 Let n(i) be the first derivative of -7/3*i**3 + 3/4*i**4 - x*i**2 + 2*i + i**5 + 4. Find a, given that n(a) = 0.
-1, 2/5, 1
Suppose 0 = 36*i - 30*i - 12. Let t(q) be the second derivative of -2/3*q**3 - 2*q**i - q + 0 - 1/12*q**4. Factor t(z).
-(z + 2)**2
Let s(b) be the first derivative of 10*b**3/3 - 2*b**2 + 48. Determine g, given that s(g) = 0.
0, 2/5
Let v(c) = -c - 1. Let x be v(-4). Suppose 0 = -x*o + 7*o. Factor -1/5*t**2 + 1/5 + o*t.
-(t - 1)*(t + 1)/5
Let c(q) = q**2 + 6*q + 5. Let w be c(-6). Let -76/11*i**3 - 4/11 - 64/11*i**2 - 26/11*i - 10/11*i**w - 4*i**4 = 0. Calculate i.
-1, -2/5
Let t(l) be the second derivative of l**7/294 + 2*l**6/105 + 3*l**5/70 + l**4/21 + l**3/42 + 23*l. Find x, given that t(x) = 0.
-1, 0
Find l such that 4/13 - 14/13*l + 2/13*l**5 - 4/13*l**3 + 16/13*l**2 - 4/13*l**4 = 0.
-2, 1
Factor -3/5 - 9/5*m**2 + 9/5*m + 3/5*m**3.
3*(m - 1)**3/5
Let i(c) = c. Let f be i(4). Factor o**2 - o**2 - 5*o**3 + 2*o**f + o**3.
2*o**3*(o - 2)
Suppose 0 = -h + 3*h + 2*x, -3*x = -h + 12. Let m be (h/6)/(3/12). Factor 2*b + 1/2*b**2 + m.
(b + 2)**2/2
Suppose 0 = -2*m + 7 - 3. Factor 3*n**2 + 19*n + 108*n**3 + 20*n - 147*n**m - 3.
3*(n - 1)*(6*n - 1)**2
Let a(v) be the third derivative of v**6/2160 - v**5/360 + v**4/144 - v**3/2 - 4*v**2. Let c(b) be the first derivative of a(b). What is x in c(x) = 0?
1
Let z(s) be the first derivative of 7*s**6/3 - 342*s**5/25 + 128*s**4/5 - 176*s**3/15 - 48*s**2/5 + 32*s/5 + 6. Determine v, given that z(v) = 0.
-2/5, 2/7, 1, 2
Suppose 0*q - 2*q - v - 5 = 0, -3*q = -5*v - 25. Let z be (-18)/(-7) + -2 - q. Factor -6/7*f**4 + 2/7 + 4/7*f**2 + 2/7*f**5 - 6/7*f + z*f**3.
2*(f - 1)**4*(f + 1)/7
Let z = 7/33 + 41/429. What is u in 2/13*u**3 + 2/13*u + 0 + z*u**2 = 0?
-1, 0
Solve -108*b**4 - 99*b**4 + 208*b**4 + 8 + b**3 - 6*b**2 - 4*b = 0 for b.
-2, 1, 2
Let k(h) = 7*h**4 - 24*h**3 - 31*h**2 + 11*h + 37. Let v(j) = 3*j**4 - 12*j**3 - 15*j**2 + 6*j + 18. Let d(p) = 6*k(p) - 13*v(p). Factor d(a).
3*(a - 1)*(a + 1)*(a + 2)**2
Let r(d) be the third derivative of d**8/504 + d**7/315 - d**6/36 - d**5/18 + d**4/9 + 4*d**3/9 + 7*d**2. Solve r(l) = 0 for l.
-2, -1, 1, 2
Let x(b) be the third derivative of b**8/1176 + b**7/245 + b**6/140 + b**5/210 - 4*b**2. Determine k, given that x(k) = 0.
-1, 0
Let l be 28/21 - (-3355)/6. Let i = l + -550. Find t, given that 21/2*t**2 - 3*t + 15/2*t**5 - 9/2*t**3 - i*t**4 + 0 = 0.
-1, 0, 2/5, 1
Let z(y) be the second derivative of -y**6/6 + y**5 + 6*y. Solve z(b) = 0 for b.
0, 4
Let t(c) = c**2 - c - 4. Let d be t(3). Factor 6/5*k**3 - 6/5*k**4 + 2/5*k**5 + 0*k - 2/5*k**d + 0.
2*k**2*(k - 1)**3/5
Let d(o) be the third derivative of 1/60*o**6 + 0*o + 0*o**4 + 4*o**2 - 1/30*o**5 + 0*o**3 + 0. What is b in d(b) = 0?
