second derivative of k(n). Find i, given that o(i) = 0.
0
Let z = -11 + 10. Let b be (z/(-4))/((-15)/(-160)). Factor -8*o**2 + 32/3*o - 16/3 - 1/3*o**4 + b*o**3.
-(o - 2)**4/3
Let d be (3/(27/6))/((-6)/(-18)). Suppose 0 + 0*m + 1/4*m**d = 0. Calculate m.
0
Let c = 34/59 + -52/295. Factor 0*w + 3/5*w**3 + 0 + c*w**2.
w**2*(3*w + 2)/5
Let k(u) be the first derivative of 2*u - 1/2*u**4 - 2/3*u**3 + u**2 + 5. Factor k(n).
-2*(n - 1)*(n + 1)**2
Suppose -2*i = -6*i + 3*j + 5, -2*i = 4*j - 30. Factor 3*f + 2*f**2 - i*f + 4*f - f**2.
f*(f + 2)
Suppose -5*q + 8 + 7 = 0. Let x(a) be the third derivative of -4*a**2 + 1/24*a**6 - 5/24*a**4 + 1/3*a**q + 0*a + 0 - 1/30*a**5. Find y such that x(y) = 0.
-1, 2/5, 1
Let g(u) be the first derivative of -u**8/7560 + u**7/3780 + u**6/1620 - u**5/540 + 2*u**3/3 - 3. Let t(n) be the third derivative of g(n). Factor t(y).
-2*y*(y - 1)**2*(y + 1)/9
Let r(f) be the second derivative of 7*f**8/5760 - f**7/720 - f**6/180 - f**5/180 - f**4/12 + 4*f. Let b(z) be the third derivative of r(z). Solve b(k) = 0.
-2/7, 1
Let c(p) be the third derivative of 0*p + 1/60*p**5 - 1/12*p**4 + 1/6*p**3 - 8*p**2 + 0. Suppose c(b) = 0. What is b?
1
Suppose -3*o = -8*o. Let n(j) be the first derivative of 0*j + 1/2*j**4 + 1 - 2/3*j**3 + o*j**2. Let n(q) = 0. What is q?
0, 1
Let y(o) be the third derivative of -1/16*o**4 - 1/12*o**3 + 0 + 1/30*o**5 - 6*o**2 + 0*o. Let y(q) = 0. Calculate q.
-1/4, 1
Let y = -9 - -11. Factor 0*u + 2/5 - 2/5*u**y.
-2*(u - 1)*(u + 1)/5
Let f = -7/12 + 5/6. Let q(s) be the first derivative of 0*s - 1/8*s**4 - f*s**2 + 2 + 1/3*s**3. Factor q(p).
-p*(p - 1)**2/2
Let m(a) = 5*a**2 - 9*a. Suppose 6*r + 6 = 24. Let n(k) = -26*k**2 + 46*k. Let f(v) = r*n(v) + 16*m(v). Factor f(y).
2*y*(y - 3)
Factor 5/3*d + 1/3*d**2 + 0.
d*(d + 5)/3
Let g be 13/3 + 2/(-6). Let n = g - 2. Determine o so that o**2 + 0*o**n - 3 + 2 = 0.
-1, 1
Let n(z) be the second derivative of z**6/135 - z**5/45 - z**4/18 + 4*z**3/27 + 4*z**2/9 + 5*z. Find b such that n(b) = 0.
-1, 2
Let h(u) be the third derivative of u**7/42 + u**6/24 - u**5/6 - 67*u**2. Factor h(v).
5*v**2*(v - 1)*(v + 2)
Let r = -16 - -18. Factor 2*z**4 + 11*z + 10*z**4 + 11*z**r - 19*z + z**2 + 32*z**3.
4*z*(z + 1)*(z + 2)*(3*z - 1)
Factor t + 3/4 + 1/4*t**2.
(t + 1)*(t + 3)/4
Let p be (-9)/(-15)*(2 + 3). Let r(q) be the second derivative of 0 - 2/21*q**p - 1/7*q**2 + 1/105*q**6 + 1/35*q**5 + q + 0*q**4. Factor r(x).
2*(x - 1)*(x + 1)**3/7
Suppose 2*c = 0, -8 = -3*d - d + 4*c. Find g such that -4*g + 0*g**2 + 0*g**2 + d + 2*g**2 + 0*g = 0.
1
Let h(p) be the second derivative of p**4/24 - p. Determine v so that h(v) = 0.
0
Let l = 1444/15 + -278/3. Factor 27/5*w**3 + 12/5*w**4 + l*w**2 + 0 + 3/5*w.
3*w*(w + 1)**2*(4*w + 1)/5
Let v(w) be the first derivative of 4*w**3/7 + 15*w**2/14 + 3*w/7 + 7. Factor v(y).
