Let k(a) be the second derivative of 0*a**2 + 0 + 2/3*a**4 - 2/3*a**3 + 2*a + 21/20*a**i. Let k(o) = 0. What is o?
-2/3, 0, 2/7
Suppose -9*a**3 + 12*a**3 - a**3 = 0. What is a?
0
Let t(j) be the second derivative of -j**6/120 + 3*j**5/40 - 2*j**3/3 + 7*j. Let v(n) be the second derivative of t(n). Factor v(x).
-3*x*(x - 3)
Let f(c) be the first derivative of 3 + 4/7*c + 6/7*c**3 - 5/14*c**4 + 2/35*c**5 - c**2. Factor f(w).
2*(w - 2)*(w - 1)**3/7
Factor -3/4*g**5 + 0 - 21/4*g**2 - 15/4*g**4 - 3/2*g - 27/4*g**3.
-3*g*(g + 1)**3*(g + 2)/4
Let g be (-14 - (-1586)/117)/(4/(-18)). Factor 0 + 3/8*s + 3/8*s**g.
3*s*(s + 1)/8
Let l(a) be the second derivative of -a**6/6 - 3*a**5/4 - 5*a**4/12 + 5*a**3/2 + 5*a**2 + 14*a. Factor l(c).
-5*(c - 1)*(c + 1)**2*(c + 2)
Suppose 13/2*g + 3 - 4*g**2 = 0. Calculate g.
-3/8, 2
Let z(r) be the second derivative of r**5/10 + 5*r**4/6 - 2*r**3 - 12*r + 3. Let z(h) = 0. What is h?
-6, 0, 1
Let q = -4 + 8. Find w such that w**5 - 3*w - 2*w**3 + 2*w**4 - 2*w**4 + q*w = 0.
-1, 0, 1
Factor 19*f**3 - 26*f**3 - 24*f**2 + 11*f**3 - 16 + 36*f.
4*(f - 4)*(f - 1)**2
Let q(k) = 6*k**3 - 9*k**2 + 4*k + 5. Let j(o) = -7*o**3 + 10*o**2 - 4*o - 6. Suppose h - 9 = y, 2*y + 0*y + h + 6 = 0. Let l(n) = y*j(n) - 6*q(n). Factor l(t).
-t*(t - 2)**2
Let h(u) = 3*u**4 - 9*u**3 + 3*u**2 + 3. Let y(i) = i**4 - 4*i**3 + 2*i**2 + 1. Let v(x) = -4*h(x) + 9*y(x). Solve v(b) = 0.
-1, 1
Find s such that -26/7*s**2 - 22/7*s**3 - 4/7*s + 0 = 0.
-1, -2/11, 0
Let i(x) be the third derivative of x**2 + 0 + 0*x**3 + 0*x + 1/120*x**6 + 0*x**4 - 1/120*x**5. Determine v, given that i(v) = 0.
0, 1/2
What is j in -16/7 + 40/7*j - 4*j**2 + 6/7*j**3 = 0?
2/3, 2
Let v(h) be the third derivative of 0 + h**2 + 0*h - 1/84*h**8 - 4/105*h**7 + 7/60*h**5 + 1/12*h**4 + 1/40*h**6 + 0*h**3. Determine z so that v(z) = 0.
-2, -1/2, 0, 1
Let b be 1/((-21)/(-6) + -3). Let g = b + 1. Solve -m**g - 1/2 + m + 1/2*m**4 + 0*m**2 = 0.
-1, 1
Suppose -2*k + 32 = -w - 3*w, 2*k + w = 22. Factor -6*h**4 + 11 + 6*h**3 - 3 - k*h + h**5 + 5*h**3 - 2*h**2.
(h - 2)**3*(h - 1)*(h + 1)
Let b(o) be the second derivative of -o**4/18 + o**3/3 + 6*o. Factor b(f).
-2*f*(f - 3)/3
Suppose i + 96 = 5*i. Suppose 5*d + 2*x = -x + i, -d = -2*x + 3. Factor 2*y**2 - 6*y**d + 3*y**3 - y + 2*y**3.
-y*(y - 1)**2
Let v(g) be the first derivative of -3*g**5/10 + g**4/3 + g**3 - 2*g**2 + 7*g + 3. Let d(f) be the first derivative of v(f). Determine w, given that d(w) = 0.
-1, 2/3, 1
Let z(o) = -o + 1. Let v(i) = -2*i**2 - 4*i + 6. Let t(h) = 2*v(h) - 4*z(h). Factor t(w).
-4*(w - 1)*(w + 2)
Let s(f) = f + 8. Let l be s(-8). Let x be 1/(l + 0 + 3). Factor 1/3*y**3 + y**2 + x + y.
