1/3*y**4.
y*(y - 1)*(y + 1)**2/3
Let d(c) be the second derivative of 0*c**2 + 0 + 1/4*c**4 + 3/8*c**5 + 9*c - 3/4*c**3. What is p in d(p) = 0?
-1, 0, 3/5
Let y(l) be the second derivative of l**10/105840 - l**8/11760 + l**6/2520 - l**4/2 + 7*l. Let u(c) be the third derivative of y(c). Factor u(g).
2*g*(g - 1)**2*(g + 1)**2/7
Let a(l) be the second derivative of l**6/20 + 3*l**5/40 - l**4/8 - l**3/4 + 3*l. Factor a(r).
3*r*(r - 1)*(r + 1)**2/2
Solve 2 - 9*b + 15*b**2 - 2 - 18*b**2 = 0 for b.
-3, 0
Let p(a) be the third derivative of a**8/4480 - a**7/480 + a**6/240 + a**5/12 - 4*a**2. Let z(m) be the third derivative of p(m). Factor z(k).
3*(k - 2)*(3*k - 1)/2
Let m(u) = -u**3 + 3*u**2 - 2*u + 3. Let a be m(2). Let k = 415/118 + -1/59. Factor j**2 + 7/2*j**a - 1 - k*j.
(j - 1)*(j + 1)*(7*j + 2)/2
Let m be 2 + -1 + ((-1958)/180)/11. Let d(t) be the second derivative of -1/27*t**3 - m*t**5 + 0*t**2 + t - 1/27*t**4 + 0. Factor d(k).
-2*k*(k + 1)**2/9
Let w(d) = d**3 - 11*d**2 + 3*d + 5. Let l be w(10). Let c = l - -197/3. Factor 0*i + 0*i**3 - c*i**5 - 2/3*i**4 + 0 + 0*i**2.
-2*i**4*(i + 1)/3
Let d = 6/43 + 56/215. Factor -d*o + 0 - 4/5*o**4 + 4/5*o**2 + 0*o**3 + 2/5*o**5.
2*o*(o - 1)**3*(o + 1)/5
Solve 11*h**4 - 121*h**4 + 250*h**5 - 2*h + 10*h**4 - 28*h**2 - 120*h**3 = 0 for h.
-1/5, 0, 1
Let s be -5*(-6)/15*-2. Let f be 93/54 + 6/s. What is v in 0 - 2/9*v**2 - 4/9*v + f*v**3 = 0?
-1, 0, 2
Suppose -5*g + 4*g = u - 9, -25 = -3*u - g. Factor i**3 - 9*i**4 - 2*i**2 + u*i**3 - i**2 + 3*i**5.
3*i**2*(i - 1)**3
Let p(u) be the second derivative of 1/33*u**3 + 0 - 3*u + 1/66*u**4 - 2/11*u**2. Determine d, given that p(d) = 0.
-2, 1
Let r(g) be the first derivative of -g**6/6 - 4*g**5/5 - g**4/4 + 10*g**3/3 + 2*g**2 - 8*g + 35. Solve r(i) = 0.
-2, 1
Let f(v) = -v**2 + 9*v + 26. Let u be f(11). Factor 0 + 0*t**2 - 1/2*t**u + 0*t - 1/2*t**3.
-t**3*(t + 1)/2
Find c, given that 240/7*c**2 + 256/7*c**4 + 52/7*c + 4/7 + 64*c**3 = 0.
-1, -1/4
Let r(g) = -g**3 - 4*g**2 + 9. Let m be r(-3). Factor k + 1/2*k**2 + m.
k*(k + 2)/2
Let o = 5 - 1. Suppose -o*u + u = 0. Determine y, given that u*y**2 + y**2 - 3*y**2 - 10*y + 2*y - 8 = 0.
-2
Factor 2*h**2 - h**2 + 5 - 6.
(h - 1)*(h + 1)
Let a(j) be the third derivative of j**9/5040 + j**8/560 + j**7/210 - j**4/8 + 9*j**2. Let c(u) be the second derivative of a(u). Suppose c(g) = 0. What is g?
-2, 0
Let r(v) be the second derivative of -1/18*v**4 + 0*v**3 + 0 - 1/63*v**7 - 1/10*v**5 - 3*v - 1/15*v**6 + 0*v**2. Factor r(h).
-2*h**2*(h + 1)**3/3
Let r(o) be the first derivative of 7*o**6/180 + o**5/30 + o**3/3 - 2. Let x(b) be the third derivative of r(b). Suppose x(n) = 0. Calculate n.
-2/7, 0
Let r(g) = -191*g**3 - 89*g**2 + 96*g - 16. Let s(a) = 95*a**3 + 45*a**2 - 48*a + 8. Let f(d) = -3*r(d) - 5*s(d). Factor f(u).
2*(u + 1)*(7*u - 2)**2
Suppose -11*q + 15 = -6*q. Solve 0 - 2/5*g**2 + 2/5*g**4 + 2/5*g**q - 2/5*g = 0 for g.
-1, 0, 1
Suppose -76*y + 78*y = 10. Determine l, given that 1/4*l + 13/4*l**3 + 0 + l**y + 3/2*l**2 + 3*l**4 = 0.