3*(y + 1)*(4*y + 1)/7
Let j(b) = 8*b - 7. Let r(a) = -a**2 + 1. Let h(z) = z**2 - 6*z - 6. Let k be h(6). Let s(t) = -2*t + 2. Let v be s(2). Let f(n) = k*r(n) + v*j(n). Factor f(g).
2*(g - 2)*(3*g - 2)
Let t = -187/4 - -47. Let h(k) be the first derivative of -k - 1 + 1/3*k**3 + 1/2*k**2 - t*k**4. Suppose h(n) = 0. What is n?
-1, 1
Solve 0*b + 0*b + 9*b**2 - 6*b - 3*b**3 = 0.
0, 1, 2
Solve 0 + 8/11*u**2 - 2*u = 0 for u.
0, 11/4
Let z(j) be the first derivative of 1 + 0*j + 3/2*j**2 + 10/3*j**3. Let p(x) = 3*x**2 + x. Let h(i) = 14*p(i) - 4*z(i). Factor h(a).
2*a*(a + 1)
Let m be 14*(10/25)/2. Let u = 3 - m. What is p in u*p**3 - 2/5 + p - 4/5*p**2 = 0?
1, 2
Let t(l) be the third derivative of -l**6/1080 + l**4/72 + l**3/2 + l**2. Let w(r) be the first derivative of t(r). Factor w(a).
-(a - 1)*(a + 1)/3
Let g(t) be the first derivative of -4*t**3/3 + 4*t - 1. Factor g(f).
-4*(f - 1)*(f + 1)
Suppose 0 = -3*r + 12, 2*a - 3*r + 1 + 3 = 0. Let o(b) = -2*b**2 + b + 3. Let x(u) = -3*u**2 + 3. Let v(z) = a*x(z) - 3*o(z). Suppose v(j) = 0. What is j?
-1, 1/2
Suppose 0 = t + 2. Let s(z) = -z**3 + z**2 - 1. Let d(h) = 8*h**4 - 10*h**2 + 2*h + 2. Let y(o) = t*s(o) - d(o). Suppose y(m) = 0. What is m?
-1, 0, 1/4, 1
Let b(z) be the first derivative of z**3/2 - 3*z**2 + 9*z/2 + 10. What is q in b(q) = 0?
1, 3
Let j be (-6)/(-4)*(-2)/(-180). Let m(x) be the third derivative of 0 - 1/8*x**4 + 0*x + 1/3*x**3 + j*x**5 + x**2. Let m(i) = 0. What is i?
1, 2
Let b(j) be the third derivative of 0*j**3 - 1/150*j**5 + 0*j + 0*j**4 + 2/525*j**7 + 0 + 3*j**2 - 1/300*j**6. Solve b(y) = 0.
-1/2, 0, 1
Let l(d) be the third derivative of -d**7/70 - d**6/40 + d**5/20 + d**4/8 - 4*d**2. Factor l(o).
-3*o*(o - 1)*(o + 1)**2
Let l(p) be the third derivative of -p**7/630 - p**6/180 - 6*p**2. Find n such that l(n) = 0.
-2, 0
Let k(y) be the first derivative of 1/15*y**5 + 0*y**3 + 0*y**2 + 1 + 0*y + 0*y**4. Factor k(v).
v**4/3
Factor -11*f**2 - 8*f**2 + 15*f**2.
-4*f**2
Let o(r) be the second derivative of -r**7/231 + r**6/33 - 9*r**5/110 + 7*r**4/66 - 2*r**3/33 - 2*r. Factor o(a).
-2*a*(a - 2)*(a - 1)**3/11
Let y(j) = -j**2 - 35*j - 286. Let m be y(-22). Factor -2/13*r**2 + m - 4/13*r + 6/13*r**3.
2*r*(r - 1)*(3*r + 2)/13
Suppose -12*t = -11*t - 6. Factor 2*n**3 + n**3 + t*n**2 + 3*n + 0*n**2.
3*n*(n + 1)**2
Factor 2 - 2*b + 2 + 0 - b**2 - 5.
-(b + 1)**2
Let h(t) = -t**3 + 5*t**2 - 4. Let r be h(4). Suppose -5*c + r + 3 = 0. What is m in -m**2 + 2*m**3 - 1 + 2*m**2 + m - c*m**3 = 0?
-1, 1
Let s(w) = w. Let t(i) = -i**2 + 8*i - 6. Let r(m) = 3*s(m) - t(m). Solve r(l) = 0 for l.
2, 3
Let d = 0 + 0. Factor -i - 2*i + 10*i**2 - 7*i**2 + d*i.
