/7*o = 0.
-1, 0, 1
Determine m, given that -11/3*m**2 + 12 - 8*m - 1/3*m**3 = 0.
-6, 1
Factor -4/3 + 6*x + 8/3*x**3 - 8*x**2.
2*(x - 2)*(2*x - 1)**2/3
Let i(p) be the second derivative of p**7/147 + p**6/21 + p**5/10 + p**4/14 + 16*p. Factor i(k).
2*k**2*(k + 1)**2*(k + 3)/7
Suppose -14*f + 7 + 35 = 0. Factor 1/5*o**2 - 1/5*o**f + 0*o + 0.
-o**2*(o - 1)/5
Suppose -4*d + 18 = 2*l, -d = -5*l - 2*d + 63. Suppose -2*a + 3*r = -19, -2*a + r + l = 2*a. Factor 1 + j**4 + 5*j**2 - 5*j - 4*j**3 + j**a + j.
(j - 1)**4
Let y(f) be the second derivative of -f**6/45 - f**5/30 + f**4/18 + f**3/9 + f. Factor y(i).
-2*i*(i - 1)*(i + 1)**2/3
Factor 1/4*n + 1/4*n**5 - 1/2*n**3 + 0 + 0*n**2 + 0*n**4.
n*(n - 1)**2*(n + 1)**2/4
Factor 0 + 0*n - 3/7*n**3 + 3/7*n**2.
-3*n**2*(n - 1)/7
Let m(a) be the first derivative of -a**6/9 + a**5/15 + a**4/4 - a**3/9 - a**2/6 + 19. What is b in m(b) = 0?
-1, -1/2, 0, 1
Let p(t) be the third derivative of t**5/12 + 25*t**4/24 - 5*t**3 + 25*t**2. Determine l so that p(l) = 0.
-6, 1
Let r(w) be the first derivative of w**3/3 - 3*w**2/2 + 4*w + 8. Let v be r(2). Let -2/3 + v*c**2 + 4/3*c**3 + 0*c = 0. Calculate c.
-1, 1/2
Let h(y) be the second derivative of y**5/90 - y**4/36 + y**2/2 + 2*y. Let o(c) be the first derivative of h(c). Let o(a) = 0. Calculate a.
0, 1
Let b = -1917/20 - -96. Let k(w) be the second derivative of -b*w**5 + 0 + 5/2*w**3 - 1/4*w**4 - 9/2*w**2 - 2*w. Factor k(g).
-3*(g - 1)**2*(g + 3)
Let i(m) be the first derivative of m**4/32 + m**3/8 + 20. Find n such that i(n) = 0.
-3, 0
Let p(u) be the second derivative of -u**6/6 - u**5/2 - 5*u**4/12 - 3*u - 12. Factor p(a).
-5*a**2*(a + 1)**2
Let x = 85/62 + 4/31. Let d be ((-4)/(-10))/((-8)/(-10)). Find b, given that -d*b + 0 - x*b**2 = 0.
-1/3, 0
Factor k**3 - 4*k**3 + 0*k**3.
-3*k**3
Let a be (-1)/((-15)/6)*5. Let t(s) = -s**3 + s + 3. Let p be t(0). Factor -a*n + 5*n**2 - p*n**2 - 4*n**2.
-2*n*(n + 1)
Let q(h) be the second derivative of h**5/45 + h**4/54 + 3*h. Factor q(c).
2*c**2*(2*c + 1)/9
Let m = 163/30 - 16/3. Let l(b) be the second derivative of 1/6*b**4 + 0 - m*b**5 + 1/3*b**3 - b**2 + b. Determine w, given that l(w) = 0.
-1, 1
Let g be ((-3)/(-36))/((-5)/(-10)). Let i(a) be the second derivative of 0*a**3 - g*a**4 + a**2 + a + 0. Factor i(r).
-2*(r - 1)*(r + 1)
Let r(x) be the third derivative of -5*x**8/336 - 10*x**2. Determine g, given that r(g) = 0.
0
Suppose -4*x + 9*x = 10. Factor 3*t**2 + t**x - 5*t**2 + 2*t.
-t*(t - 2)
Let g(j) be the first derivative of j**5/25 - j**4/10 - 2*j**3/15 - 3*j - 3. Let t(n) be the first derivative of g(n). Factor t(z).
2*z*(z - 2)*(2*z + 1)/5
Solve 78*q**2 + 1 + 126*q**3 + 31/2*q = 0 for q.
-2/7, -1/6
Let f(j) = -j**2 - j + 1. Let v(z) = 3*z**3 - 30*z**2 + 78*z - 78. Let h(w) = -3*f(w) + v(w). Find l such that h(l) = 0.
