ative of q**7/8820 + q**4/24 + 3*q**2. Let g(r) be the second derivative of l(r). Factor g(h).
2*h**2/7
Let z(s) be the second derivative of -s**8/1680 - s**7/2520 + s**6/540 - s**3/2 - s. Let a(q) be the second derivative of z(q). What is w in a(w) = 0?
-1, 0, 2/3
Let m(s) be the second derivative of s**6/360 - s**4/24 + 5*s**3/6 + 2*s. Let t(q) be the second derivative of m(q). Determine a, given that t(a) = 0.
-1, 1
Let u(a) = a. Suppose 2*n - 2 - 2 = 0. Let o(v) = -v**3 + 2*v. Let d(r) = n*u(r) - 2*o(r). Find s, given that d(s) = 0.
-1, 0, 1
Let p = -1/198 + 109/1980. Let o(g) be the second derivative of -1/24*g**4 + 0*g**3 + 2*g + 0 + 0*g**2 - 1/60*g**6 - p*g**5. Factor o(q).
-q**2*(q + 1)**2/2
Let y(h) = 2 - 6*h + 0*h - 12*h**2 + 4*h**2. Let l(u) = u**2 + u. Let t be -2 + 1 + -5 + 5. Let i(d) = t*y(d) - 6*l(d). Suppose i(n) = 0. What is n?
-1, 1
Factor 0*p**4 - 9*p**2 - 7*p**4 - 9*p**3 - 2*p**5 - p + 4*p**2.
-p*(p + 1)**3*(2*p + 1)
Let q(j) = j**3 - 10*j**2 + 7*j - 3. Suppose p = 5*p - 20. Let h(u) = u**3 - 11*u**2 + 7*u - 3. Let a(f) = p*h(f) - 6*q(f). Factor a(y).
-(y - 3)*(y - 1)**2
Let g(x) be the second derivative of 0 + 0*x**2 + 2/21*x**3 - 1/42*x**4 - 3*x. Solve g(t) = 0.
0, 2
Let u(i) be the first derivative of -1/4*i**2 - 1/2*i**4 + 5/6*i**3 + 0*i + 1. Solve u(x) = 0.
0, 1/4, 1
Let h(a) be the second derivative of 1/24*a**3 + 6*a - 1/8*a**2 - 1/80*a**5 + 0 + 1/48*a**4. Let h(r) = 0. Calculate r.
-1, 1
Let g(s) be the third derivative of -s**10/453600 + s**9/181440 + s**5/20 + 2*s**2. Let z(m) be the third derivative of g(m). Factor z(l).
-l**3*(l - 1)/3
Let r(f) be the first derivative of -f**3/15 - f**2/5 + 3*f/5 + 3. Factor r(i).
-(i - 1)*(i + 3)/5
Determine j, given that 0 + 2/3*j**3 - 10/3*j**2 + 4*j = 0.
0, 2, 3
Suppose 0 = -w + 2*b + 83, -5*w + 788 = 5*b + 298. Factor 2*m**4 + w*m - 93*m.
2*m**4
Solve 16*a**4 + 26*a**4 + 5*a**3 + 5*a**5 - 52*a**4 = 0.
0, 1
Let n(x) = x**2 - 3*x - 8. Let q be n(-2). Factor 0*w**q + 0*w**4 + 0*w - 1/4*w**3 + 0 + 1/4*w**5.
w**3*(w - 1)*(w + 1)/4
Suppose 0*f - 5*f + 20 = 0. Let z be 14/(-4)*f/(-7). Factor 3*v - 2*v - 4*v**z + 3*v**2.
-v*(v - 1)
Let v(a) = 2*a**4 - 2*a**3 - a**2 - 3. Let j(r) = -3*r**4 + 4*r**3 + 2*r**2 + 5. Suppose -1 = x - 4. Let b = x - 6. Let l(h) = b*j(h) - 5*v(h). Factor l(i).
-i**2*(i + 1)**2
Let h(m) be the second derivative of -m**7/10080 + m**6/2880 - m**4/3 + 2*m. Let c(k) be the third derivative of h(k). Solve c(g) = 0 for g.
0, 1
Factor 1/2*b - 1/2*b**3 + 0 + 0*b**2.
-b*(b - 1)*(b + 1)/2
Factor 10*t**2 - 6*t**3 + 5*t**2 - 18*t**2 - 3*t**4.
-3*t**2*(t + 1)**2
Let y(c) = -10*c**4 - c**3 + 10*c**2 + 12*c + 11. Let n(m) = -m**4 + m**2 + m + 1. Let z(b) = -44*n(b) + 4*y(b). Solve z(v) = 0 for v.