3*i*(i - 1)
Let r(a) be the third derivative of 1/420*a**6 + 0*a - 2*a**2 + 0*a**3 + 0 - 1/84*a**4 + 0*a**5. Find w such that r(w) = 0.
-1, 0, 1
Let f(z) be the third derivative of z**7/70 - 3*z**6/20 + 13*z**5/20 - 3*z**4/2 + 2*z**3 + 41*z**2. Factor f(t).
3*(t - 2)**2*(t - 1)**2
Let h = 21 + -83/4. Suppose 3*n + 15 = -4*p, -3*n - 20 = n. Suppose p + 1/4*v**4 - 1/4*v**2 - 1/4*v**3 + h*v = 0. What is v?
-1, 0, 1
Let s(u) = 4*u**3 + 4*u**2 - 12*u. Let r(l) = 4*l**3 + 4*l**2 - 11*l. Let v(o) = 4*r(o) - 3*s(o). Factor v(t).
4*t*(t - 1)*(t + 2)
Let c(o) = -8*o**2 + o - 2. Let q(x) = 23*x**2 - 2*x + 7. Let j(r) = 8*c(r) + 3*q(r). Let i(m) = -4*m**2 - 2*m - 4. Let b(t) = -6*i(t) - 5*j(t). Factor b(s).
-(s - 1)**2
Let h be (4/6 + -1)*(-1 - 0). Let -o**2 - 1/3*o**4 - o**3 - h*o + 0 = 0. Calculate o.
-1, 0
Let g be 3*(14/4 + -3). Let t = -7/6 - -8/3. Solve 1/2*a**5 + 0 + 0*a + g*a**4 + 1/2*a**2 + t*a**3 = 0 for a.
-1, 0
Suppose 5*v - 17 - 4 = 3*a, -v - 2*a = 1. Let h(n) be the second derivative of 1/2*n**4 - n**2 - 7/6*n**v + 0 + 7/15*n**6 - 2*n + 5/4*n**5. Solve h(k) = 0.
-1, -2/7, 1/2
Let t(p) = p**2. Let b(n) = n**5 - 4*n**3 - 2*n**2 + 3*n - 2. Let q(s) = b(s) + 4*t(s). Factor q(d).
(d - 1)**3*(d + 1)*(d + 2)
Let t(v) be the third derivative of -v**5/45 + v**4/9 + 2*v**3/3 + 14*v**2. Find p, given that t(p) = 0.
-1, 3
Suppose -x = -2*h - 3*x - 4, 0 = 5*h - x - 20. Let a(y) be the first derivative of -2/7*y + 2/21*y**h - 1/14*y**4 + 1/7*y**2 + 1. Let a(o) = 0. Calculate o.
-1, 1
Let j(h) = h - 4. Let u be j(6). Let g(v) be the third derivative of 0 + 0*v**3 + 0*v + 1/240*v**6 - 1/120*v**5 - u*v**2 - 1/24*v**4. Factor g(i).
i*(i - 2)*(i + 1)/2
Let r(y) be the third derivative of y**8/2240 + y**7/280 + y**6/120 - y**4/12 + 5*y**2. Let x(w) be the second derivative of r(w). Factor x(k).
3*k*(k + 1)*(k + 2)
Let x(w) be the third derivative of -w**5/60 + w**3/3 - 6*w**2. Let s(l) = -2 - 2 + 3. Let h(g) = -2*s(g) - x(g). Factor h(o).
o**2
Let 34*n**2 - 4*n**3 + 4*n**5 - 3*n**5 - 34*n**2 = 0. What is n?
-2, 0, 2
Let x be (-64)/(-10) + (-4)/10. Let q = x - 4. Factor 0*r**5 - r - 5*r**2 + 4*r**q + 4*r**5 - 11*r**4 + 9*r**3.
r*(r - 1)**3*(4*r + 1)
Let q be (-12)/(-24) + 2/12. Let 2/9*k**3 + 4/9 - 2/9*k - q*k**2 + 2/9*k**4 = 0. Calculate k.
-2, -1, 1
Suppose j - 3*g - 20 + 3 = 0, -5*j + 5*g = -35. Determine x so that 0 + 3/7*x**j + 3/7*x = 0.
-1, 0
Let o(k) be the first derivative of -7 - 1/8*k**3 + 1/16*k**2 + 3/40*k**5 + 0*k + 1/32*k**4 - 1/24*k**6. Suppose o(g) = 0. Calculate g.
-1, 0, 1/2, 1
Let w(b) = 3*b**2 - 3*b. Let t(u) be the third derivative of 0 - 2*u**2 + 0*u + 1/24*u**4 + 0*u**3 - 1/60*u**5. Let d(z) = -4*t(z) - 2*w(z). Factor d(a).
-2*a*(a - 1)
Factor -119 - 2*z**3 + 12*z**2 - 