2
Let s(b) be the first derivative of -b**6/200 + 7*b**5/300 - b**4/60 - b**2/2 - 5. Let u(d) be the second derivative of s(d). Factor u(l).
-l*(l - 2)*(3*l - 1)/5
Let h(v) = -5*v**3 - 41*v**2 - 6*v + 30. Let w(u) = u**3 + 8*u**2 + u - 6. Let g(q) = 4*h(q) + 22*w(q). Solve g(k) = 0.
-6, -1, 1
Let h(x) be the third derivative of -x**9/15120 + x**8/1680 - x**7/504 + x**6/360 - 5*x**4/12 + x**2. Let g(n) be the second derivative of h(n). Factor g(i).
-i*(i - 2)*(i - 1)**2
Let w(l) = -l**4 + l. Let z(h) = 6*h**4 - 2*h**3 - 3*h**2 - 4*h + 7. Let i(d) = d - 1. Let m(u) = 3*i(u) + z(u). Let t(a) = m(a) + 5*w(a). Factor t(c).
(c - 2)**2*(c + 1)**2
Factor -4*t + 2 - t + t**2 + 2*t**2 + 0*t.
(t - 1)*(3*t - 2)
Let f = -3/1841 + -38610/31297. Let j = f + 135/68. Factor -1/2 - 1/4*c**2 + j*c.
-(c - 2)*(c - 1)/4
Let r(d) be the second derivative of -d**4/18 + d**3/9 + 2*d**2 - 2*d. Factor r(f).
-2*(f - 3)*(f + 2)/3
Let i be (-35)/10*24/(-14). Suppose 0 = 6*d - 4*d - i. Factor 0*m**2 + 3*m**2 + 5*m**3 + 9*m**4 + 4*m**3 + d*m**5.
3*m**2*(m + 1)**3
Let v(y) = y**3 - 4*y**2 + 2*y - 3. Let z be v(3). Let x(h) = -h - 3. Let p be x(z). Factor 2*f**4 - f**p + f**2 + 3*f**3 + f**3.
f**2*(f + 1)*(2*f + 1)
Find f, given that -1 - 1/2*f**3 + 3/2*f + 0*f**2 = 0.
-2, 1
Suppose -8 = i - 5*i. Determine v so that -2 - 8*v - 6 + 10 + 2*v**4 - 4*v**i + 16*v**3 - 8*v**5 = 0.
-1, 1/4, 1
Let s = 1 - 2. Let p = 2 - s. Determine k so that -2*k + 4 - 4*k**2 + 4*k + p*k - 3*k - 2*k**3 = 0.
-2, -1, 1
Let p be (-23 - -19)/((-38)/5). Factor 0 + 2/19*g**2 + p*g**3 + 0*g + 8/19*g**4.
2*g**2*(g + 1)*(4*g + 1)/19
Let z = 17 + -15. Factor 7*u - 2*u**3 - 2*u**2 + z*u**4 - 3*u - 2*u.
2*u*(u - 1)**2*(u + 1)
Let u(m) = m - 23. Let n be u(26). Determine p, given that 1/7*p**5 + 2/7 - 4/7*p**2 + 1/7*p + 2/7*p**4 - 2/7*p**n = 0.
-2, -1, 1
Factor 4*f - 1 + 3 + 3 + 3 - 12*f**2.
-4*(f - 1)*(3*f + 2)
Let g(b) = -b**4 + b**3 - b**2 + b - 1. Let y(x) = -8*x**4 - 22*x**3 + 32*x**2 - 2*x + 2. Let t(f) = 10*g(f) + y(f). Determine s, given that t(s) = 0.
-1, 2/3
Solve -1/2*y**5 - 6*y**2 - 2*y - 3*y**4 + 0 - 13/2*y**3 = 0 for y.
-2, -1, 0
Let r(j) = j**3 + 12*j**2 - 2*j - 21. Let q be r(-12). Let o be q/9 + -2 - -2. Factor -m + m**2 + o - 1/3*m**3.
-(m - 1)**3/3
Factor -1/3*u - 2/3 + 2/3*u**2 + 1/3*u**3.
(u - 1)*(u + 1)*(u + 2)/3
Suppose -2*k = 2*k - 8. Factor p**3 - p**2 - 2*p**4 - k*p**5 + 3*p**4 + p**5 + 0*p**2.
-p**2*(p - 1)**2*(p + 1)
Let b(u) = -8*u**2 - 16*u + 4. Let v(y) = 7*y**2 + 16*y - 3. Let l(q) = -3*b(q) - 4*v(q). Factor l(j).
-4*j*(j + 4)
Let u(a) = -a - 5. Let d be u(-5). Suppose 0 = -d*c + 4*c - 4. Find z such that z + c + 1/4*z**2 = 0.
