4/18 + n**2/6 + 6*n. Suppose w(c) = 0. Calculate c.
-1, 1
Suppose 4/5*m**2 - 4/5*m + 0 = 0. What is m?
0, 1
Let w(p) be the first derivative of 0*p**2 + 1/120*p**6 + 0*p + p**3 - 4 + 0*p**5 - 1/8*p**4. Let q(d) be the third derivative of w(d). Factor q(g).
3*(g - 1)*(g + 1)
Let a be 0 + (-1 - (-4 - 0)). Factor -2*q - q**3 + 4*q - q + a*q.
-q*(q - 2)*(q + 2)
Let m(p) = -p**3 - 5*p**2 + 2. Let v be m(-5). Suppose -4*c**2 - 2*c**2 + 2*c**2 + v*c**2 + 2*c = 0. What is c?
0, 1
What is u in 4/7*u**2 + 6/7*u + 0*u**4 + 2/7*u**5 - 8/7*u**3 - 4/7 = 0?
-2, -1, 1
Suppose -4 = -y - y. Factor -14/5*z**y - 2*z**4 + 2/5*z**5 + 0 + 18/5*z**3 + 4/5*z.
2*z*(z - 2)*(z - 1)**3/5
Let d(t) = -2*t**4 - 30*t**3 - 30*t**2 - 22. Let w(v) = -v**3 - v**2 - 1. Let r(j) = -2*d(j) + 44*w(j). Determine b so that r(b) = 0.
-2, 0
Let m(z) = 2*z**2 + 26*z - 8. Let d be m(-13). Let j = -8 - d. Suppose j + 0*n - 2/3*n**3 + 2/3*n**5 + 2/3*n**2 - 2/3*n**4 = 0. Calculate n.
-1, 0, 1
Let j(a) be the second derivative of -1/9*a**2 - 1/9*a**3 - 3*a - 1/18*a**4 + 0 - 1/90*a**5. Factor j(m).
-2*(m + 1)**3/9
Let -2*o**2 - 2*o**2 - 10*o - 2*o**2 + o**2 = 0. What is o?
-2, 0
Let -5*a**2 + 5*a**3 - 4*a**5 + 5*a**4 + 11*a**5 - 6*a**5 - 6*a**5 = 0. What is a?
-1, 0, 1
Suppose 5*x - 10 - 5 = 0. Find w, given that -3*w**2 + 0*w - 3/2*w**x + 0 = 0.
-2, 0
Let x = -193 - -45. Let h be -3 - 1/(36/x). Solve 2/9*t**5 + 10/9*t - 20/9*t**2 - h*t**4 - 2/9 + 20/9*t**3 = 0.
1
Let u(y) be the third derivative of -y**5/90 + y**3/9 - 38*y**2. Suppose u(t) = 0. Calculate t.
-1, 1
Let s(r) be the third derivative of 0 + 0*r**3 - 5*r**2 + 0*r**4 + 1/200*r**6 - 2/175*r**7 + 0*r + 0*r**5. Factor s(g).
-3*g**3*(4*g - 1)/5
Let o = -30/11 + 178/33. Find s, given that -o + 49/3*s**3 - 42*s**2 + 20*s = 0.
2/7, 2
Suppose 5*v + 5 = 25. Let y(j) = -j**2 + 4*j + 2. Let m be y(v). Suppose -4/5*i**m + 1/5*i**5 + 0 - 4/5*i**4 + 6/5*i**3 + 1/5*i = 0. What is i?
0, 1
Let t(h) be the first derivative of 1/12*h**3 - 1/2*h**2 + 1 + 2*h + 1/24*h**4. Let j(v) be the first derivative of t(v). Let j(w) = 0. What is w?
-2, 1
Factor 3*g**2 + 10*g - 4*g**2 - 4*g**2 - 5.
-5*(g - 1)**2
Let j(w) = -7*w**2 - 2*w + 4. Let z be (114/12)/(1/2). Let u(g) = 33*g**2 - 11*g**2 - z + 6*g + 7. Let f(y) = 16*j(y) + 5*u(y). What is m in f(m) = 0?
-2, 1
Let f(l) = -9*l**3 + 2*l**2 - 5*l + 4. Let x(t) = -10*t**3 + t**2 - 6*t + 5. Let p(y) = 5*f(y) - 4*x(y). Factor p(u).
-u*(u - 1)*(5*u - 1)
Solve -17*i - 12*i**2 + 2*i**4 + 2*i**4 + 9*i = 0.
-1, 0, 2
Let a(p) be the second derivative of -p**7/231 + p**5/22 - 4*p**3/33 + 2*p + 18. Solve a(r) = 0 for r.
-2, -1, 0, 1, 2
Let c(a) be the second derivative of 6*a - 1/16*a**4 + 3/80*a**5 + 0*a**3 + 0 + 0*a**2. Let c(i) = 0. What is i?