3
Let -3*x - 76*x - 11*x - 405 - 5*x**2 = 0. What is x?
-9
Factor 24/11*h + 2/11*h**3 - 12/11*h**2 - 16/11.
2*(h - 2)**3/11
Let f(v) = -71*v**2 - 75*v - 1. Let j(x) = x**2 + x - 1. Let o(c) = -f(c) - 3*j(c). Determine a so that o(a) = 0.
-1, -1/17
Find z such that 63*z + 32 - 87*z + 4*z**2 + 4 = 0.
3
What is k in -4/7*k - 4/7 + 4/7*k**3 + 3/7*k**2 + 1/7*k**4 = 0?
-2, -1, 1
Let o(z) = 13*z**2 + 4*z - 9. Suppose 8*a - 18 = 11*a. Let c(f) = 7*f**2 + 2*f - 5. Let v(s) = a*o(s) + 11*c(s). Suppose v(n) = 0. Calculate n.
-1
Solve 10*s**2 + 1 - 3*s + 0 - 5*s**2 - 9*s**2 = 0 for s.
-1, 1/4
Suppose n - 3 = -1. Suppose -u**3 - 4*u**2 + 3*u**3 - u**n + u**2 + 2*u = 0. Calculate u.
0, 1
Let -38*v**2 + 6*v**3 - 3*v + v**4 + 12 + 11*v**4 + 14*v**2 - 2*v**5 - v**5 = 0. What is v?
-1, 1, 4
Let z(r) be the third derivative of -7*r**5/80 - 3*r**4/32 + 18*r**2. Factor z(g).
-3*g*(7*g + 3)/4
Let c be 0/(-2 + (2 - 3)). Let u(y) be the third derivative of -1/24*y**4 + 0*y**3 + 3*y**2 + 0*y - 1/60*y**5 + c. Suppose u(v) = 0. What is v?
-1, 0
Let u(p) be the second derivative of -p**6/50 + 9*p**5/100 - 2*p**3/5 - 6*p. Factor u(a).
-3*a*(a - 2)**2*(a + 1)/5
Let w(f) be the third derivative of 2/3*f**3 + 0*f + 1/60*f**6 - 6*f**2 - 1/6*f**4 + 0 - 1/20*f**5 + 1/210*f**7. Factor w(v).
(v - 1)**2*(v + 2)**2
Suppose 0 = 6*c + 2*c - 8. Let m(u) be the first derivative of 0*u - c - 1/2*u**6 - 3/5*u**5 + 3/4*u**4 + u**3 + 0*u**2. Factor m(t).
-3*t**2*(t - 1)*(t + 1)**2
Let p be (-16)/12*(-15)/4. Let r(u) be the first derivative of -2 - 1/3*u**2 + 2/9*u**3 + 0*u + 1/6*u**4 - 2/15*u**p. Determine t, given that r(t) = 0.
-1, 0, 1
Factor -220/21*z**2 + 2/3*z**3 + 0 - 64/21*z.
2*z*(z - 16)*(7*z + 2)/21
Let g be (-16)/(-36)*((-4 - -2) + 5). Factor -2/3*c**4 + g*c**3 - 2/3*c**2 + 0*c + 0.
-2*c**2*(c - 1)**2/3
Let w(s) be the third derivative of s**5/240 - s**4/96 - 12*s**2. Let w(o) = 0. What is o?
0, 1
Let o(s) be the third derivative of -s**5/12 - 5*s**4/6 - 3*s**2. Solve o(v) = 0.
-4, 0
Let m = -309 - -311. Find u such that u**m + 4/5*u - 4/5 - 3/5*u**3 = 0.
-1, 2/3, 2
Let f(u) = -u**2 - 5*u + 2. Let g be f(-5). Factor 2*r**4 + 4*r - 7*r**2 + 3*r**3 - 3*r**4 - 1 + r**g + r**3.
-(r - 1)**4
Let f(g) be the first derivative of g**8/420 - g**6/30 + g**5/15 + 5*g**3/3 - 1. Let a(o) be the third derivative of f(o). What is l in a(l) = 0?
-2, 0, 1
Let s(m) be the third derivative of m**10/75600 + m**9/7560 + m**8/2016 + m**7/1260 + m**5/20 - 3*m**2. Let u(p) be the third derivative of s(p). Factor u(h).
2*h*(h + 1)**2*(h + 2)
Let n(j) = -j**4 + j**3 + 1. Let s(d) = -6*d**4 - 6*d**3 - 12*d**2 + 8*d + 20. Let v(l) = 4*n(l) - s(l). Factor v(c).
2*(c - 1)*(c + 2)**3
Suppose 0 = 11*y - 6*y + 80. Let s be (3/6)/((-2)/y). Factor 1/2*i - 1/2*i**3 - 2*i**5 + s*i**4 - 5/2*i**2 + 1/2.