0, 1
Suppose 0*y = 3*h + 2*y + 36, 3*h - 4*y + 54 = 0. Let r be (-12)/(-42) - 3/h. Factor 0*v - 1/2*v**2 + r.
-(v - 1)*(v + 1)/2
Let l(k) be the second derivative of k**4/12 - k**3/2 - 19*k - 3. Factor l(a).
a*(a - 3)
Suppose -3*x + 32 = -1. Suppose 0 = -3*n + 2*b + 15, -2*n + 2 = 5*b + x. Factor 0*j**2 + 0 - 2/5*j + 2/5*j**n.
2*j*(j - 1)*(j + 1)/5
Let v(x) be the first derivative of x**6/360 - x**5/90 + x**4/72 + x**2/2 - 3. Let z(s) be the second derivative of v(s). Factor z(c).
c*(c - 1)**2/3
Suppose -3*x = 5*d - 22, 23 + 1 = 5*d + x. Suppose -8 = k - d*k + 2*c, 0 = -3*k + 5*c - 1. Determine f, given that -2 + 2 - 2*f**k = 0.
0
Let m(z) be the second derivative of -z**4/9 - 2*z**3/3 - 4*z**2/3 + 5*z. Factor m(w).
-4*(w + 1)*(w + 2)/3
Factor -1/2*f**3 - 1/4*f**2 + 0 + 1/4*f.
-f*(f + 1)*(2*f - 1)/4
Let u(p) = 2*p**2 - 6*p - 11. Let a(s) = 4*s**2 - 10*s - 21. Let c(f) = -6*a(f) + 14*u(f). Find q, given that c(q) = 0.
-1, 7
Let w be 0 - (4 + -13 + 4). Let f(i) be the second derivative of 1/10*i**w + 0 + 1/30*i**6 + 0*i**4 - 1/2*i**2 + 2*i - 1/3*i**3. Factor f(h).
(h - 1)*(h + 1)**3
Let u(a) = 2*a**4 + a**3 - 3 - 4*a**4 + 3*a**4 + 2*a + 8*a**2. Let v(r) = 4*r**4 + 5*r**3 + 31*r**2 + 8*r - 11. Let f(c) = 22*u(c) - 6*v(c). Factor f(p).
-2*p*(p + 1)**2*(p + 2)
Factor 0*v**2 + 0*v**4 - 1/4*v**5 + 1/4*v**3 + 0 + 0*v.
-v**3*(v - 1)*(v + 1)/4
Let x(w) be the first derivative of 2*w**3/15 + 2*w**2/5 - 13. Suppose x(n) = 0. Calculate n.
-2, 0
Let b(x) = 19*x**2 + 29*x + 24. Let v(g) = 13*g**2 + 19*g + 16. Let j(o) = 5*b(o) - 7*v(o). Find m, given that j(m) = 0.
-2, -1
Let c(d) = d - 2. Let p be c(-7). Let j be (6/p)/((-6)/27). Solve 2*h**j + 4/3*h**4 + 0 + 1/3*h**5 + 4/3*h**2 + 1/3*h = 0.
-1, 0
Let x(t) = -7*t**2 + 8*t - 3. Let y(b) = 2*b**2 - 33*b + 13 - 3*b**2 + 16*b**2 + 12*b**2. Let k(u) = 18*x(u) + 4*y(u). Determine h so that k(h) = 0.
1/3
Let c(d) be the second derivative of d**6/75 + 9*d**5/50 + 7*d**4/15 - 2*d - 3. Let c(w) = 0. What is w?
-7, -2, 0
Let j be (124/310)/(1 + 2/(-5)). Determine d, given that d**4 - 1/3*d**5 + d - 1/3 - j*d**2 - 2/3*d**3 = 0.
-1, 1
Let k(s) be the second derivative of 1/90*s**6 + 0 + 3*s + 1/6*s**2 + 2/9*s**3 + 1/6*s**4 + 1/15*s**5. Let k(n) = 0. Calculate n.
-1
Let j(y) be the third derivative of -y**8/3360 + y**7/420 - y**6/144 + y**5/120 - y**3/3 + y**2. Let h(a) be the first derivative of j(a). Factor h(c).
-c*(c - 2)*(c - 1)**2/2
Let p(c) be the second derivative of c**4/27 + 20*c**3/27 + 50*c**2/9 + 14*c. Factor p(d).
4*(d + 5)**2/9
Let t(u) be the first derivative of 0*u**2 + 0*u + 9 + 4/3*u**3. Determine i so that t(i) = 0.
0
Let i(p) be the second derivative of -1/5*p**2 - p + 0 - 2/15*p**4 + 4/15*p**3. Find b, given that i(b) = 0.