0, 1
Let y(i) be the second derivative of 0*i**3 + 0 + 1/60*i**4 + 5*i + 0*i**2. Find o such that y(o) = 0.
0
Let f(k) = -8*k**2 - 6*k. Let i(b) be the first derivative of 3*b**3 + 7*b**2/2 - 4. Let u(z) = -7*f(z) - 6*i(z). Factor u(s).
2*s**2
Let u be 0 + 0 + 3 - -2. Let f(l) be the third derivative of 1/120*l**6 + 1/140*l**7 - 1/40*l**u - 1/24*l**4 + 0*l + 0 + 0*l**3 - l**2. Factor f(i).
i*(i - 1)*(i + 1)*(3*i + 2)/2
Let v(l) be the first derivative of 2*l**3/3 - 3*l**2 + 4*l + 2. Factor v(a).
2*(a - 2)*(a - 1)
Let n = -4/163 - -283/4890. Let y(z) be the second derivative of n*z**5 + 0 + 2*z - 1/135*z**6 - 1/18*z**4 + 0*z**2 + 1/27*z**3. Let y(r) = 0. Calculate r.
0, 1
Let b(l) = l**5 - 6*l**4 - l**3 - 6*l. Let k(c) = c**5 - 5*c**4 - c**3 - 5*c. Let n(q) = -5*b(q) + 6*k(q). Solve n(t) = 0 for t.
-1, 0, 1
Suppose -4*n + 6 = 2*t, 5*n - 35 = 3*t - 0*t. Let z = n - 1. Factor -i**5 - 2*i**3 + 0*i**5 + z*i**5.
2*i**3*(i - 1)*(i + 1)
Let k(d) be the first derivative of 4*d**3/3 - 8*d**2 + 16*d - 7. Factor k(z).
4*(z - 2)**2
Let m(g) be the second derivative of g**7/14 - 3*g**5/20 - 28*g. Factor m(z).
3*z**3*(z - 1)*(z + 1)
Factor -1 - 6*t**2 - 3*t + 0*t - 3*t + t**2.
-(t + 1)*(5*t + 1)
Let r(n) = 2*n - 7. Let f be r(5). Let 2*q**2 - q**f + 4*q**5 - q**5 - 4*q**4 + 0*q**4 = 0. Calculate q.
-2/3, 0, 1
Let s = -14/33 + -21/11. Let k = 31/12 + s. Factor 1/4*d**2 - k*d - 1/2.
(d - 2)*(d + 1)/4
Suppose 0 = -2*y + 5*t + 15, t + 6 = -t. Let n(c) be the second derivative of y + 1/3*c**3 + c**2 - 2*c - 1/6*c**4 - 1/10*c**5. Let n(l) = 0. What is l?
-1, 1
Suppose 5 + 15 = 10*h. Let b(l) be the first derivative of 0*l**h - 3 + 1/6*l**3 + 0*l. Factor b(r).
r**2/2
Let f(z) be the first derivative of z**3 + 9*z - 3 + 9/2*z**2 + 1/12*z**4. Let f(d) = 0. Calculate d.
-3
Suppose -23 = 4*w - w - 5*x, w + 3 = -3*x. Let i be (-16)/w*1 + -2. Factor 2/3*n**4 + 0 + 2/3*n - i*n**3 - 2/3*n**2.
2*n*(n - 1)**2*(n + 1)/3
Let j(f) = 15*f**3 - f**2. Let n be j(1). Suppose 0*u**2 + 9 + 4*u**2 - n*u + 7 + 30*u = 0. Calculate u.
-2
Let i(x) be the second derivative of -x**6/150 + x**5/50 + x**4/60 - x**3/15 - 4*x + 2. Solve i(w) = 0 for w.
-1, 0, 1, 2
Let y be 3/14 - 6/(-21). Factor 1/2 + 0*i - y*i**2.
-(i - 1)*(i + 1)/2
Let c(o) be the first derivative of 4*o**5/5 - 4*o**3 + 4*o**2 - 4. Factor c(h).
4*h*(h - 1)**2*(h + 2)
Let j(q) = -q - 20. Let l be j(-20). Factor -1/3*v**3 - 1/3*v**5 + 0 + l*v + 0*v**2 + 2/3*v**4.
-v**3*(v - 1)**2/3
Let w(r) be the second derivative of 3/5*r**3 - 9/50*r**6 - 2/35*r**7 - 3/50*r**5 + 2/5*r**4 + 0 - 6*r + 3/10*r**2. Let w(x) = 0. What is x?
-1, -1/4, 1
Factor -21/2*k**2 + 0 - 12*k + 3/2*k**3.