-1, 0, 1
Let q(a) be the second derivative of 7*a + 8/9*a**3 - 16/3*a**2 - 1/18*a**4 + 0. Suppose q(u) = 0. Calculate u.
4
Find f, given that 5/2*f**2 + 0 - 5*f = 0.
0, 2
Let a(z) be the first derivative of z**7/3360 + z**6/720 - z**5/480 - z**4/48 - z**3 - 1. Let y(b) be the third derivative of a(b). Factor y(n).
(n - 1)*(n + 1)*(n + 2)/4
Let h(r) be the second derivative of 0 + 3/20*r**5 + 1/18*r**4 + 0*r**3 + 7/90*r**6 + 3*r + 0*r**2. Suppose h(q) = 0. What is q?
-1, -2/7, 0
Let n(r) be the third derivative of r**5/270 + r**4/36 + 2*r**3/27 + 3*r**2. Factor n(g).
2*(g + 1)*(g + 2)/9
Let n = 10 + -8. Let r(h) be the second derivative of 2*h**n + 0 + 1/3*h**4 - 5/3*h**3 + 2*h. Factor r(d).
2*(d - 2)*(2*d - 1)
Solve 12*v**3 - 193*v + 4*v**2 - 8 - 2*v**4 - 30*v**2 + 217*v = 0 for v.
1, 2
Let p(m) be the third derivative of m**5/12 - 5*m**4/24 - 5*m**3 + 13*m**2. Suppose p(f) = 0. What is f?
-2, 3
Suppose -9*v + 11*v = 18. Suppose v = 4*m - 3. Solve 8/7*d**2 + 4/7*d**4 - 2/7*d + 0 - 10/7*d**m = 0 for d.
0, 1/2, 1
Let s be (2/(-4))/((-3)/12). Factor 5*w - 4*w + w**s + w**3 - 3*w**2.
w*(w - 1)**2
Suppose -15 = 3*b, -2*b + 12 = -2*w - 6*b. Factor -3/2*f**2 + 0*f - 9/4*f**3 - 3/4*f**w + 0.
-3*f**2*(f + 1)*(f + 2)/4
Let c(v) be the second derivative of 1/147*v**7 + 2/105*v**6 - 1/21*v**4 + 3*v + 0*v**5 + 0 + 0*v**2 - 1/21*v**3. Factor c(x).
2*x*(x - 1)*(x + 1)**3/7
Let g(o) be the first derivative of o**7/4620 - o**6/1980 - 2*o**3 - 6. Let a(w) be the third derivative of g(w). Factor a(q).
2*q**2*(q - 1)/11
Let z(m) be the first derivative of -m**4/12 + m**3/2 - m**2 - 4*m + 4. Let s(g) be the first derivative of z(g). Factor s(o).
-(o - 2)*(o - 1)
Let u = -10 + 4. Let q = -4 - u. Solve 8/3*d**4 - 7/3*d + d**5 - q*d**2 + 4/3*d**3 - 2/3 = 0 for d.
-1, -2/3, 1
Find x such that 3*x + 15 + 15*x**2 - 3*x**2 + 62*x + 8*x**2 = 0.
-3, -1/4
Let i(r) be the third derivative of r**6/80 + 29*r**5/360 + r**4/6 + r**3/9 + 14*r**2. Find m such that i(m) = 0.
-2, -1, -2/9
Factor -2/23 + 8/23*p + 10/23*p**2.
2*(p + 1)*(5*p - 1)/23
Let k be 59/(-150) - 22/(-55). Let j(z) be the third derivative of 0*z - 1/525*z**7 - z**2 + k*z**5 + 1/60*z**4 + 0 + 0*z**3 - 1/300*z**6. Factor j(o).
-2*o*(o - 1)*(o + 1)**2/5
Suppose 4*l - d - 17 = -0*d, 3*l + 2*d + 1 = 0. Let t(z) be the second derivative of 4/15*z**l - 2*z + 1/30*z**4 + 4/5*z**2 + 0. Factor t(r).
2*(r + 2)**2/5
Let h(q) be the first derivative of q**6/120 - 3*q**5/40 + q**4/4 - 4*q**3/3 + 3. Let i(k) be the third derivative of h(k). Factor i(p).
3*(p - 2)*(p - 1)
Let h = 4 - 3. Suppose 2*y - 4*i + 9*i = -h, 2*y + 4*i = 0. Factor g**3 + 5*g**y - 5*g**2.
g**3
Factor -8/9 - 1/9*w**4 - 1/9*w**3 + 4/9*w + 2/3*w**2.
-(w - 2)*(w - 1)*(w + 2)**2/9
Let n = -135 + 137. Let x(j) be the third derivative of -1/105*j**7 - 1/60*j**6 + 0*j**3 + 1/12*j**4 + 0*j + 1/30*j**5 + 3*j**n + 0. Factor x(l).
