5 + 3*a**2 - 1/210*a**m + 1/120*a**6. Factor h(i).
-i*(i - 1)**2*(i + 1)
Let z be (5 + -2)*2/3. Factor -8 - 4 + 10*s**2 - 4*s**z - 3*s**2.
3*(s - 2)*(s + 2)
Let w(d) = 4*d**4 - 4*d**3 - 8*d**2 - 3. Let x(o) be the first derivative of -o - 3. Let z(k) = w(k) - 3*x(k). Determine m, given that z(m) = 0.
-1, 0, 2
Let m be (-2)/9 - (-110)/9. Suppose 3*t - m + 3 = 0. Find d, given that -6 - 5*d - d + t*d**3 - 2*d - d = 0.
-1, 2
Let n be (-16)/(-20)*2/48. Let f(o) be the third derivative of o**2 + n*o**5 + 0 + 0*o - 1/6*o**4 + 1/3*o**3. Factor f(u).
2*(u - 1)**2
Factor 1/6*t**2 + 49/6 + 7/3*t.
(t + 7)**2/6
Let d(i) be the second derivative of 0 - 1/6*i**4 + i**2 + 1/3*i**3 - 1/10*i**5 - 3*i. Factor d(p).
-2*(p - 1)*(p + 1)**2
Let a(r) be the second derivative of -r**7/2520 + r**6/360 - r**5/120 + r**4/4 + 4*r. Let m(l) be the third derivative of a(l). Suppose m(h) = 0. Calculate h.
1
Factor -2/5*b**3 + 0 + 0*b**2 + 2/5*b.
-2*b*(b - 1)*(b + 1)/5
Let y(c) be the second derivative of c + 0 + 5/3*c**6 + 145/42*c**4 - 40/21*c**3 - 47/14*c**5 - 1/3*c**7 + 4/7*c**2. Factor y(d).
-2*(d - 1)**3*(7*d - 2)**2/7
Let s(m) be the first derivative of 1/2*m**2 + 0*m + 3 - 1/120*m**6 - 1/60*m**5 + 0*m**4 + 0*m**3. Let y(h) be the second derivative of s(h). Factor y(u).
-u**2*(u + 1)
Let g(l) be the first derivative of l**5 - 15*l**4/4 + 10*l**3/3 + 42. Solve g(t) = 0 for t.
0, 1, 2
Let f = -4 + 7. Factor 4 + u + 2*u + f*u**2 - 4.
3*u*(u + 1)
Let h(a) = 8*a**5 - 12*a**4 - 6*a**3 + 2*a**2 - 6*a + 6. Let s(j) = 23*j**5 - 35*j**4 - 17*j**3 + 7*j**2 - 17*j + 17. Let p(d) = -17*h(d) + 6*s(d). Factor p(t).
2*t**2*(t - 2)**2*(t + 1)
Let t be (-5)/(-15) + 8/3. Suppose 2*u + t = 5. Let n(y) = -y**2 - y - 1. Let z(h) = 2*h**2 + 3*h + 2. Let f(q) = u*n(q) + z(q). Factor f(p).
(p + 1)**2
Let o(b) be the third derivative of -b**6/280 + b**5/28 - b**4/7 + 2*b**3/7 - 10*b**2. Let o(l) = 0. Calculate l.
1, 2
Solve 12*l - 90/7*l**2 + 27/7*l**3 - 24/7 = 0 for l.
2/3, 2
Let m(v) be the second derivative of -v**2 - 1/6*v**4 + 2*v + 2/3*v**3 + 0. Determine u so that m(u) = 0.
1
Factor -4/9 - 2/9*k**2 - 2/3*k.
-2*(k + 1)*(k + 2)/9
Let r be (-11)/90 + 2/9. Let s(u) be the second derivative of 0 + 1/2*u**4 - u**3 - r*u**5 + u**2 - u. Solve s(h) = 0.
1
Let p be (-15)/(-30) - 2/(-12). Solve -1/3*x**5 + 1/3 - p*x**2 - 1/3*x + 1/3*x**4 + 2/3*x**3 = 0.
-1, 1
Let l(n) = -n**2 - 11*n - 7. Let q be l(-7). Suppose -4*d - 2*b + q = 3, -14 = -3*d - 2*b. Factor -o**d + 0*o**4 - 3*o**2 + 4*o**2.
-o**2*(o - 1)*(o + 1)
Let b(a) be the second derivative of a**4/42 + a**3/21 - 10*a. What is w in b(w) = 0?
-1, 0
Let w(x) be the second derivative of 2/15*x**5 + x + 0*x**2 + 0 - 2/9*x**4 - 1/45*x**6 + 0*x**3. Suppose w(a) = 0. What is a?
