Let d(f) be the second derivative of -1/60*f**6 + 0*f**3 - 1/40*f**5 + 0*f**2 + 1/24*f**4 - 6*f + 0 + 1/84*f**7. Let d(y) = 0. Calculate y.
-1, 0, 1
Let s be 1976/480 - (-6)/45. Find n such that s*n - 1/2 - 10*n**2 + 4*n**3 = 0.
1/4, 2
Let n be (3417/42)/(2/(-4)). Let w = n - -163. Factor -w*q**2 + 0 - 2/7*q.
-2*q*(q + 1)/7
Suppose -r - 17 = -5*m + m, 2*r + 22 = 4*m. Find c, given that 16/5 - 8*c + 28/5*c**2 - 6/5*c**m = 0.
2/3, 2
Let i(v) = 5*v**4 + 7*v**3 + 6*v**2 - 4*v. Let l(d) = -9*d**4 - 13*d**3 - 11*d**2 + 7*d. Let s(n) = 7*i(n) + 4*l(n). Let s(y) = 0. What is y?
-2, -1, 0
Let b(h) = -h + 3. Let v be b(0). Let -x**4 + x**3 + 3*x**3 - 7*x**v - 2*x**2 = 0. Calculate x.
-2, -1, 0
Let t be (-2 + 9/3)/(3/6). Let p(n) be the second derivative of 1/6*n**3 - 4*n + 0 + 1/2*n**t - 1/2*n**4. Let p(b) = 0. Calculate b.
-1/3, 1/2
Let p(y) = -y**5 + 3*y**4 + y**3 - 7*y**2. Let o(i) = -i**5 + i**3 - i**2. Let k(n) = -4*o(n) + p(n). Factor k(v).
3*v**2*(v - 1)*(v + 1)**2
Let r(c) be the second derivative of 0 - 1/30*c**5 + 1/9*c**3 + 1/18*c**4 - 6*c - 1/45*c**6 + 0*c**2. Solve r(q) = 0.
-1, 0, 1
Let m be (-21)/(-14) + (2 - 2). What is c in m + 3/2*c**2 - 3*c = 0?
1
Factor 32*r**2 + 14*r**2 + 40*r + 10 - 2 + 14*r**3.
2*(r + 1)*(r + 2)*(7*r + 2)
Let r(q) be the second derivative of 0 + 1/24*q**4 - 1/12*q**3 + 6*q - 1/2*q**2. Determine y so that r(y) = 0.
-1, 2
Let p be (-2 - (-56)/(-6))*3. Let r = p - -36. Suppose 8/5*j**4 - 24/5*j**3 + 0 + 18/5*j**r - 4/5*j = 0. Calculate j.
0, 1/2, 2
Let h(y) = -y**5 + 5*y**4 - 2*y**2 + 2*y. Let v(x) = 3*x**5 - 16*x**4 + 5*x**2 - 7*x. Let f(i) = -7*h(i) - 2*v(i). Factor f(m).
m**2*(m - 2)**2*(m + 1)
Let h(z) = 7*z**2 + 5*z + 3. Let q(c) = c**2 - c - 1. Let m(f) = -2*h(f) - 6*q(f). Solve m(t) = 0 for t.
-1/5, 0
Let d(i) = 3*i**2 - 5*i - 3. Let b be d(4). Find c, given that 27*c**3 + b*c**3 - 13*c**3 + 21*c**3 - 6*c - 9*c**2 = 0.
-1/4, 0, 2/5
Let x(s) = -4*s - 4. Let l be x(-2). Find c such that -2*c**3 + 4*c**l - 5*c**4 - 1 + 2*c + 2*c**4 = 0.
-1, 1
Let c(q) be the second derivative of -1/10*q**6 - 5*q - 2*q**3 + 0 - 3/2*q**4 + 3/4*q**5 + 12*q**2. Factor c(o).
-3*(o - 2)**3*(o + 1)
Let t(s) be the third derivative of -s**5/24 - 5*s**4/24 - 5*s**3/12 + s**2 + 26. Factor t(h).
-5*(h + 1)**2/2
Determine t so that -4/9*t**2 + 4/9*t**3 + 0 - 4/9*t + 4/9*t**4 = 0.
-1, 0, 1
Solve 3/4*i**4 - 3/4*i**3 + 3/4*i**5 + 0*i + 0 - 3/4*i**2 = 0.
-1, 0, 1
Determine r so that 0*r**2 + 0*r - 1/2*r**4 + 0 + 3/2*r**3 = 0.
0, 3
Let g(u) be the third derivative of u**6/40 + 3*u**5/20 + u**4/4 - 15*u**2 - 2*u. Find k such that g(k) = 0.
-2, -1, 0
Let t = -11 - -18. Suppose b - x - 3 = 0, -5*x + t = 4*b - 5. Factor -3/5 + 0*u**2 + 3/5*u**4 + 6/5*u**b - 6/5*u.
