 -18/5*h**3 - 36/5*h**2 - 4/5 - a*h = 0. Calculate h.
-1, -2/3, -1/3
Let g(n) be the second derivative of 5*n**4/4 + 25*n**3/3 - 20*n**2 + 15*n. Determine d, given that g(d) = 0.
-4, 2/3
Let u(o) be the first derivative of 1/15*o**5 - 1/9*o**3 + 0*o**2 + 0*o - 2 - 1/12*o**4 + 1/18*o**6. Factor u(g).
g**2*(g - 1)*(g + 1)**2/3
Let h(v) be the third derivative of v**5/360 - v**4/72 - v**3/12 + 14*v**2 + 3*v. What is f in h(f) = 0?
-1, 3
Factor 2*o**3 - 29*o**3 + 3*o**5 + 16*o**4 - 7*o**5 + 8*o**2 + 7*o**3.
-4*o**2*(o - 2)*(o - 1)**2
Let y(w) be the second derivative of w**6/210 - w**4/84 - 7*w. Factor y(k).
k**2*(k - 1)*(k + 1)/7
Suppose 3*k - 6*k + 6 = 0. Let p(d) be the third derivative of 0 + 0*d + 1/8*d**5 + 13/240*d**6 + 1/105*d**7 + 3*d**k + 1/12*d**3 + 7/48*d**4. Solve p(f) = 0.
-1, -1/4
Let w = -16/15 - -68/45. Let r be (-15)/(-5) + (-75)/27. What is o in 0 - r*o**3 - 2/3*o**4 + 0*o + w*o**2 = 0?
-1, 0, 2/3
Let m(k) = k**3 - 2*k**2 + 2. Let d be m(2). Factor 2*j + 1 - d*j**3 - 1 + 0.
-2*j*(j - 1)*(j + 1)
Suppose -4*t - 2*h = -3*t + 9, 3*t - 6 = 5*h. Let c be (105/6)/5 + t. Factor -1/2*p**2 + c*p**4 - 1/2*p + 0 + 1/2*p**3.
p*(p - 1)*(p + 1)**2/2
Factor 0*r**3 - r**3 - 3*r + 4*r**3.
3*r*(r - 1)*(r + 1)
Suppose -3*i = -3*p - 0 + 3, 3*i = -2*p + 22. Factor 0 - 3/5*n + 3/5*n**2 + 3/5*n**3 - 3/5*n**i.
-3*n*(n - 1)**2*(n + 1)/5
Let v(x) = -2*x + 14. Let d be v(7). Suppose 5*p + 0 - 15 = 0. Factor 7/4*l**2 - 2*l**p + d - 4*l**4 - 1/4*l.
-l*(l + 1)*(4*l - 1)**2/4
Let n(q) = -6*q**2 - q. Let k(d) = d + 0*d - 2*d - 7*d**2. Let z(t) = -5*k(t) + 6*n(t). Factor z(a).
-a*(a + 1)
Let o(c) be the second derivative of -c**4/3 + 2*c**2 - 2*c. Factor o(s).
-4*(s - 1)*(s + 1)
Let r(n) = -23*n + 184. Let x be r(8). Find u, given that -1/4 + x*u**3 + 0*u + 1/2*u**2 - 1/4*u**4 = 0.
-1, 1
Let x(u) = -u**5 - 3*u**4 + 2*u**2 + 2*u + 2. Let g(m) = -2*m**5 - 4*m**4 + 3*m**2 + 3*m + 3. Let i(n) = -2*g(n) + 3*x(n). Factor i(k).
k**4*(k - 1)
Let g(q) be the first derivative of -2*q**3/21 + 2*q/7 - 1. Factor g(b).
-2*(b - 1)*(b + 1)/7
Let o(f) be the third derivative of f**7/315 + f**6/180 - f**5/30 - f**4/36 + 2*f**3/9 + 12*f**2. Let o(i) = 0. Calculate i.
-2, -1, 1
Let y(k) be the first derivative of k**5/30 - k**2/2 + 1. Let l(m) be the second derivative of y(m). Factor l(d).
2*d**2
Suppose 4*k - 12 = k. Solve 4*l**3 + 4*l - 9*l**2 - k*l**3 + 2*l**3 + 3*l**2 = 0 for l.
0, 1, 2
Let f(t) = 110*t**4 - 220*t**3 + 45*t**2 + 45*t - 45. Let j(c) = -5*c**4 + 10*c**3 - 2*c**2 - 2*c + 2. Let u(p) = -2*f(p) - 45*j(p). Factor u(i).
5*i**3*(i - 2)
Let p(t) be the third derivative of t**8/4200 + t**7/1050 + t**6/900 + 2*t**3/3 + 3*t**2. Let c(x) be the first derivative of p(x). Factor c(o).
