n**5/10 + 7*n**4/18 - 5*n**3/9 + n**2/3 + 3*n + 1. Let o(h) be the first derivative of z(h). Factor o(t).
-2*(t - 1)**2*(3*t - 1)/3
Let r be ((-2)/(-10))/(28/35). Let s(m) be the second derivative of r*m**2 + 0 + 1/40*m**5 + 1/4*m**3 - 2*m + 1/8*m**4. Factor s(n).
(n + 1)**3/2
Suppose 4*c - 4*u - 16 = 0, 6 = c - 4*u - 10. Suppose 2*n + c*n = 0. Let -1/3*a**2 + 0 + n*a = 0. Calculate a.
0
Suppose 0 = 12*w - 5*w. Determine v so that 1/4*v**3 + v + w + v**2 = 0.
-2, 0
Find h, given that 24/5*h - 3/5*h**5 + 36/5*h**2 + 6/5*h**3 + 0 - 9/5*h**4 = 0.
-2, -1, 0, 2
Let v(t) be the third derivative of 0*t + t**2 + 0 + 0*t**3 + 0*t**4 - 1/120*t**6 + 0*t**5. Factor v(f).
-f**3
Suppose -8 = 5*z - 28. Suppose -3*n + 3*w = -0*n - 3, z*w - 8 = -2*n. Solve 4/5*g + 2/5*g**n + 2/5 = 0 for g.
-1
Let x(m) be the second derivative of m**7/42 - m**6/6 + 9*m**5/20 - 7*m**4/12 + m**3/3 - 22*m. Factor x(o).
o*(o - 2)*(o - 1)**3
Suppose z + 4*z = 30. Let m be (8/24)/(8/z). Factor 1/4*s**3 - m*s - 1/4*s**2 + 1/4*s**4 + 0.
s*(s - 1)*(s + 1)**2/4
Let t(f) be the second derivative of 11/80*f**5 + 5/16*f**4 + 1/40*f**6 + 1/4*f**2 + 3/8*f**3 + 4*f + 0. Factor t(k).
(k + 1)**3*(3*k + 2)/4
Let g(i) = -i**4 + 7*i**3 + 12*i**2 - i - 8. Let m(w) = -12*w**4 + 76*w**3 + 132*w**2 - 12*w - 88. Let f(l) = 32*g(l) - 3*m(l). Find s, given that f(s) = 0.
-1, 1, 2
Let j(g) = -g**2 + g + 1. Let h(b) = -3*b**2 + 4*b + 2. Let q(f) = -3*h(f) + 6*j(f). Factor q(v).
3*v*(v - 2)
Let u(z) = -11*z**3 + 24*z**2 - 39*z + 6. Let k(l) = -l**3 - l**2 + l + 1. Let y(o) = 6*k(o) - u(o). Factor y(j).
5*j*(j - 3)**2
Let a(j) be the third derivative of j**8/224 - j**7/70 - 15*j**2. Factor a(m).
3*m**4*(m - 2)/2
Let a(k) be the first derivative of -k**8/336 + k**7/70 - k**6/40 + k**5/60 + k**2 - 1. Let o(f) be the second derivative of a(f). Factor o(c).
-c**2*(c - 1)**3
Let y(p) be the first derivative of p**6/3 - 6*p**5/5 + 3*p**4/2 - 2*p**3/3 + 6. Find v, given that y(v) = 0.
0, 1
Suppose 2*k = 5*h - 14, -k = 4*h - 1 - 18. Let d(y) = 2*y - 3. Let o be d(h). Factor -o*n - 2 + n**3 - 4*n**3 + 8*n**3 - n**2 + 3*n**4.
(n - 1)*(n + 1)**2*(3*n + 2)
Let w be 4/20 + (-57)/(-15). Factor w*b**3 + 0*b**2 - 5*b + 7*b - 8*b**2 + 2*b.
4*b*(b - 1)**2
Let w be 4/(-22) + 414/99. Let i(t) be the first derivative of 2*t + 0*t**3 + 3/2*t**2 - 1/4*t**w - 3. Solve i(f) = 0.
-1, 2
Let w be (-3)/(-2)*2 + -3. Let -t**2 - 8*t + 6 + w - t**2 + 4*t**2 = 0. Calculate t.
1, 3
Let k be 6*(2/(-4) - (-28)/35). Factor 0*q**4 + 3/5*q**2 + 0*q - k*q**3 + 0 + 12/5*q**5.
3*q**2*(q + 1)*(2*q - 1)**2/5
Let m be 1/3*0/6. Let q be (0 - m)/((-3)/3). Factor q + 2/9*n**2 + 2/9*n.
2*n*(n + 1)/9
Factor 15/4*y**2 - 9/4*y**3 + 0 + 3/4*y**5 - 3/4*y**4 - 3/2*y.