-2
Let v = 51 - 51. Find n such that 0*n - 2/3*n**2 + v = 0.
0
Let w = 11 - 5. Find b such that -6*b**3 - 1 + 0 - 3*b**4 + w*b + 4 = 0.
-1, 1
Let g(y) be the first derivative of -y**5/30 - y**4/3 - 4*y**3/3 - 2*y**2 + 8. Let l(r) be the second derivative of g(r). Let l(p) = 0. Calculate p.
-2
Let s(r) be the third derivative of -r**5/420 - r**4/168 + 13*r**2. What is a in s(a) = 0?
-1, 0
Suppose 0 = -5*n + 2*m - 5, 3*n + m - 8 = 0. Let i(s) be the first derivative of 1/12*s**3 + 1/4*s - 1/4*s**2 + n. Find y such that i(y) = 0.
1
Let z be -1 + -2 + -8 + 7 - -6. Let r(v) be the first derivative of 2*v**4 + 4 + 10/3*v**3 + 0*v + v**z. Solve r(n) = 0 for n.
-1, -1/4, 0
Let h(s) be the second derivative of -s**8/2240 - s**7/210 - s**6/48 - s**5/20 - s**4/12 - 3*s. Let d(l) be the third derivative of h(l). Factor d(q).
-3*(q + 1)**2*(q + 2)
Suppose 2*v = -2*p, 20 = 5*v - 2*p - 8. Let 4*g**4 + g + 3*g**3 + v*g**2 - g**2 - 3*g**4 = 0. Calculate g.
-1, 0
Let d be (-8)/2 - (-2 + (-6)/3). Let w(r) be the third derivative of 0*r**4 + 1/6*r**3 + 1/210*r**7 - 1/30*r**5 + 0*r + d + 0*r**6 - 4*r**2. Factor w(k).
(k - 1)**2*(k + 1)**2
Let m(d) = -2 - 2 - 5*d + 1 - 1 + d**3 + 2*d**2. Let r be m(-3). Solve 2*h + 3*h + r*h - 6*h + h**2 = 0.
-1, 0
Suppose 0 = x - 2*x + 13. Let f = -9 + x. Suppose -6/5*k**5 + 2/5 - 14/5*k**f + 2*k + 12/5*k**2 - 4/5*k**3 = 0. What is k?
-1, -1/3, 1
Find b such that -3/2*b**3 + 0 + 0*b - 3/2*b**2 = 0.
-1, 0
Let s be 1/(4*3/8). Let 0*h + 0 + s*h**2 = 0. Calculate h.
0
Determine u, given that -30*u**2 - 19*u**3 - 5*u**4 + 200*u - 125 + 38*u**3 - 36*u**3 - 23*u**3 = 0.
-5, 1
Let w be 1 - (3 - (-1)/((-9)/30)). Factor 0*v + 2/3*v**2 + 0 + w*v**3.
2*v**2*(2*v + 1)/3
Let h(n) be the second derivative of n**4/6 + 2*n**3/3 + n**2 + 4*n. Determine z so that h(z) = 0.
-1
Let i = 353/730 - -6/365. Find s, given that 1/2*s**3 + 3/2*s**2 + i + 3/2*s = 0.
-1
Let r(f) be the first derivative of 2*f**3/3 + f**2 - f + 4. Let v be r(-2). Determine q so that 0 + 0*q + 1/3*q**4 - 1/3*q**v + 0*q**2 = 0.
0, 1
Suppose 338*m - 16 = 334*m. What is r in 0*r + 0 + 4/7*r**5 + 4/7*r**m + 0*r**3 + 0*r**2 = 0?
-1, 0
Let l(z) be the second derivative of -5*z**4/12 + 5*z**3 - 25*z**2/2 + 51*z. Factor l(w).
-5*(w - 5)*(w - 1)
Let l(o) be the second derivative of o**7/840 + o**6/360 - o**3/2 - 2*o. Let a(f) be the second derivative of l(f). Factor a(q).
q**2*(q + 1)
Let n = -1/63 - -85/63. Factor 2/3*j**2 - n*j + 2/3.
2*(j - 1)**2/3
Let a be ((-2)/6)/(10/(-30)). Suppose 10*d + a - 3*d**2 - d**4 - 9*d - 1 + 3*d**3 = 0. Calculate d.
0, 1
Let d = 2557/18 - 142. Let w(q) be the third derivative of -1/180*q**6 - 1/18*q**4 - 1/36*q**5 + 0 + 3*q**2 + 0*q - d*q**3. Factor w(k).
-(k + 1)**2*(2*k + 1)/3
Determine t, given that 0 + 0*t - 2/5*t**3 - 2/5*t**2 = 0.
-1, 0
Suppose 7*s = 4*s - 9, i + 18 = -4*s. Let w = 8 + i. Factor -3/2 - 3*v - 3/2*v**w.