2*o**2*(o + 1)**2/5
Let z(d) be the second derivative of -d**6/90 - d**5/60 + d**4/12 + 5*d**3/18 + d**2/3 - 13*d. Solve z(j) = 0.
-1, 2
Let x(b) = b**3 - b. Let g(q) = -4*q**3 + 10*q**2 - 12*q + 6. Let w(l) = g(l) + 2*x(l). Factor w(t).
-2*(t - 3)*(t - 1)**2
Let w = -1897/6 - -317. Determine y so that -3/2*y**3 + 7/6*y**5 + 1/3*y + 5/6*y**4 + 0 - w*y**2 = 0.
-1, 0, 2/7, 1
Let x(c) be the second derivative of 0*c**5 + 0*c**3 - 3*c + 0 + 0*c**2 + 0*c**4 - 1/30*c**6. Factor x(o).
-o**4
Let m = 3/52 + 199/156. Let i = 315 + -944/3. Find f, given that m + i*f**2 - 4/3*f = 0.
2
Let v be ((-9)/6)/(((-3)/8)/1). Let b(d) be the first derivative of 1/4*d + 0*d**2 + v - 1/12*d**3. Factor b(r).
-(r - 1)*(r + 1)/4
Let b = 84 - 78. Let n(q) be the third derivative of 1/9*q**3 + 0 + q**2 - 1/8*q**4 + 1/36*q**5 - 1/90*q**7 + 0*q + 1/40*q**b. Solve n(c) = 0.
-1, 2/7, 1
Let h(k) = -k**3 - 4*k**2 - 2*k - 6. Let g be h(-4). Let m be 1/(-3) - 14/(-6). Determine j, given that -2*j + j**3 - j**m + 3*j**g + 3*j = 0.
-1, 0
Let y = 3 - 0. Determine x so that -2*x**y - 2*x**4 + 2*x**3 + 2*x**2 = 0.
-1, 0, 1
Let m(q) = 0*q + 0 + 6 - 2*q + 6. Let l be m(6). Factor l + 0*j - 1/4*j**4 + 1/4*j**3 + 1/2*j**2.
-j**2*(j - 2)*(j + 1)/4
Suppose u - 7 = -3*y + 4*y, 2*y = 4*u - 22. Suppose v = u - 0. Factor -1/4*n - 1/2*n**2 + 1/2*n**v + 0 + 1/4*n**3.
n*(n - 1)*(n + 1)*(2*n + 1)/4
Let m(h) be the first derivative of -1/48*h**4 - 1/24*h**3 + 1/2*h**2 + 2 - 1/240*h**5 + 0*h. Let g(k) be the second derivative of m(k). Solve g(u) = 0.
-1
Let y be (-2)/7 + (-48)/(-70). Factor -y*x**4 + 0*x**2 + 0*x + 0 - 2/5*x**3.
-2*x**3*(x + 1)/5
Let r = -13 + 15. Let 2*b**2 - b**2 - 2*b**2 - 2*b**r = 0. What is b?
0
Factor -2*f - 83*f**2 + 83*f**2 + 2*f**3.
2*f*(f - 1)*(f + 1)
Let i(v) = 2*v + 40. Let c be i(-20). Let w(o) be the second derivative of c + 1/48*o**4 + 1/8*o**2 + 2*o - 1/12*o**3. Factor w(f).
(f - 1)**2/4
Let i = -10/7 - -47/28. Let u be (1 - 1)*(2 - 1). Let u + i*s + 1/4*s**2 = 0. What is s?
-1, 0
Let -103 - 26*d**2 + 10*d**2 + 119 - 12*d**3 + 12*d = 0. Calculate d.
-4/3, -1, 1
Let o be ((-3)/9)/((-132)/18 + 6). Find b, given that -o*b + 0 - 1/4*b**2 = 0.
-1, 0
Let w(i) be the first derivative of -5*i**4/4 - 3*i**3/2 + 3*i**2 + i + 4. Let a(q) be the first derivative of w(q). Suppose a(j) = 0. Calculate j.
-1, 2/5
Let l(r) be the first derivative of -1/900*r**6 - 2/3*r**3 + 1/300*r**5 + 1 + 0*r + 0*r**2 + 0*r**4. Let n(g) be the third derivative of l(g). Factor n(f).
-2*f*(f - 1)/5
Let k(j) = -j**3 - 12*j**2 + 12*j - 9. Let t(v) = 12*v**2 - 12*v + 8. Let f(l) = -4*k(l) - 5*t(l). Factor f(u).
4*(u - 1)**3
Suppose z + 21 = 5*x, -x - 2*x + 15 = -3*z. Factor x*k - 2*k**5 - 6*k - 4*k**4 + 4*k**3 - 2 + 2*k**4 + 4*k**2.
