). Let l = 504 + -502. Determine n, given that -2/3*n**5 + 0*n + 4/3*n**4 + k*n**l - 2/3*n**3 + 0 = 0.
0, 1
Let g(q) = -3*q**3 + 7*q**2 + 4. Let m(u) = u**2 + 1. Let n(a) = g(a) - 4*m(a). Factor n(y).
-3*y**2*(y - 1)
Let r(o) be the third derivative of 0 + 0*o - 1/36*o**4 + o**2 + 2/3*o**3 - 1/1080*o**6 - 1/120*o**5. Let d(v) be the first derivative of r(v). Factor d(a).
-(a + 1)*(a + 2)/3
Let w(k) be the third derivative of k**10/105840 + k**9/17640 - k**7/2205 + k**4/8 + 2*k**2. Let o(d) be the second derivative of w(d). Factor o(p).
2*p**2*(p - 1)*(p + 2)**2/7
Factor -4*v + 0 + 4/3*v**3 + 8/3*v**2.
4*v*(v - 1)*(v + 3)/3
Let a be -6 - 1056/(-56) - 6. Let -24/7*o + 3/7*o**2 + a = 0. Calculate o.
4
Let r be (-4)/140*-5*2. Determine z so that 6/7*z**2 + r + 6/7*z + 2/7*z**3 = 0.
-1
Let v be 2*((-5)/15)/(2/(-9)). Factor -1/3*a**v + 2/3 - 1/3*a**4 + a**2 + 5/3*a.
-(a - 2)*(a + 1)**3/3
Factor 1/2*n**3 - 1/2*n + 0*n**2 + 1/4 - 1/4*n**4.
-(n - 1)**3*(n + 1)/4
Let l(d) = 2*d**2 - 2*d - 2. Let p be l(2). Suppose b - 9 = -p*b. Solve 2/3*a + 4*a**b + 11/3*a**2 + 0 = 0 for a.
-2/3, -1/4, 0
Let d(h) be the second derivative of h**4/12 - 2*h**2 - 20*h. Factor d(u).
(u - 2)*(u + 2)
Let o(h) = -10*h**3 + 101*h**2 - 200*h - 125. Let s(f) = -20*f**3 + 203*f**2 - 400*f - 250. Let i(g) = 13*o(g) - 6*s(g). Factor i(v).
-5*(v - 5)**2*(2*v + 1)
Suppose -2*y + 5*s - 4 = 0, 4*y + 18 = 5*s - 0*s. Let v be 2 - (-2)/y*-2. Determine u, given that -26/7*u**4 - 4/7*u + v*u**3 + 2/7*u**2 + 0 + 10/7*u**5 = 0.
-2/5, 0, 1
Suppose -14/9*r**5 + 16/9*r**2 - 8*r**3 + 0 + 20/3*r**4 + 0*r = 0. What is r?
0, 2/7, 2
Let g(w) be the third derivative of w**6/75 - w**5/50 - 3*w**4/20 - 2*w**3/15 + 7*w**2. What is f in g(f) = 0?
-1, -1/4, 2
Let q be 1*(-124)/(-28) - (-7 + 11). Let -6/7*t**4 + 9/7*t + 6/7*t**2 + q*t**5 + 0 - 12/7*t**3 = 0. What is t?
-1, 0, 1, 3
Let s = -21 + 14. Let j(k) = k**2 + 8*k + 9. Let g be j(s). Find t such that 0*t**3 - 2/7 + 0*t - 2/7*t**4 + 4/7*t**g = 0.
-1, 1
Let i = 8 + -4. Suppose -i*p = -0*p - 224. Determine o so that -14*o**3 + 0*o**5 + p*o**2 - 48*o - 18*o**3 + 16 + 9*o**4 - o**5 = 0.
1, 2
Let n(f) = -26*f**2 - 2*f - 2. Let z be n(-2). Let x = 512/5 + z. Factor 8/5*t + x + 6/5*t**2.
2*(t + 1)*(3*t + 1)/5
Let i = 6/83 - 25/1494. Let v(l) be the second derivative of -l + 0 - i*l**4 - 1/3*l**2 - 2/9*l**3. Find w such that v(w) = 0.
-1
Let a = -6 + 9. Suppose -a*w = -w - 8. Factor -8/7*p**3 + 10/7*p**2 + 2/7*p**w + 0 - 4/7*p.
2*p*(p - 2)*(p - 1)**2/7
Find j such that 0 - 1/3*j**3 + 4/3*j**2 + 0*j = 0.
0, 4
Let -135*d**2 - 164*d**3 + 30*d + 9*d**3 - 33*d**4 + 2*d**4 + d**4 + 40 = 0. Calculate d.