(y + 1)**3/3
Let z(c) be the third derivative of -3/70*c**7 + 1/112*c**8 + 0 + 3/40*c**6 - 1/20*c**5 + 0*c + 0*c**3 + 0*c**4 - 3*c**2. Factor z(y).
3*y**2*(y - 1)**3
Let j be ((-322)/21)/((-2)/3). Let c = 38 - j. Determine u, given that 0*u - c*u**3 + 0 - 2*u**2 - 63/2*u**4 - 49/4*u**5 = 0.
-2, -2/7, 0
Let n(l) = -15*l**2 - 7*l + 22. Let a(g) = -5*g**2 - 2*g + 7. Let s(o) = 7*a(o) - 2*n(o). Factor s(w).
-5*(w - 1)*(w + 1)
Let r(w) = 5*w**3 - 7*w**2 + 12*w - 6. Let p(y) = -19*y**3 + 29*y**2 - 48*y + 22. Let x(q) = 6*p(q) + 22*r(q). Find c, given that x(c) = 0.
0, 2, 3
Let z(l) = -l**3 - 25*l**2 + 25*l - 6. Let x(t) = t**2 - t**2 - 8*t - t**2 + 9*t**2 + 2. Let u(v) = -7*x(v) - 2*z(v). Factor u(r).
2*(r - 1)**3
Factor -8/13 - 72/13*i - 162/13*i**2.
-2*(9*i + 2)**2/13
Factor 18/7*t**5 - 30/7*t**4 + 2*t**3 - 2/7*t**2 + 0*t + 0.
2*t**2*(t - 1)*(3*t - 1)**2/7
Let r(l) = l - 11. Let b be r(15). Let p(a) be the first derivative of 0*a + 4/27*a**3 + 1/9*a**2 + 1/18*a**4 + b. Factor p(q).
2*q*(q + 1)**2/9
Let x(p) be the first derivative of 0*p + 0*p**2 - 3 + 1/20*p**4 + 1/15*p**3. Find z, given that x(z) = 0.
-1, 0
Let s(q) be the second derivative of 0*q**3 + 0 + 0*q**6 + 1/252*q**7 - 1/120*q**5 + 0*q**4 - 2*q + 0*q**2. Factor s(f).
f**3*(f - 1)*(f + 1)/6
Find o such that 54/5 - 54/5*o + 18/5*o**2 - 2/5*o**3 = 0.
3
Let o = -40 + 42. Let m(c) be the second derivative of 4/21*c**3 - 5/42*c**4 + 0 - 1/7*c**o + 2*c + 1/35*c**5. Factor m(b).
2*(b - 1)**2*(2*b - 1)/7
Let q(i) be the second derivative of -i**6/6 + i**5/4 - 13*i. Solve q(x) = 0.
0, 1
Suppose 2*y + 11 = d, -5*y - 20 = -5. Determine i, given that 0*i**2 + 14*i + 0*i**2 - d*i + 7*i**2 + 2 = 0.
-1, -2/7
Let l be (-18)/(-52) + (10/65 - 0). What is i in -l*i + 1 - 1/2*i**2 = 0?
-2, 1
Suppose -2*d = -5*d + a + 12, -4*a = -d - 7. Suppose 4*u - d = 11. Factor -1/3*l**5 - 2/3*l**2 + 0*l**3 + 0 + 1/3*l + 2/3*l**u.
-l*(l - 1)**3*(l + 1)/3
Find c, given that -14*c + 5*c**3 + 9*c - c**2 + c**2 = 0.
-1, 0, 1
Let q(y) be the third derivative of -1/150*y**5 - 1/900*y**6 - 1/60*y**4 + 1/3*y**3 - 2*y**2 + 0*y + 0. Let i(g) be the first derivative of q(g). Factor i(o).
-2*(o + 1)**2/5
Let k(u) = -15*u**5 - 8*u**4 + 11*u**2 - 11*u. Let y(v) = -3*v + 2*v**4 - 2*v**4 - 4*v**5 + 3*v**2 - 2*v**4. Let f(d) = -6*k(d) + 22*y(d). Factor f(x).
2*x**4*(x + 2)
Let d(t) = -20*t**2 - 9*t + 2*t**3 - 19*t**3 + 0*t**4 + 13*t**4 + 15*t**2. Let w(b) = 6*b**4 - 8*b**3 - 2*b**2 - 4*b. Let q(n) = 4*d(n) - 9*w(n). Factor q(i).
-2*i**2*(i - 1)**2
Let -9/5*i - 6/5 - 3/5*i**2 = 0. Calculate i.
-2, -1
Let h = 9 - 5. Let t(b) be the first derivative of -1/15*b**3 - 1 + 0*b**2 + 0*b**h + 1/25*b**5 + 0*b. Let t(a) = 0. What is a?