0, 2
Let m be (38/3)/(91/(-21)). Let d = m - -368/117. Factor 4/9*x**4 + 0 + 0*x**3 - d*x**5 - 4/9*x**2 + 2/9*x.
-2*x*(x - 1)**3*(x + 1)/9
Let u(h) be the first derivative of h**8/336 - h**7/42 + h**6/20 + h**5/15 - h**4/3 - h**2/2 - 2. Let a(b) be the second derivative of u(b). Factor a(i).
i*(i - 2)**3*(i + 1)
Let d = 0 + 0. Let a = 48/217 - -2/31. Factor 4/7*w**2 + 0 + a*w**4 + 6/7*w**3 + d*w.
2*w**2*(w + 1)*(w + 2)/7
Let m(r) = 4*r**2 + 2*r + 1. Let o be m(-1). Let a be (-4)/(9 + o)*-15. Factor 0 + 1/3*u**a + 0*u - u**4 + u**3 - 1/3*u**2.
u**2*(u - 1)**3/3
Let t = 9 - 3. Let x(a) = -a**3 + 5*a**2 + 8*a - 8. Let f be x(t). Factor 2/3*y**3 + 2/3*y**f + 2/9*y**5 + 0*y + 2/9*y**2 + 0.
2*y**2*(y + 1)**3/9
Let v(b) = -35*b**3 - 10*b**2 - 5*b - 30. Let u(j) = -j**3 - 1. Let m(n) = 30*u(n) - v(n). Let m(p) = 0. Calculate p.
-1, 0
Let b(k) be the second derivative of k**8/47040 - k**7/17640 - k**6/5040 + k**5/840 - 5*k**4/6 + 2*k. Let j(g) be the third derivative of b(g). Factor j(f).
(f - 1)**2*(f + 1)/7
Let w(r) = r**3 - r**2 - 3*r. Let a be w(3). Let h be (-2 - -2)/(a - 5). Suppose -1/4*y**3 - 3/4*y**2 + h - 1/2*y = 0. Calculate y.
-2, -1, 0
Let c(m) be the second derivative of m**8/6720 - m**6/1440 - m**3/3 + m. Let x(s) be the second derivative of c(s). Factor x(n).
n**2*(n - 1)*(n + 1)/4
Let r(a) = 2*a**4 - 8*a**3 - 2*a**2 + 8*a + 12. Let h(x) = x**3 - x**2 - 1. Let m(q) = 4*h(q) + r(q). Determine u, given that m(u) = 0.
-1, 2
Let d(k) be the second derivative of -5*k**7/168 - 17*k**6/120 - k**5/5 - k**4/12 + 10*k. Let d(s) = 0. Calculate s.
-2, -1, -2/5, 0
Suppose -1/5*d**2 - 1/5*d + 1/5 + 1/5*d**3 = 0. Calculate d.
-1, 1
Factor -5/4*y**2 + 0 + 1/2*y + 3/4*y**3.
y*(y - 1)*(3*y - 2)/4
Suppose 24 = 4*h + 8. Let q(y) = y**3 - y + 1. Let c(m) = 5*m**3 - m**2 - 4*m + 4. Let t(a) = h*q(a) - c(a). Factor t(k).
-k**2*(k - 1)
Let g(y) be the third derivative of y**6/960 + 3*y**2. Factor g(l).
l**3/8
Determine r, given that -9*r**4 + 6*r + 18*r**2 - 3*r**2 - 6*r**3 - 6*r**4 = 0.
-1, -2/5, 0, 1
Suppose -56 = -5*t - 3*t. Let n(r) be the third derivative of 1/5*r**5 + 0*r + 0 + 9/10*r**6 - 2*r**2 + 81/70*r**t + 0*r**3 + 0*r**4. Solve n(q) = 0 for q.
-2/9, 0
Let a(r) be the second derivative of 0*r**4 + 0*r**2 + 1/9*r**3 + 0 - 1/120*r**5 - 2*r. Factor a(x).
-x*(x - 2)*(x + 2)/6
Let f(t) be the first derivative of -t**6/3 - 4*t**5/5 + t**4 + 8*t**3/3 - t**2 - 4*t - 8. Let f(r) = 0. Calculate r.
-2, -1, 1
Let u(w) be the first derivative of -w**9/10584 + w**7/1470 - w**5/420 - 2*w**3/3 + 2. Let p(g) be the third derivative of u(g). Suppose p(b) = 0. What is b?
-1, 0, 1
Let j(v) be the third derivative of v**6/40 - v**4/8 - 6*v**2. Factor j(q).
3*q*(q - 1)*(q + 1)
Let j be 2 + 4 + (-42)/8. What is s in -3/4*s**2 - 9/4*s + j + 9/4*s**3 = 0?