-4, -1, -2/3, 1/2
Let u = 86 - 41. Let h be 18/(-3)*2/(-4). Factor -5*l + 2*l**h + 3*l - 46*l**2 + u*l**2 + l**4.
l*(l - 1)*(l + 1)*(l + 2)
Factor -7*u - 26*u**2 + 32*u**2 - 2*u**3 + 7*u.
-2*u**2*(u - 3)
Factor -2/3*q**3 + 2/3*q**4 + 0 + 0*q + 2/9*q**2 - 2/9*q**5.
-2*q**2*(q - 1)**3/9
Factor 0*k + 2/7*k**3 + 0 + 0*k**2.
2*k**3/7
Let g be (-1)/(-4)*4 + 5. Factor -19*a - 5*a + 18 + 6*a - g*a + 8*a**2.
2*(2*a - 3)**2
Let w(y) be the first derivative of y**6/12 - 3*y**4/8 + y**3/3 - 30. Solve w(a) = 0.
-2, 0, 1
Let s(g) be the first derivative of 1 + 1/10*g**5 - 1/3*g**3 - 1/6*g**4 + g**2 + 2*g. Let a(v) be the first derivative of s(v). Factor a(f).
2*(f - 1)**2*(f + 1)
Let -2*u**3 - 14*u + 5*u**2 - 6*u**2 - 4*u - 11*u**2 = 0. What is u?
-3, 0
Let m(f) be the second derivative of 5*f - 1/12*f**4 - 1/3*f**3 + 0*f**2 + 1/20*f**5 + 0. What is n in m(n) = 0?
-1, 0, 2
Let o be 1/4 - 33/(-22). Factor 1/2 - o*a + 5/4*a**2.
(a - 1)*(5*a - 2)/4
Let s(v) be the first derivative of 0*v + 0*v**2 - 2 + 0*v**3 + 1/32*v**4. Factor s(i).
i**3/8
Let d(k) be the third derivative of 0*k + 31/30*k**5 - 7/40*k**6 - 25/12*k**4 + 0 + 2*k**2 + 4/3*k**3. Let a(n) = n. Let f(y) = 6*a(y) + d(y). Factor f(j).
-(j - 2)*(3*j - 2)*(7*j - 2)
Suppose 3*s = 4 - 4. Let 0*x + 2/5*x**2 + s = 0. What is x?
0
Let m(i) be the second derivative of i**7/1260 - i**5/180 - 2*i**3/3 + 2*i. Let r(y) be the second derivative of m(y). Factor r(l).
2*l*(l - 1)*(l + 1)/3
Let l(z) be the second derivative of z**4/12 - 2*z**3/3 + 2*z**2 + 4*z. Find c, given that l(c) = 0.
2
Let u(h) be the first derivative of h**8/672 - h**7/210 + h**5/60 - h**4/48 - h**2/2 - 3. Let d(y) be the second derivative of u(y). Factor d(a).
a*(a - 1)**3*(a + 1)/2
Let g(s) be the third derivative of 0 + 1/300*s**5 + 0*s + 1/15*s**3 - 1/40*s**4 - s**2. Factor g(z).
(z - 2)*(z - 1)/5
Let c(w) be the third derivative of w**5/270 + w**4/36 + 2*w**3/27 - 14*w**2. Determine r, given that c(r) = 0.
-2, -1
Let n(c) = 5 - 2*c + 5 - 8. Let s(j) = j**4 - j**3 - j**2 - 2*j + 3. Let g(r) = 3*n(r) - 2*s(r). Factor g(d).
-2*d*(d - 1)**2*(d + 1)
Let y(o) be the third derivative of o**8/110880 - o**7/27720 - o**5/20 + o**2. Let f(v) be the third derivative of y(v). Factor f(z).
2*z*(z - 1)/11
Let h = 167 - 665/4. Determine x, given that -3/4*x - 3/2*x**2 + 0 - h*x**3 = 0.
-1, 0
Let w be 5/((-900)/178) - -1. Let i(s) be the third derivative of 1/18*s**4 - 3*s**2 + 0*s + 1/105*s**7 + 0 - 1/30*s**5 - w*s**6 + 0*s**3. Solve i(o) = 0 for o.
-1, 0, 2/3, 1
Let v(m) be the second derivative of -m**6/36 + m**5/12 - 18*m. Factor v(w).
-5*w**3*(w - 2)/6
Let y(p) be the first derivative of 0*p + 3/5*p**5 - 3/4*p**4 + 2 + 3/2*p**2 - p**3. Determine m, given that y(m) = 0.
-1, 0, 1
Let n = 1/165 + 29/660. Let u(h) be the second derivative of -1/60*h**6 + 0*h**3 - 1/24*h**4 + 0*h**2 + 0 - 3*h - n*h**5. Factor u(z).