-2*(k - 1)**2*(k + 1)**3
Suppose 4*n - 5*t - 18 = 0, 4 = 3*n + 4*t - 3*t. Factor 2*o**n - o**4 - 2*o**5 + 2*o**3 + 0*o**4 + o**4 - 2*o**4.
-2*o**2*(o - 1)*(o + 1)**2
Let g(v) = 7*v**2 + 4*v + 4. Let x(o) = -8*o**2 - 5*o - 5. Let j(k) = 5*g(k) + 4*x(k). Factor j(u).
3*u**2
Suppose 3*k = -0*k + 288. Let n be 1/(-3) - k/(-18). Factor 2*j**3 - 2*j - j + j - n*j**3 - 5*j**2.
-j*(j + 1)*(3*j + 2)
Let n be (-10 - -10)/(-9 - -4). Factor 6/5*b + 2/5*b**2 + n.
2*b*(b + 3)/5
Let o be (-6 - 2)*(-5)/4. Suppose 0*d + d + 5*s - 22 = 0, 0 = d - 3*s + o. Factor -10*x**3 + x**d - 2*x - 3*x**2 - 6*x**2 - 4*x**4.
-2*x*(x + 1)**2*(2*x + 1)
Let z be -4*(0 - (-3)/4). Let a(r) be the second derivative of r**3/3 - r**2 - 2*r. Let o(v) = v**2 + v - 3. Let t(n) = z*a(n) + 2*o(n). Factor t(y).
2*y*(y - 2)
Let a(b) be the first derivative of 3*b**4/8 + 2*b**3 + 9*b**2/4 - 4. Suppose a(g) = 0. Calculate g.
-3, -1, 0
Let u(b) be the third derivative of b**5/10 + 9*b**4/8 + 2*b**3 - 19*b**2. Determine m so that u(m) = 0.
-4, -1/2
Let b = 248/21 - 78/7. Factor 0*x + 0 + b*x**3 - 2/3*x**2.
2*x**2*(x - 1)/3
Let j = -4 + 4. Suppose j*r = r. Factor -2/7*w**5 + 0*w**3 - 2/7*w**4 + 0*w**2 + r*w + 0.
-2*w**4*(w + 1)/7
Let q(u) be the second derivative of -5/6*u**4 + 1/2*u**5 + 0 - 1/2*u**2 - 1/6*u**6 - u + 1/42*u**7 + 5/6*u**3. What is a in q(a) = 0?
1
Let c(g) be the second derivative of -g**5/60 - g**4/36 + 2*g. Let c(w) = 0. Calculate w.
-1, 0
Let z(x) be the second derivative of 5/84*x**4 - 3/140*x**5 - 1/14*x**2 + 8*x + 0 - 1/42*x**3. Factor z(y).
-(y - 1)**2*(3*y + 1)/7
Let j be 38/(-12) + 1/6. Let w = j - -5. Suppose -4*h**3 + w*h**4 + 2*h**2 - 2 + 2 = 0. What is h?
0, 1
Solve -4/3*a**3 - 2/3*a**2 + 0 + 2*a**4 + 0*a = 0 for a.
-1/3, 0, 1
Let y(l) be the second derivative of l**7/21 + l**6/15 + 11*l. Solve y(q) = 0 for q.
-1, 0
Find f such that 20*f + f**3 + 13 - 4 + 7*f**2 - 5*f = 0.
-3, -1
Let j(d) be the third derivative of 0 - 1/72*d**4 + 1/180*d**6 - 1/630*d**7 + 1/90*d**5 - 1/1008*d**8 - 5*d**2 + 0*d - 1/18*d**3. Suppose j(f) = 0. Calculate f.
-1, 1
Let r(v) = -v**3 + 3*v**2 + 7*v - 9. Let d be r(4). Let u(h) be the second derivative of 0 - 1/6*h**4 - 2*h - 3/4*h**d - 1/2*h**2. Factor u(f).
-(f + 2)*(4*f + 1)/2
Let w = -29 + 581/20. Let r(l) be the second derivative of 1/8*l**3 + 1/168*l**7 + 4*l + 0 - w*l**5 + 1/4*l**2 - 1/24*l**4 + 0*l**6. Factor r(u).
(u - 2)*(u - 1)*(u + 1)**3/4
Let c be 1/(30*2)*61. Let d = c - 4/15. Factor -3/4*f**2 + 0 + d*f.
-3*f*(f - 1)/4
Let v(a) be the second derivative of a**5/10 - a**4/6 - 2*a**3/3 - 11*a. Let v(m) = 0. Calculate m.
-1, 0, 2
Let v be ((-1)/3)/(25/(-50)). Determine t, given that -2/3*t**5 + 0*t**2 - v*t**3 + 4/3*t**4 + 0*t + 0 = 0.
0, 1
Factor 7*u**4 + u**4 - 12*u**3 - 4*u**4 + 12*u - 8 + 4*u**2.
4*(u - 2