et n(u) be the first derivative of p(u). Factor n(l).
-2*l*(l + 1)/3
Let z(f) be the second derivative of -f**4/60 - f**3/5 - 9*f**2/10 - 16*f. Determine x so that z(x) = 0.
-3
Factor 0 - 9/4*w**2 - 3/8*w**3 + 0*w.
-3*w**2*(w + 6)/8
Let q(c) = -c**2 + c + 3. Let z be q(0). Let l(r) = 21*r**2 + 24*r + 6. Let v(m) = m. Let o(j) = z*v(j) + l(j). Factor o(h).
3*(h + 1)*(7*h + 2)
Factor -5*j - j - 5*j**2 - j**2 - 2 + 0 - 2*j**3.
-2*(j + 1)**3
Suppose -2*l - 1 = -3*l. Let a be -2 + 0 - -5 - l. Let a*x**3 - 4*x**3 - x + 3*x = 0. Calculate x.
-1, 0, 1
Let x(y) be the first derivative of -y**4/12 - 2*y**3/9 - y**2/6 + 5. Factor x(f).
-f*(f + 1)**2/3
Let c = 193/4 + -48. Suppose 7 = 2*a + 3. Factor 3/4*u - c - 1/2*u**a - 1/4*u**5 + 3/4*u**4 - 1/2*u**3.
-(u - 1)**4*(u + 1)/4
Let 0 + 5/2*b**3 + b + 9/2*b**2 - 9/2*b**4 - 7/2*b**5 = 0. Calculate b.
-1, -2/7, 0, 1
Let l(f) be the third derivative of 5*f**2 + 0*f**5 - 1/630*f**7 + 0*f**4 + 0 + 0*f**3 + 0*f**6 + 0*f - 1/2016*f**8. Determine r so that l(r) = 0.
-2, 0
Let d(c) be the first derivative of 2*c - 6 - 16/3*c**3 - 9/4*c**4 - 5/2*c**2. Let d(z) = 0. What is z?
-1, 2/9
Solve -27 - 12*p**3 + 36*p - 52*p**4 + 6*p**2 + 22*p**4 + 27*p**4 = 0.
-3, 1
Factor 0 + 1/2*f + 1/6*f**2.
f*(f + 3)/6
Suppose 2*r = 3*r + 3*v - 7, 3*v + 17 = 5*r. Factor -r*k**3 - 2/3*k**4 - 8*k - 8/3 - 26/3*k**2.
-2*(k + 1)**2*(k + 2)**2/3
Let d be 0 + 1 + (3 - -1). Let q be (18/10 + -2)/(6/(-135)). Solve 1/4 + 7/4*v + 2*v**4 + q*v**2 + d*v**3 = 0 for v.
-1, -1/2
Let w(f) be the first derivative of 0*f**4 - 4 + 0*f**2 + 1/6*f**3 - 1/4*f - 1/20*f**5. Determine o, given that w(o) = 0.
-1, 1
Solve -84*s**3 - 55*s**4 + 30*s**4 - 41*s**4 - 15*s**5 - 24*s**2 = 0.
-2, -2/5, 0
Let i(q) be the first derivative of -q**7/2940 + q**6/630 + 2*q**3/3 - 1. Let h(b) be the third derivative of i(b). Determine o so that h(o) = 0.
0, 2
Let y(c) be the third derivative of -1/36*c**3 + 7*c**2 + 0 + 1/360*c**5 - 1/720*c**6 + 1/144*c**4 + 0*c. Solve y(n) = 0.
-1, 1
Factor 2*m**4 - 14*m**3 + 14*m**3.
2*m**4
Let o(m) be the second derivative of m**8/1400 + m**7/2100 - m**3/2 - 3*m. Let v(z) be the second derivative of o(z). Suppose v(y) = 0. Calculate y.
-1/3, 0
Let y be (11/(44/(-24)))/(-2). Solve -5/4*n**2 + 0 - 1/2*n - 3/4*n**y = 0.
-1, -2/3, 0
Let q(a) be the second derivative of a + 1/66*a**4 + 0 - 2/33*a**3 + 0*a**2. Find b, given that q(b) = 0.
0, 2
Let g(y) be the third derivative of -y**6/120 + y**5/40 - 5*y**3/6 + 5*y**2. Let n(i) be the first derivative of g(i). Suppose n(x) = 0. Calculate x.
0, 1
Factor 2/9*h**3 - 2/3*h**2 - 2/9*h + 2/3.
2*(h - 3)*(h - 1)*(h + 1)/9
Let j be ((-2)/(-5))/(4/(-40)). Let c be (-22)/j - 4/(-8). Factor 0*k**3 + 2*k**3 + c*k + 3*k**2 - 5*k.
k*(k + 1)*(2*k + 1)
Let p = 5 + -3. Suppose -17*n**3 - 2*n**2 - p*n + 2 + 19*n**3 + 0*n**2 = 0. Calculate n.