-(i - 1)**3*(2*i + 1)**2/2
Let a = -2105/4 + 527. Factor 9/4*l**3 + 9/4*l**4 + 0*l + a*l**2 + 0 + 3/4*l**5.
3*l**2*(l + 1)**3/4
Suppose s + 2*j = -0 + 37, -101 = -3*s - j. Let q = 35 - s. Let 2/3*c**q + 0 + 0*c = 0. What is c?
0
Let b(z) be the first derivative of -3 - z**2 + 0*z + 0*z**3 - 1/240*z**5 - 1/96*z**4. Let u(o) be the second derivative of b(o). Factor u(q).
-q*(q + 1)/4
Suppose -37 + 469 = -6*f. Let v be (-16)/(-3)*(-6)/f. Factor v*p**3 + 0*p**4 + 0 - 2/9*p - 2/9*p**5 + 0*p**2.
-2*p*(p - 1)**2*(p + 1)**2/9
Factor 3/2 - 3/4*b**2 + 3/4*b.
-3*(b - 2)*(b + 1)/4
Let d = -3 - -2. Let h be 0 + (0 - (-1 + d)). Find u, given that -3/4*u + 0 - 3/2*u**h - 3/4*u**3 = 0.
-1, 0
Let m(o) be the first derivative of -1 - 1/20*o**5 + 0*o**3 + 0*o**2 + 2*o + 0*o**4. Let n(p) be the first derivative of m(p). Let n(d) = 0. What is d?
0
Let y(h) be the first derivative of h**4/12 + 2*h**3/9 + h**2/6 - 5. Suppose y(r) = 0. What is r?
-1, 0
Let n(w) = 5*w**3 - 8*w**2 + 7*w + 2. Let a(c) = -135*c**3 + 215*c**2 - 190*c - 55. Let i(r) = -2*a(r) - 55*n(r). Let i(o) = 0. What is o?
0, 1
Let d(v) = 5*v**2 + 5*v + 8. Let q(l) = 11*l**2 + 11*l + 17. Suppose 0 = -5*k + 19 + 46. Let t(n) = k*d(n) - 6*q(n). Factor t(p).
-(p - 1)*(p + 2)
Let u = 112 - 110. Let 3/5*x**3 + 0 - 3/5*x**5 - 3/5*x**u + 0*x + 3/5*x**4 = 0. What is x?
-1, 0, 1
Let y(n) = n**2 + n + 4. Let q(m) = 3 + 4*m**2 + 7 + 6 + 5*m. Let l(h) = -6*q(h) + 22*y(h). Find g such that l(g) = 0.
-2
Let t(d) be the third derivative of -1/60*d**4 + 2/75*d**5 + 0*d + 0 + 0*d**3 - 4/525*d**7 + 1/300*d**6 - d**2. Suppose t(a) = 0. Calculate a.
-1, 0, 1/4, 1
Let w(d) be the third derivative of 0*d**3 - 1/15*d**6 + 2/15*d**5 + 0*d**4 + 0 + 1/105*d**7 + 3*d**2 + 0*d. Factor w(x).
2*x**2*(x - 2)**2
Let s(y) be the third derivative of -y**7/1155 - y**6/110 - 2*y**5/55 - 2*y**4/33 - 6*y**2. Suppose s(b) = 0. Calculate b.
-2, 0
Let k(h) = -h**4 + 6*h**3 + 2*h**2 + 6*h + 5. Suppose -3 = 3*o - 6. Let y(t) = t**3 + t + 1. Let s(u) = o*k(u) - 6*y(u). Factor s(i).
-(i - 1)**2*(i + 1)**2
Let j(k) = -k**3 + k**2 - k + 4. Let w be j(0). Suppose r + r = -u + 10, 0 = w*r - 3*u - 30. Factor 4*f**2 + 4 - r*f - 4*f**2 + 2*f**3.
2*(f - 1)**2*(f + 2)
Let b(i) be the second derivative of 7*i**6/6 - 33*i**5/4 + 55*i**4/12 + 115*i**3/2 + 45*i**2 + 2*i - 13. Factor b(p).
5*(p - 3)**2*(p + 1)*(7*p + 2)
Suppose 4 = -0*f - 5*f + i, -f + 2*i = 8. Let c be (-2 - 36/(-16)) + f. Find d, given that c*d + 1/2*d**2 + 1/4*d**3 + 0 = 0.
-1, 0
Let o(w) be the third derivative of w**5/150 + w**4/10 + 3*w**3/5 + w**2. Factor o(a).
2*(a + 3)**2/5
Factor 2/11*o**3 + 0 + 0*o**2 - 2/11*o.