-2*l*(l - 1)*(l + 1)**2
Solve -15*m + m**3 - 3*m**3 - 5 - 15*m**2 + 3*m**3 - 6*m**3 = 0.
-1
Let r(o) be the first derivative of -2*o**3/27 - 2*o**2/3 - 16*o/9 + 36. Determine z so that r(z) = 0.
-4, -2
Let a(p) be the third derivative of -p**5/12 - 5*p**4/4 - 15*p**3/2 + 10*p**2. Factor a(i).
-5*(i + 3)**2
Let r(n) = -2*n**3 + 9*n**2 - n + 1. Let q be r(6). Let x = q + 567/5. Factor -2/5*s + 2/5*s**3 + 2/5*s**2 - x.
2*(s - 1)*(s + 1)**2/5
Let y = 117 + -581/5. Suppose 2/5*m**2 + 2/5 - y*m = 0. What is m?
1
Let f(w) be the second derivative of -w**6/40 - 3*w**5/40 + w**4/16 + w**3/4 - 20*w. Factor f(n).
-3*n*(n - 1)*(n + 1)*(n + 2)/4
Let v(h) be the second derivative of -h**4/6 + h**3/2 - h**2/2 + 3*h. Factor v(q).
-(q - 1)*(2*q - 1)
Find u, given that -24*u**5 - 24*u**3 + 18*u**2 - 50*u**3 - 4*u + 20*u**3 + 2*u + 62*u**4 = 0.
0, 1/4, 1/3, 1
Factor -5*k + 0*k**2 + 25*k + 3*k**2 - 2*k.
3*k*(k + 6)
Factor 775*q - 152*q**2 + 7*q**3 + 260*q - 232*q + 242.
(q - 11)**2*(7*q + 2)
Let w(s) = 5*s**3 + 7*s**3 - 11*s**3 + 9*s - 5 + 11*s**2. Let r be w(-10). Factor 2/11*o + 0 + 0*o**2 + 2/11*o**r - 4/11*o**3 + 0*o**4.
2*o*(o - 1)**2*(o + 1)**2/11
Let w = -9 + 9. Let r(z) be the second derivative of 0*z**4 - 1/60*z**5 + w*z**2 - 1/90*z**6 + 2*z + 0*z**3 + 0. Factor r(l).
-l**3*(l + 1)/3
Let 13*d**2 + 18 + 17*d**2 - 15*d - 54*d = 0. Calculate d.
3/10, 2
Let t(f) = -f**3 + 3*f**2 + 2*f - 2. Let n be t(4). Let g be (-1)/(-5) - 18/n. Factor -i**2 - 8*i**4 + 7*i**4 + g*i**3 - 4*i**3.
-i**2*(i + 1)**2
Let t(o) be the first derivative of -o**3/15 + o**2/10 + 6*o/5 + 56. Factor t(y).
-(y - 3)*(y + 2)/5
Let j = -366 + 369. Factor -1/4*n**2 + 0*n - 2*n**5 - j*n**4 + 0 - 3/2*n**3.
-n**2*(2*n + 1)**3/4
Suppose 33*z = 38*z. Let o(p) be the first derivative of -2 - 1/8*p**2 + z*p**3 + 0*p + 1/16*p**4. Determine l so that o(l) = 0.
-1, 0, 1
Let z be (-20)/4 - (0 + -1). Let f(n) = n**2 + 5*n + 4. Let h be f(z). Suppose 0 + 1/4*r**4 + h*r + 1/4*r**2 - 1/2*r**3 = 0. Calculate r.
0, 1
Suppose 2*f - 1 - 2 = -3*b, 3*b - 3 = -3*f. Factor -3*s**2 - 3 + 2*s + 9*s**2 - b.
2*(s + 1)*(3*s - 2)
Let j = 12 - 9. Let f be -4*12/(-16) - j. Factor 0*m - 8/5*m**4 + f + 2/5*m**2 - 6/5*m**3.
-2*m**2*(m + 1)*(4*m - 1)/5
Factor 12/7 - 3/7*a**2 + 0*a.
-3*(a - 2)*(a + 2)/7
Let b(i) be the third derivative of 9/560*i**8 + 11/100*i**6 - 12/175*i**7 + 1/40*i**4 - 2/25*i**5 + 0*i**3 - 3*i**2 + 0 + 0*i. Factor b(a).
3*a*(a - 1)**2*(3*a - 1)**2/5
Let o(k) = -4*k**2 + 21*k - 17. Let v(g) be the first derivative of 2*g**3/3 - 5*g**2 + 8*g - 7. Let t(y) = -4*o(y) - 9*v(y). Factor t(b).
-2*(b - 2)*(b - 1)
Determine v, given that 2/7*