-1, 1
Suppose 3*q - 5*x = -x, -12 = -4*x. Let f(u) be the second derivative of 1/18*u**q - u + 0*u**2 + 0 + 1/9*u**3. Factor f(l).
2*l*(l + 1)/3
Solve -9*x**5 + 3*x**4 + 16*x**5 - 10*x**5 - 3*x**2 + 3*x**3 = 0.
-1, 0, 1
Let a = 335 - 333. Factor 2*g**3 - 1/2*g**4 - 3*g**2 + a*g - 1/2.
-(g - 1)**4/2
Factor 6/13*s - 2/13 + 8/13*s**2.
2*(s + 1)*(4*s - 1)/13
Let g(i) be the third derivative of 0*i + 0 - 1/180*i**5 - 4*i**2 + 1/18*i**3 + 1/72*i**4 - 1/360*i**6. Suppose g(c) = 0. What is c?
-1, 1
Let b(t) be the third derivative of 2*t**7/105 - t**5/15 - 8*t**2. Factor b(j).
4*j**2*(j - 1)*(j + 1)
Let s(h) = -4*h**5 - h**4 - h**3 - 4*h**2 - 5*h + 5. Let z(b) = 6*b**5 + 2*b**4 + 2*b**3 + 6*b**2 + 8*b - 8. Let x(f) = 8*s(f) + 5*z(f). Factor x(k).
-2*k**2*(k - 1)**2*(k + 1)
Let y = -2 - -2. Let n(f) = -f + 3. Let w be n(y). Find c, given that -3*c**w - 7*c + 2*c**3 + 8*c = 0.
-1, 0, 1
Suppose -5*v + 7 = -3. Let z be 16/12 - (-2)/3. Solve 3*u**2 + u**3 - u**4 + 2*u**v - 6*u**z + u**3 = 0.
0, 1
Let c(u) be the third derivative of u**7/735 - u**6/420 - 2*u**2. Solve c(g) = 0 for g.
0, 1
Let s = -24 + 56. Let i be ((-4)/16)/((-6)/s). Solve 1/3*g**2 + i + 4/3*g = 0.
-2
Let w(b) = 5*b**3 - 9*b**2 + 5*b + 5. Let k(x) = -4*x**3 + 10*x**2 - 6*x - 6. Let n(q) = -5*k(q) - 6*w(q). Solve n(g) = 0.
0, 2/5
Let m(y) be the second derivative of -y**5/70 + 5*y**4/84 - y**3/21 - y. Suppose m(s) = 0. Calculate s.
0, 1/2, 2
Let o(j) be the first derivative of -j**6/27 + j**4/6 - 4*j**3/27 - 7. Suppose o(u) = 0. Calculate u.
-2, 0, 1
Let d(z) be the first derivative of 7*z**7/30 + 7*z**6/30 + z**5/15 - 3*z**2/2 - 8. Let a(y) be the second derivative of d(y). Factor a(b).
b**2*(7*b + 2)**2
Let t(f) be the first derivative of 0*f**4 + 2/21*f**3 + 0*f**2 - 2/35*f**5 + 0*f - 6. Find a, given that t(a) = 0.
-1, 0, 1
Solve 0*x**3 + 0*x + 0 - 1/3*x**4 + 1/3*x**2 = 0.
-1, 0, 1
Let h(d) = -d**3 + 7*d**2 - d + 10. Let w be h(7). Factor -w*n - 4*n**2 - 12 + 18 + n**2 + 6*n.
-3*(n - 2)*(n + 1)
Let j(x) be the third derivative of x**6/30 + x**3/3 + 2*x**2. Let r(w) = w**4 - 13*w**3 - 7. Let z be 7/(0/1 + -1). Let m(b) = z*j(b) - 2*r(b). Factor m(i).
-2*i**3*(i + 1)
Determine z, given that 1/2*z + 0 + z**2 + 1/2*z**3 = 0.
-1, 0
Find y such that 5*y**4 - 47*y**3 + 11 - 1 + 45*y**2 + 22*y**3 - 35*y = 0.
1, 2
Let r = 20 + -12. Factor 4*w**2 - r*w - 3*w**2 + 5*w**3 - w**3 + 3*w**2.
4*w*(w - 1)*(w + 2)
Let u(x) be the third derivative of -x**6/24 + x**4/24 - 3*x**2. Let g be u(-1). Factor 2*o**4 + o**2 - g*o**2 + 5*o**3 + 7*o**2 - 2*o**2.
o**2*(o + 2)*(2*o + 1)
Let l(m) = -3*m**5 + 9*m**4 - 6*m**3 - 12*m**2 + 3*m - 3. Let g(z) = -3*z**5 + 9*z**4 - 6*z**3 - 11*z**2 + 4*z - 3. Let x(b) = 6*g(b) - 5*l(b). Factor x(i).