3*(u - 1)*(u + 1)**3/5
Let n(g) be the third derivative of -g**6/8 + 5*g**5/6 - 5*g**4/24 - 5*g**3 + 15*g**2. Factor n(x).
-5*(x - 3)*(x - 1)*(3*x + 2)
Let n = -81 - -81. Determine h so that n + 2/3*h**2 - 2/3*h**3 - 2/3*h**4 + 2/3*h = 0.
-1, 0, 1
Let o(d) be the second derivative of -d**6/15 - 7*d**5/40 - d**4/12 + d**3/12 - d. Factor o(v).
-v*(v + 1)**2*(4*v - 1)/2
Suppose -d + 12 = 2*d - 4*g, 3*d - 5*g - 9 = 0. Let b be 3/2*d/6. Factor 1/2 + 1/2*w**b - w.
(w - 1)**2/2
Suppose -25 = -5*j - 15. Let f(s) be the first derivative of -2*s**2 + 9/8*s**4 - j*s + 2 + 1/2*s**3. Factor f(p).
(p - 1)*(3*p + 2)**2/2
Let y be (-4)/(-6) + (-39)/(-9). Suppose i = -4 + y, -5*i = 4*t - 13. Factor -v + 1/2 + 1/2*v**t.
(v - 1)**2/2
Let z(p) be the first derivative of 2*p**3/9 + p**2/3 + 2. Factor z(u).
2*u*(u + 1)/3
Let b(z) = z**3 - z**2 + z + 1. Let n be (5 - 6/2) + -3. Let y(v) = -3*v**3 + 4*v**2 - 7*v - 2. Let u(d) = n*y(d) - 4*b(d). Factor u(q).
-(q - 1)**2*(q + 2)
Let n(w) = -3*w**2 + 10*w - 13. Let m(i) = -i**2 + 4*i - 6. Let x(h) = 15*m(h) - 6*n(h). Factor x(q).
3*(q - 2)*(q + 2)
Suppose 0*h + 5*u = 2*h + 16, -2*u = h - 10. Suppose -6 = -d - h*d. Solve 6/7*z**d - 4/7*z + 0 = 0 for z.
0, 2/3
Let x = -15 + 15. Let p(q) be the first derivative of 1/12*q**3 - 2 + 1/16*q**4 + 0*q**2 + x*q - 1/24*q**6 - 1/20*q**5. Determine y so that p(y) = 0.
-1, 0, 1
Let h(u) be the first derivative of -u**7/1260 - u**6/360 - u**5/360 - 7*u**2/2 + 5. Let w(v) be the second derivative of h(v). Factor w(z).
-z**2*(z + 1)**2/6
Let o(m) = 22*m + 200. Let d be o(-9). Factor -2/3*j**d + 0*j + 2/3.
-2*(j - 1)*(j + 1)/3
Let f(m) be the third derivative of -m**8/1176 + m**6/420 - 5*m**2. Factor f(r).
-2*r**3*(r - 1)*(r + 1)/7
Let -36/5*u + 0 - 6/5*u**3 + 42/5*u**2 = 0. Calculate u.
0, 1, 6
Let i(l) be the first derivative of -l**6/8 + 3*l**5/4 - 15*l**4/8 + 5*l**3/2 - 15*l**2/8 + 3*l/4 + 1. Factor i(v).
-3*(v - 1)**5/4
Suppose 2*c + 13 = 5*w, -c - 17 = -5*w - 3*c. Let v be (w/15)/((-6)/(-245)). Factor v*h**4 - 34/3*h + 4/3 - 175/6*h**3 + 31*h**2.
(h - 2)*(h - 1)*(7*h - 2)**2/6
Let l(a) be the third derivative of -a**8/84 + 8*a**7/105 - a**6/5 + 4*a**5/15 - a**4/6 - 21*a**2. Find g such that l(g) = 0.
0, 1
Factor 22/9*y**3 - 22/9*y + 4/9 - 4/9*y**2.
2*(y - 1)*(y + 1)*(11*y - 2)/9
Factor 2/5*q**4 - 1/5*q**3 + 0*q**2 - 1/5*q**5 + 0*q + 0.
-q**3*(q - 1)**2/5
Let j(k) be the second derivative of 5*k + 0 - 1/30*k**3 - 3/50*k**5 - 1/15*k**4 - 2/75*k**6 - 1/210*k**7 + 0*k**2. Factor j(r).
-r*(r + 1)**4/5
Factor -4*h + h + h**4 + 2*h**3 + 4 - h - 3*h**2.
(h - 1)**2*(h + 2)**2
Let h(j) be the second derivative of -2*j + 0*j**3 + 1/96*j**4 - 1/2*j**2 + 0 + 1/120*j**5 + 1/480*j**6. Let c(d) be the first derivative of h(d). Factor c(r).
r*(r + 1)**2/4
Solve 2/3*w**3 - 2/3*w**5 + 0 + 4/3*w**4 - 4/3*w**2 + 0*w = 0.