-z**2*(z + 1)**2/2
Let d(h) be the first derivative of h**6/14 - 3*h**5/5 + 45*h**4/28 - 13*h**3/7 + 6*h**2/7 + 13. Factor d(x).
3*x*(x - 4)*(x - 1)**3/7
Let m be 7 + -3 - (0 + 7). Let x(u) = 0*u + 2*u + 1 + u**2 - 2*u**2. Let y(o) = o**2 - 3*o - 1. Let b(a) = m*x(a) - 2*y(a). Factor b(f).
(f - 1)*(f + 1)
Factor 3*l**2 - 25/3 + 5*l + 1/3*l**3.
(l - 1)*(l + 5)**2/3
Let x be (30/4)/((-1)/(-2)). Let i be (-1)/1 - x/(-5). Factor -b**2 - i*b**3 - b**4 + 0*b**2 + 0*b**3.
-b**2*(b + 1)**2
Let y(a) be the first derivative of a**5/270 - a**4/108 - 2*a**3/27 - a**2 + 1. Let f(n) be the second derivative of y(n). Let f(g) = 0. What is g?
-1, 2
Let g be (12/18)/((-2)/(-15)). Suppose 0 = 5*t + 3*z - 4*z - 51, g*z + 5 = 0. Factor -2*j + t*j**2 - 6*j + 30*j**2 - 50*j**3.
-2*j*(5*j - 2)**2
Suppose -33*s**2 + 15*s**4 - 7*s**3 + 12 - 5*s**3 - 7*s**3 + 6*s**5 + 12*s + 7*s**3 = 0. What is s?
-2, -1/2, 1
Let k be 16/9 + (-18)/(-81). Let t(c) be the second derivative of 0 + 3*c - 1/36*c**4 + 1/9*c**3 + 0*c**k. Suppose t(j) = 0. Calculate j.
0, 2
Let u = -14 + 16. Factor u*c**2 - 1 - 2*c + 0*c + 2 - 5.
2*(c - 2)*(c + 1)
Factor 0 + 0*p**2 - 5/2*p**4 + 0*p + 5*p**3.
-5*p**3*(p - 2)/2
Let h(w) be the second derivative of -w**5/70 - w**4/42 + 2*w**3/21 - 5*w. Factor h(d).
-2*d*(d - 1)*(d + 2)/7
Let r(m) be the first derivative of -2*m**5/7 - 32*m**4/21 - 16*m**3/7 + 32*m/21 - 43. Determine i so that r(i) = 0.
-2, -2/3, 2/5
Let j = 788/1155 - 6/385. Factor -2/3*o**4 - j*o**2 + 0 + 4/3*o**3 + 0*o.
-2*o**2*(o - 1)**2/3
Let s(j) be the first derivative of j**3/5 - 13*j**2/10 - 2*j - 40. Solve s(o) = 0 for o.
-2/3, 5
Let p be 2/((-1)/(-40)*-2). Let n be ((-24)/p)/(2/10). Let 0 + 4/5*y + 18/5*y**2 + 14/5*y**n = 0. What is y?
-1, -2/7, 0
Let f(a) be the first derivative of 1/20*a**5 - 5 + 0*a - 1/12*a**3 - 1/16*a**4 + 1/8*a**2. Factor f(n).
n*(n - 1)**2*(n + 1)/4
Let x be 1*-8*4/(-8). Factor i**5 + 4 - 2*i**3 + i + x*i**2 - 6*i**2 - 3 + i**4.
(i - 1)**2*(i + 1)**3
Factor -4/7 - 10/7*r**3 - 18/7*r**2 - 2*r - 2/7*r**4.
-2*(r + 1)**3*(r + 2)/7
Suppose 4*c - 16 = 2*x - 4*x, 4*c + 4*x = 24. Factor 3*l**2 - 2*l**2 - 2*l**3 + 2*l - c*l**2 + 3*l**2 - 2*l**4.
-2*l*(l - 1)*(l + 1)**2
Suppose -9*d + 1 = -17. Let w be 1 + 0 - 2/4. Factor -1/4*s**d - 1/4*s + w.
-(s - 1)*(s + 2)/4
Let s(i) be the third derivative of -i**8/3360 + i**7/1260 - i**4/12 - 2*i**2. Let y(v) be the second derivative of s(v). Factor y(j).
-2*j**2*(j - 1)
Let f(o) be the second derivative of 3*o**5/20 + 3*o**4/4 - 2*o**3 - 5*o. Suppose f(d) = 0. Calculate d.
-4, 0, 1
Let h(g) = -g**2 - 2*g - 1. Let c be h(-2). Let m be c + 2 - 3/5. Suppose -8/5*x**3 + 2/5 - m*x**2 + 8/5*x = 0. What is x?
-1, -1/4, 1
Let f(s) be the third derivative of s*