3*k*(k - 8)*(k + 1)/2
Let 0*j + 0*j**2 + 8/3*j**4 + 8/3*j**3 + 0 + 2/3*j**5 = 0. Calculate j.
-2, 0
Let y(q) be the third derivative of q**7/525 - q**6/100 + q**5/50 - q**4/60 + 6*q**2. Factor y(i).
2*i*(i - 1)**3/5
Let u(t) be the first derivative of 1/24*t**3 - 1/16*t**4 + 3/80*t**5 + 0*t**2 + 2*t + 1 - 1/120*t**6. Let g(y) be the first derivative of u(y). Factor g(b).
-b*(b - 1)**3/4
Suppose -4*n - 5*p - 18 = -3*n, -3*n + p = -10. Suppose 7*a**2 - 6*a**4 + 2*a**4 - 2*a**5 - 3*a**2 + n*a = 0. What is a?
-1, 0, 1
Let d be 12/56*(-3)/(-27). Let j(n) be the second derivative of d*n**7 - 1/6*n**4 + 2*n - 1/6*n**3 + 0 + 1/15*n**6 + 0*n**5 + 0*n**2. Factor j(z).
z*(z - 1)*(z + 1)**3
Let 5/4*k**2 + k - 1/4 = 0. What is k?
-1, 1/5
Determine u, given that -10*u**3 + 52/5*u**2 - 2*u + 0 + 8/5*u**4 = 0.
0, 1/4, 1, 5
Let p(h) be the first derivative of h**5/5 - h**4 + 4*h**3/3 + 6. Factor p(o).
o**2*(o - 2)**2
Let x(a) = 29*a**4 + 135*a**3 + 154*a**2 + 85*a + 26. Let t(d) = 6*d**4 + 27*d**3 + 31*d**2 + 17*d + 5. Let f(r) = -11*t(r) + 2*x(r). Let f(p) = 0. What is p?
-1, -3/8
Let p(j) = 3*j**4 + 8*j**3 - 13*j**2 - 12*j + 10. Let l(b) = -15*b**4 - 39*b**3 + 66*b**2 + 61*b - 51. Let u(k) = -4*l(k) - 22*p(k). Solve u(s) = 0 for s.
-4, -1, 2/3, 1
Let w be (8/30)/(10/75). Solve -3/5*u + 1/5*u**3 + 0 + 2/5*u**w = 0 for u.
-3, 0, 1
Let d(m) be the first derivative of m**8/210 + m**7/140 - m**6/180 - m**3/3 - 1. Let n(v) be the third derivative of d(v). Suppose n(f) = 0. What is f?
-1, 0, 1/4
Let g(i) be the first derivative of -i**4/18 - 4*i**3/27 + 5*i**2/9 + 4*i/3 + 41. Let g(k) = 0. What is k?
-3, -1, 2
Let a = -45 - -50. Find i, given that -2/3*i**4 - 4/3*i**3 + 2/3*i**a - 2/3 + 4/3*i**2 + 2/3*i = 0.
-1, 1
Let d(n) be the third derivative of -n**7/2520 + n**6/540 - n**5/360 - n**3 - 9*n**2. Let v(z) be the first derivative of d(z). Factor v(t).
-t*(t - 1)**2/3
Let l(q) be the first derivative of -3*q**4/4 - q**3 - 12. Find k such that l(k) = 0.
-1, 0
Let a(w) be the second derivative of w**4 + 0 + 0*w**3 + 0*w**2 - 6*w + 4/5*w**5 + 2/15*w**6. Factor a(p).
4*p**2*(p + 1)*(p + 3)
Suppose -138/11*s**3 - 1920/11*s + 6/11*s**4 + 1008/11*s**2 - 3072/11 = 0. Calculate s.
-1, 8
Let j(a) be the first derivative of a**7/210 - a**5/30 + a**3/6 + a**2/2 - 2. Let x(d) be the second derivative of j(d). Factor x(v).
(v - 1)**2*(v + 1)**2
Let h be (-7)/5*(-14)/49. Factor -h*c**3 + 0 + 0*c + 2/5*c**2.
-2*c**2*(c - 1)/5
Let l be -2 + 9*4/6. Suppose -l*t = -1 - 11. Factor a**4 - 15*a + 2*a**t + 15*a.
a**3*(a + 2)
Let g(c) = -4*c**3 + 10*c**2 + 26*c - 21. Let d(b) = b**3 - 2*b**2 - 5*b + 4. Let v(z) = 33*d(z) + 6*g(z). Let v(t) = 0. Calculate t.
-1, 2/3, 1
Let g(n) be the third derivative of n**5/90 - n**4/36 + 8*n**2. Determine r so that g(r) = 0.
0, 1
Let z(j) = j**3 - 5*j**2 + 5*j - 2. Let r be z(4). Let c be (-5)/r*8/(-70)