-1, 0, 1, 2
Factor -12*f + 5*f**2 + f - 14*f + 5*f.
5*f*(f - 4)
Let s(f) = 2*f + 8. Let j be s(-3). Suppose j*v + 5*r = 25, 3 = 3*v + 5*r - 22. Factor -2/5*o**2 + v + 0*o.
-2*o**2/5
Let j(v) = -v**3 + 8*v**2 - v + 3. Let q be j(8). Let p be (-1)/q*30/9. Let -4/3*u**3 + 2/3*u**5 + 4/3*u**2 - 2/3 + 2/3*u - p*u**4 = 0. What is u?
-1, 1
Suppose 9*x = 3*x - 12. Let b be 2/(7 + x + -4). Determine d so that -4/3 - 5/3*d**b - 8/3*d - 1/3*d**3 = 0.
-2, -1
Let j(b) be the third derivative of -1/180*b**6 - 11*b**2 + 1/72*b**4 + 1/1008*b**8 + 0 + 0*b - 1/90*b**5 + 1/630*b**7 + 1/18*b**3. Factor j(t).
(t - 1)**2*(t + 1)**3/3
Suppose 0 = -19*p + 52 - 52. Factor -2/9*w**4 + 4/9*w**3 - 2/9*w**2 + 0*w + p.
-2*w**2*(w - 1)**2/9
Let w(z) be the second derivative of z**4/78 + z**3/39 - 4*z. Solve w(u) = 0.
-1, 0
Let o(h) be the third derivative of -h**7/525 + h**5/50 + h**4/30 - 41*h**2. Suppose o(n) = 0. Calculate n.
-1, 0, 2
Let w(u) = -3*u**3 - 35*u**2 - 56*u - 29. Let x(s) = -s**3 - 17*s**2 - 28*s - 15. Let q(d) = -3*w(d) + 5*x(d). Factor q(j).
4*(j + 1)**2*(j + 3)
Suppose -37*h + 112 = 1. Solve -24/7*p**h + 18/7*p**4 - 8/7 + 24/7*p - 10/7*p**2 = 0.
-1, 2/3, 1
Let k(l) = l**3 + 6*l**2 + l + 6. Let w be k(-6). Let g = 37 - 35. Factor -2/5*h**3 + 0*h + w + 2/5*h**g.
-2*h**2*(h - 1)/5
Let k(u) be the first derivative of u**4/20 - u**2/10 + 7. Determine d so that k(d) = 0.
-1, 0, 1
Let r(z) = -4*z + 40. Let o be r(10). Factor 0*c + 2/5*c**4 + o*c**3 - 2/5*c**2 + 0.
2*c**2*(c - 1)*(c + 1)/5
Let r(j) be the second derivative of 0 - 1/4*j**5 + j**2 + 7*j - 1/6*j**4 + 5/6*j**3. Find f, given that r(f) = 0.
-1, -2/5, 1
Let p = -15 - -24. Let x = p + -7. Factor -5 - 14*u**3 + 1 - 6*u - 24*u**x + 8.
-2*(u + 1)**2*(7*u - 2)
Let p(v) be the first derivative of v**7/315 - v**6/90 + v**4/18 - v**3/9 - v**2/2 + 2. Let h(c) be the second derivative of p(c). Factor h(j).
2*(j - 1)**3*(j + 1)/3
Suppose -10 = 7*v - 12*v. Factor 0 + 2/13*t + 2/13*t**v.
2*t*(t + 1)/13
Find x such that -10/13*x - 8/13 - 2/13*x**2 = 0.
-4, -1
Suppose -3 = 3*i - 0*i, -4*r = -5*i - 873. Let t = r + -1071/5. Determine d so that -4/5 + 2*d**4 + t*d**3 - 6/5*d**2 - 14/5*d = 0.
-1, -2/5, 1
Let b(c) be the second derivative of -c**7/2 - 9*c**6/5 - 327*c**5/140 - 9*c**4/7 - 2*c**3/7 + 5*c. Factor b(u).
-3*u*(u + 1)**2*(7*u + 2)**2/7
Suppose -4*x = x + 5*c - 10, 20 = x - 5*c. Factor 2*i - i**3 - 2 - 2*i**x - i**4 + 4*i**2 - i**4 - 4*i + 5*i**3.
-2*(i - 1)**2*(i + 1)**3
Let i = -8/5 + 26/15. Let v(b) be the second derivative of b - i*b**5 - 4/9*b**3 - 1/3*b**4 + 0 - 1/45*b**6 - 1/3*b**2. Factor v(w).
-2*(w + 1)**4/3
Let q(v) be the first derivative of -4 - 2/3*v + 2/27*v**3 - 2/9*v**2. Determi