-1, -1/2, 0
Let j(k) be the second derivative of 4*k**4/21 - 2*k**3/7 - 2*k**2/7 - 2*k. Factor j(a).
4*(a - 1)*(4*a + 1)/7
Let h(j) be the third derivative of -j**6/60 + j**5/10 + 3*j**4/4 - 9*j**3 + j**2 + 3. Factor h(w).
-2*(w - 3)**2*(w + 3)
Suppose 17 = -c + 3*j, 0 = 2*c + 2*c + 5*j + 51. Let h be 0 - (-7)/(c/(-4)). Factor -9*o**h + o**3 + 3*o**2 - o**4 + 2*o - o**4 + 5*o**3.
-2*o*(o - 1)**3
Let q(b) = -b - 2. Let h be q(-4). Let w = 43/5 - 81/10. Factor 5/4*n**3 + 1/4*n + h*n**2 - w.
(n + 1)**2*(5*n - 2)/4
Let x(k) be the first derivative of 3*k**4/32 - k**3 + 3*k**2 - 39. Find n, given that x(n) = 0.
0, 4
Let j(n) = 2*n**2 + 16*n - 15. Let z be j(-9). Factor 0 - 1/2*i + i**z + 0*i**2 - 1/2*i**5 + 0*i**4.
-i*(i - 1)**2*(i + 1)**2/2
Let l(h) be the first derivative of 2*h**6/3 - 3*h**4 + 8*h**3/3 - 5. Factor l(y).
4*y**2*(y - 1)**2*(y + 2)
Suppose -4*m = b + 3 - 8, m = 5*b + 17. Let s = -1 - b. Determine v so that 0 - v**2 + 8 + 2*v - 4 - 5*v**s = 0.
-2/3, 1
Let q(i) = -3*i**3 + 2*i**2 - 4*i - 5. Let a(h) = -4*h**3 + 3*h**2 - 6*h - 7. Let j(t) = -5*a(t) + 7*q(t). Let j(k) = 0. What is k?
-2, 0, 1
Let o be 3/(8/(-2) - -5). Let u(s) be the first derivative of 1/25*s**5 - 2/15*s**o + 1/5*s + 2 - 1/30*s**6 + 1/10*s**4 - 1/10*s**2. Factor u(t).
-(t - 1)**3*(t + 1)**2/5
Suppose 5*y = 13 - 8. Let a(p) be the first derivative of y + 2/7*p - 2/21*p**3 + 0*p**2. Factor a(w).
-2*(w - 1)*(w + 1)/7
Let -480/17*f**2 - 2048/17 - 1792/17*f - 2/17*f**4 - 52/17*f**3 = 0. What is f?
-8, -2
Let u be (-10)/(-2) - (-1 + 4). Let q(y) be the second derivative of y + 0*y**3 + 1/50*y**5 + 1/75*y**6 + 0*y**u + 0 + 0*y**4. Factor q(x).
2*x**3*(x + 1)/5
Find l such that 0*l - 4/3*l**3 + 2*l**4 + 2/3 - 8/3*l**2 + 4/3*l**5 = 0.
-1, 1/2, 1
Factor 3/2*d**4 + 0 + 3*d - 3/2*d**2 - 3*d**3.
3*d*(d - 2)*(d - 1)*(d + 1)/2
Let s = 197 + -1377/7. Let 2/7*h**2 + 2/7*h**5 - s*h**4 - 2/7*h**3 + 0*h + 0 = 0. What is h?
-1, 0, 1
Let n(x) be the first derivative of 4/7*x + 6/35*x**5 + 13/14*x**4 + 11/7*x**2 + 6 + 38/21*x**3. Determine y, given that n(y) = 0.
-2, -1, -1/3
Let j(i) = -i**3 - 5*i**2 - 5*i - 2. Let t be j(-4). Suppose 3 + 1 = t*f. Factor 4*k + 2*k**2 + k**2 - k**2 - k**f + 4.
(k + 2)**2
Let z(m) be the first derivative of -1/50*m**5 + 0*m**2 + 1 + 2*m + 1/15*m**3 + 1/30*m**4 - 1/75*m**6. Let i(p) be the first derivative of z(p). Factor i(u).
-2*u*(u - 1)*(u + 1)**2/5
Let k(v) be the first derivative of v**3 - v**2/2 - 2*v + 9. Suppose k(b) = 0. Calculate b.
-2/3, 1
Let x(j) be the third derivative of j**6/240 - j**5/40 - j**4/12 - j**2. Determine k, given that x(k) = 0.
-1, 0, 4
What is q in 4/7*q - 4/7*q**2 + 0 - 8/7*q**3 = 0?
-1, 0, 1/2
Let l(p) = -p**4 + p**3 - p. Let n(d) = 6*d**4 - 7*d**3 - d**2 + 7*d. Let o(x) = 20*l(x) + 4*n(x). Find v such that o(v) = 0.
-1, 0, 1, 2
Suppose -b - 1 + 0 = 0. Let d be 3 - b*3/(-9). Find l, given that -50/3*l**5 - 64/3*l - 190/