1/2
Let s be ((-8)/(-60))/(88/20 + -4). Find q such that 2/3 - s*q**2 - 1/3*q = 0.
-2, 1
Let v(h) be the first derivative of -4*h + 7 - 4/3*h**3 + 4*h**2. Factor v(l).
-4*(l - 1)**2
Let q(u) be the second derivative of -u**9/7560 + u**8/2240 - u**6/720 + u**4/3 - 5*u. Let b(t) be the third derivative of q(t). Solve b(v) = 0 for v.
-1/2, 0, 1
Factor 0 - 8/7*w - 24/7*w**2 - 18/7*w**3.
-2*w*(3*w + 2)**2/7
Let w be (2/20)/(12/45). Let c(a) be the first derivative of 2 + 5/3*a**3 - w*a**2 - 1/2*a. Solve c(y) = 0.
-1/4, 2/5
Let f be 202*2/16 - -1. Let c = -26 + f. Determine j, given that 0 + j**4 + 3/2*j**3 + 1/4*j**5 + c*j + j**2 = 0.
-1, 0
Let r = -209 + 427/2. Factor -1/2*t**4 - 1 + 5/2*t**3 - r*t**2 + 7/2*t.
-(t - 2)*(t - 1)**3/2
Factor 10*h**3 + 7*h**2 - 2*h**3 - 6*h - 5*h**3 - 4*h**2.
3*h*(h - 1)*(h + 2)
Let k(p) = 7*p**3 - p. Let i be k(1). Let z be (4/i)/((-2)/(-6)). Factor -8 - 62*j**3 - 53*j**z - 18*j**5 - 72*j**3 - 61*j**2 - 78*j**4 - 48*j.
-2*(j + 1)**3*(3*j + 2)**2
Let a(x) be the second derivative of x**7/21 - 2*x**6/45 - 2*x**5/5 + 4*x**4/9 + 13*x - 2. Determine z, given that a(z) = 0.
-2, 0, 2/3, 2
Suppose 5 = -5*a - 0, a + 19 = -3*t. Let x be 18/(-4)*4/t. Factor -5*v**4 - x + 3*v**4 + 6*v**2 - v**4.
-3*(v - 1)**2*(v + 1)**2
Let y(r) = 5*r + 21. Let d(j) = -3*j - 11. Let o(c) = -7*d(c) - 4*y(c). Let f be o(7). Let f + 2/5*h - 2/5*h**2 = 0. Calculate h.
0, 1
Factor 2/7*c**2 + 4/7 + 6/7*c.
2*(c + 1)*(c + 2)/7
Let z be 15/(-6)*12/(-5). Let p = 8 - z. Factor 0*x**p - 2/11*x**3 + 0 + 0*x - 2/11*x**4.
-2*x**3*(x + 1)/11
Suppose 4*s = 2*s. Let a(x) be the second derivative of s - 3*x + 0*x**4 + 0*x**2 + 1/20*x**5 - 1/6*x**3. Factor a(w).
w*(w - 1)*(w + 1)
Let s(a) be the third derivative of a**8/1176 - a**6/420 - 24*a**2. Find w such that s(w) = 0.
-1, 0, 1
Suppose -36*l + 3*l**2 + 0*l**3 - 24 - 3*l**3 - 21*l**2 + 0 = 0. Calculate l.
-2
Let r(c) be the third derivative of -c**8/120960 - c**7/15120 - c**6/4320 - c**5/60 + 2*c**2. Let y(k) be the third derivative of r(k). Solve y(o) = 0.
-1
What is a in 18000*a + 6834 + 1960*a**3 + 7548*a**4 + 5*a**5 - 7383*a**4 + 9800*a**2 + 3166 = 0?
-10, -2, -1
Let j(h) be the first derivative of h**6/120 - h**4/24 - h**2/2 + 3. Let z(k) be the second derivative of j(k). What is t in z(t) = 0?
-1, 0, 1
Let c(v) = 4*v**2. Let o be c(1). Suppose -4*n = 2*m - 14, -m + 25 = o*n + 6. Solve -n - g**3 + 7 + 2*g - g**3 - g**4 = 0.
-1, 1
Let h(y) = -4*y**2 + 20*y + 15. Let u(p) = -p**2 + 5*p + 4. Let i(t) = 2*h(t) - 9*u(t). Factor i(l).
(l - 6)*(l + 1)
Let l be ((-15)/6 + 3)*2. Let f(p) be the first derivative of 1/3*p**2 - l - 1/27*p**6 + 4/27*p**3 + 2/9*p - 1/9*p**4 - 2/15*p**5. Factor f(y).
-2*(y - 1)*(y + 1)**4/9
Suppose 0 = -3*n + 3*z + 53 + 25, -n + 5*z = -22.