-1, 0, 1
Suppose -w = -5*w + 12. Suppose 10 = -0*f + 2*f. What is h in h**w + h**5 + 2*h - h - f*h**3 + 2*h**3 = 0?
-1, 0, 1
Let x(b) be the third derivative of b**7/42 - b**6/8 - b**5/3 + 53*b**2. Let x(l) = 0. What is l?
-1, 0, 4
Let z be (-484)/462 - 8/(-6). Let 0*i - z*i**3 + 0 - 6/7*i**2 = 0. What is i?
-3, 0
Suppose 3*k + f = 5*k - 32, -3*k + 48 = -5*f. Let i be (-24)/k*2/(-6). Factor 1/2*g**2 - i*g**3 - 1/2 + 1/2*g.
-(g - 1)**2*(g + 1)/2
Suppose 20*c = 23*c. Let n(j) be the third derivative of -1/1512*j**8 + 0*j + 0*j**7 - 1/108*j**4 + 0*j**5 + 1/270*j**6 + 0*j**3 + c + 2*j**2. Factor n(r).
-2*r*(r - 1)**2*(r + 1)**2/9
Let i(m) be the third derivative of m**7/7560 + m**4/12 + 7*m**2. Let l(h) be the second derivative of i(h). Find a such that l(a) = 0.
0
Suppose -4/13*p + 2/13*p**2 + 2/13 = 0. What is p?
1
Let v be (-1 + 43/42)/(1/2). Let j(q) be the second derivative of 0 + v*q**3 + 2*q + 2/7*q**2 - 1/42*q**4. Factor j(n).
-2*(n - 2)*(n + 1)/7
Let s(f) be the third derivative of 0 + 1/30*f**5 - 1/60*f**6 + 0*f**3 + 0*f - 1/105*f**7 + 1/12*f**4 + f**2. Factor s(h).
-2*h*(h - 1)*(h + 1)**2
Let k(l) be the first derivative of -l**4/5 + 6*l**3/5 + l**2 + 51. Suppose k(o) = 0. What is o?
-1/2, 0, 5
Suppose -15*k + 11*k = 0. Factor k - 1/6*u**3 + 1/6*u**2 - 1/6*u**4 + 0*u + 1/6*u**5.
u**2*(u - 1)**2*(u + 1)/6
Let q(l) be the third derivative of l**8/36960 - l**7/6930 + l**6/3960 - 7*l**4/24 + l**2. Let x(y) be the second derivative of q(y). Factor x(k).
2*k*(k - 1)**2/11
Find o, given that 0*o**3 + 0*o**2 - 3/7*o**4 + 0 + 6/7*o**5 + 0*o = 0.
0, 1/2
Let c(g) = -3*g**3 + g**2 + 2*g - 2. Let q(k) = -10*k**3 + 4*k**2 + 6*k - 7. Let p(u) = -14*c(u) + 4*q(u). Determine h so that p(h) = 0.
-2, 0, 1
Let h(u) be the third derivative of u**10/70560 + u**9/35280 - u**8/15680 - u**7/5880 + u**4/8 - 3*u**2. Let y(s) be the second derivative of h(s). Factor y(w).
3*w**2*(w - 1)*(w + 1)**2/7
Let t(w) be the first derivative of w**6/1620 + w**5/270 + w**4/108 + w**3 + 1. Let z(c) be the third derivative of t(c). Suppose z(b) = 0. What is b?
-1
Let z(h) be the first derivative of -h**3 - 4 + 6*h + 3/2*h**2. Suppose z(v) = 0. What is v?
-1, 2
Let i be 20/(-6)*(-4)/(-80)*-4. Factor -2/3*v**2 - 4/3*v - i.
-2*(v + 1)**2/3
Let r be (-2)/5 - (-34)/10. Factor -4*y**3 + r + 16*y + 2*y**4 - 6*y**2 + 5 - 8*y.
2*(y - 2)**2*(y + 1)**2
Factor 0*u**4 + 2/9*u**5 + 0*u**2 + 0 - 4/9*u**3 + 2/9*u.
2*u*(u - 1)**2*(u + 1)**2/9
Suppose l + 3 = 5*b - 3*b, 3*l - 21 = -4*b. Suppose 5*z - 27 = -y, -y - z - l = -2*z. Suppose -r**2 + 2*r**y - 5 - 8*r + r**2 + 11 = 0. Calculate r.
1, 3
Let l be (-45)/99*2/(-5). Factor 0*y + 0 - l*y**3 - 4/11*y**2 + 6/11*y**4.
2*y**2*(y - 1)*(3*y + 2)/11
Let s**2 - 15*s**4 - s**3 + 24*s**4 - 10*s**4 + s**5 = 0. Calculate s.
-1, 0, 1
Let r(s) be the third derivative of s**7/105 + s**6/30 - s**4/6 - s**3/3 + 9*s**2. Fa