3*y*(y - 1)**3*(y + 2)/4
Let k(n) be the third derivative of n**8/84 + 8*n**7/105 + n**6/5 + 4*n**5/15 + n**4/6 + 26*n**2. Factor k(c).
4*c*(c + 1)**4
Let a(k) be the first derivative of 4*k + 1/5*k**3 + 1/30*k**4 + 2/5*k**2 + 3. Let o(g) be the first derivative of a(g). Determine n, given that o(n) = 0.
-2, -1
Factor -8/11*h**2 + 8/11*h + 2/11*h**3 + 0.
2*h*(h - 2)**2/11
Let a(r) be the second derivative of 5*r - 1/27*r**4 + 2/9*r**2 + 0 + 1/9*r**3 - 1/30*r**5. Factor a(c).
-2*(c - 1)*(c + 1)*(3*c + 2)/9
Let x(v) = -9*v**2 + 38*v + 11. Let l(r) be the second derivative of -r**4/4 + 13*r**3/6 + 2*r**2 + 6*r. Let o(j) = -11*l(j) + 4*x(j). Factor o(w).
-3*w*(w - 3)
Let q = -6058/15 - -404. Let w(y) be the first derivative of 0*y**2 - 1/3*y**4 + 2/9*y**3 + 0*y - 3 + q*y**5. Let w(r) = 0. What is r?
0, 1
Let y = 281/566 + 1/283. Let 0 + y*n - 1/4*n**2 - 1/4*n**3 = 0. What is n?
-2, 0, 1
Suppose -4*k = 5*g + 28, 6*k - 4 = -g + 2*k. Let x be (-22)/g + (-1)/(-4). Factor 5*o**3 - o**x - 7*o - 8*o**2 - 2*o**3 + 15*o.
2*o*(o - 2)**2
Let k(d) = -3*d**3 - 2*d**2 - d. Let h be k(-1). Factor 3*n**2 - 3*n**2 + h*n**2.
2*n**2
Let k be 4/5*(-25)/10. Let i be ((-3)/k)/(108/96). Factor 2*c**2 - i*c**3 + 8/3*c - 8/3 - 2/3*c**4.
-2*(c - 1)**2*(c + 2)**2/3
Let x(j) = -j**4 - 2*j**3 + 6*j**2 - 4*j + 1. Let h be 6/9*3*-1. Let n(o) = -2*o**4 - o**3 + 6*o**2 - 4*o + 1. Let c(u) = h*n(u) + 3*x(u). Factor c(m).
(m - 1)**4
Let c be 9/(-25)*(-75)/30. Let s(w) be the second derivative of 0 - 6*w**3 - 6*w**2 - c*w**5 + 3*w - 13/4*w**4 - 1/10*w**6. Factor s(f).
-3*(f + 1)**2*(f + 2)**2
Factor -8/5*h**4 + h**5 + 0*h + 2/5*h**2 + 1/5*h**3 + 0.
h**2*(h - 1)**2*(5*h + 2)/5
Let -2/9*p**2 + 4/9*p + 2/3 = 0. Calculate p.
-1, 3
Let d(v) be the second derivative of 3*v**5/20 - v**4/4 - 11*v**3/6 - 3*v. Let p(x) = x. Let c(z) = -d(z) - 5*p(z). Solve c(s) = 0.
-1, 0, 2
Let d(f) = -3*f**2 - 2*f + 1. Let y(x) = -16*x**2 - 11*x + 5. Suppose b - 18 = -4*b + 2*z, -4*b + 3*z = -13. Let j(l) = b*y(l) - 22*d(l). Factor j(r).
2*(r - 1)*(r + 1)
Let s(d) be the third derivative of 2*d**7/105 + d**6/15 + d**5/15 - 9*d**2. Determine r, given that s(r) = 0.
-1, 0
Let q(c) be the first derivative of c**3/2 - 3*c**2/4 - 3*c + 1. Factor q(o).
3*(o - 2)*(o + 1)/2
Let x be 196/(-10) + 22/(-55). Let l be ((-6)/(-10))/((-4)/x). Suppose -2*n + 2*n**4 + 2/3*n**5 - 2/3 - 4/3*n**2 + 4/3*n**l = 0. What is n?
-1, 1
Let q(i) be the third derivative of -i**8/224 - i**7/35 - i**6/20 + i**5/20 + 5*i**4/16 + i**3/2 + 10*i**2. Suppose q(g) = 0. What is g?
-2, -1, 1
Let s(q) be the third derivative of q**10/30240 - q**8/6720 - q**4/24 + 3*q**2. Let g(n) be the second derivative of s(n). Let g(v) = 0. What is v?
-1, 0, 1
Let l(n) = -9*n - 4. Let h(j) = -j**2 + j + 1. Let r(x) = 10*h(x) + 2*l(x). Determine w so that r(w) = 0.