-3*(i - 1)**4*(i + 1)
Let p(z) = -z**3 + 6*z**2 - 3*z + 12. Let w be p(8). Let u be 1/(-4) + (-115)/w. Find b such that 0*b + u*b**2 + 2/7*b**3 + 0 = 0.
-2, 0
Let b(x) be the second derivative of -8*x + 0 - 1/16*x**4 - 1/24*x**3 + 3/8*x**2 + 1/80*x**5. Factor b(c).
(c - 3)*(c - 1)*(c + 1)/4
Let u(x) be the third derivative of x**8/336 - x**7/210 - x**6/120 + x**5/60 + 4*x**2. Factor u(p).
p**2*(p - 1)**2*(p + 1)
Let a = 83 + -83. Let f(q) be the first derivative of -1/12*q**6 + 1/8*q**4 + 1/10*q**5 + 0*q + a*q**2 - 3 - 1/6*q**3. Factor f(y).
-y**2*(y - 1)**2*(y + 1)/2
Let m(t) = -3*t**2 + 2*t + 4. Let r(c) = 12 - 1 - 9*c**2 + 2*c + 5*c. Let v(n) = 11*m(n) - 4*r(n). Factor v(q).
3*q*(q - 2)
Suppose -5*n = -j + 28, 3*j - 5*n - 3 - 31 = 0. Find d, given that -d + 1/2*d**j + 1/2*d**2 + 0 = 0.
-2, 0, 1
Factor -5*f**3 - 408*f - 2127*f - 10096 - 889 - 195*f**2.
-5*(f + 13)**3
Let w(a) = 4*a**2 - 17*a + 6. Let b be w(4). Factor 4*v**3 + 0 + 8/3*v**4 + 0*v + 3/2*v**b.
v**2*(4*v + 3)**2/6
Let j(r) be the third derivative of r**8/560 + r**7/140 + r**6/120 - r**3 + 7*r**2. Let n(h) be the first derivative of j(h). Determine q so that n(q) = 0.
-1, 0
Let j(t) be the second derivative of t**5/4 - 35*t**3/6 + 15*t**2 - 32*t. Factor j(k).
5*(k - 2)*(k - 1)*(k + 3)
Let f(u) = u**2 + 8*u - 7. Let p be f(-9). Let -4*w - w**2 - 2*w - p*w**2 = 0. What is w?
-2, 0
Let s(h) be the second derivative of -h**4/38 + 4*h**3/57 - h**2/19 + 21*h. Factor s(q).
-2*(q - 1)*(3*q - 1)/19
Let y(u) = -u + 6. Let v be y(6). Factor 2*h**3 + 0*h**5 - h**5 + h + v*h**5 - 2*h.
-h*(h - 1)**2*(h + 1)**2
Let g(q) be the first derivative of -q**7/420 - q**6/240 + q**5/120 + q**4/48 + q**2 + 3. Let f(i) be the second derivative of g(i). Solve f(k) = 0.
-1, 0, 1
Suppose 3*c = -11 + 11. Factor 1/3*v**2 + c*v + 0.
v**2/3
Let d(o) be the first derivative of o**5/120 + o**4/24 + o**2 - 1. Let c(x) be the second derivative of d(x). Factor c(w).
w*(w + 2)/2
Let b(i) be the second derivative of i**6/75 - i**5/50 - i**4/30 + i**3/15 + 6*i. Suppose b(m) = 0. Calculate m.
-1, 0, 1
Let q = -6 + 15. Factor -10*z**3 - 12*z**4 - 6*z**2 - 11*z + q*z - 11*z**3 + 5*z.
-3*z*(z + 1)**2*(4*z - 1)
Determine v, given that 3*v**3 + 0 + 1/2*v + 2*v**4 + 2*v**2 + 1/2*v**5 = 0.
-1, 0
Let f(l) = -17*l**3 + 5*l**2 + 13*l. Let n(i) = 8*i**3 - 2*i**2 - 6*i. Let s(b) = 6*f(b) + 13*n(b). Factor s(h).
2*h**2*(h + 2)
Let s be (84/70)/((-9)/(-6)). Factor s*r - 4/5 - 1/5*r**2.
-(r - 2)**2/5
Suppose 0 = 6*q - 2*q - 4*i + 8, -5*q - 5*i = -40. Let l(r) be the second derivative of -1/21*r**4 + 0 + 0*r**2 + 0*r**q - r + 1/70*r**5. Solve l(a) = 0 for a.
0, 2
Let y(x) be the first derivative of x**4/30 