-3*(v + 1)**2/2
Let r(n) be the third derivative of -n**7/70 - n**6/20 + n**5/5 + n**4 - 39*n**2. Factor r(p).
-3*p*(p - 2)*(p + 2)**2
Factor -4/7*l + 0 + 2/7*l**3 + 2/7*l**2.
2*l*(l - 1)*(l + 2)/7
Determine p, given that 5*p**2 - 2*p**3 + 2*p**3 - 2*p**4 + 3*p**2 = 0.
-2, 0, 2
Let z(s) be the second derivative of s**5/80 - s**4/24 - s. Factor z(r).
r**2*(r - 2)/4
Let m(w) = 3*w**2 + 8*w - 16. Let k(g) = -g**2 - 4*g + 8. Let i(x) = 5*k(x) + 3*m(x). Factor i(u).
4*(u - 1)*(u + 2)
Let t(q) be the third derivative of q**8/1512 + q**7/189 + q**6/90 - q**5/135 - 7*q**4/108 - q**3/9 - 12*q**2. Determine l so that t(l) = 0.
-3, -1, 1
Let q(x) be the second derivative of 2*x + 0 - 1/21*x**3 - x**2 - 1/42*x**4 - 1/210*x**5. Let h(w) be the first derivative of q(w). Factor h(g).
-2*(g + 1)**2/7
Let k(g) be the third derivative of -1/24*g**4 + 1/120*g**6 - 1/210*g**7 + 0*g**3 + 0 + 1/60*g**5 - g**2 + 0*g. Factor k(f).
-f*(f - 1)**2*(f + 1)
Find a, given that 2/23*a**5 - 4/23*a**4 + 0*a**3 + 0 - 2/23*a + 4/23*a**2 = 0.
-1, 0, 1
Let h be 2*(-2 - -10)/48. Find d, given that 0 - 1/3*d + h*d**2 = 0.
0, 1
Let v(n) = 5*n**3 - 26*n**2 + 4*n - 5. Let s be 3/(-6) - (-67)/2. Let a(r) = r**3 - 5*r**2 + r - 1. Let f(y) = s*a(y) - 6*v(y). Factor f(m).
3*(m - 1)**3
Let l(z) be the second derivative of -27*z**5/20 - 3*z**4/4 + 5*z**3/2 - 3*z**2/2 - 5*z. Suppose l(i) = 0. Calculate i.
-1, 1/3
Let x(r) = -7*r**3 + r**2 + 3*r + 2. Let t be x(-1). Factor 12*a**3 + t*a**2 + 6 + a**4 + a**4 + 17*a**2 + 20*a.
2*(a + 1)**3*(a + 3)
Solve 1/2 - 1/6*i**2 + 1/3*i = 0 for i.
-1, 3
Factor -15/2*l**3 - 5/2*l**2 + 0 + 5/2*l**4 + 15/2*l.
5*l*(l - 3)*(l - 1)*(l + 1)/2
Let y = -24 - -17. Let k(n) = 5*n**5 - 3*n**4 - n**3 - n**2 - 4. Let h(g) = 9*g**5 - 6*g**4 - g**3 - 2*g**2 - 7. Let u(a) = y*k(a) + 4*h(a). Factor u(c).
c**2*(c - 1)**3
Let b(c) = 9*c**2 + c + 5. Let z = 8 + -4. Let v be 1/z + 19/4. Let f(r) = -5*r**2 - r - 3. Let y(w) = v*f(w) + 3*b(w). Factor y(h).
2*h*(h - 1)
Let u(z) be the third derivative of 49*z**6/120 - 7*z**5/15 + z**4/6 + 2*z**2. Solve u(r) = 0.
0, 2/7
Let t(g) = 7*g - g + 3*g**2 - 6*g - 1. Let x be t(1). Suppose 7/3*q**x - 2/3 - 5/3*q = 0. What is q?
-2/7, 1
Let k(i) be the first derivative of -3*i**4/28 - 4*i**3/21 + i**2/14 + 2*i/7 + 39. Factor k(z).
-(z + 1)**2*(3*z - 2)/7
Let l be 1 - -3 - (-2)/(-1). Let d(u) be the third derivative of 1/90*u**5 + 0*u**3 + 0*u + 0 + 1/36*u**4 - u**l. Factor d(q).
2*q*(q + 1)/3
Let a(h) be the second derivative of -2*h + 1/4*h**4 + 0 + 0*h**3 + 3/20*h**5 + 0*h**2. Factor a(s).
3*s**2*(s + 1)
Let g(o) = -o**2 + 22*o - 48. Suppose -5*d - 45 = -0*d. Let k(h) = -3*h**2 + 87*h - 192. Let t(v) = d*g(v) + 2*k(v). Suppose t(p) = 0. Cal