-1, 1/3, 1
Let w be (-1 - -1)/(2 + 2 + -5). Factor 1/2*h**4 + 0 - h**3 + w*h + 1/2*h**2.
h**2*(h - 1)**2/2
Let r(x) be the third derivative of 8/135*x**6 + 0*x + 0*x**4 + 0*x**3 + 0 - 2/135*x**5 - 11/135*x**7 + 7/216*x**8 - 4*x**2. Let r(d) = 0. What is d?
0, 2/7, 1
Let b(q) be the third derivative of -q**8/504 + 2*q**7/315 + q**6/180 - q**5/45 - 5*q**2. Solve b(d) = 0.
-1, 0, 1, 2
Let h(u) be the second derivative of 8*u**7/49 - 12*u**6/35 - 3*u**5/20 + 23*u**4/28 - 9*u**3/14 + 3*u**2/14 + 3*u. Determine q so that h(q) = 0.
-1, 1/4, 1
Solve 1/4*f**2 - 3/4*f + 1/2 = 0 for f.
1, 2
Let u = 70 - 67. Let p(r) be the first derivative of r + 1/3*r**u + r**2 + 3. Factor p(q).
(q + 1)**2
Let t(m) = -3*m**4 - 16*m**3 - 46*m**2 + 8*m + 89. Let d(k) = 2*k**4 + 11*k**3 + 31*k**2 - 5*k - 59. Let u(j) = -8*d(j) - 5*t(j). Factor u(v).
-(v - 1)*(v + 3)**3
Let j(c) be the third derivative of -c**7/12600 + c**6/1800 + 5*c**4/24 + c**2. Let s(b) be the second derivative of j(b). Factor s(h).
-h*(h - 2)/5
Let s(a) be the first derivative of -a**4/16 + a**3/4 - a + 4. Let s(y) = 0. What is y?
-1, 2
Let x(u) = u + 6. Let v be x(-6). Factor r**5 + 2*r**4 + 3*r**3 + v*r**2 - 3*r**5 - r**3 - 2*r**2.
-2*r**2*(r - 1)**2*(r + 1)
Let s(t) = 11*t**3 + 8*t**2 + t + 4. Suppose h = -2*h - 3. Let x(r) = -r**3 - 1. Let d(w) = h*s(w) - 6*x(w). Let d(n) = 0. Calculate n.
-1, 2/5
Let z = -13 - -25. Suppose -10*k = -6*k - z. Factor 0 - 6/7*u**k + 0*u - 4/7*u**2 - 2/7*u**4.
-2*u**2*(u + 1)*(u + 2)/7
Let u(d) = d**3 - d**2 - 1. Let v(l) = -33*l**2 + 40*l**3 + 3 + 5*l - 10*l**2 + 12*l. Let s(z) = -5*u(z) - v(z). Let s(f) = 0. Calculate f.
1/3, 2/5
Let t(w) be the first derivative of w**5/15 - 5*w**4/12 + 8*w**3/9 - 2*w**2/3 + 6. Factor t(j).
j*(j - 2)**2*(j - 1)/3
Let c be (-2)/(-4)*(0 + 12). Let r = -1 + c. Determine d, given that -4*d**2 + 2 - 2*d - 2*d**4 + 4*d**3 + 4*d**4 + 0*d**5 - 2*d**r = 0.
-1, 1
Let -2/7*f**3 - 6/7*f**2 - 4/7*f + 0 = 0. Calculate f.
-2, -1, 0
Let v(m) = 7*m**3 - 5*m**2 + 3*m - 5. Let d(t) = -3*t**3 + 2*t**2 - t + 2. Let q(r) = -15*d(r) - 6*v(r). Solve q(h) = 0 for h.
-1, 0, 1
Let f(g) = -g - 9*g + 9*g**3 - 2*g - 5*g**2 + 13. Let z(q) = -14*q**3 + 8*q**2 + 18*q - 20. Let i(s) = 8*f(s) + 5*z(s). Let i(x) = 0. Calculate x.
-2, 1
Let i(f) be the first derivative of 2*f**5/45 - 2*f**3/27 - 13. Factor i(l).
2*l**2*(l - 1)*(l + 1)/9
Determine u, given that -1/5*u**4 + 2/5*u**2 + 1/5*u**5 - 2/5*u**3 - 1/5 + 1/5*u = 0.
-1, 1
Let p(y) be the third derivative of 5*y**8/168 - y**7/35 - y**6/30 + 20*y**2. Factor p(n).
2*n**3*(n - 1)*(5*n + 2)
Let t(s) be the third derivative of s**3/2 + s**2. Let l = 12 + -9. Let x(z) = -z**2 - z + 1. Let n(o) = l*x(o) + t(o). Factor n(k).
-3*(k -