-1, 1/5
Let a = 50 - 249/5. Let r = -23/35 + 6/7. Factor -r*z**2 + 2/5*z - a.
-(z - 1)**2/5
Let o(k) be the first derivative of -20*k**3/27 - 7*k**2/9 + 2*k/3 - 36. Suppose o(c) = 0. What is c?
-1, 3/10
Suppose -2*b + 18 = 3*j - 4, -4*b + 34 = j. Let w = b - 4. Factor 2*m**3 + 1/2*m**2 + m**5 + 0 + 0*m + 5/2*m**w.
m**2*(m + 1)**2*(2*m + 1)/2
Let t(u) be the second derivative of -u**5/25 + 2*u**3/15 - 3*u. Determine l, given that t(l) = 0.
-1, 0, 1
Suppose -3*j + 3*l = 12, -4*j + 2 = 4*l - 14. Suppose j = 3*m - 3 - 3. Let -8*r**2 + 0*r**5 - 8*r**4 - m*r**5 - 12*r**3 - 2*r + 0*r**4 = 0. Calculate r.
-1, 0
Factor 9*l**2 - 35*l**2 + 8*l - 2*l**2.
-4*l*(7*l - 2)
Let q(j) = 16*j**4 - 12*j**3 - 4*j**2 + 12*j. Let y(m) = m**4 + m**2 + m. Let a(u) = q(u) - 12*y(u). Factor a(w).
4*w**2*(w - 4)*(w + 1)
Suppose 3*s - 3*g - 1 = 11, 20 = 5*s + 3*g. Suppose 3*y + 4 = s*y. Factor 3/4*p**2 + 1/4*p**y + 1/4*p + 0 + 3/4*p**3.
p*(p + 1)**3/4
Let p(v) = -3*v**2 - 7*v + 2. Let j(m) = m**2 + m. Let t be -4 - (-2)/4*0. Let g(k) = t*j(k) - p(k). Let g(w) = 0. What is w?
1, 2
Let z(m) be the first derivative of -3/5*m**2 + 2/5*m + 2/5*m**3 - 6 - 1/10*m**4. Determine i, given that z(i) = 0.
1
Let t(i) be the first derivative of -i**6/1620 - i**5/180 - i**4/54 + 2*i**3/3 - 3. Let w(g) be the third derivative of t(g). Factor w(a).
-2*(a + 1)*(a + 2)/9
Let l(s) be the second derivative of s**4/6 + 2*s**3/3 + 7*s. Find p such that l(p) = 0.
-2, 0
Let z(j) = j**3 + 11*j**2. Let w be z(-11). Let v be 1*(w/4 - -2). Let 4/3 + 2/3*n**v - 2*n = 0. What is n?
1, 2
Let l(i) be the first derivative of i**6/10 - i**4/2 + 3*i**2/2 + 3*i - 2. Let c(j) be the first derivative of l(j). Factor c(b).
3*(b - 1)**2*(b + 1)**2
Let m = 22 - 20. Let k(v) be the first derivative of 10/3*v**3 + 3*v**2 + m - 4*v. Solve k(l) = 0 for l.
-1, 2/5
Let i(a) be the first derivative of 11/8*a**4 - 1/2*a**2 - 2 + 5/6*a**3 + 0*a + 2/5*a**5. Find d such that i(d) = 0.
-2, -1, 0, 1/4
Solve 4*p**2 - 9 + p**2 - 2*p**2 - 3 = 0.
-2, 2
Suppose s = -4*j + 2, -3*j + 12 - 2 = 5*s. Factor -8/3*x - x**s - 4/3.
-(x + 2)*(3*x + 2)/3
Let z(y) = -13*y**2 + 1. Let w be z(-1). Let p be -1 - (-3 - w/(-2)). Solve 0*m**2 + m**4 + 2*m**2 - 8*m**3 - 3*m**4 + p*m**5 = 0.
-1, 0, 1/4, 1
Let n be (24/10)/((-3)/50). Let b be (n/(-70))/(2/7). Solve 2/5*i**2 + 8/5 - 16/5*i - b*i**4 + 14/5*i**3 + 2/5*i**5 = 0 for i.
-1, 1, 2
Suppose -3*y - n - 53 = -0*n, 3*y - 3*n = -57. Let u(p) = -p. Let x(t) = -t**2 + 6*t - 2. Let h(i) = y*u(i) - 2*x(i). What is f in h(f) = 0?
-2, -1
Let j(l) be the third derivative of 0 + 0*l - 1/24*l**3 + 1/480*l**6 + l**2 - 1/96*l**4 + 1/240*l**5. Factor j(u).
(u - 1)*(u + 1)**2/4
Let p(u) be the first derivative of 2/5*u**